# Aperiodic Life 3.7.4: complete preset catalogue Editable narrative source. Stable headings are read by build_catalogue.py; edit prose beneath them. Exact rules, seeds, references and measurements are in catalogue-source.json. ## cover ### Abstract This catalogue documents all 89 curated configurations in Aperiodic Life 3.7.4: 22 on the Einstein-hat tiling, 21 on Penrose rhombs, 36 on the hexagonal lattice and 10 on the square lattice. Every entry has its exact rule, initialisation, production-engine illustrations, computational evidence and attribution. All 56 complete rule-sets are registered, and all 12 named rule presets are described separately. ### Scope of originality The catalogue identifies 55 configurations original to this package for which no exact precedent was found in the literature reviewed to 14 October 2026. A further package search result, P09, may be Owens and Stepney’s published fireworks oscillator [5,6]; its identity remains unresolved. Four deliberate package constructions, 25 published examples and four adaptations complete the 89 entries. Each adaptation names its parent pattern or rule and states what changed. ### Authorship and status AI generated following prompts by Murdoch J. Gabbay. Catalogue revision 2, 14 October 2026, for Aperiodic Life 3.7.4. The software package was vibe-coded by Murdoch J. Gabbay. This catalogue reports computational checks and source comparisons; it is not a peer-reviewed paper. Each reproduced pattern and rule names its source with a numbered reference. ## scope ### What is included Every entry in discoveries.js appears once, with a stable identifier and a linked rule reference. The 12 named options in the separate rule selector also appear. The Custom option, arbitrary painted states and arbitrary random seeds are not finite preset lists. Penrose sun/star selects geometry, not a cellular-automaton pattern. Spectre and Goucher API-only tables are distinguished from the UI presets. ### Original to this package, or already known? ORIGINAL TO THIS PACKAGE identifies a configuration generated by this package’s search, with no exact precedent identified in the literature reviewed to 14 October 2026. It does not attribute an established update rule or travelling mechanism to this package, and the review cannot exclude unexamined or unpublished earlier work. CONSTRUCTED HERE identifies a deliberate assembly and names its underlying rule or principle. PUBLISHED names the author, pattern or mechanism and numbered source. ADAPTATION names that predecessor, its source and the change. P09 is labelled POSSIBLE PUBLISHED MATCH, not original. ### What has been compared The audit uses Owens and Stepney’s Penrose catalogue [5,6], Goucher’s Penrose-glider paper [4], Edmond’s paper and compendium [2,3], the hexagonal seed records identified in X23-X35, Stephen Silver’s Life Lexicon [24,25,26,27,29,30,32], and retained exact-state comparisons. Eleven hexagonal precedents have executable comparison records. Coverage is incomplete: the wider hexagonal databases and unpublished work have not been exhausted. A failed search or inaccessible web page is not evidence of originality. ### How to use this document Start with the plain-language rule guide, then the neighbourhood diagrams and rule-status definitions. Tiling directories link to every illustrated configuration. H, P, X and S label Hat, Penrose, hexagonal and square entries; C01-C04 retain the earlier catalogue’s constructed-example labels. R01-R56 denote complete rule-sets. U01-U12 denote rule-selector templates, which need a chosen graph. These labels are document references, not standard names. ## rules ### Update convention Each polygon is one cell. All cells update simultaneously using the states before the update. A complete rule specifies the tiling, neighbour relation, transition rule and total state count C. A B/S string alone does not specify all four. The cell itself is never counted as its neighbour. ### Worked example: R40 R40 is B234/S245 with C = 5 on the shared-edge hexagonal graph. An empty cell is born with exactly 2, 3 or 4 live neighbours. A live cell survives with exactly 2, 4 or 5. The six neighbours are precisely the edge-sharing hexagons. Thus R40:S5 means survival with exactly five of those six neighbours live. S5 is one clause, not an entire rule. The example is X08, the ten-step knightship launcher. ### States and refractory time State 0 is empty and state 1 is live. Only state 1 contributes to B/S neighbour counts. With C = 2, a live cell that fails survival becomes 0. With C > 2, it becomes state 2; refractory states then advance one step each generation, regardless of neighbours, through 2, 3, ..., C-1 and back to 0. A refractory cell cannot be born until it is 0 again. In R40 the death sequence is 1, 2, 3, 4, 0. ### Exact counts, not thresholds B12 means one or two neighbours, not twelve. B2/S has no survival counts, whereas B2/S0 permits survival with zero live neighbours. A multi-digit count is bracketed, for example B[10]/S[9,10]. None of R01-R56 needs a multi-digit B/S count. By contrast, priority-table conditions n_i >= k mean at least k neighbours in state i, including i = 0. ### Priority tables are different Named TABLE rules count each neighbour state separately and take the first matching ordered row. All conditions in that row must hold. No match gives state 0. The higher states are signals, with no automatic refractory ageing. The complete ordered rows, including defaults and state totals, appear in the rule register. ## evidence ### Exact cycles and regular-lattice spaceships A stationary cycle satisfies F^p(S) = S on the same graph; its least positive p is its period. A transient of a steps means that the first recurrent phase is F^a(S). Equality concerns the entire labelled state. On an infinite translation-invariant lattice, F^p(S) = T_d(S) with nonzero displacement d and a verified empty exterior implies F^(kp)(S) = T_(kd)(S). The hexagonal unbounded reference supplies such exact certificates for the identified moving cycles. ### Aperiodic motion is finite evidence A translated cluster on an aperiodic graph need not encounter the same surroundings forever. The Hat and Penrose travel records therefore state finite horizons. They do not prove an immortal Einstein glider. Exact stationary cycles do recur on their fixed finite graph; boundary separation is reported where measured. ### Launchers, emitters, guns and puffers A launcher produces outgoing bodies once. A recurring emitter regenerates a source over the tested interval. An indefinite gun claim needs a repeatable source and proof that outgoing bodies never interfere with later emissions. H03 is a finite aperiodic emitter. The identified hexagonal gun and puffers have separate separation certificates; a growing puffer’s complete state is not a spaceship. ### Measurements N counts all nonzero cells; L counts state-1 cells. They differ for multistate rules. Cycle territory is the union of nonzero sites throughout a cycle. Boundary distance counts graph steps, with the outermost cells at zero. Polygon matches use the tolerances recorded in the evidence; they are not symbolic geometric proofs. ### Figures All 267 pattern panels are snapshots from the production engine and retain every nonzero cell. Pale cells are optional immediate zero-state context. Stationary cycle panels use one fixed view and scale; other panels are independently centred and scaled without rotation. The caption states the convention. Colours identify states. Every snapshot retains a complete-state hash and exact polygon coordinates in the source data. ## neighbours ### Definition Shared-edge means a common boundary segment of positive length. Touch means edge or boundary-point contact, including a corner meeting another tile’s edge at a T-junction. The examined cell is excluded. Hat and Penrose neighbour counts vary with position. ### Regular lattices A square touch neighbourhood has eight cells: four sharing edges and four diagonal corner contacts. A square edge neighbourhood has four. All ten curated square configurations use touch. The hexagonal edge and touch graphs coincide: at each vertex only three hexagons meet and every pair shares an edge. There are exactly six neighbours. ### Coordinates and borders Hexagonal axial neighbours differ by (1,0), (1,-1), (0,-1), (-1,0), (-1,1), or (0,1). A cell (q,r) has centre (sqrt(3)(q+r/2), 3r/2). Square coordinates are integer column/row coordinates. Hat/Penrose tile IDs depend on the released builder, depth and seed. A border parameter b locks cells at graph-boundary distance less than b to state 0. There is no wraparound; external missing cells are not additional state-0 neighbours in a priority table. ## status ### Complete rule identifiers R01-R56 each fixes the tiling, neighbour relation, transition and C. The seed, patch size and locked border then specify an experiment. The same B/S digits on different graphs or with different C values describe different automata. R40:S5 uniquely identifies one survival clause; R15.1 identifies row 1 of the ordered R15 table. ### Standard, previously used, or original? Binary birth/survival, Generations refractory rules and ordered state-count tables are established formalisms. A rule card names its documented earlier author or user and the publication that contains it. If the package transfers standard counts to a different graph, the card names that standard rule and graph change. If no earlier use of a complete graph/update/state-count specification was identified, the card says so explicitly and dates that statement to 14 October 2026. An adapted table names its parent: R13 derives its mature mechanism from Edmond’s Spectre relay [2,3]; R14 derives from his Hat B table R11 [2,3]. R15 was evolved in this package; Edmond’s work is background for its search framework, not a source for that exact table. ### Rules and patterns have separate credit R10 and R11 are Edmond’s published Hat rules. H02 and H03 are separately searched launch/source seeds under those rules and their known travelling mechanism. Calling B3/S23 Conway does not attribute a Hat, Penrose or hexagonal arrangement to Conway. The XOR construction uses a known additive principle. Each entry gives both its pattern status and a link to the rule’s status. ### Unresolved identity P09, penrose-conway-p12, matches the period 12, territory 33 and minimum population 6 of Owens and Stepney’s fireworks oscillator r-p12-33-6. These invariants do not determine identity. The exact geometric comparison is unresolved, and the pattern is not claimed original [5,6]. ## reproduce ### From the application Use the version 3.7.4 release accompanying this catalogue. Open aperiodic-life-standalone.html, locate the entry by title in Curated configurations, and press Load. The lower-case identifier printed on the page is its discoveries.js key. Step through the generations shown. Save state preserves all labelled states. The live website may later run a different release. ### Machine-readable initial states The PDF attachment catalogue-data.json contains every preset, exact seed, rule and measurement. The repository’s geometry/diagrams.json additionally records complete snapshot geometry, graph hashes and the realised initial states of random fields. Where a long seed is not printed in full, the record key, population and SHA-256 of the canonical seed list identify the attached exact data. PDF readers may hide attachments; the same data is provided as a normal file beside this PDF. ### Rebuilding the catalogue The editable prose is catalogue.md. catalogue-source.json contains exact definitions, seeds, attributions and bibliography. build_catalogue.py reads both and produces the PDF plus catalogue-data.json. Install the optional documentation dependencies in requirements.txt, then run python3 docs/catalogue/build_catalogue.py from the repository root. The application itself still needs no installation or npm dependencies. ### Regenerating scientific figures Run node docs/catalogue/export_geometry.js to regenerate every snapshot from core.js and discoveries.js. Then rebuild the PDF. Re-run node research/verify-catalog.js and the cited specialised verifiers when changing seeds, geometry or dynamics. A larger aperiodic depth changes tile IDs: transfer by verified polygon correspondence, not by assuming the same numerical ID means the same location. ## integrity ### Double-checks All 89 curated presets are included exactly once, all 12 named UI rule presets are inventoried, and all 56 complete rule definitions are mapped to their entries. Every panel is regenerated from the release engine. The full catalogue verifier and the eleven published hexagonal source comparisons were rerun. Independent period/displacement and aperiodic structure checks from the previous catalogue remain applicable to the unchanged seeds