From 2172943239af745ce43ede68afafb8d8783d7011 Mon Sep 17 00:00:00 2001 From: Cinna Davis Date: Fri, 23 Oct 2026 05:35:50 -0500 Subject: [PATCH] Prove round-three owned high-contact floors with every native warp cut --- research/monotone-owned-centre-floor/PROOF.md | 116 + .../monotone-owned-centre-floor/README.md | 79 + .../monotone-owned-centre-floor/SOURCES.json | 36 + .../monotone-owned-centre-floor/TASK.json | 75 + .../monotone-owned-centre-floor/VERIFY.json | 36 + .../WITNESSES.json | 3265 +++++++++++++++++ .../monotone-owned-centre-floor/verify.py | 239 ++ 7 files changed, 3846 insertions(+) create mode 100644 research/monotone-owned-centre-floor/PROOF.md create mode 100644 research/monotone-owned-centre-floor/README.md create mode 100644 research/monotone-owned-centre-floor/SOURCES.json create mode 100644 research/monotone-owned-centre-floor/TASK.json create mode 100644 research/monotone-owned-centre-floor/VERIFY.json create mode 100644 research/monotone-owned-centre-floor/WITNESSES.json create mode 100644 research/monotone-owned-centre-floor/verify.py diff --git a/research/monotone-owned-centre-floor/PROOF.md b/research/monotone-owned-centre-floor/PROOF.md new file mode 100644 index 0000000000..2e7f70b7c4 --- /dev/null +++ b/research/monotone-owned-centre-floor/PROOF.md @@ -0,0 +1,116 @@ +# Sharp high-contact floor in the round-three word + +Prepared by Cinna Davis / 1337isnot1337 with substantial OpenAI Codex +assistance; Apache-2.0. This is a written scoped proof with exact finite +witnesses, not a proof-kernel check or a new multiplication theorem. + +## Statement + +Use the exact scalar opcode, coefficient, order and persistent-field incidence +of Cao Yifan's round-three word in `SOURCES.json`, separately in either +orientation. At every scalar event, all its persistent operands have one +common binary frame subspace in F2^9. Between consecutive scalar contacts on +a persistent field, with no intervening native warp, require containment in +chronological order. The main entrance subspaces stay fixed. The helper +entrances/exits, all scalar contact subspaces and all native warp boundaries +may otherwise vary. In particular, do not impose a relation across any native +warp and do not require final endpoints in this relaxation. + +Then each of the eight high owned contacts has dimension at least eight. The +original word simultaneously attains eight at all of them, so these bounds are +sharp. For a center job between that high contact and the zero subspace, its +rank is therefore at least eight. Retaining all eight jobs gives paid rank +mass at least 64 and, at every positive rank exponent t, center moment at +least 8 times 8^t. This is a bound on the center contribution. It does not +optimize the remaining paid/helper moment. + +In the forward orientation the contact is the persistent source of an owned +COPY immediately before the descending center job. In the backward orientation +it is the persistent destination of the owned output ADD immediately after +the ascending job. `verify.py` checks these actual macro boundaries and the +initial/final owned CLEARs adjacent to the high side. + +## Path lemma + +Matarener's PR5060 (`research/owned-centre-wire-floor/PROOF.md`, Lemma1) +already uses forward joins and backward meets to force contact subspaces, +and proves a complete nested owned-wire floor with fixed warps and helpers. +The containment propagation below is the same elementary invariant. The new +source-specific coverage removes all native relations and helper boundaries, +retains only fixed main entrance seeds, and supplies explicit path witnesses +for the newer round-three word. It proves the high-contact floor in that +larger domain, not the predecessor's full owned-wire conclusion there. + +Associate a vertex with each main entrance and scalar contact. For each +persistent field, draw an edge from its previous entrance/contact to the next +scalar contact. A native warp terminates that chain: its output begins a new +unconstrained chain, and no relation across the warp is retained. Identifying +the two operands of a scalar ADD at one contact gives their common subspace. +No edge for a productive helper target or final endpoint is needed. + +If v lies in a fixed main entrance space and a directed path leads from that +entrance to contact q, then v lies in the space at q. This follows by induction +on the path length, using the containment hypothesis on every edge. Thus k +linearly independent fixed entrance vectors with paths to q force dimension +at least k, regardless of all other contacts, helper choices and native maps. + +This argument uses the common physical frame of scalar operands, not their +data coefficients or nonzero logical dependence. Data cancellation does not +remove a required physical contact. Splitting operands into independent gauges +requires a different paid scalar interface and falls outside this statement. + +## Source-bound witnesses + +The source has 632 persistent fields, of which 224 are main and 408 are +independent arbitrary helpers. Raw event ordinals below omit `climb` events +and start at zero. The graph contains 31,630 distinct monotone edges in each +orientation. Every one of the 240 native events per orientation is cut. +All owned scalar contacts, including the low scatter/gather side, are released +while proving the high-side floor. Helper spaces do not supply witness seeds. + +| Persistent role | Forward high event | Backward high event | Original frame ID | Eight independent entrance vectors | +| --- | ---: | ---: | ---: | --- | +| 92 | 10344 | 10367 | 254 | 276, 351, 266, 74, 44, 193, 247, 14 | +| 57 | 10370 | 10393 | 274 | 304, 379, 259, 67, 37, 131, 254, 14 | +| 81 | 10396 | 10419 | 619 | 471, 386, 73, 506, 164, 194, 254, 388 | +| 224 | 10422 | 10445 | 279 | 471, 386, 73, 506, 164, 194, 304, 74 | +| 11 | 10448 | 10471 | 621 | 268, 274, 164, 194, 146, 289, 67, 388 | +| 240 | 10474 | 10497 | 280 | 268, 274, 146, 289, 304, 379, 164, 247 | +| 9 | 10500 | 10523 | 624 | 268, 274, 146, 289, 471, 386, 67, 14 | +| 256 | 10526 | 10549 | 281 | 247, 145, 290, 196, 268, 274, 471, 304 | + +Each integer encodes a nine-bit binary vector. `WITNESSES.json` records the +actual fixed entrance role and every graph vertex on each path. It contains +128 paths and 2,204 links across both orientations. The verifier checks every +seed, chronological link, target, binary rank and equality of the resulting +eight-dimensional span with the original high contact. The path lemma proves +the bound for arbitrary candidate subspaces, without enumerating them. + +The original full source has paid histogram +`{1:2201, 2:412, 3:510, 4:127, 5:40, 8:8}` and productive-helper