and engine; the evidence records state their actual horizons. ### Reproducibility and scope The embedded catalogue data and repository source identify the exact engine and discovery file by SHA-256. The PDF deliberately does not embed its containing release archive. That would create a circular dependency. Build and verification output paths are described in the catalogue README. Source claims are qualified separately from the runtime checks. ### Corrections and citation Cite Aperiodic Life 3.7.4, the stable preset ID, the full rule including C, and the graph. A useful earlier-match report supplies a dated source, complete multistate seed, rule and neighbourhood, and an explicit transformation or phase match. Please submit corrections and patches to the project repository. Neither this software nor this computational catalogue establishes global priority or replaces independent verification. ## pattern:hat-wake-traveller ### Verified behaviour A compact traveller under a separately evolved four-state priority table. The six-cell catalogue seed is verified for 293 generations on the depth-5 Hat touch graph. A polygon-preserving placement of the same labelled seed on the depth-6 patch remains nonzero for 1,000 generations, visits 2,447 tiles, and displaces its nonzero-cell centroid by 1,071.983213 coordinate units; at most nine cells are nonzero at any instant. ### Interpretation and limits Finite aperiodic travel only: neither indefinite flight nor historical priority is established. The instantaneous support may have two connected components. The 341 failed state projections distinguish the observed mature local transitions from six stored reference tables, not every possible travelling mechanism. The state-3 wake is not proven necessary for transport. No earlier exact configuration or table was identified in the reviewed sources. ### Pattern provenance and credit The table arose in a fresh random evolutionary lineage (evaluation 358893, epoch 11). Four rows reproduce the retained seven-row trajectory. No exact precedent was identified in the literature reviewed to 14 October 2026. Edmond’s published framework and gliders remain prior work [2,3]. ## pattern:hat-edmond-a-six-way-launcher ### Verified behaviour A connected six-cell launch under Edmond's unchanged Hat A table produces six independently evolving compact travelling bodies. From generation 60 through 180, independently evolving the six separated bodies reconstructs the complete labelled state at every generation. Each body has a checked translated return of its occupied polygons and three surrounding empty neighbour rings. ### Interpretation and limits A finite one-off launcher, not a repeating gun. The rule and glider mechanism were published by James Edmond; the contribution catalogued here is the searched launch configuration. No claim of an indefinitely traversable outgoing corridor or historical priority is made. All proper nonempty subsets fail to reproduce the checked full endpoint, which does not establish globally minimal seed size among all placements. ### Pattern provenance and credit The package found this interacting six-cell seed. The local rule and travelling mechanism belong to Edmond [2,3]. Failure of all 31 initial bipartitions and all proper seed subsets to reproduce the checked outcome does not prove global seed minimality. ## pattern:hat-edmond-b-periodic-emitter ### Verified behaviour A three-cell seed under Edmond's Hat B table reaches a 56-cell source C at parent generation 30. For the complete nonzero state, F^40(C) is the disjoint union of C and a 23-cell emitted packet E. The packet decomposes into four independently travelling bodies in two streams, with successive bodies in each stream delayed by 20 generations. Independent cohort evolution reconstructs every source state from time 0 through 180. Source time 0 is parent generation 30, so source time 180 corresponds to parent generation 210. ### Interpretation and limits This verifies four complete 40-generation emission intervals on the checked finite substrate, not a least source period of 40 or perpetual gun operation. The source is the entire state at parent generation 30 and needs no external feed during the checked interval. An earlier 38-cell crop is not this certificate. James Edmond’s Hat B table and gliders are the published rule and mechanism [2, 3]; no exact precedent for this emitting seed was identified in the literature reviewed to 14 October 2026. ### Pattern provenance and credit The package found this three-cell source seed under Edmond’s unchanged Hat B rule. Credit for the rule and travelling mechanism belongs to Edmond [2,3]. No exact precedent for this emitting configuration was identified in the literature reviewed to 14 October 2026. ## pattern:hat-b2s1-c3-rotor-p39 ### Verified behaviour An exact least-period-39 oscillator under B2/S1 with three states and edge adjacency. The complete labelled state advances by a 120-degree clockwise rotation after every 13 generations. The recurrent support consists of 39 Hat tiles, all of whose state histories have least temporal period 39. ### Interpretation and limits The rotation maps the recurrent occupied territory and its induced adjacency graph. It does not assert rotational symmetry of the entire Hat tiling. Instantaneous support can be disconnected. This is a bounded rotating oscillator with zero net translation, not a spaceship. ### Pattern provenance and credit Found by the package’s compact-seed oscillator search under three-state B2/S1 on the shared-edge graph. The retained phase is an exact period-39 rotating wave. Its original search record identifies trial 44 of the B2/S1 edge-orbit follow-up. No exact precedent identified in the literature reviewed to 14 October 2026. ## pattern:hat-b2s23-c6-rotor-p219 ### Verified behaviour An exact least-period-219 oscillator under B2/S23 with six states and edge adjacency. The complete labelled state advances by a 120-degree clockwise rotation after every 73 generations. Its recurrent support has 300 tiles, each with least temporal period 219, so the period is not just the least common multiple of independent shorter clocks. ### Interpretation and limits The verified rotational relation concerns the recurrent support and its induced graph, not a symmetry of the whole Hat tiling. The object is a bounded oscillator, not a translating glider; instantaneous support can be disconnected. ### Pattern provenance and credit Found by the package’s compact-seed oscillator search under six-state B2/S23 on the shared-edge graph. The retained phase is an exact period-219 rotating wave. Its original pilot record identifies trial 122 for that rule and state count. No exact precedent identified in the literature reviewed to 14 October 2026. ## pattern:hat-b2s13-c4-clock-p11 ### Verified behaviour A two-live-cell seed produces an exact least-period-11 oscillator under B2/S13 with four states and edge adjacency. The union of occupied tiles over a cycle contains eight tiles. Using the same two-cell seed, every state count C from 4 through 255 was independently checked to give least period 2C+3, with the same eight-tile support and an identically zero 12-tile exterior halo. ### Interpretation and limits The family formula is computationally verified for 4 <= C <= 255; no extrapolation beyond that range is claimed. C counts state 0 as well as live and refractory states. The browser exposes state counts only through 32, although the core supports the larger checked range. ### Pattern provenance and credit Developed from an eight-tile clock found by the package’s B2/S13 search at ten states (trial 1730). The catalogue keeps the same two-live-cell phase and changes the state count to four, giving period 11. The relation period = 2C + 3 was then checked for C = 4 through 255. No exact precedent identified in the literature reviewed to 14 October 2026. ## pattern:hat-directional-transient-83 ### Verified behaviour A ten-cell labelled phase under B2/S1 with ten states and touch adjacency generates a directional transient. No live cells remain from generation 75; the remaining refractory states have all vanished at generation 83. Its total visited support contains 344 tiles, and its maximum instantaneous nonzero population is 76. ### Interpretation and limits Complete extinction is verified. This is not a glider or spaceship. The seed contains nine state-1 cells and one state-7 refractory cell, so describing it as ten live cells would be incorrect. The occupied support is not connected at every time. ### Pattern provenance and credit Selected from the package’s Hat B/S motion search and reduced to a ten-cell complete phase, including one refractory cell. The reduction preserves the retained parent state at generation 40. All activity ends at generation 83; the example is a directional transient, not a glider. No exact precedent identified in the literature reviewed to 14 October 2026. ## pattern:hat-conway-p6 ### Verified behaviour An isolated oscillator of exact least period 6 under B3/S23 with two states on the Hat touch graph. The union of occupied tiles over its complete cycle has 15 tiles, while the instantaneous live population ranges from 10 to 13. ### Interpretation and limits The standard rule-family name does not imply that this Hat configuration was published previously. No exact precedent was identified in the literature reviewed to 14 October 2026; unexamined or unpublished earlier work may exist. The full labelled state, not a population count or partial image, is used for recurrence verification. ### Pattern provenance and credit Extracted from a deterministic soup by the package’s oscillator miner: source seed hat-touch-B3/S23-2-osc-v3-2285, density 0.35. The isolated component has period 6. No exact precedent identified in the literature reviewed to 14 October 2026. ## pattern:hat-conway-p9 ### Verified behaviour An isolated oscillator of exact least period 9 under B3/S23 with two states on the Hat touch graph. The union of occupied tiles over its complete cycle has 11 tiles, while the instantaneous live population ranges from 8 to 9. ### Interpretation and limits The standard rule-family name does not imply that this Hat configuration was published previously. No exact precedent was identified in the literature reviewed to 14 October 2026; unexamined or unpublished earlier work may exist. The full labelled state, not a population count or partial image, is used for recurrence verification. ### Pattern provenance and credit Extracted from the package’s deterministic Conway-rule soup hat-touch-osc-61 at density 0.30. The whole soup has period 18; the isolated catalogue component has period 9. The name credits Conway’s B3/S23 rule, not authorship of this hat configuration. No exact precedent identified in the literature reviewed to 14 October 2026. ## pattern:hat-conway-p26 ### Verified behaviour An isolated oscillator of exact least period 26 under B3/S23 with two states on the Hat touch graph. The union of occupied tiles over its complete cycle has 14 tiles, while the instantaneous live population ranges from 6 to 10. ### Interpretation and limits The standard rule-family name does not imply that this Hat configuration was published previously. No exact precedent was identified in the literature reviewed to 14 October 2026; unexamined or unpublished earlier work may exist. The full labelled state, not a population count or partial image, is used for recurrence verification. ### Pattern provenance and credit Extracted from the package’s deterministic Conway-rule soup hat-touch-osc-27 at density 0.35. The isolated catalogue component has period 26. The name credits Conway’s B3/S23 rule, not authorship of this hat configuration. No exact precedent identified in the literature reviewed to 14 October 2026. ## pattern:hat-edge-conway-p15 ### Verified behaviour An isolated oscillator of exact least period 15 under B3/S23 with two states on the Hat shared-edge graph. The union of occupied tiles over its complete cycle has 31 tiles, while the instantaneous live population ranges from 24 to 29. ### Interpretation and limits The standard rule-family name does not imply that this Hat configuration was published previously. No exact precedent was identified in the literature reviewed to 14 October 2026; unexamined or unpublished earlier work may exist. The full labelled state, not a population count or partial image, is used for recurrence verification. ### Pattern provenance and credit Extracted from a deterministic soup by the package’s oscillator miner: source seed hat-edge-B3/S23-2-osc-v3-467, density 0.35. This is an exact period-15 component on the shared-edge hat graph, using Conway’s B3/S23 counts. No exact precedent identified in the literature reviewed to 14 October 2026. ## pattern:hat-seeds-p8 ### Verified behaviour An isolated oscillator of exact least period 8 under B2/S with two states on the Hat shared-edge graph. The union of occupied tiles over its complete cycle has 12 tiles, while the instantaneous live population ranges from 4 to 5. ### Interpretation and limits The standard rule-family name does not imply that this Hat configuration was published previously. No exact precedent was identified in the literature reviewed to 14 October 2026; unexamined or unpublished earlier work may exist. The full labelled state, not a population count or partial image, is used for recurrence verification. ### Pattern provenance and credit Extracted from a deterministic soup by the package’s oscillator miner: source seed hat-edge-B2/S-2-osc-v3-97, density 0.04. The four-live-cell catalogue phase has period 8 on the shared-edge hat graph. Seeds names the B2/S rule family; it does not identify a published source for this particular configuration. No exact precedent identified in the literature reviewed to 14 October 2026. ## pattern:hat-b23-p20 ### Verified behaviour An isolated oscillator of exact least period 20 under B23/S with two states on the Hat shared-edge graph. The union of occupied tiles over its complete cycle has 32 tiles, while the instantaneous live population ranges from 10 to 16. ### Interpretation and limits The standard rule-family name does not imply that this Hat configuration was published previously. No exact precedent was identified in the literature reviewed to 14 October 2026; unexamined or unpublished earlier work may exist. The full labelled state, not a population count or partial image, is used for recurrence verification. ### Pattern provenance and credit Extracted from a deterministic soup by the package’s oscillator miner: source seed hat-edge-B23/S-2-osc-v3-333, density 0.12. The whole soup has period 60; the isolated catalogue component has period 20. No exact precedent identified in the literature reviewed to 14 October 2026. ## pattern:hat-b23-p24 ### Verified behaviour An isolated oscillator of exact least period 24 under B23/S with two states on the Hat shared-edge graph. The union of occupied tiles over its complete cycle has 21 tiles, while the instantaneous live population ranges from 8 to 11. ### Interpretation and limits The standard rule-family name does not imply that this Hat configuration was published previously. No exact precedent was identified in the literature reviewed to 14 October 2026; unexamined or unpublished earlier work may exist. The full labelled state, not a population count or partial image, is used for recurrence verification. ### Pattern provenance and credit Extracted from a deterministic soup by the package’s oscillator miner: source seed hat-edge-B23/S-2-osc-v3-748, density 0.10. The eight-live-cell catalogue phase has period 24. No exact precedent identified in the literature reviewed to 14 October 2026. ## pattern:hat-b23-p28 ### Verified behaviour An isolated oscillator of exact least period 28 under B23/S with two states on the Hat shared-edge graph. The union of occupied tiles over its complete cycle has 37 tiles, while the instantaneous live population ranges from 14 to 20. ### Interpretation and limits The standard rule-family name does not imply that this Hat configuration was published previously. No exact precedent was identified in the literature reviewed to 14 October 2026; unexamined or unpublished earlier work may exist. The full labelled state, not a population count or partial image, is used for recurrence verification. ### Pattern provenance and credit Extracted from a deterministic soup by the package’s oscillator miner: source seed hat-edge-B23/S-2-osc-v3-694, density 0.16. The whole soup has period 56; the isolated catalogue component has period 28. No exact precedent identified in the literature reviewed to 14 October 2026. ## pattern:hat-two-row-relay ### Verified behaviour A two-cell seed travels under the three-state, two-row rule R13. Generations 60–235 match James Edmond’s Spectre relay [2, 3] after state relabelling. Verified through 235 finite generations; the complete support can split. ### Interpretation and limits The checked mature trajectories agree; the complete transition rules do not. R13 and Edmond’s Spectre table [3] have different ignition and transition conditions outside that trajectory. Finite travel does not prove indefinite propagation. ### Pattern provenance and credit R13 was obtained by simplifying the package’s evolved wake rule R15. Its mature trajectory matches James Edmond’s Spectre relay in The Glider Compendium [3], with package states (0,1,2) mapped to Edmond states (0,3,1). The global transition conditions and ignition differ. Edmond’s paper [2] supplies the published framework; this entry does not claim an independent discovery of the reproduced travelling mechanism. ## pattern:hat-edmond-b-glider ### Verified behaviour A two-cell seed launches a compact Hat glider under James Edmond’s published B priority table. Verified through 307 generations with a dead boundary buffer; no immortality or first-discovery claim. The recorded trajectory contains at most 13 nonzero cells and stays at least 4 graph rings from the boundary. ### Interpretation and limits The package verifies this particular placement through generation 307 with at least four boundary rings. The Hat B rule and travelling behaviour are published by James Edmond [2, 3]; neither indefinite travel nor independent historical priority is inferred from this finite run. ### Pattern provenance and credit James Edmond — Hat B; seed placement found for Aperiodic Life [2, 3, 18]. Uses Edmond’s published Hat B transition rule and previously demonstrated travelling behaviour. Aperiodic Life independently selected this two-cell placement on its own finite hat patch; its tile numbering and recorded trajectory are not an import of Edmond’s saved run. The package’s finite replay does not establish indefinite propagation. ## pattern:hat-edmond-a-glider ### Verified behaviour A two-cell seed launches a compact Hat glider under James Edmond’s published A priority table. Verified through 307 generations with a dead boundary buffer; no immortality or first-discovery claim. The recorded trajectory contains at most 14 nonzero cells and stays at least 4 graph rings from the boundary. ### Interpretation and limits The package verifies this particular placement through generation 307 with at least four boundary rings. James Edmond’s Hat A rule and travelling behaviour appear in The Glider Compendium [3] and paper [2]. Aperiodic Life’s different seed placement does not establish a new glider discovery. ### Pattern provenance and credit James Edmond — Hat A; seed placement found for Aperiodic Life [2, 3, 18]. Uses Edmond’s published Hat A transition rule and previously demonstrated travelling behaviour. Aperiodic Life independently selected this two-cell placement on its own finite hat patch; its tile numbering and recorded trajectory are not an import of Edmond’s saved run. The package’s finite replay does not establish indefinite propagation. ## pattern:hat-edmond-c-glider ### Verified behaviour A two-cell seed launches a compact Hat glider under James Edmond’s published C priority table. Verified through 311 generations with a dead boundary buffer; no immortality or first-discovery claim. The recorded trajectory contains at most 18 nonzero cells and stays at least 4 graph rings from the boundary. ### Interpretation and limits The package checks this placement through generation 311 with at least four boundary rings. A finite translated local neighbourhood is not a proof that the full future substrate will repeat. James Edmond’s Hat C rule and travelling behaviour are published in The Glider Compendium [3] and paper [2]. ### Pattern provenance and credit James Edmond — Hat C; seed placement found for Aperiodic Life [2, 3, 18]. Uses Edmond’s published Hat C transition rule and previously demonstrated travelling behaviour. Aperiodic Life independently selected this two-cell placement on its own finite hat patch; its tile numbering and recorded trajectory are not an import of Edmond’s saved run. The package’s finite replay does not establish indefinite propagation. ## pattern:hat-simple-glider ### Verified behaviour R14 is a three-state modification of James Edmond’s Hat B rule R11 [2, 3]. It reproduces the tested compact flights after relabelling, but differs on other inputs. The recorded trajectory contains at most 13 nonzero cells and stays at least four graph rings from the boundary. ### Interpretation and limits Agreement holds for the checked trajectories, not every input. A retained counterexample separates R14 from Edmond’s Hat B rule R11 [3]. Finite agreement does not prove endless travel. ### Pattern provenance and credit R14 modifies James Edmond’s Hat B rule R11 [2, 3]: remove the state unreachable from the checked two-cell launch, relabel parent state 3 as 2, and drop the empty-neighbour birth condition. These changes give three states and preserve the checked launches, but alter other inputs. The parent rule and travelling mechanism are Edmond’s; the package contributes this simplification, without claiming that no earlier equivalent simplification exists. ## pattern:hat-edmond-c-triple-launcher ### Verified behaviour Two cells under Edmond’s C rule emit three separated compact travellers. Their complete independent evolutions reproduce the whole configuration through generation 160, with no leftover debris. This is a finite launcher, not a repeating gun. The recorded trajectory contains at most 39 nonzero cells and stays at least 34 graph rings from the boundary. ### Interpretation and limits This is a finite launch, not a repeating gun. Edmond’s Glider Compendium [3] already demonstrates Hat C triple emission; the package independently selected a placement and verifies its finite evolution. ### Pattern provenance and credit James Edmond — Hat C triple launch; seed placement found for Aperiodic Life [2, 3, 18]. Edmond’s compendium already demonstrates a two-cell Hat C seed producing three gliders. This catalogue entry uses the same published rule with a placement independently selected on Aperiodic Life’s patch. Its three separated travellers are verified through the stated finite horizon. It is a reproduction of published launch behaviour, not a claim to the first triple launcher or a repeating gun. ## pattern:hat-b1-field ### Verified behaviour A deterministic pseudorandom B1/S field with two states, touch adjacency, density 0.12, random seed hat-touch-B1/S-2 and eight locked dead boundary rings remains dynamically active through 3,000 generations on the 7,921-tile depth-4 Hat patch. ### Interpretation and limits A constructed finite-board demonstration of collective activity, not a compact discovered structure or a novel rule. Persistence to 3,000 does not prove nonperiodic behaviour, indefinite persistence on an infinite tiling, or lack of a finite-board eventual cycle. It is classified as a package construction, C04. ### Pattern provenance and credit A reproducible pseudorandom field constructed for the package’s rule survey, using seed hat-touch-B1/S-2, density 0.12 and an eight-ring dead border. It was selected because it remains active through 3,000 generations. This is a finite-board demonstration of collective dynamics, not an attributed compact pattern or a claim of a newly discovered rule. ## pattern:penrose-b2-c6-twelve-launcher ### Verified behaviour Three initially live cells produce twelve compact bodies whose independent evolutions reconstruct the entire configuration at every generation from 90 through 130. All twelve have observed translated full-state/polygon returns; five also have a verified matching three-ring neighbourhood return. ### Interpretation and limits A finite, placement-dependent one-off launcher in the B2/S six-state travelling family R22, illustrated by P13. It is neither a repeating gun nor evidence for a new propagating mechanism. Locally matching transplants do not necessarily preserve the twelve-body outcome. ### Pattern provenance and credit Three live cells selected by the connected/phased-seed campaign launch twelve independent compact bodies from generation 90 to 130, with a minimum observed boundary distance of seven graph steps. All twelve have translated full-state and polygon returns, while five have radius-three halo returns within that horizon. All six nonempty proper seed subsets differ at generation 130. This is a finite launcher using the package travelling family R22 (P13), not a new glider mechanism or repeating gun. Larger locally matching placements need not preserve this outcome. No exact precedent was identified in the literature reviewed to 14 October 2026. ## pattern:penrose-b2-c5-five-launcher ### Verified behaviour Three initially live cells yield five compact five-state travelling bodies. From generation 120 through 