histogram +`{4:28, 7:7, 8:47, 9:326}` in both directions. These are reconstructed as +baseline controls, including every center. They are not a claimed new invoice. +No solver, power approximation or floating tolerance enters the certificate. + +## Decision and limits + +The independent-contact/shared-native-map proposal in +[the preceding claim](https://github.com/CrocSwap/integer-mult-bounds/discussions/4611#discussioncomment-19139586) +released the high COPY chart while keeping the opposite owned chart at zero. +Its proposed center reduction is impossible under monotone persistent paths. +The proof already holds in a relaxation that forgets every shared-map equation. +No MILP is required to decide that center reduction. + +Other bridges or productive boundaries might still improve while all centers +retain rank eight. This theorem proves no whole-profile optimum. Moving the +low center side can also change the job rank, which is then a relative rank +between two nonzero spaces rather than the dimension bounded here. Nonmonotone +transitions, changed scalar chronology, split scalar contacts, phase/general +gauges, changed main entrances and sharing different owned macros need separate +analysis. In particular the previous common-kernel prototype allowed +nonmonotone edges and is not excluded by this theorem. + +The source-specific finite statement is distinct from native all-column +realization, precision, movement, owned erasure, compilation and the outer +integer-recovery theorem. Those are not reverified or strengthened here. The +selected conditional kappa remains 0.00302015. diff --git a/research/monotone-owned-centre-floor/README.md b/research/monotone-owned-centre-floor/README.md new file mode 100644 index 0000000000..be65e8d4ab --- /dev/null +++ b/research/monotone-owned-centre-floor/README.md @@ -0,0 +1,79 @@ +# Monotone owned-center high-contact floor + +Each of the eight owned high contacts in the actual round-three word must +have dimension at least eight under fixed main entrances, the fixed scalar +word and monotone persistent-field contact subspaces. This remains true after +discarding every native warp relation, freeing all helper boundaries and +freeing the other scalar contacts. The source attains all eight bounds. + +Consequently, releasing only the high side of the centers while keeping the +other side at zero cannot reduce their paid rank mass below 64. The proof +does not give a global moment optimum or a higher kappa. The selected +conditional result at the base commit is kappa 0.00302015. + +Read [PROOF.md](PROOF.md) for the mathematical argument, exact hypotheses, +source-contact table and limits. [WITNESSES.json](WITNESSES.json) contains +128 independent entrance-vector paths with 2,204 links, covering both actual +orientations and all eight owned lifetimes separately. Only fixed main +entrances supply seeds; no clean logical helper input is assumed. + +Reproduce with standard Python 3.12 or later: + +```sh +python3 -B scripts/research_package.py --package research/monotone-owned-centre-floor +python3 -I -B research/monotone-owned-centre-floor/verify.py +python3 -I -O -B research/monotone-owned-centre-floor/verify.py +``` + +The registered commands include the normal and optimized exact checks, the +complete source paid/helper baseline and 144 corruption, rank-seven-hyperplane +and warp-cut controls. `verify.py --write` regenerates the deterministic +witness artifact. Verification does not write it. This needs no solver, +network, imported predecessor executable or optional package. + +Source: Cao Yifan / intqwq's round-three word, retained in +`research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz`, with compressed and +decompressed SHA256 bindings. The source manifest pins the base and exact live +input; all frozen predecessor bytes remain unchanged. Retain Cinna Davis's +native/controller/retiming lineage, Dugongue's transported-frame work, zxv, +Jacob Alan Sussman and the source's complete predecessor attribution. + +This continues the owned-contact question from the +[bounded common-kernel prototype](https://github.com/1337isnot1337/integer-mult-bounds/tree/8052b4818738986960c5b243097b3fffb6d21139/research/owned-centre-kernel-retiming) +and [independent-contact claim](https://github.com/CrocSwap/integer-mult-bounds/discussions/4611#discussioncomment-19139586). +The former permits nonmonotone transitions and is not excluded by this proof. +The pending nearest-Clifford/split-contact work in +[discussion #5125](https://github.com/CrocSwap/integer-mult-bounds/discussions/5125) +also has a different boundary. Canonical investigation update: +[the scoped finding](https://github.com/CrocSwap/integer-mult-bounds/discussions/4611#discussioncomment-19143793). + +Matarener's [PR5060 owned-wire floor](https://github.com/CrocSwap/integer-mult-bounds/pull/5060) +already proves a complete nested C-wire floor for the older #4470 word with +fixed native warps and helper boundaries, including variable low contacts. +Its interval-propagation/path argument is prior work. The present result +extends the high-contact part to the actual round-three word with every warp +relation removed and all helper boundaries free, using explicit paths seeded +only by main entrances. It does not extend PR5060's complete C-wire floor to +that larger domain. In particular, its open low-side/helper-boundary question +must not be reported as solved here. + +Prepared by Cinna Davis / 1337isnot1337 with substantial OpenAI Codex +assistance; no subagents. Apache-2.0. Evidence is author-checked, not independent +human or proof-kernel acceptance. A package merge would not select a frontier. + +## Open next questions + +- Can changing both sides of an owned center job improve the complete moment? + The high-side floor does not settle its relative rank. First reconstruct + both owned macro itineraries with one variable low chart, charge all changed + persistent bridges and the full center rank power, and gate the complete + baseline before solving. Actual frame/phase, ownership, cleanup, precision + and compiler/outer charges remain obligations. +- Can a changed scalar word or nonmonotone paid itinerary remove the forced + entrance paths at a favorable total cost? Name the exact edit or descending + bridge, emit both orientations, and reconstruct every paid/helper child. + The present proof and the old floating common-kernel failure do not decide + that question. + +The structured questions, stopping rule and scope change are in +[TASK.json](TASK.json). No extra search is claimed by this package. diff --git a/research/monotone-owned-centre-floor/SOURCES.json b/research/monotone-owned-centre-floor/SOURCES.json new file mode 100644 index 0000000000..2bc8edc670 --- /dev/null +++ b/research/monotone-owned-centre-floor/SOURCES.json @@ -0,0 +1,36 @@ +{ + "schema_version": 1, + "base_commit": "20a1e31bc6009b9b3f4d084bbaadc6350e34fcba", + "files": [ + { + "path": "certificates/selected-result.json", + "usage": "provenance", + "git_blob": "c35482cd9035843b15a634cc8276a7e1e40e8395", + "sha256": "6fe0a099b89aa2aed796a13c3a21dafc63f3388ebf397464e44e0451893b9375" + }, + { + "path": "docs/research/agent-task-catalog.json", + "usage": "provenance", + "git_blob": "f126dd2e2dad2b669e75d1d0d0bd05c600725602", + "sha256": "f7a48bfa2659b88378282a8eee7d9fe52cdf505594124c4d1686b58510fffd72" + }, + { + "path": "research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz", + "usage": "input", + "git_blob": "46d929df83817b85a5387bcdb9745e0627d6366e", + "sha256": "7679daa4ec6a40f56fc7f0202379a6f454310e94945aba4f48beaaaafb838d05" + }, + { + "path": "research/owned-centre-wire-floor/README.md", + "usage": "provenance", + "git_blob": "ffd10d3c4314d3bdc80aad56d606b73e1bb4d820", + "sha256": "f2fdd6c91d98b692dac91e7a6cd6c8f09094cd2259ed3737ec429b147499c0a3" + }, + { + "path": "research/owned-centre-wire-floor/PROOF.md", + "usage": "provenance", + "git_blob": "e6033ac5ddedc4152c2553499021b262f81f75bd", + "sha256": "4fddcb9d3595870dd6ba9a0819e19ba50d9748b3cd643b978f43aef8750dcaf5" + } + ] +} diff --git a/research/monotone-owned-centre-floor/TASK.json b/research/monotone-owned-centre-floor/TASK.json new file mode 100644 index 0000000000..ce3e8ce5fc --- /dev/null +++ b/research/monotone-owned-centre-floor/TASK.json @@ -0,0 +1,75 @@ +{ + "schema_version": 1, + "task_id": "centre-path-sharing", + "priority_revision": 7, + "base_commit": "20a1e31bc6009b9b3f4d084bbaadc6350e34fcba", + "original_card": { + "id": "centre-path-sharing", + "question": "Can the 64-per-call centre path (eight rank-8 COPY/ERASE totals through the private temporary) be shared across calls or shrunk?", + "starting_points": [ + "docs/research/research-family-status.md", + "research/complex-local-word-ceiling/README.md", + "research/split-centres-global/proofs/PR386-BIT-GEOMETRY.txt", + "certificates/selected-result.json" + ], + "methods": [ + "Derive a fully charged favorable relaxation for sharing one centre path across k calls, including restoration, hosting and precision.", + "Prove a lower bound on copied information per call for the selected decoder contract." + ], + "acceptance_gate": "Show the changed centre charge and copy profile per call with every added restoration or hosting cost charged, and its ceiling via ceiling.ceiling(centre=...). A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.", + "first_step": { + "command": [ + "python3", + "-B", + "research/complex-local-word-ceiling/verify.py" + ], + "expected": "PASS_COMPLEX_LOCAL_WORD_CEILING", + "inspect": "Read the selected word's per-call local profile, its packing ceiling and the lever table; run levers.py for the ideal budget of the lever you target.", + "scope": "Positive control and planning budget only; this is not a new construction or full cold replay." + }, + "first_experiment": "Write the per-call centre charge and copy children for sharing across k = 2 calls, charge the sharing overhead, and screen it; stop this route if even the ideal sharing gains under 10%. Ideal budgets: free 2.80x, shared by two 1.90x (levers.py).", + "bottleneck_link": "The centre path consumes 64 of about 99.6 unpaid coordinates per call, i.e. about 64% of the raw deficit.", + "allowed_variations": [ + "One sharing pattern across a fixed number of calls.", + "One reduced copied-total contract for the existing decoder.", + "If the coverage law, template or guard changes, derive an applicable fully charged replacement bound instead of applying the incumbent ceiling outside its scope." + ], + "scope_change_triggers": [ + "Removing copies without a replacement contract for the decoder's copied totals.", + "Continuing a partial cost improvement while leaving the same unpriced consumer, restoration or central-readout obligation unresolved; refresh the family expansion decision first. Local product-retiming evidence has a narrow scope and is not a ban on changed graphs or contracts." + ], + "overlap_terms": [ + "centre path", + "copied totals", + "private temporary", + "shared centre", + "batching" + ] + }, + "scope_status": "refined", + "actual_scope": "Prove sharp rank-eight floors at every owned high contact of the actual round-three word, for arbitrary monotone contact subspaces and all native warp relations removed.", + "scope_change_reason": "Resumes the independent owned-COPY/shared-map handoff. Before solving, exact paths already exclude lowering the high side; the card historical sharing/ceiling experiment does not cover this changed-source invariant.", + "bottleneck_link": "Eight rank-eight owned center jobs remain a paid rank mass of at least64 when their opposite chart stays zero. This closes the high-contact-only monotone retiming route without a solver.", + "budget_minutes": 60, + "stop_rule": "Finish exact source-bound floor and explicit path witnesses; do not launch the precluded high-side-only MILP or infer a universal moment optimum.", + "outcome": "completed", + "evidence": "PROOF.md, WITNESSES.json; normal and optimized registered replay with source baseline and144 controls.", + "author": "Cinna Davis / 1337isnot1337, with substantial OpenAI Codex assistance", + "ai_assistance": "Substantial OpenAI Codex assistance in proof, implementation, experiments and writing. No subagents or human/kernel proof acceptance claimed.", + "open_questions": [ + { + "question": "Can releasing the zero-side charts of a center macro lower the complete paid-minus-productive moment?", + "why_it_matters": "The high-side floor alone does not bound rank of a transition between two nonzero charts.", + "first_step": "Derive both orientation owned macro itineraries with a variable low chart, reprice all adjacent persistent transports and use full center rank powers.", + "blocked_by": "A common physical contact chart for every scatter/gather operation, owned restoration, native phases and full supplier/outer costs." + }, + { + "question": "Can a changed scalar word or nonmonotone paid itinerary avoid the eight independent entrance paths?", + "why_it_matters": "Those are hypotheses of the floor; the previous common-kernel search permits nonmonotone edges and is not excluded by this theorem.", + "first_step": "Name the exact edited scalar event or descending bridge, emit both full literal words and reconstruct every paid/helper child before search.", + "blocked_by": "Exact endpoint, native absolute-phase and fully