240 the five independently simulated bodies reproduce the complete state; each has an observed full-state translated return with matching tile polygons and three neighbourhood rings. ### Interpretation and limits A finite one-off launch using the B2/S travelling family; no repeating source or indefinite continuation has been established. ### Pattern provenance and credit This three-live-cell launch and its depth-11 placement were located by the package's connected-seed search and polygon-matched transplants. Its five emitted bodies use the B2/S five-state family R21 (P12), with finite verification through generation 240. This identifies the origin of this recorded launch, not a first-discovery claim for the rule or propagating mechanism. Goucher’s earlier published Penrose gliders use a different rule [4]. ## pattern:penrose-b2-c6-six-launcher ### Verified behaviour Three initially live cells yield six compact six-state travelling bodies. From generation 120 through 200 their independent evolutions reproduce the complete state; each has an observed full-state translated return with matching tile polygons and three neighbourhood rings. ### Interpretation and limits A finite one-off launch using the B2/S travelling family; no repeating source or indefinite continuation has been established. ### Pattern provenance and credit This three-live-cell launch and its depth-11 placement were located by the package's connected-seed search and polygon-matched transplants. Its six emitted bodies use the B2/S six-state family R22 (P13), with finite verification through generation 200. This identifies the origin of this recorded launch, not a first-discovery claim for the rule or propagating mechanism. Goucher’s earlier published Penrose gliders use a different rule [4]. ## pattern:penrose-edge-b23s23-p822 ### Verified behaviour An exact least-period-822 stationary oscillator starts from nineteen live tiles and visits a total of forty-six tiles. Thirty-nine individual sites have least temporal period 822, excluding an explanation solely as independent smaller-period oscillators. ### Interpretation and limits Uses B23/S23 with edge adjacency, not ordinary Conway B3/S23 on the contact graph. The rule, graph and complete state are essential to the identity. ### Pattern provenance and credit Recovered in the package's focused B23/S23 edge search, then transplanted from depth 7 to depth 8. The recorded full period is 822 and 39 individual sites have that period. Owens–Stepney is earlier work on Penrose oscillators, but its Conway touch-graph catalogue does not establish authorship of this different-rule edge-graph pattern. No exact precedent was identified in the literature reviewed to 14 October 2026. Earlier Penrose oscillator catalogue: Owens and Stepney [5]. ## pattern:penrose-conway-c3-p14 ### Verified behaviour Four live and two refractory tiles initiate an exact least-period-14 stationary oscillator, using three-state B3/S23 Generations on the contact graph. ### Interpretation and limits This is a three-state rule. A binary Penrose oscillator of the same period is not thereby a precedent for the same pattern. ### Pattern provenance and credit Recovered in the package's multistate oscillator survey and transplanted from depth 7 to depth 8. This is a three-state B3/S23 Generations oscillator; it must not be identified with a published binary Penrose oscillator merely by period. No exact precedent was identified in the literature reviewed to 14 October 2026. Earlier Penrose oscillator catalogue: Owens and Stepney [5]. ## pattern:penrose-conway-p4 ### Verified behaviour An eleven-live-tile phase belongs to a least-period-4 contact-graph Conway oscillator; twelve tiles occur in its cycle support and its live population ranges from nine to twelve. ### Interpretation and limits Owens and Stepney’s Penrose Life catalogue [5] is relevant earlier work. An exact identification with its illustrated patterns has not been established; independent recovery from soup is not proof of originality. ### Pattern provenance and credit The package record recovers this exact phase from deterministic soup penrose-touch-B3/S23-2-osc-v3-6566, density 0.16. It has 12 support tiles and minimum population 9. Penrose Conway oscillators were catalogued by Owens and Stepney, but an exact identification with their illustrated patterns has not been established; this is a package search attribution, not a worldwide originality claim. Earlier Penrose oscillator catalogue: Owens and Stepney [5]. ## pattern:penrose-conway-p5 ### Verified behaviour An eight-live-tile phase belongs to a least-period-5 contact-graph Conway oscillator with eighteen-tile cycle support and live population between eight and ten. ### Interpretation and limits Its support and minimum population differ from the published r-p5-14-7 juggler, excluding that particular invariant match. Other possible antecedents have not been ruled out. ### Pattern provenance and credit The exact phase is recorded under soup penrose-touch-B3/S23-2-osc-v3-1151, density 0.35. It has 18 support tiles and minimum population 8. It is not identified with the published r-p5-14-7 juggler: those support/population invariants differ. No exact earlier match was identified in the literature reviewed to 14 October 2026. Earlier Penrose oscillator catalogue: Owens and Stepney [5]. ## pattern:penrose-conway-p7 ### Verified behaviour An eleven-live-tile phase belongs to a least-period-7 contact-graph Conway oscillator; twenty tiles occur during the cycle and the live population ranges from seven to eleven. ### Interpretation and limits Owens and Stepney’s Penrose oscillator catalogue [5] is directly relevant; exact earlier-pattern identity remains unresolved. ### Pattern provenance and credit The package soup replay records seed penrose-touch-osc-149, density 0.16, and this exact isolated period-7 phase. It has 20 support tiles and minimum population 7. No exact earlier match was identified in Owens and Stepney’s Penrose oscillator catalogue [5] in the review to 14 October 2026. ## pattern:penrose-conway-p12 ### Verified behaviour A six-live-tile phase belongs to a least-period-12 contact-graph Conway oscillator with thirty-three-tile cycle support and live population between six and fourteen. ### Interpretation and limits The published fireworks oscillator has matching period, territory and minimum population, but those invariants do not uniquely identify an oscillator. The possible antecedent remains unresolved; no originality claim is made. ### Pattern provenance and credit POSSIBLE PUBLISHED ANTECEDENT: the Owens-Stepney fireworks pattern r-p12-33-6 shares its period, territory and minimum population [5,6]. Complete phase-and-neighbourhood identity has not been established. Treat priority as unresolved, not original. ## pattern:penrose-edge-conway-p4 ### Verified behaviour A twenty-three-live-tile phase initiates a least-period-4 edge-graph Conway oscillator with twenty-five-tile cycle support and live population between twenty-two and twenty-five. ### Interpretation and limits The edge graph differs from the generalised Moore/contact graph used in the cited Owens–Stepney catalogue. Shared rule notation and period do not establish identity. ### Pattern provenance and credit The exact phase is recorded under soup penrose-edge-B3/S23-2-osc-v3-4732, density 0.30. This example uses edge adjacency, unlike the generalised Moore contact graph in the cited Penrose Conway catalogue. Same rule name or period alone does not identify an earlier exact pattern; no exact precedent was identified in the literature reviewed to 14 October 2026. Earlier Penrose oscillator catalogue: Owens and Stepney [5]. ## pattern:penrose-b2-c4-compact-traveller ### Verified behaviour A seven-nonzero-tile phased seed remains connected and compact through 220 generations, traversing 193.270 tile-edge units with seven to eleven nonzero tiles. Generations 102 and 164 have a complete-state translated return with matching three-ring local neighbourhoods. ### Interpretation and limits Finite propagation only: a translated return of the occupied state and three surrounding graph rings does not prove that the aperiodic tiling ahead continues to provide equivalent neighbourhoods indefinitely. Adam P. Goucher’s Penrose gliders [4] use a different transition rule. ### Pattern provenance and credit The package retains an explicit source phase and a polygon-preserving transplant verifier. It is a 4-state B2/S live-front/refractory-wake example with a finite 220-generation certificate. Earlier published Penrose gliders use a different rule; no exact-pattern identity with them is asserted. The general refractory idea is established, and no worldwide first-discovery claim is made for this Penrose phase. Earlier Penrose glider work under a different rule: Goucher [4]. ## pattern:penrose-b2-c5-compact-traveller ### Verified behaviour An eleven-nonzero-tile phased seed remains connected and compact through 220 generations, traversing 192.391 tile-edge units with eleven to fourteen nonzero tiles. Generations 59 and 161 have a complete-state translated return with matching three-ring local neighbourhoods. ### Interpretation and limits Finite propagation only: a translated return of the occupied state and three surrounding graph rings does not prove that the aperiodic tiling ahead continues to provide equivalent neighbourhoods indefinitely. Adam P. Goucher’s Penrose gliders [4] use a different transition rule. ### Pattern provenance and credit The recorded depth-10 phase is taken from the package's five-state traveller campaign. It is a 5-state B2/S live-front/refractory-wake example with a finite 220-generation certificate. Earlier published Penrose gliders use a different rule; no exact-pattern identity with them is asserted. The general refractory idea is established, and no worldwide first-discovery claim is made for this Penrose phase. Earlier Penrose glider work under a different rule: Goucher [4]. ## pattern:penrose-b2-c6-compact-traveller ### Verified behaviour A fourteen-nonzero-tile phased seed remains connected and compact through 220 generations, traversing 192.268 tile-edge units with fourteen to eighteen nonzero tiles. Generations 80 and 143 have a complete-state translated return with matching three-ring local neighbourhoods. ### Interpretation and limits Finite propagation only: a translated return of the occupied state and three surrounding graph rings does not prove that the aperiodic tiling ahead continues to provide equivalent neighbourhoods indefinitely. Adam P. Goucher’s Penrose gliders [4] use a different transition rule. ### Pattern provenance and credit The recorded depth-10 phase is taken from the package's six-state traveller campaign. It is a 6-state B2/S live-front/refractory-wake example with a finite 220-generation certificate. Earlier published Penrose gliders use a different rule; no exact-pattern identity with them is asserted. The general refractory idea is established, and no worldwide first-discovery claim is made for this Penrose phase. Earlier Penrose glider work under a different rule: Goucher [4]. ## pattern:penrose-b24-c4-launcher-traveller ### Verified behaviour A phased seed of twenty-seven nonzero tiles (ten live and seventeen refractory) produces eight B4 births by generation 14 before settling into a compact B2/S-type wave. The complete configuration traverses 171.841 tile-edge units through generation 200, becoming continuously connected from generation 27. ### Interpretation and limits The added B4 clause affects launch; the mature recurrent body belongs to the B2/S family. The recorded seed and launch are distinct catalogue objects, not a new recurrent glider mechanism. ### Pattern provenance and credit The package's altered-rule search supplied this 27-cell phased launcher. Eight B4 births affect its launch; its mature travelling core belongs to the package's B2/S family. This attributes the recorded seed and launch mechanism, not a new recurrent glider core or a proved immortal Penrose glider. No external exact-pattern source has been established. ## pattern:penrose-b2s4-c5-survival-launcher ### Verified behaviour Seven initially live tiles undergo two S4 survivals by generation 7 and launch a five-state B2/S-type wave. The configuration traverses 170.831 tile-edge units in 200 generations, becoming continuously connected from generation 14. ### Interpretation and limits S4 affects ignition but does not establish a new mature travelling mechanism. This is a finite one-off launch. ### Pattern provenance and credit This seven-live-cell seed comes from the package's Penrose traveller search. Two S4 survivals distinguish its launch before it settles into the established B2/S-type wave. The exact seed, clause ablation and finite traversal are documented; no exact precedent for this launch was identified in