funded compiler/precision/outer obligations." + } + ], + "upstream_checked_commit": "20a1e31bc6009b9b3f4d084bbaadc6350e34fcba", + "canonical_thread": "https://github.com/CrocSwap/integer-mult-bounds/discussions/4611#discussioncomment-19143793" +} diff --git a/research/monotone-owned-centre-floor/VERIFY.json b/research/monotone-owned-centre-floor/VERIFY.json new file mode 100644 index 0000000000..597645af04 --- /dev/null +++ b/research/monotone-owned-centre-floor/VERIFY.json @@ -0,0 +1,36 @@ +{ + "schema_version": 1, + "status": "ready", + "python": "3.12", + "requirements": [], + "inputs": [ + "research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz" + ], + "commands": [ + { + "argv": [ + "{python}", + "-I", + "-W", + "error", + "-B", + "{package}/verify.py" + ], + "timeout_seconds": 30, + "checks": "Exact source baseline,128 independent main entrance paths,2204 literal links,144 corruption/hyperplane/warp-cut controls." + }, + { + "argv": [ + "{python}", + "-I", + "-O", + "-W", + "error", + "-B", + "{package}/verify.py" + ], + "timeout_seconds": 30, + "checks": "Same source-bound proof and controls with assertions disabled." + } + ] +} diff --git a/research/monotone-owned-centre-floor/WITNESSES.json b/research/monotone-owned-centre-floor/WITNESSES.json new file mode 100644 index 0000000000..47d6e68cf7 --- /dev/null +++ b/research/monotone-owned-centre-floor/WITNESSES.json @@ -0,0 +1,3265 @@ +{ + "directions": { + "backward": { + "cut_native_events": 240, + "monotone_edges": 31630, + "path_links": 1102, + "targets": [ + { + "event": 10367, + "frame": 254, + "lower_dimension": 8, + "node": 10999, + "role": 92, + "witnesses": [ + { + "entrance_role": 50, + "path": [ + 50, + 9697, + 9737, + 9738, + 9753, + 9764, + 9783, + 9791, + 9814, + 9821, + 9825, + 9833, + 9834, + 9846, + 9847, + 10931, + 10999 + ], + "vector": 276 + }, + { + "entrance_role": 108, + "path": [ + 108, + 9701, + 9737, + 9738, + 9753, + 9764, + 9783, + 9791, + 9814, + 9821, + 9825, + 9833, + 9834, + 9846, + 9847, + 10931, + 10999 + ], + "vector": 351 + }, + { + "entrance_role": 34, + "path": [ + 34, + 9695, + 9733, + 9734, + 9751, + 9763, + 9764, + 9783, + 9791, + 9814, + 9821, + 9825, + 9833, + 9834, + 9846, + 9847, + 10931, + 10999 + ], + "vector": 266 + }, + { + "entrance_role": 32, + "path": [ + 32, + 9542, + 9582, + 9583, + 9598, + 9609, + 9628, + 9636, + 9659, + 9666, + 9670, + 9678, + 9679, + 9691, + 9692, + 10930, + 10931, + 10999 + ], + "vector": 74 + }, + { + "entrance_role": 45, + "path": [ + 45, + 9546, + 9582, + 9583, + 9598, + 9609, + 9628, + 9636, + 9659, + 9666, + 9670, + 9678, + 9679, + 9691, + 9692, + 10930, + 10931, + 10999 + ], + "vector": 44 + }, + { + "entrance_role": 22, + "path": [ + 22, + 9703, + 9741, + 9742, + 9752, + 9767, + 9781, + 9794, + 9803, + 9813, + 9814, + 9821, + 9825, + 9833, + 9834, + 9846, + 9847, + 10931, + 10999 + ], + "vector": 193 + }, + { + "entrance_role": 102, + "path": [ + 102, + 9388, + 9428, + 9429, + 9443, + 9454, + 9473, + 9481, + 9504, + 9511, + 9515, + 9523, + 9524, + 9536, + 9537, + 10929, + 10930, + 10931, + 10999 + ], + "vector": 247 + }, + { + "entrance_role": 25, + "path": [ + 25, + 9080, + 9120, + 9121, + 9135, + 9146, + 9165, + 9173, + 9196, + 9203, + 9207, + 9215, + 9216, + 9228, + 9229, + 10927, + 10928, + 10929, + 10930, + 10931, + 10999 + ], + "vector": 14 + } + ] + }, + { + "event": 10393, + "frame": 274, + "lower_dimension": 8, + "node": 11025, + "role": 57, + "witnesses": [ + { + "entrance_role": 69, + "path": [ + 69, + 10314, + 10354, + 10355, + 10369, + 10380, + 10399, + 10407, + 10430, + 10437, + 10441, + 10449, + 10450, + 10462, + 10463, + 10937, + 11025 + ], + "vector": 304 + }, + { + "entrance_role": 96, + "path": [ + 96, + 10318, + 10354, + 10355, + 10369, + 10380, + 10399, + 10407, + 10430, + 10437, + 10441, + 10449, + 10450, + 10462, + 10463, + 10937, + 11025 + ], + "vector": 379 + }, + { + "entrance_role": 5, + "path": [ + 5, + 10312, + 10350, + 10351, + 10367, + 10379, + 10380, + 10399, + 10407, + 10430, + 10437, + 10441, + 10449, + 10450, + 10462, + 10463, + 10937, + 11025 + ], + "vector": 259 + }, + { + "entrance_role": 3, + "path": [ + 3, + 10160, + 10200, + 10201, + 10215, + 10226, + 10245, + 10253, + 10276, + 10283, + 10287, + 10295, + 10296, + 10308, + 10309, + 10936, + 10937, + 11025 + ], + "vector": 67 + }, + { + "entrance_role": 8, + "path": [ + 8, + 10164, + 10200, + 10201, + 10215, + 10226, + 10245, + 10253, + 10276, + 10283, + 10287, + 10295, + 10296, + 10308, + 10309, + 10936, + 10937, + 11025 + ], + "vector": 37 + }, + { + "entrance_role": 4, + "path": [ + 4, + 10316, + 10358, + 10359, + 10368, + 10383, + 10397, + 10410, + 10419, + 10429, + 10430, + 10437, + 10441, + 10449, + 10450, + 10462, + 10463, + 10937, + 11025 + ], + "vector": 131 + }, + { + "entrance_role": 84, + "path": [ + 84, + 10006, + 10046, + 10047, + 10061, + 10072, + 10091, + 10099, + 10122, + 10129, + 10133, + 10141, + 10142, + 10154, + 10155, + 10935, + 10936, + 10937, + 11025 + ], + "vector": 254 + }, + { + "entrance_role": 25, + "path": [ + 25, + 9080, + 9120, + 9121, + 9135, + 9146, + 9165, + 9173, + 9196, + 9203, + 9207, + 9215, + 9216, + 9228, + 9229, + 10933, + 10934, + 10935, + 10936, + 10937, + 11025 + ], + "vector": 14 + } + ] + }, + { + "event": 10419, + "frame": 619, + "lower_dimension": 8, + "node": 11051, + "role": 81, + "witnesses": [ + { + "entrance_role": 99, + "path": [ + 99, + 10622, + 10662, + 10663, + 10677, + 10688, + 10707, + 10715, + 10738, + 10745, + 10749, + 10757, + 10758, + 10770, + 10771, + 10943, + 11051 + ], + "vector": 471 + }, + { + "entrance_role": 43, + "path": [ + 43, + 10626, + 10662, + 10663, + 10677, + 10688, + 10707, + 10715, + 10738, + 10745, + 10749, + 10757, + 10758, + 10770, + 10771, + 10943, + 11051 + ], + "vector": 386 + }, + { + "entrance_role": 13, + "path": [ + 13, + 10618, + 10619, + 10654, + 10655, + 10677, + 10688, + 10707, + 10715, + 10738, + 10745, + 10749, + 10757, + 10758, + 10770, + 10771, + 10943, + 11051 + ], + "vector": 73 + }, + { + "entrance_role": 78, + "path": [ + 78, + 10620, + 10658, + 10659, + 10675, + 10687, + 10688, + 10707, + 10715, + 10738, + 10745, + 10749, + 10757, + 10758, + 10770, + 10771, + 10943, + 11051 + ], + "vector": 506 + }, + { + "entrance_role": 52, + "path": [ + 52, + 10468, + 10508, + 10509, + 10523, + 10534, + 10553, + 10561, + 10584, + 10591, + 10595, + 10603, + 10604, + 10616, + 10617, + 10942, + 10943, + 11051 + ], + "vector": 164 + }, + { + "entrance_role": 41, + "path": [ + 41, + 10472, + 10508, + 10509, + 10523, + 10534, + 10553, + 10561, + 10584, + 10591, + 10595, + 10603, + 10604, + 10616, + 10617, + 10942, + 10943, + 11051 + ], + "vector": 194 + }, + { + "entrance_role": 84, + "path": [ + 84, + 10006, + 10046, + 10047, + 10061, + 10072, + 10091, + 10099, + 10122, + 10129, + 10133, + 10141, + 10142, + 10154, + 10155, + 10941, + 10942, + 10943, + 11051 + ], + "vector": 254 + }, + { + "entrance_role": 56, + "path": [ + 56, + 9234, + 9274, + 9275, + 9289, + 9300, + 9319, + 9327, + 9350, + 9357, + 9361, + 9369, + 9370, + 9382, + 9383, + 10939, + 10940, + 10941, + 10942, + 10943, + 11051 + ], + "vector": 388 + } + ] + }, + { + "event": 10445, + "frame": 279, + "lower_dimension": 8, + "node": 11077, + "role": 224, + "witnesses": [ + { + "entrance_role": 99, + "path": [ + 99, + 10622, + 10662, + 10663, + 10677, + 10688, + 10707, + 10715, + 10738, + 10745, + 10749, + 10757, + 10758, + 10770, + 10771, + 10949, + 11077 + ], + "vector": 471 + }, + { + "entrance_role": 43, + "path": [ + 43, + 10626, + 10662, + 10663, + 10677, + 10688, + 10707, + 10715, + 10738, + 10745, + 10749, + 10757, + 10758, + 10770, + 10771, + 10949, + 11077 + ], + "vector": 386 + }, + { + "entrance_role": 13, + "path": [ + 13, + 10618, + 10619, + 10654, + 10655, + 10677, + 10688, + 10707, + 10715, + 10738, + 10745, + 10749, + 10757, + 10758, + 10770, + 10771, + 10949, + 11077 + ], + "vector": 73 + }, + { + "entrance_role": 78, + "path": [ + 78, + 10620, + 10658, + 10659, + 10675, + 10687, + 10688, + 10707, + 10715, + 10738, + 10745, + 10749, + 10757, + 10758, + 10770, + 10771, + 10949, + 11077 + ], + "vector": 506 + }, + { + "entrance_role": 52, + "path": [ + 52, + 10468, + 10508, + 10509, + 10523, + 10534, + 10553, + 10561, + 10584, + 10591, + 10595, + 10603, + 10604, + 10616, + 10617, + 10948, + 10949, + 11077 + ], + "vector": 164 + }, + { + "entrance_role": 41, + "path": [ + 41, + 10472, + 10508, + 10509, + 10523, + 10534, + 10553, + 10561, + 10584, + 10591, + 10595, + 10603, + 10604, + 10616, + 10617, + 10948, + 10949, + 11077 + ], + "vector": 194 + }, + { + "entrance_role": 69, + "path": [ + 69, + 10314, + 10354, + 10355, + 10369, + 10380, + 10399, + 10407, + 10430, + 10437, + 10441, + 10449, + 10450, + 10462, + 10463, + 10947, + 10948, + 10949, + 11077 + ], + "vector": 304 + }, + { + "entrance_role": 32, + "path": [ + 32, + 9542, + 9582, + 9583, + 9598, + 9609, + 9628, + 9636, + 9659, + 9666, + 9670, + 9678, + 9679, + 9691, + 9692, + 10945, + 10946, + 10947, + 10948, + 10949, + 11077 + ], + "vector": 74 + } + ] + }, + { + "event": 10471, + "frame": 621, + "lower_dimension": 8, + "node": 11103, + "role": 11, + "witnesses": [ + { + "entrance_role": 47, + "path": [ + 47, + 10776, + 10816, + 10817, + 10831, + 10842, + 10861, + 10869, + 10892, + 10899, + 10903, + 10911, + 10912, + 10924, + 10925, + 10955, + 11103 + ], + "vector": 268 + }, + { + "entrance_role": 37, + "path": [ + 37, + 10780, + 10816, + 10817, + 10831, + 10842, + 10861, + 10869, + 10892, + 10899, + 10903, + 10911, + 10912, + 10924, + 10925, + 10955, + 11103 + ], + "vector": 274 + }, + { + "entrance_role": 52, + "path": [ + 52, + 10468, + 10508, + 10509, + 10523, + 10534, + 10553, + 10561, + 10584, + 10591, + 10595, + 10603, + 10604, + 10616, + 10954, + 10955, + 11103 + ], + "vector": 164 + }, + { + "entrance_role": 41, + "path": [ + 41, + 10472, + 10508, + 10509, + 10523, + 10534, + 10553, + 10561, + 10584, + 10591, + 10595, + 10603, + 10604, + 10616, + 10954, + 10955, + 11103 + ], + "vector": 194 + }, + { + "entrance_role": 36, + "path": [ + 36, + 10772, + 10773, + 10808, + 10809, + 10831, + 10842, + 10861, + 10869, + 10892, + 10899, + 10903, + 10911, + 10912, + 10924, + 10925, + 10955, + 11103 + ], + "vector": 146 + }, + { + "entrance_role": 21, + "path": [ + 21, + 10774, + 10812, + 10813, + 10829, + 10841, + 10842, + 10861, + 10869, + 10892, + 10899, + 10903, + 10911, + 10912, + 10924, + 10925, + 10955, + 11103 + ], + "vector": 289 + }, + { + "entrance_role": 3, + "path": [ + 3, + 10160, + 10200, + 10201, + 10215, + 10226, + 10245, + 10253, + 10276, + 10283, + 10287, + 10295, + 10296, + 10308, + 10953, + 10954, + 10955, + 11103 + ], + "vector": 67 + }, + { + "entrance_role": 56, + "path": [ + 56, + 9234, + 9274, + 9275, + 9289, + 9300, + 9319, + 9327, + 9350, + 9357, + 9361, + 9369, + 9370, + 9382, + 10951, + 10952, + 10953, + 10954, + 10955, + 11103 + ], + "vector": 388 + } + ] + }, + { + "event": 10497, + "frame": 280, + "lower_dimension": 8, + "node": 11129, + "role": 240, + "witnesses": [ + { + "entrance_role": 47, + "path": [ + 47, + 10776, + 10816, + 10817, + 10831, + 10842, + 10861, + 10869, + 10892, + 10899, + 10903, + 10911, + 10912, + 10924, + 10925, + 10961, + 11129 + ], + "vector": 268 + }, + { + "entrance_role": 37, + "path": [ + 37, + 10780, + 10816, + 10817, + 10831, + 10842, + 10861, + 10869, + 10892, + 10899, + 10903, + 10911, + 10912, + 10924, + 10925, + 10961, + 11129 + ], + "vector": 274 + }, + { + "entrance_role": 36, + "path": [ + 36, + 10772, + 10773, + 10808, + 10809, + 10831, + 10842, + 10861, + 10869, + 10892, + 10899, + 10903, + 10911, + 10912, + 10924, + 10925, + 10961, + 11129 + ], + "vector": 146 + }, + { + "entrance_role": 21, + "path": [ + 21, + 10774, + 10812, + 10813, + 10829, + 10841, + 10842, + 10861, + 10869, + 10892, + 10899, + 10903, + 10911, + 10912, + 10924, + 10925, + 10961, + 11129 + ], + "vector": 289 + }, + { + "entrance_role": 69, + "path": [ + 69, + 10314, + 10354, + 10355, + 10369, + 10380, + 10399, + 10407, + 10430, + 10437, + 10441, + 10449, + 10450, + 10462, + 10959, + 10960, + 10961, + 11129 + ], + "vector": 304 + }, + { + "entrance_role": 96, + "path": [ + 96, + 10318, + 10354, + 10355, + 10369, + 10380, + 10399, + 10407, + 10430, + 10437, + 10441, + 10449, + 10450, + 10462, + 10959, + 10960, + 10961, + 11129 + ], + "vector": 379 + }, + { + "entrance_role": 52, + "path": [ + 52, + 10468, + 10508, + 10509, + 10523, + 10534, + 10553, + 10561, + 10584, + 10585, + 10587, + 10601, + 10602, + 10606, + 10614, + 10615, + 10960, + 10961, + 11129 + ], + "vector": 164 + }, + { + "entrance_role": 102, + "path": [ + 102, + 9388, + 9428, + 9429, + 9443, + 9454, + 9473, + 9481, + 9504, + 9511, + 9515, + 9523, + 9524, + 9536, + 10957, + 10958, + 10959, + 10960, + 10961, + 11129 + ], + "vector": 247 + } + ] + }, + { + "event": 10523, + "frame": 624, + "lower_dimension": 8, + "node": 11155, + "role": 9, + "witnesses": [ + { + "entrance_role": 47, + "path": [ + 47, + 10776, + 10816, + 10817, + 10831, + 10842, + 10861, + 10869, + 10892, + 10899, + 10903, + 10911, + 10912, + 10924, + 10967, + 11155 + ], + "vector": 268 + }, + { + "entrance_role": 37, + "path": [ + 37, + 10780, + 10816, + 10817, + 10831, + 10842, + 10861, + 10869, + 10892, + 10899, + 10903, + 10911, + 10912, + 10924, + 10967, + 11155 + ], + "vector": 274 + }, + { + "entrance_role": 36, + "path": [ + 36, + 10772, + 10773, + 10808, + 