the literature reviewed to 14 October 2026. ## pattern:penrose-b26s-c4-birth-launcher ### Verified behaviour An eighteen-nonzero-tile phased seed uses one B6 birth at the first update, then self-cleans into a four-state B2/S-type wave. It traverses 175.890 tile-edge units in 200 generations and remains connected from generation 5. ### Interpretation and limits The extra B6 birth is an ignition event. The eventual travelling body uses the established B2/S mechanism; no indefinite continuation is established. ### Pattern provenance and credit The package search supplied this eighteen-cell phased seed. One B6 birth genuinely affects the launch; its eventual recurrent wave uses the B2/S four-state mechanism R20 (P11). It is a separately recorded launcher rather than evidence of a new recurrent rule mechanism. No exact precedent was identified in the literature reviewed to 14 October 2026. ## pattern:penrose-b27s4-c4-dual-clause-launcher ### Verified behaviour Twenty-six live tiles use four B7 births at the first update and seven S4 survivals by generation 4, then self-clean into a four-state B2/S-type wave. The configuration traverses 177.349 tile-edge units in 200 generations, becoming continuously connected from generation 6. ### Interpretation and limits Both added clauses affect launch, but the mature core belongs to the B2/S family. This is neither a new recurrent rule mechanism nor a repeating gun. ### Pattern provenance and credit The recorded 26-live-cell launch comes from the package's altered-rule campaign. Both added clauses fire during launch: B7 births and S4 survivals. The mature core belongs to the B2/S travelling family. This identifies the package search that produced the seed; no exact precedent was identified in the literature reviewed to 14 October 2026. ## pattern:penrose-conway-diehard-293 ### Verified behaviour Fourteen initially live tiles remain nonempty through generation 292 and become completely extinct at generation 293; the maximum live population is seventy-nine. ### Interpretation and limits This is an exactly reproduced lifetime in the recorded finite patch, not a claim to a Penrose lifetime record. Earlier Penrose Life statistical studies do not by themselves identify the exact seed. ### Pattern provenance and credit This exact fourteen-cell seed is the retained extinction-at-293 result of the package's 5,000-candidate transient campaign, deterministic seed penrose-touch-B3/S23-2-transient-v1. Earlier Penrose Life lifetime studies provide context, but do not identify this exact initial state. No world-record or original-discovery claim is made. Earlier statistical investigation, not the source of this seed: Owens and Stepney [10]. ## pattern:penrose-conway-methuselah-289 ### Verified behaviour Twenty-two initially live tiles reach a four-live-tile fixed point after a transient of exactly 289 generations. ### Interpretation and limits The displayed seed is a long transient, not a moving body or an oscillator of period 289. No longest-known or first-discovery claim is justified. ### Pattern provenance and credit The exact 22-live-cell seed is the retained result of the package's 35,000-candidate campaign penrose-touch-b3s23-transient-v2. Its transient is 289 generations before a fixed point. This is a locally documented search result, not an attribution of the underlying Conway rule or a claim to the longest known Penrose transient. Earlier statistical investigation, not the source of this seed: Owens and Stepney [10]. ## pattern:penrose-b12-p840-field ### Verified behaviour A deterministic finite random field reaches a complete-state cycle of least period 840 after a transient of 51 generations. During the cycle 5,252 tiles are nonzero at some time and the live population ranges from 2,553 to 2,587. ### Interpretation and limits A package-generated field, not an indivisible local oscillator. Its period may combine smaller local periods. Neither an original rule nor a novel mechanism is claimed. ### Pattern provenance and credit The initial field is generated by the package from seed penrose-edge-B12/S-2, density 0.12 and eight dead border rings. The finite field has transient 51 and period 840. This is a reproducible seeded demonstration, not a claim to an independently indivisible period-840 oscillator or an original cellular-automaton rule. ## pattern:penrose-brain-field ### Verified behaviour A deterministic finite initial field remains active through generation 3,000 under three-state B2/S on the Penrose contact graph; generation 3,000 has 607 live tiles. ### Interpretation and limits The state transition is Brian Silverman’s established Brain rule, transferred to a different graph. This is a seeded field demonstration, not an unpreceded fixed pattern, periodicity proof, or infinite-activity proof. ### Pattern provenance and credit The B2/S three-state transition is Brian Silverman’s Brain rule, documented in Rucker and Walker’s CelLab manual [7], here applied to the Penrose touch graph instead of its usual square neighbourhood. The exact random field is package-generated from seed penrose-touch-B2/S-3 at density 0.12 with eight border rings. Its 3,000-generation observation is a finite demonstration, not a published fixed pattern or a first-discovery claim. ## pattern:hex-b245s02-c5-p6-puffer ### Verified behaviour A five-state puffer shifts by axial (−2,4) every six generations, depositing one stationary live cell each cycle. Exact separation certificates prove continued propagation on the infinite hexagonal lattice. ### Interpretation and limits Period 6 is the head-plus-deposit recurrence interval; the entire ever-growing trail is neither an oscillator nor a finite spaceship. B5 is inactive on this established puffer orbit. ### Pattern provenance and credit A moving head extracted from the three-cell mixed-state seed. Its complete period-6 recurrence and permanent separation from every deposit are certified. B5 is unused in flight; the three-cell launch uses B5 twice. This is a newly verified package example, not a claim of first discovery. ## pattern:hex-b245s02-c5-three-cell-twin-puffer-launcher ### Verified behaviour Two live cells and one refractory cell launch two opposite puffers. By generation 30 they have separated from four stationary cells; each puffer then deposits one live cell every six generations. ### Interpretation and limits This is a one-off launch of two moving emitters, not a stationary gun. Generation 30 is the first successful split among tested generations divisible by six, not a universal earliest-decomposition claim. B5 is used twice during ignition. ### Pattern provenance and credit Mixed-state exhaustive campaign, seed mixed-n3-c5-s10. Complete replay gives two opposite certified p6 puffers and four stationary live cells at generation 30. This is a finite launch, not a stationary gun. A related four-live-cell seed had remained unclassified in the earlier exhaustive campaign; no exact precedent was identified in the literature reviewed to 14 October 2026. ## pattern:hex-b2345s24-c4-p48-traveller ### Verified behaviour The complete 4-state configuration has least translated period 48, with axial displacement (-32, 16). Its recurrent orbit contains 10-23 live cells and 21-50 nonzero cells. Translation invariance gives indefinite recurrence on the unbounded hexagonal lattice. ### Interpretation and limits B5 is inactive throughout this recurrent orbit; the searched rule B2345/S24 is retained. D6/phase comparison excludes matches only within the preceding 33-entry package catalogue. Independent decomposition finds one persistent body plus short-lived sparks, not an independently repeating convoy. ### Pattern provenance and credit Seven-cell exhaustive campaign, seed n7c4s245: seven live cells settle after 16 generations into this exact period-48 ship. The displayed recurrent phase was centred for viewing. Full D6/phase comparison finds no match in the preceding 33-entry hexagonal catalogue. Independent decomposition at every phase confirms one persistent body with short-lived sparks, rather than a convoy of independently recurring ships. No worldwide priority claim is made. ## pattern:hex-b2s0-c3-three-cell-glider ### Verified behaviour The complete 3-state configuration has least translated period 2, with axial displacement (0, -1). Its recurrent orbit contains 2-3 live cells and 3-5 nonzero cells. Translation invariance gives indefinite recurrence on the unbounded hexagonal lattice. ### Interpretation and limits No earlier exact-pattern match has been identified; worldwide discovery priority is not established. The browser board is finite. Infinite-lattice conclusions, where given, concern the mathematical hexagonal lattice. ### Pattern provenance and credit Campaign small, enumerated seed 3, recorded trial 101391. Three live cells already form a period-2 spaceship in B2/S0 with three states; complete-state translation is (0,-1). The campaign enumerated connected all-live seeds of one to six cells up to translations, rotations and reflections, with all 8,192 quiescent binary birth/survival rules and state counts 2–6, subject to its documented simulation limits. This identifies the package search that produced the configuration. No exact precedent was identified in the literature reviewed to 14 October 2026. ## pattern:hex-b234s1346-c3-four-cell-launcher ### Verified behaviour The complete 3-state configuration has least translated period 8, with axial displacement (1, 1), after a 9-generation transient. Its recurrent orbit contains 7-19 live cells and 12-27 nonzero cells. Translation invariance gives indefinite recurrence on the unbounded hexagonal lattice. ### Interpretation and limits No earlier exact-pattern match has been identified; worldwide discovery priority is not established. The browser board is finite. Infinite-lattice conclusions, where given, concern the mathematical hexagonal lattice. ### Pattern provenance and credit Campaign small, enumerated seed 6, recorded trial 120894. Four live cells settle after nine generations into a period-8 spaceship translating (1,1). This is a finite launch, not a periodically emitting gun. The campaign enumerated connected all-live seeds of one to six cells up to translations, rotations and reflections, with all 8,192 quiescent binary birth/survival rules and state counts 2–6, subject to its documented simulation limits. This identifies the package search that produced the configuration. No exact precedent was identified in the literature reviewed to 14 October 2026. ## pattern:hex-b2456s1345-c4-five-cell-launcher ### Verified behaviour The complete 4-state configuration has least translated period 43, with axial displacement (-6, 3), after a 6-generation transient. Its recurrent orbit contains 5-32 live cells and 9-48 nonzero cells. Translation invariance gives indefinite recurrence on the unbounded hexagonal lattice. ### Interpretation and limits No earlier exact-pattern match has been identified; worldwide discovery priority is not established. The browser board is finite. Infinite-lattice conclusions, where given, concern the mathematical hexagonal lattice. ### Pattern provenance and credit Campaign n5, enumerated seed n5s19, recorded trial 525071. Five live cells settle after six generations into a period-43 spaceship translating (-6,3). This is a finite launch, not a periodically emitting gun. The campaign enumerated connected all-live seeds of one to six cells up to translations, rotations and reflections, with all 8,192 quiescent binary birth/survival rules and state counts 2–6, subject to its documented simulation limits. This identifies the package search that produced the configuration. No exact precedent was identified in the literature reviewed to 14 October 2026. ## pattern:hex-b23s13-c4-p9-knightship-launcher ### Verified behaviour The complete 4-state configuration has least translated period 9, with axial displacement (5, -4), after a 16-generation transient. Its recurrent orbit contains 7-15 live cells and 15-33 nonzero cells. Translation invariance gives indefinite recurrence on the unbounded hexagonal lattice. ### Interpretation and limits The term knightship identifies an oblique displacement outside the hexagonal axes and their bisectors; it does not imply that oblique hexagonal spaceships are historically new. ### Pattern provenance and credit Campaign n6, enumerated seed n6s14, recorded trial 1407298. Six live cells settle after sixteen generations into a period-9 spaceship translating (5,-4). Its oblique heading is outside the edge-axis and angle-bisector directions; this does not establish a first such hexagonal spaceship. The campaign enumerated connected all-live seeds of one to six cells up to translations, rotations and reflections, with all 8,192 quiescent binary birth/survival rules and state counts 2–6, subject to its documented simulation limits. This