10809, + 10831, + 10842, + 10861, + 10869, + 10892, + 10899, + 10903, + 10911, + 10912, + 10924, + 10967, + 11155 + ], + "vector": 146 + }, + { + "entrance_role": 21, + "path": [ + 21, + 10774, + 10812, + 10813, + 10829, + 10841, + 10842, + 10861, + 10869, + 10892, + 10899, + 10903, + 10911, + 10912, + 10924, + 10967, + 11155 + ], + "vector": 289 + }, + { + "entrance_role": 99, + "path": [ + 99, + 10622, + 10662, + 10663, + 10677, + 10688, + 10707, + 10715, + 10738, + 10745, + 10749, + 10757, + 10758, + 10770, + 10966, + 10967, + 11155 + ], + "vector": 471 + }, + { + "entrance_role": 43, + "path": [ + 43, + 10626, + 10662, + 10663, + 10677, + 10688, + 10707, + 10715, + 10738, + 10745, + 10749, + 10757, + 10758, + 10770, + 10966, + 10967, + 11155 + ], + "vector": 386 + }, + { + "entrance_role": 3, + "path": [ + 3, + 10160, + 10200, + 10201, + 10215, + 10226, + 10245, + 10253, + 10276, + 10277, + 10279, + 10293, + 10294, + 10298, + 10306, + 10307, + 10965, + 10966, + 10967, + 11155 + ], + "vector": 67 + }, + { + "entrance_role": 25, + "path": [ + 25, + 9080, + 9120, + 9121, + 9135, + 9146, + 9165, + 9173, + 9196, + 9203, + 9207, + 9215, + 9216, + 9228, + 10962, + 10963, + 10964, + 10965, + 10966, + 10967, + 11155 + ], + "vector": 14 + } + ] + }, + { + "event": 10549, + "frame": 281, + "lower_dimension": 8, + "node": 11181, + "role": 256, + "witnesses": [ + { + "entrance_role": 102, + "path": [ + 102, + 9388, + 9428, + 9429, + 9443, + 9454, + 9473, + 9481, + 9504, + 9505, + 9507, + 9521, + 9522, + 9526, + 9534, + 9535, + 10973, + 11181 + ], + "vector": 247 + }, + { + "entrance_role": 18, + "path": [ + 18, + 9392, + 9428, + 9429, + 9443, + 9454, + 9473, + 9481, + 9504, + 9505, + 9507, + 9521, + 9522, + 9526, + 9534, + 9535, + 10973, + 11181 + ], + "vector": 145 + }, + { + "entrance_role": 40, + "path": [ + 40, + 9394, + 9432, + 9433, + 9442, + 9457, + 9471, + 9484, + 9493, + 9503, + 9510, + 9514, + 9525, + 9526, + 9534, + 9535, + 10973, + 11181 + ], + "vector": 290 + }, + { + "entrance_role": 54, + "path": [ + 54, + 9386, + 9387, + 9426, + 9427, + 9442, + 9457, + 9471, + 9484, + 9493, + 9503, + 9510, + 9514, + 9525, + 9526, + 9534, + 9535, + 10973, + 11181 + ], + "vector": 196 + }, + { + "entrance_role": 47, + "path": [ + 47, + 10776, + 10816, + 10817, + 10831, + 10842, + 10861, + 10869, + 10892, + 10893, + 10895, + 10909, + 10910, + 10914, + 10922, + 10923, + 10972, + 10973, + 11181 + ], + "vector": 268 + }, + { + "entrance_role": 37, + "path": [ + 37, + 10780, + 10816, + 10817, + 10831, + 10842, + 10861, + 10869, + 10892, + 10893, + 10895, + 10909, + 10910, + 10914, + 10922, + 10923, + 10972, + 10973, + 11181 + ], + "vector": 274 + }, + { + "entrance_role": 99, + "path": [ + 99, + 10622, + 10662, + 10663, + 10677, + 10688, + 10707, + 10715, + 10738, + 10739, + 10741, + 10755, + 10756, + 10760, + 10768, + 10769, + 10971, + 10972, + 10973, + 11181 + ], + "vector": 471 + }, + { + "entrance_role": 69, + "path": [ + 69, + 10314, + 10354, + 10355, + 10369, + 10380, + 10399, + 10407, + 10430, + 10431, + 10433, + 10447, + 10448, + 10452, + 10460, + 10461, + 10970, + 10971, + 10972, + 10973, + 11181 + ], + "vector": 304 + } + ] + } + ] + }, + "forward": { + "cut_native_events": 240, + "monotone_edges": 31630, + "path_links": 1102, + "targets": [ + { + "event": 10344, + "frame": 254, + "lower_dimension": 8, + "node": 10976, + "role": 92, + "witnesses": [ + { + "entrance_role": 50, + "path": [ + 50, + 9697, + 9737, + 9738, + 9753, + 9764, + 9783, + 9791, + 9814, + 9821, + 9825, + 9833, + 9834, + 9846, + 9847, + 10931, + 10976 + ], + "vector": 276 + }, + { + "entrance_role": 108, + "path": [ + 108, + 9701, + 9737, + 9738, + 9753, + 9764, + 9783, + 9791, + 9814, + 9821, + 9825, + 9833, + 9834, + 9846, + 9847, + 10931, + 10976 + ], + "vector": 351 + }, + { + "entrance_role": 34, + "path": [ + 34, + 9695, + 9733, + 9734, + 9751, + 9763, + 9764, + 9783, + 9791, + 9814, + 9821, + 9825, + 9833, + 9834, + 9846, + 9847, + 10931, + 10976 + ], + "vector": 266 + }, + { + "entrance_role": 32, + "path": [ + 32, + 9542, + 9582, + 9583, + 9598, + 9609, + 9628, + 9636, + 9659, + 9666, + 9670, + 9678, + 9679, + 9691, + 9692, + 10930, + 10931, + 10976 + ], + "vector": 74 + }, + { + "entrance_role": 45, + "path": [ + 45, + 9546, + 9582, + 9583, + 9598, + 9609, + 9628, + 9636, + 9659, + 9666, + 9670, + 9678, + 9679, + 9691, + 9692, + 10930, + 10931, + 10976 + ], + "vector": 44 + }, + { + "entrance_role": 22, + "path": [ + 22, + 9703, + 9741, + 9742, + 9752, + 9767, + 9781, + 9794, + 9803, + 9813, + 9814, + 9821, + 9825, + 9833, + 9834, + 9846, + 9847, + 10931, + 10976 + ], + "vector": 193 + }, + { + "entrance_role": 102, + "path": [ + 102, + 9388, + 9428, + 9429, + 9443, + 9454, + 9473, + 9481, + 9504, + 9511, + 9515, + 9523, + 9524, + 9536, + 9537, + 10929, + 10930, + 10931, + 10976 + ], + "vector": 247 + }, + { + "entrance_role": 25, + "path": [ + 25, + 9080, + 9120, + 9121, + 9135, + 9146, + 9165, + 9173, + 9196, + 9203, + 9207, + 9215, + 9216, + 9228, + 9229, + 10927, + 10928, + 10929, + 10930, + 10931, + 10976 + ], + "vector": 14 + } + ] + }, + { + "event": 10370, + "frame": 274, + "lower_dimension": 8, + "node": 11002, + "role": 57, + "witnesses": [ + { + "entrance_role": 69, + "path": [ + 69, + 10314, + 10354, + 10355, + 10369, + 10380, + 10399, + 10407, + 10430, + 10437, + 10441, + 10449, + 10450, + 10462, + 10463, + 10937, + 11002 + ], + "vector": 304 + }, + { + "entrance_role": 96, + "path": [ + 96, + 10318, + 10354, + 10355, + 10369, + 10380, + 10399, + 10407, + 10430, + 10437, + 10441, + 10449, + 10450, + 10462, + 10463, + 10937, + 11002 + ], + "vector": 379 + }, + { + "entrance_role": 5, + "path": [ + 5, + 10312, + 10350, + 10351, + 10367, + 10379, + 10380, + 10399, + 10407, + 10430, + 10437, + 10441, + 10449, + 10450, + 10462, + 10463, + 10937, + 11002 + ], + "vector": 259 + }, + { + "entrance_role": 3, + "path": [ + 3, + 10160, + 10200, + 10201, + 10215, + 10226, + 10245, + 10253, + 10276, + 10283, + 10287, + 10295, + 10296, + 10308, + 10309, + 10936, + 10937, + 11002 + ], + "vector": 67 + }, + { + "entrance_role": 8, + "path": [ + 8, + 10164, + 10200, + 10201, + 10215, + 10226, + 10245, + 10253, + 10276, + 10283, + 10287, + 10295, + 10296, + 10308, + 10309, + 10936, + 10937, + 11002 + ], + "vector": 37 + }, + { + "entrance_role": 4, + "path": [ + 4, + 10316, + 10358, + 10359, + 10368, + 10383, + 10397, + 10410, + 10419, + 10429, + 10430, + 10437, + 10441, + 10449, + 10450, + 10462, + 10463, + 10937, + 11002 + ], + "vector": 131 + }, + { + "entrance_role": 84, + "path": [ + 84, + 10006, + 10046, + 10047, + 10061, + 10072, + 10091, + 10099, + 10122, + 10129, + 10133, + 10141, + 10142, + 10154, + 10155, + 10935, + 10936, + 10937, + 11002 + ], + "vector": 254 + }, + { + "entrance_role": 25, + "path": [ + 25, + 9080, + 9120, + 9121, + 9135, + 9146, + 9165, + 9173, + 9196, + 9203, + 9207, + 9215, + 9216, + 9228, + 9229, + 10933, + 10934, + 10935, + 10936, + 10937, + 11002 + ], + "vector": 14 + } + ] + }, + { + "event": 10396, + "frame": 619, + "lower_dimension": 8, + "node": 11028, + "role": 81, + "witnesses": [ + { + "entrance_role": 99, + "path": [ + 99, + 10622, + 10662, + 10663, + 10677, + 10688, + 10707, + 10715, + 10738, + 10745, + 10749, + 10757, + 10758, + 10770, + 10771, + 10943, + 11028 + ], + "vector": 471 + }, + { + "entrance_role": 43, + "path": [ + 43, + 10626, + 10662, + 10663, + 10677, + 10688, + 10707, + 10715, + 10738, + 10745, + 10749, + 10757, + 10758, + 10770, + 10771, + 10943, + 11028 + ], + "vector": 386 + }, + { + "entrance_role": 13, + "path": [ + 13, + 10618, + 10619, + 10654, + 10655, + 10677, + 10688, + 10707, + 10715, + 10738, + 10745, + 10749, + 10757, + 10758, + 10770, + 10771, + 10943, + 11028 + ], + "vector": 73 + }, + { + "entrance_role": 78, + "path": [ + 78, + 10620, + 10658, + 10659, + 10675, + 10687, + 10688, + 10707, + 10715, + 10738, + 10745, + 10749, + 10757, + 10758, + 10770, + 10771, + 10943, + 11028 + ], + "vector": 506 + }, + { + "entrance_role": 52, + "path": [ + 52, + 10468, + 10508, + 10509, + 10523, + 10534, + 10553, + 10561, + 10584, + 10591, + 10595, + 10603, + 10604, + 10616, + 10617, + 10942, + 10943, + 11028 + ], + "vector": 164 + }, + { + "entrance_role": 41, + "path": [ + 41, + 10472, + 10508, + 10509, + 10523, + 10534, + 10553, + 10561, + 10584, + 10591, + 10595, + 10603, + 10604, + 10616, + 10617, + 10942, + 10943, + 11028 + ], + "vector": 194 + }, + { + "entrance_role": 84, + "path": [ + 84, + 10006, + 10046, + 10047, + 10061, + 10072, + 10091, + 10099, + 10122, + 10129, + 10133, + 10141, + 10142, + 10154, + 10155, + 10941, + 10942, + 10943, + 11028 + ], + "vector": 254 + }, + { + "entrance_role": 56, + "path": [ + 56, + 9234, + 9274, + 9275, + 9289, + 9300, + 9319, + 9327, + 9350, + 9357, + 9361, + 9369, + 9370, + 9382, + 9383, + 10939, + 10940, + 10941, + 10942, + 10943, + 11028 + ], + "vector": 388 + } + ] + }, + { + "event": 10422, + "frame": 279, + "lower_dimension": 8, + "node": 11054, + "role": 224, + "witnesses": [ + { + "entrance_role": 99, + "path": [ + 99, + 10622, + 10662, + 10663, + 10677, + 10688, + 10707, + 10715, + 10738, + 10745, + 10749, + 10757, + 10758, + 10770, + 10771, + 10949, + 11054 + ], + "vector": 471 + }, + { + "entrance_role": 43, + "path": [ + 43, + 10626, + 10662, + 10663, + 10677, + 10688, + 10707, + 10715, + 10738, + 10745, + 10749, + 10757, + 10758, + 10770, + 10771, + 10949, + 11054 + ], + "vector": 386 + }, + { + "entrance_role": 13, + "path": [ + 13, + 10618, + 10619, + 10654, + 10655, + 10677, + 10688, + 10707, + 10715, + 10738, + 10745, + 10749, + 10757, + 10758, + 10770, + 10771, + 10949, + 11054 + ], + "vector": 73 + }, + { + "entrance_role": 78, + "path": [ + 78, + 10620, + 10658, + 10659, + 10675, + 10687, + 10688, + 10707, + 10715, + 10738, + 10745, + 10749, + 10757, + 10758, + 10770, + 10771, + 10949, + 11054 + ], + "vector": 506 + }, + { + "entrance_role": 52, + "path": [ + 52, + 10468, + 10508, + 10509, + 10523, + 10534, + 10553, + 10561, + 10584, + 10591, + 10595, + 10603, + 10604, + 10616, + 10617, + 10948, + 10949, + 11054 + ], + "vector": 164 + }, + { + "entrance_role": 41, + "path": [ + 41, + 10472, + 10508, + 10509, + 10523, + 10534, + 10553, + 10561, + 10584, + 10591, + 10595, + 10603, + 10604, + 10616, + 10617, + 10948, + 10949, + 11054 + ], + "vector": 194 + }, + { + "entrance_role": 69, + "path": [ + 69, + 10314, + 10354, + 10355, + 10369, + 10380, + 10399, + 10407, + 10430, + 10437, + 10441, + 10449, + 10450, + 10462, + 10463, + 10947, + 10948, + 10949, + 11054 + ], + "vector": 304 + }, + { + "entrance_role": 32, + "path": [ + 32, + 9542, + 9582, + 9583, + 9598, + 9609, + 9628, + 9636, + 9659, + 9666, + 9670, + 9678, + 9679, + 9691, + 9692, + 10945, + 10946, + 10947, + 10948, + 10949, + 11054 + ], + "vector": 74 + } + ] + }, + { + "event": 10448, + "frame": 621, + "lower_dimension": 8, + "node": 11080, + "role": 11, + "witnesses": [ + { + "entrance_role": 47, + "path": [ + 47, + 10776, + 10816, + 10817, + 10831, + 10842, + 10861, + 10869, + 10892, + 10899, + 10903, + 10911, + 10912, + 10924, + 10925, + 10955, + 11080 + ], + "vector": 268 + }, + { + "entrance_role": 37, + "path": [ + 37, + 10780, + 10816, + 10817, + 10831, + 10842, + 10861, + 10869, + 10892, + 10899, + 10903, + 10911, + 10912, + 10924, + 10925, + 10955, + 11080 + ], + "vector": 274 + }, + { + "entrance_role": 52, + "path": [ + 52, + 10468, + 10508, + 10509, + 10523, + 10534, + 10553, + 10561, + 10584, + 10591, + 10595, + 10603, + 10604, + 10616, + 10954, + 10955, + 11080 + ], + "vector": 164 + }, + { + "entrance_role": 41, + "path": [ + 41, + 10472, + 10508, + 10509, + 10523, + 10534, + 10553, + 10561, + 10584, + 10591, + 10595, + 10603, + 10604, + 10616, + 10954, + 10955, + 11080 + ], + "vector": 194 + }, + { + "entrance_role": 36, + "path": [ + 36, + 10772, + 10773, + 10808, + 10809, + 10831, + 10842, + 10861, + 10869, + 10892, + 10899, + 10903, + 10911, + 10912, + 10924, + 10925, + 10955, + 11080 + ], + "vector": 146 + }, + { + "entrance_role": 21, + "path": [ + 21, + 10774, + 10812, + 10813, + 10829, + 10841, + 10842, + 10861, + 10869, + 10892, + 10899, + 10903, + 10911, + 10912, + 10924, + 10925, + 10955, + 11080 + ], + "vector": 289 + }, + { + "entrance_role": 3, + "path": [ + 3, + 10160, + 10200, + 10201, + 10215, + 10226, + 10245, + 10253, + 10276, + 10283, + 10287, + 10295, + 10296, + 10308, + 10953, + 10954, + 10955, + 11080 + ], + "vector": 67 + }, + { + "entrance_role": 56, + "path": [ + 56, + 9234, + 9274, + 9275, + 9289, + 9300, + 9319, + 9327, + 9350, + 9357, + 9361, + 9369, + 9370, + 9382, + 10951, + 10952, + 10953, + 10954, + 10955, + 11080 + ], + "vector": 388 + } + ] + }, + { + "event": 10474, + "frame": 280, + "lower_dimension": 8, + "node": 11106, + "role": 240, + "witnesses": [ + { + "entrance_role": 47, + "path": [ + 47, + 10776, + 10816, + 10817, + 10831, + 10842, + 10861, + 10869, + 10892, + 10899, + 10903, + 10911, + 10912, + 10924, + 10925, + 10961, + 11106 + ], + "vector": 268 + }, + { + "entrance_role": 37, + "path": [ + 37, + 10780, + 10816, + 10817, + 10831, + 10842, + 10861, + 10869, + 10892, + 10899, + 10903, + 10911, + 10912, + 10924, + 10925, + 10961, + 11106 + ], + "vector": 274 + }, + { + "entrance_role": 36, + "path": [ + 36, + 10772, + 10773, + 10808, + 10809, + 10831, + 10842, + 10861, + 10869, + 10892, + 10899, + 10903, + 10911, + 10912, + 10924, + 10925, + 10961, + 11106 + ], + "vector": 