identifies the package search that produced the configuration. No exact precedent was identified in the literature reviewed to 14 October 2026. ## pattern:hex-b234s245-c5-p10-knightship-launcher ### Verified behaviour The complete 5-state configuration has least translated period 10, with axial displacement (1, 2), after a 12-generation transient. Its recurrent orbit contains 7-24 live cells and 22-58 nonzero cells. Translation invariance gives indefinite recurrence on the unbounded hexagonal lattice. ### Interpretation and limits Deleting S5 changes R40 to B234/S24 with C = 5 and the same six edge-sharing neighbours. Applied from generation 0 to this seed, that changed rule fails to produce the recorded spaceship. S5 is enabled throughout the original run, although it is needed only during launch and never fires in the eventual cycle. This is a one-off launcher, not a repeating gun. ### Pattern provenance and credit Campaign n6, enumerated seed n6s78, recorded trial 2166518. Six live cells settle after twelve generations into a period-10 spaceship translating (1,2). Survival clause S5 acts during the launch, although inactive in the eventual orbit; removing it before launch destroys the example. This is a finite launch, not a gun. The campaign enumerated connected all-live seeds of one to six cells up to translations, rotations and reflections, with all 8,192 quiescent binary birth/survival rules and state counts 2–6, subject to its documented simulation limits. This identifies the package search that produced the configuration. No exact precedent was identified in the literature reviewed to 14 October 2026. ## pattern:hex-conway-p2 ### Verified behaviour The complete configuration has least period 2, with 4-4 live cells and 4-4 nonzero cells. Its full cycle visits 7 distinct lattice sites. The exact finite return proves indefinite periodic continuation on the unbounded hexagonal lattice. ### Interpretation and limits No earlier exact-pattern match has been identified; worldwide discovery priority is not established. The browser board is finite. Infinite-lattice conclusions, where given, concern the mathematical hexagonal lattice. ### Pattern provenance and credit Recovered campaign provenance: deterministic soup seed hex-conway-v31-2, B3/S23 with six edge neighbours, hexagonal depth 32, density 0.12, transient 6, period 2. The archived soup campaign covered indices 0–4,999 and used a 1,200-generation limit. Exact full-orbit comparison with the archived result confirms the curated pattern. The old campaign archive was examined in the handover workspace; it is not part of the fresh release. “Conway” describes the birth/survival rule notation and is not a claim that John Conway discovered this hexagonal pattern. This identifies the package search that produced the configuration. No exact precedent was identified in the literature reviewed to 14 October 2026. ## pattern:hex-conway-p3 ### Verified behaviour The complete configuration has least period 3, with 19-21 live cells and 19-21 nonzero cells. Its full cycle visits 21 distinct lattice sites. The exact finite return proves indefinite periodic continuation on the unbounded hexagonal lattice. ### Interpretation and limits No earlier exact-pattern match has been identified; worldwide discovery priority is not established. The browser board is finite. Infinite-lattice conclusions, where given, concern the mathematical hexagonal lattice. ### Pattern provenance and credit Recovered campaign provenance: deterministic soup seed hex-conway-v31-3851, B3/S23 with six edge neighbours, hexagonal depth 32, density 0.35, transient 28, period 3. The archived soup campaign covered indices 0–4,999 and used a 1,200-generation limit. Exact full-orbit comparison with the archived result confirms the curated pattern. The old campaign archive was examined in the handover workspace; it is not part of the fresh release. “Conway” describes the birth/survival rule notation and is not a claim that John Conway discovered this hexagonal pattern. This identifies the package search that produced the configuration. No exact precedent was identified in the literature reviewed to 14 October 2026. ## pattern:hex-conway-p6 ### Verified behaviour The complete configuration has least period 6, with 19-23 live cells and 19-23 nonzero cells. Its full cycle visits 25 distinct lattice sites. The exact finite return proves indefinite periodic continuation on the unbounded hexagonal lattice. ### Interpretation and limits No earlier exact-pattern match has been identified; worldwide discovery priority is not established. The browser board is finite. Infinite-lattice conclusions, where given, concern the mathematical hexagonal lattice. ### Pattern provenance and credit Recovered campaign provenance: deterministic soup seed hex-conway-v31-2813, B3/S23 with six edge neighbours, hexagonal depth 32, density 0.35, transient 39, period 6. The archived soup campaign covered indices 0–4,999 and used a 1,200-generation limit. Exact full-orbit comparison with the archived result confirms the curated pattern. The old campaign archive was examined in the handover workspace; it is not part of the fresh release. “Conway” describes the birth/survival rule notation and is not a claim that John Conway discovered this hexagonal pattern. This identifies the package search that produced the configuration. No exact precedent was identified in the literature reviewed to 14 October 2026. ## pattern:hex-conway-p4 ### Verified behaviour The complete configuration has least period 4, with 14-15 live cells and 14-15 nonzero cells. Its full cycle visits 16 distinct lattice sites. The exact finite return proves indefinite periodic continuation on the unbounded hexagonal lattice. At every cycle phase, 2 further steps give a half-turn of the complete labelled state about the same fixed centre. ### Interpretation and limits No earlier exact-pattern match has been identified; worldwide discovery priority is not established. The browser board is finite. Infinite-lattice conclusions, where given, concern the mathematical hexagonal lattice. ### Pattern provenance and credit Oscillator miner source seed 272632, radius 8, initial density 60%, soup transient 19; the displayed phase is offset 1 within the resulting orbit. The computational evidence files listed for this entry retain the replayable initial state and resulting cycle. Known rule notation does not establish authorship of this exact pattern. This identifies the package search that produced the configuration. No exact precedent was identified in the literature reviewed to 14 October 2026. ## pattern:hex-conway-p5 ### Verified behaviour The complete configuration has least period 5, with 14-16 live cells and 14-16 nonzero cells. Its full cycle visits 19 distinct lattice sites. The exact finite return proves indefinite periodic continuation on the unbounded hexagonal lattice. ### Interpretation and limits No earlier exact-pattern match has been identified; worldwide discovery priority is not established. The browser board is finite. Infinite-lattice conclusions, where given, concern the mathematical hexagonal lattice. ### Pattern provenance and credit Oscillator miner source seed 1045970, radius 6, initial density 67%, soup transient 10; the displayed phase is offset 0 within the resulting orbit. The computational evidence files listed for this entry retain the replayable initial state and resulting cycle. Known rule notation does not establish authorship of this exact pattern. This identifies the package search that produced the configuration. No exact precedent was identified in the literature reviewed to 14 October 2026. ## pattern:hex-conway-p8 ### Verified behaviour The complete configuration has least period 8, with 22-25 live cells and 22-25 nonzero cells. Its full cycle visits 27 distinct lattice sites. The exact finite return proves indefinite periodic continuation on the unbounded hexagonal lattice. ### Interpretation and limits No earlier exact-pattern match has been identified; worldwide discovery priority is not established. The browser board is finite. Infinite-lattice conclusions, where given, concern the mathematical hexagonal lattice. ### Pattern provenance and credit Oscillator miner source seed 511247, radius 9, initial density 46%, soup transient 25; the displayed phase is offset 6 within the resulting orbit. The computational evidence files listed for this entry retain the replayable initial state and resulting cycle. Known rule notation does not establish authorship of this exact pattern. This identifies the package search that produced the configuration. No exact precedent was identified in the literature reviewed to 14 October 2026. ## pattern:hex-b34s234-p269 ### Verified behaviour The complete configuration has least period 269, with 25-50 live cells and 25-50 nonzero cells. Its full cycle visits 53 distinct lattice sites. The exact finite return proves indefinite periodic continuation on the unbounded hexagonal lattice. Twenty-nine individual sites have least period 269, so the period is not merely a combination of independent shorter clocks. ### Interpretation and limits No earlier exact-pattern match has been identified; worldwide discovery priority is not established. The browser board is finite. Infinite-lattice conclusions, where given, concern the mathematical hexagonal lattice. ### Pattern provenance and credit Oscillator miner source seed 15338, radius 6, initial density 18%, soup transient 182; the displayed phase is offset 266 within the resulting orbit. The computational evidence files listed for this entry retain the replayable initial state and resulting cycle. Known rule notation does not establish authorship of this exact pattern. This identifies the package search that produced the configuration. No exact precedent was identified in the literature reviewed to 14 October 2026. ## pattern:hex-b245s3-p57-pulsator ### Verified behaviour The complete configuration has least period 57, with 9-99 live cells and 9-99 nonzero cells. Its full cycle visits 231 distinct lattice sites. The exact finite return proves indefinite periodic continuation on the unbounded hexagonal lattice. ### Interpretation and limits No earlier exact-pattern match has been identified; worldwide discovery priority is not established. The browser board is finite. Infinite-lattice conclusions, where given, concern the mathematical hexagonal lattice. ### Pattern provenance and credit Binary campaign seed 20261011, trial 2586, mode 1, transient 7, chosen cycle phase offset 34. The computational evidence files listed for this entry retain the initial state and verification evidence. This identifies the package search that produced the configuration. No exact precedent was identified in the literature reviewed to 14 October 2026. ## pattern:hex-b24s3-p128-rotor ### Verified behaviour The complete configuration has least period 128, with 9-34 live cells and 9-34 nonzero cells. Its full cycle visits 118 distinct lattice sites. The exact finite return proves indefinite periodic continuation on the unbounded hexagonal lattice. At every cycle phase, 64 further steps give a half-turn of the complete labelled state about the same fixed centre. ### Interpretation and limits No earlier exact-pattern match has been identified; worldwide discovery priority is not established. The browser board is finite. Infinite-lattice conclusions, where given, concern the mathematical hexagonal lattice. ### Pattern provenance and credit Binary campaign seed 908020261011, trial 53543, mode 3, transient 25, chosen cycle phase offset 67. The computational evidence files listed for this entry retain the initial state and verification evidence. This identifies the package search that produced the configuration. No exact precedent was identified in the literature reviewed to 14 October 2026. ## pattern:hex-b234s3-p4104 ### Verified behaviour The complete configuration has least period 4104, with 12-36 live cells and 12-36 nonzero cells. Its full cycle visits 50 distinct lattice sites. The exact finite return proves indefinite periodic continuation on the unbounded hexagonal lattice. Twenty-six individual sites have least period 4104, excluding an explanation solely as independent shorter clocks. ### Interpretation and limits No earlier exact-pattern match has been identified; worldwide discovery priority is not established. The browser board is finite. Infinite-lattice conclusions, where given, concern the mathematical hexagonal lattice. ### Pattern provenance and credit Binary campaign seed 60520261011, trial 127, mode 2, transient 802, chosen cycle phase offset 2268. The computational evidence files listed for this entry retain the initial state and verification evidence. This identifies the package search that produced the configuration. No exact precedent was identified in the literature reviewed to 14 October 2026. ## pattern:hex-b2s3456-c7-p372-rotor ### Verified behaviour The complete configuration has least period 372, with 7-13 live cells and 12-21 nonzero cells. Its full cycle visits 37 distinct lattice sites. The exact finite return proves indefinite periodic continuation on the unbounded hexagonal lattice. At every cycle phase, 62 further steps give a 60-degree rotation of the complete labelled state about the same fixed centre. ### Interpretation and limits No earlier exact-pattern match has been identified; worldwide discovery priority is not established. The browser board is finite. Infinite-lattice conclusions, where given, concern the mathematical hexagonal lattice. ### Pattern provenance and credit Generations campaign first, random seed 7522551138070962214, trial 75416, original rule B25/S3456, source transient 13. The displayed rule B2/S3456 removes B5, which is inactive throughout the verified periodic orbit. Rule simplification certifies the selected complete-state orbit; it does not assert that the original preperiodic soup takes the same route under the simplified rule. This identifies the package search that produced the configuration. No exact precedent was identified in the literature reviewed to 14 October 2026. ## pattern:hex-b24s16-c3-p248-breather ### Verified behaviour The complete configuration has least period 248, with 9-124 live cells and 13-209 nonzero cells. Its full cycle visits 1281 distinct lattice sites. The exact finite return proves indefinite periodic continuation on the unbounded hexagonal lattice. At every cycle phase, 124 further steps give a half-turn of the complete labelled state about the same fixed centre. ### Interpretation and limits No earlier exact-pattern match has been identified; worldwide discovery priority is not established. The browser board is finite. Infinite-lattice conclusions, where given, concern the mathematical hexagonal lattice. ### Pattern provenance and credit The rule used in the original search was B24/S16, C = 3; this thirteen-cell recurrent phase was retained. No exact earlier pattern match was identified in the literature reviewed to 14 October 2026. Its period-248 recurrence has been independently replayed on the unbounded lattice; this does not establish discovery priority. ## pattern:hex-b23s13-c5-p138-traveller ### Verified behaviour The complete 5-state configuration has least translated period 138, with axial displacement (0, -8). Its recurrent orbit contains 9-40 live cells and 26-103 nonzero cells. Translation invariance gives indefinite recurrence on the unbounded hexagonal lattice. ### Interpretation and limits No earlier exact-pattern match has been identified; worldwide discovery priority is not established. The browser board is finite. Infinite-lattice conclusions, where given, concern the mathematical hexagonal lattice. ### Pattern provenance and credit Generations campaign million, random seed 7529271334792788165, trial 106888, original rule B235/S13, source transient 53. The displayed rule B23/S13 removes B5, which is inactive throughout the verified travelling orbit. Rule simplification certifies the selected complete-state orbit; it does not assert that the original preperiodic soup takes the same route under the simplified rule. This identifies the package search that produced the configuration. No exact precedent was identified in the literature reviewed to 14 October 2026. ## pattern:hex-b234s13-c4-p23-traveller ### Verified behaviour The complete 4-state configuration has least translated period 23, with axial displacement (10, -5). Its recurrent orbit contains 15-30 live cells and 29-62 nonzero cells. Translation invariance gives indefinite recurrence on the unbounded hexagonal lattice. ### Interpretation and limits No earlier exact-pattern match has been identified; worldwide discovery priority is not established. The browser board is finite. Infinite-lattice conclusions, where given, concern the mathematical hexagonal lattice. ### Pattern provenance and credit Generations campaign first, random seed 7522551138070962214, trial 50, original rule B2345/S135, source transient 15. The displayed rule B234/S13 removes B5 and S5, which are inactive throughout the verified travelling orbit. Rule simplification certifies the selected complete-state orbit; it does not assert that the original preperiodic soup takes the same route under the simplified rule. This identifies the package search that produced the configuration. No exact precedent was identified in the literature reviewed to 14 October 2026. ## pattern:hex-b2s35-p5-traveller ### Verified behaviour A 12-cell phase of the published B2/S35 hexagonal spaceship translates by one axial cell every five generations; the complete state return is exact. ### Interpretation and limits The exact translated recurrence establishes indefinite travel on the unbounded uniform hexagonal lattice, before any finite-board boundary effect. A different phase or orientation is not a separate discovery. ### Pattern provenance and credit John Cerkan’s 22 January 2016 B2/S35 RLE [15] is 2bo$o3bo$2bo$bo2bo$6bo$2bo2bo$4bo!. Full-orbit comparison under (q,r)=(x,y-x) proves exact equivalence: phase shift 2, rotation by one 60-degree step, no reflection, translation (3,0). Carter Bays’s 2005 paper [11, 19], Figure 3, describes the same rule, period and displacement; its drawing was not independently transcribed. Independent recovery by the package does not make this a new spaceship. ## pattern:hex-b245s3-p10-traveller ### Verified behaviour This nine-cell two-state spaceship translates by two axial cells every ten generations. Its exact recurrence and the use of every B245/S3 rule clause are verified. ### Interpretation and limits All B245/S3 clauses are used somewhere in the cycle. The finite browser board eventually truncates travel; the unbounded-lattice cycle follows from exact translation recurrence. ### Pattern provenance and credit The exact executable source is Golly’s QuickLife hexagonal example [14], RLE obo$4bo$2bo$bo2bobo$3bo$5bo!. The catalogue is D6-equivalent under (q,r)=(x,y-x); full-state replay verifies period 10 and a two-cell displacement. Carter Bays’s 2005 paper [11, 19], Figure 4, describes the rule and motion. Golly’s page does not name Bays; the executable-source comparison and the earlier scholarly account are separate evidence. ## pattern:hex-b235s146-c4-launcher-traveller ### Verified behaviour A twelve-cell seed uses three launch-only clauses before settling at generation 21 into an exact period-10 traveller that advances five axial cells per cycle. ### Interpretation and limits This is a one-off launch from the X23 spaceship seed, not a gun. Under R44, births at five live edge-neighbours and survivals at four or six occur only during ignition. Absence from the final cycle does not make those clauses dispensable for launch. John Cerkan’s RLE [15] supplies the parent seed; the changed-rule dynamics are package results. ### Pattern provenance and credit The twelve live-cell coordinates are identical to X23, the B2/S35 spaceship matched to John Cerkan’s published RLE [15]. Carter Bays gives an earlier account of the parent rule and motion [11], Figure 3. The update changes from binary R34 to B235/S146 with four states, R44. The seed settles after 21 generations into a period-10 spaceship translating (-5,0). This is a verified package adaptation; worldwide first discovery of the altered dynamics is not established. ## pattern:hex-b235s134-c5-launcher-traveller ### Verified behaviour The twelve-cell X23 spaceship seed, now under five-state rule R43, uses seven essential B5 births, then condenses into an eight-to-ten-cell period-4 traveller at generation 58. ### Interpretation and limits Seven births with exactly five live edge-neighbours occur during ignition, last entering generation 32; removing R43:B5 before launch changes the example. This is a one-off launch from John Cerkan’s published X23 seed [15], with a changed rule. Worldwide first discovery of the altered dynamics is not established. ### Pattern provenance and credit The twelve live-cell coordinates are identical to X23, the B2/S35 spaceship matched to John Cerkan’s published RLE [15]. Carter Bays gives an earlier account of the parent rule and motion [11], Figure 3. The update changes from binary R34 to B235/S134 with five states, R43. The seed settles after 58 generations into a period-4 spaceship translating (2,0). The package establishes this adaptation and verifies its launch and complete-state recurrence. ## pattern:hex-b245s35-p25-traveller ### Verified behaviour An exact B245/S35 spaceship: its complete state shifts by axial (1,1) every 25 generations, with 9–24 live cells during the cycle. ### Interpretation and limits Rediscovery, reorientation and changing the displayed phase do not establish originality. The exact complete-state recurrence guarantees the unbounded-lattice spaceship; the finite display eventually meets its boundary. ### Pattern provenance and credit Published by muzik (2019), independently rediscovered by this package’s search [9]. Outer-totalistic hexagonal rules with spaceships [9] credits muzik (2019) for B245/S35H RLE b3o$bobo$4o$bo!. Independent full-orbit comparison with the catalogue succeeds after phase shift 5, rotation by four 60-degree steps, no reflection and translation (1,1), using (q,r)=(x,y-x). Thus the package’s binary campaign seed 20261011, trial 483, mode 3, transient 57 recovered an already published spaceship. The displayed phase and orientation are not a distinct discovery. ## pattern:hex-b2s34-p48-rotor ### Verified behaviour Six live cells expand and rearrange into a half-turn after 24 generations, returning exactly after 48. The cycle has 6–16 live cells. ### Interpretation and limits This is one independently evolving component of the pair published by drc. Extracting a component does not make it a new oscillator. The original discoverer, as distinct from this retrieved publication, is not asserted. ### Pattern provenance and credit Published by drc (2016), independently rediscovered by this package’s search [20]. The 18 January 2016 RLE o16bo$obo12b2o$2b2o10bobo$5bo9bo! contains two independently oscillating six-cell components. Catalogue coordinates translated by axial (2,-1) reproduce its first component exactly at generation zero. Extracting that independent component does not create a new oscillator. The package independently recovered it in binary campaign seed 20261011, trial 194, mode 4. Dean Hickerson also mentions earlier work on the rule, but the audit does not assign him priority for this particular oscillator. ## pattern:hex-b246s246-c4-p30-gun ### Verified behaviour A 12-live-cell seed rebuilds its core every 30 generations while emitting three period-3 spaceships in different directions. Published by confocaloid; ships eventually reach this finite board's edge. ### Interpretation and limits The certificate establishes indefinitely repeated three-way emission on the unbounded hexagonal lattice, not perpetual operation on the finite browser board. Confocaloid published the gun and seed in Hexagonal Generations [8]; the package contributes verification, not authorship. ### Pattern provenance and credit Published by confocaloid (2024) [8]. The package independently verifies indefinite three-way emission. Confocaloid published the twelve-live-cell seed 3A$4A$.3A$2.2A! on 14 October 2024 in Hexagonal Generations Rules. Direct comparison confirms that the catalogue retains exactly the published initial states, after coordinate conversion and translation. The package adds a complete-state emission certificate for the period-30 core and three permanently separating output streams; that verification is not authorship of the gun. ## pattern:hex-b25s34-p20-puffer ### Verified behaviour The engine advances ten axial cells every 20 generations and leaves a period-2 oscillator behind. Published by Naszvadi, with an earlier pattern noted by Dmitry Maitak. The finite board eventually ends the trail. ### Interpretation and limits The result is an unbounded-lattice puffer certificate. The finite browser eventually ends the trail. Naszvadi’s retrieved 2024 seed is exactly matched; Maitak reports an earlier 2023 occurrence, but the first discoverer is unconfirmed, and no exact seed comparison with that earlier report is available [21, 22]. ### Pattern provenance and credit Published by Naszvadi (2024); Dmitry Maitak points to an earlier 2023 occurrence [16, 21, 22]. The package independently verifies its persistent oscillator trail. Naszvadi’s 1 February 2024 post supplies the exact twenty-three-cell RLE used here and describes it as probably known. Dmitry Maitak’s later response links to a 2023 occurrence. This audit confirms the 2024 source and the report of earlier publication, but does not establish the original discoverer or independently compare the linked 2023 seed. Initial-state comparison confirms translation-only equivalence to the 2024 RLE. The package adds a certificate of period-20 translated core recurrence and independently separating period-2 deposits. ## pattern:hex-b2s1-c3-p999-rotor ### Verified behaviour A three-state rotating wave first returns after 999 generations, making a 120-degree turn every 333. Published by c0b0p0; all refractory states are part of the rotation. ### Interpretation and limits The full cycle contains 21–129 nonzero cells but only 11–80 live cells. Counting only live cells would discard the refractory information needed for a correct recurrence. The exact published seed is replayed without a novelty claim. ### Pattern provenance and credit Published by c0b0p0 (2014); independently replayed and verified for this package [8]. The Hexagonal Generations Rules post by c0b0p0 dated 27 February 2014 supplies this exact B2/S1 three-state period-999 rotor RLE. The catalogue retains every live and refractory initial state under (q,r)=(x,y-x), followed only by a centring translation. The full-state dynamics are therefore a replay of the published object, not a new package discovery. ## pattern:hex-b23s4-p13-traveller ### Verified behaviour John Cerkan's B23/S4 spaceship returns exactly with axial shift (1,1) every 13 generations, using at most 15 live cells. ### Interpretation and limits The verified translation recurrence establishes a spaceship on the unbounded lattice. The package does not claim discovery of the seed or its dynamics. ### Pattern provenance and credit Published by John Cerkan (2020); independently replayed and verified for this package [9]. John Cerkan’s 15 March 2020 post in Outer-totalistic hexagonal rules with spaceships gives RLE o3bo$bo2bo$2b3o$2bo2bo! for B23/S4H. The catalogue is exactly this nine-cell published seed after (q,r)=(x,y-x) and a centring translation. The exact period and displacement were independently replayed. The published seed is in Cerkan’s 15 March 2020 contribution to the thread in reference [9]. ## pattern:hex-b2s1-c3-p158-traveller ### Verified behaviour Published by c0b0p0: this three-state spaceship changes shape dramatically and doubles back locally, then repeats its complete state shifted by axial (-11,22) after 158 generations. ### Interpretation and limits The live population sequence happens to repeat after 79 steps, but population is not a state: the least complete-state translational period is 158. The published c0b0p0 seed includes refractory states and is not a package discovery. ### Pattern provenance and credit Published by c0b0p0 (2014); independently replayed and verified for this package [8]. The Hexagonal Generations Rules post by c0b0p0 dated 27 February 2014 supplies this exact B2/S1 three-state period-158 spaceship RLE. The catalogue retains every live and refractory initial state under (q,r)=(x,y-x), followed only by a centring translation. The full-state dynamics are therefore a replay of the published object, not a new package discovery. ## pattern:hex-b2s34-wall-repair ### Verified behaviour Dean Hickerson's oscillating wall repairs one missing cell. Its damaged evolution rejoins the pristine period-5 wall exactly at generation 44, after the exterior debris has disappeared. ### Interpretation and limits The evidence concerns this specific one-cell defect. It does not establish recovery from arbitrary damage. Dean Hickerson’s 20 January 2016 post [15] supplies this damaged seed and describes its repair. ### Pattern provenance and credit Self-repairing wall published by Dean Hickerson (2016) [15, 23]. The package independently verifies recovery of the complete state. The 20 January 2016 post supplies the exact damaged-wall RLE used here. Direct coordinate comparison confirms the catalogue changes only embedding and centring. Independent replay of damaged and pristine walls shows full-state reunion at generation 44, including exterior debris. Hickerson describes earlier investigations of the rule, but this audit dates the retrieved public example to 2016 rather than assigning an unverified earlier discovery date. ## pattern:hex-b2s34-p2044-billiard ### Verified behaviour Dean Hickerson's narrow B2/S34 enclosure contains a bouncing, branching signal with exact period 2,044. The construction illustrates an XOR-like one-dimensional evolution inside a hexagonal board. ### Interpretation and limits This is a published bounded oscillator, not a newly discovered XOR mechanism. Exact recurrence includes the walls as well as the moving internal signal. ### Pattern provenance and credit Period-2044 billiard table published by Dean Hickerson (2016); independently verified for this package [15, 23]. The 20 January 2016 post supplies the exact B2/S34H period-2044 billiard-table RLE used here and describes the one-dimensional XOR behaviour inside its walls. Direct coordinate comparison confirms the catalogue changes only embedding and centring. The package’s long complete-state replay verifies the published oscillator; it does not establish a new oscillator or a new XOR mechanism. ## pattern:hex-parity-seven-copy ### Verified behaviour Under binary B135/S0246 the next state is the XOR of the centre and its six neighbours. At times 2^k the evolution equals the XOR of seven translations of the seed. For this seed these seven copies are disjoint at times 8, 16 and 32, with 21 live cells. ### Interpretation and limits At other times, populations may exceed 21 and translated copies can overlap modulo 2. ### Pattern provenance and credit The three-live-cell initial pattern was assembled for the package, not mined from a soup or imported as an attributed published pattern. B135/S0246 computes the XOR of the centre and six neighbours. Over GF(2), powers of two of this linear update yield translated copies, giving the seven-copy demonstration once their supports are disjoint. The package claims this illustrative arrangement and its exact verification only; neither XOR replication nor the underlying algebra is a new principle. No external source is asserted for this particular seed. ## pattern:square-block ### Verified behaviour The four-cell block is unchanged after every update: an exact period-1 still life in Conway Life. ### Interpretation and limits This is a standard still life. Its fixed-state identity is exact and is independent of the distant finite boundary. ### Pattern provenance and credit The standard four-cell block appears in Martin Gardner’s original Conway Life article (1970) [13] and Stephen Silver’s Life Lexicon [24]. The package changes only its placement. These sources are cited for the published pattern, without assigning an individual discoverer. ## pattern:square-blinker ### Verified behaviour The smallest Conway oscillator alternates between horizontal and vertical lines. ### Interpretation and limits Exact first return at generation 2 establishes the least temporal period. It is a standard published oscillator. ### Pattern provenance and credit Stephen Silver’s Life Lexicon [24] credits the blinker to John H. Conway. The period-2 three-cell oscillator also appears in Martin Gardner’s original Conway Life article [13]. The package uses its standard horizontal phase, translated for display. ## pattern:square-pulsar ### Verified behaviour A symmetric 48-cell Conway oscillator with exact first-return period 3. ### Interpretation and limits The quoted period is for the complete state, not merely its population or appearance. This is the classical published pulsar. ### Pattern provenance and credit Stephen Silver’s Life Lexicon [25] credits the pulsar to John H. Conway. Martin Gardner’s original Conway Life article [13] describes its 48-cell phase. The package uses that published phase; placement and playback settings are package choices. ## pattern:square-pentadecathlon ### Verified behaviour A compact Conway oscillator whose complete state first returns after 15 generations. ### Interpretation and limits The complete state first returns after 15 updates. The package supplies a phase of the classical oscillator, not a newly discovered seed. ### Pattern provenance and credit Stephen Silver’s Life Lexicon, entry “pentadecathlon” [25], credits John H. Conway’s 1970 investigation of short rows. This is the published twelve-cell oscillator phase; the ten-cell row is a predecessor, not the displayed phase. ## pattern:square-glider ### Verified behaviour The traditional Conway glider translates by one square in each axis every four generations. ### Interpretation and limits Translation symmetry of the unbounded square lattice makes the verified translated recurrence repeat indefinitely there. On the finite browser board the glider eventually reaches the boundary. ### Pattern provenance and credit Stephen Silver’s Life Lexicon, entry “glider” [26], explicitly credits Richard K. Guy. The package seed is a rotated and translated standard glider phase. No discovery year is asserted here. ## pattern:square-lwss ### Verified behaviour The nine-cell LWSS translates two squares horizontally every four Conway generations. ### Interpretation and limits The infinite-lattice conclusion follows from the exact translated recurrence. The finite browser board is not infinite and eventually obstructs the flight. ### Pattern provenance and credit Stephen Silver’s Life Lexicon, entry “LWSS” [27], credits John H. Conway’s 1970 discovery of the lightweight spaceship. The package uses the published nine-cell phase, translated for display, under ordinary B3/S23. ## pattern:square-highlife-replicator ### Verified behaviour At generation 12, the complete state is exactly the disjoint union of two copies of the 12-cell initial seed, translated by (-2,-2) and (2,2) in square coordinates. This is the established B36/S23 HighLife replicator. ### Interpretation and limits The direct check establishes the stated replication event. It does not by itself prove independent binary doubling forever: copies later interact, and the finite board limits growth. ### Pattern provenance and credit David Eppstein’s Replicators: HighLife [17] credits this replicator to Nathan Thompson in 1994. David Bell subsequently documented and investigated HighLife; he is not credited as this seed’s discoverer. The package uses the published twelve-cell seed [28] and independently checks its two-copy return after twelve generations. ## pattern:square-diehard ### Verified behaviour A famous seven-cell Conway methuselah that vanishes exactly at generation 130. ### Interpretation and limits This is an extinction transient, not an oscillator. The retained seed matches the classical published diehard; no individual discoverer is assigned without a source. ### Pattern provenance and credit The seven-cell seed matches diehard in Stephen Silver’s Life Lexicon [29] exactly after translation. Its extinction at generation 130 is independently checked. The consulted source does not establish an individual discoverer; no personal attribution or new-discovery claim is made. ## pattern:square-r-pentomino ### Verified behaviour The standard five-cell seed remains active through generation 1,103 on the supplied finite board. Independent square-lattice replay first differs from that board at generation 641; at generation 1,103 the infinite-lattice and finite-board populations are 116 and 111 respectively. ### Interpretation and limits The browser uses a finite 301 by 301 board with a permanently dead outer ring. The endpoint and population of that run must not be presented as the infinite-plane final census; escaping objects can encounter its boundary. ### Pattern provenance and credit Martin Gardner’s original Conway Life article [13] documents John H. Conway’s study of the R-pentomino; Stephen Silver’s Life Lexicon [30] records the same five-cell shape. Its finite-board check establishes activity through generation 1,103, not equality with the infinite-plane final census. ## pattern:square-acorn ### Verified behaviour The published seven-cell seed remains active through generation 5,206 on the supplied finite board. Independent square-lattice replay first differs from that board at generation 812; at generation 5,206 the infinite-lattice and finite-board populations are 633 and 620 respectively. ### Interpretation and limits The browser uses a finite 301 by 301 board with a permanently dead outer ring. Activity at generation 5,206 is a finite-board observation, not a certification of the infinite-plane ash or its stabilisation time. ### Pattern provenance and credit Robert Wainwright’s Lifeline No. 3 (1971), page 12 [31], credits Acorn to Charles L. Corderman; Wainwright supplied the name. Stephen Silver’s Life Lexicon [32] records the same seven-cell seed. The package translates it for display and checks finite-board activity through 5,206 generations, not the infinite-plane final ash.