146 + }, + { + "entrance_role": 21, + "path": [ + 21, + 10774, + 10812, + 10813, + 10829, + 10841, + 10842, + 10861, + 10869, + 10892, + 10899, + 10903, + 10911, + 10912, + 10924, + 10925, + 10961, + 11106 + ], + "vector": 289 + }, + { + "entrance_role": 69, + "path": [ + 69, + 10314, + 10354, + 10355, + 10369, + 10380, + 10399, + 10407, + 10430, + 10437, + 10441, + 10449, + 10450, + 10462, + 10959, + 10960, + 10961, + 11106 + ], + "vector": 304 + }, + { + "entrance_role": 96, + "path": [ + 96, + 10318, + 10354, + 10355, + 10369, + 10380, + 10399, + 10407, + 10430, + 10437, + 10441, + 10449, + 10450, + 10462, + 10959, + 10960, + 10961, + 11106 + ], + "vector": 379 + }, + { + "entrance_role": 52, + "path": [ + 52, + 10468, + 10508, + 10509, + 10523, + 10534, + 10553, + 10561, + 10584, + 10585, + 10587, + 10601, + 10602, + 10606, + 10614, + 10615, + 10960, + 10961, + 11106 + ], + "vector": 164 + }, + { + "entrance_role": 102, + "path": [ + 102, + 9388, + 9428, + 9429, + 9443, + 9454, + 9473, + 9481, + 9504, + 9511, + 9515, + 9523, + 9524, + 9536, + 10957, + 10958, + 10959, + 10960, + 10961, + 11106 + ], + "vector": 247 + } + ] + }, + { + "event": 10500, + "frame": 624, + "lower_dimension": 8, + "node": 11132, + "role": 9, + "witnesses": [ + { + "entrance_role": 47, + "path": [ + 47, + 10776, + 10816, + 10817, + 10831, + 10842, + 10861, + 10869, + 10892, + 10899, + 10903, + 10911, + 10912, + 10924, + 10967, + 11132 + ], + "vector": 268 + }, + { + "entrance_role": 37, + "path": [ + 37, + 10780, + 10816, + 10817, + 10831, + 10842, + 10861, + 10869, + 10892, + 10899, + 10903, + 10911, + 10912, + 10924, + 10967, + 11132 + ], + "vector": 274 + }, + { + "entrance_role": 36, + "path": [ + 36, + 10772, + 10773, + 10808, + 10809, + 10831, + 10842, + 10861, + 10869, + 10892, + 10899, + 10903, + 10911, + 10912, + 10924, + 10967, + 11132 + ], + "vector": 146 + }, + { + "entrance_role": 21, + "path": [ + 21, + 10774, + 10812, + 10813, + 10829, + 10841, + 10842, + 10861, + 10869, + 10892, + 10899, + 10903, + 10911, + 10912, + 10924, + 10967, + 11132 + ], + "vector": 289 + }, + { + "entrance_role": 99, + "path": [ + 99, + 10622, + 10662, + 10663, + 10677, + 10688, + 10707, + 10715, + 10738, + 10745, + 10749, + 10757, + 10758, + 10770, + 10966, + 10967, + 11132 + ], + "vector": 471 + }, + { + "entrance_role": 43, + "path": [ + 43, + 10626, + 10662, + 10663, + 10677, + 10688, + 10707, + 10715, + 10738, + 10745, + 10749, + 10757, + 10758, + 10770, + 10966, + 10967, + 11132 + ], + "vector": 386 + }, + { + "entrance_role": 3, + "path": [ + 3, + 10160, + 10200, + 10201, + 10215, + 10226, + 10245, + 10253, + 10276, + 10277, + 10279, + 10293, + 10294, + 10298, + 10306, + 10307, + 10965, + 10966, + 10967, + 11132 + ], + "vector": 67 + }, + { + "entrance_role": 25, + "path": [ + 25, + 9080, + 9120, + 9121, + 9135, + 9146, + 9165, + 9173, + 9196, + 9203, + 9207, + 9215, + 9216, + 9228, + 10962, + 10963, + 10964, + 10965, + 10966, + 10967, + 11132 + ], + "vector": 14 + } + ] + }, + { + "event": 10526, + "frame": 281, + "lower_dimension": 8, + "node": 11158, + "role": 256, + "witnesses": [ + { + "entrance_role": 102, + "path": [ + 102, + 9388, + 9428, + 9429, + 9443, + 9454, + 9473, + 9481, + 9504, + 9505, + 9507, + 9521, + 9522, + 9526, + 9534, + 9535, + 10973, + 11158 + ], + "vector": 247 + }, + { + "entrance_role": 18, + "path": [ + 18, + 9392, + 9428, + 9429, + 9443, + 9454, + 9473, + 9481, + 9504, + 9505, + 9507, + 9521, + 9522, + 9526, + 9534, + 9535, + 10973, + 11158 + ], + "vector": 145 + }, + { + "entrance_role": 40, + "path": [ + 40, + 9394, + 9432, + 9433, + 9442, + 9457, + 9471, + 9484, + 9493, + 9503, + 9510, + 9514, + 9525, + 9526, + 9534, + 9535, + 10973, + 11158 + ], + "vector": 290 + }, + { + "entrance_role": 54, + "path": [ + 54, + 9386, + 9387, + 9426, + 9427, + 9442, + 9457, + 9471, + 9484, + 9493, + 9503, + 9510, + 9514, + 9525, + 9526, + 9534, + 9535, + 10973, + 11158 + ], + "vector": 196 + }, + { + "entrance_role": 47, + "path": [ + 47, + 10776, + 10816, + 10817, + 10831, + 10842, + 10861, + 10869, + 10892, + 10893, + 10895, + 10909, + 10910, + 10914, + 10922, + 10923, + 10972, + 10973, + 11158 + ], + "vector": 268 + }, + { + "entrance_role": 37, + "path": [ + 37, + 10780, + 10816, + 10817, + 10831, + 10842, + 10861, + 10869, + 10892, + 10893, + 10895, + 10909, + 10910, + 10914, + 10922, + 10923, + 10972, + 10973, + 11158 + ], + "vector": 274 + }, + { + "entrance_role": 99, + "path": [ + 99, + 10622, + 10662, + 10663, + 10677, + 10688, + 10707, + 10715, + 10738, + 10739, + 10741, + 10755, + 10756, + 10760, + 10768, + 10769, + 10971, + 10972, + 10973, + 11158 + ], + "vector": 471 + }, + { + "entrance_role": 69, + "path": [ + 69, + 10314, + 10354, + 10355, + 10369, + 10380, + 10399, + 10407, + 10430, + 10431, + 10433, + 10447, + 10448, + 10452, + 10460, + 10461, + 10970, + 10971, + 10972, + 10973, + 11158 + ], + "vector": 304 + } + ] + } + ] + } + }, + "payload_sha256": "cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd", + "scope": "FIXED_SCALAR_WORD_MONOTONE_CONTACT_FLOOR_ONLY", + "source_sha256": "7679daa4ec6a40f56fc7f0202379a6f454310e94945aba4f48beaaaafb838d05" +} diff --git a/research/monotone-owned-centre-floor/verify.py b/research/monotone-owned-centre-floor/verify.py new file mode 100644 index 0000000000..8905ae5388 --- /dev/null +++ b/research/monotone-owned-centre-floor/verify.py @@ -0,0 +1,239 @@ +#!/usr/bin/env python3 +"""Exact monotone owned-centre floor. Standard library only. + +Cinna Davis / 1337isnot1337, substantial OpenAI Codex assistance. Apache-2.0. +Scientific word: Cao Yifan's round-three word and its credited predecessors. +All native warp relations and all helper boundary constraints are discarded. +""" +from collections import Counter, defaultdict, deque +from copy import deepcopy +import argparse +import gzip +import hashlib +import json +from pathlib import Path + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] +SOURCE = 'research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz' +SOURCE_SHA = '7679daa4ec6a40f56fc7f0202379a6f454310e94945aba4f48beaaaafb838d05' +PAYLOAD_SHA = 'cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd' + + +def need(condition, message): + if not condition: + raise ValueError(message) + + +def basis(vectors): + pivots = {} + for value in vectors: + v = value + while v: + p = v.bit_length() - 1 + if p in pivots: + v ^= pivots[p] + else: + pivots[p] = v + break + return [pivots[p] for p in sorted(pivots)] + + +def span(vectors): + out = {0} + for v in vectors: + out |= {x ^ v for x in tuple(out)} + return frozenset(out) + + +def load_source(): + data = (ROOT / SOURCE).read_bytes() + need(hashlib.sha256(data).hexdigest() == SOURCE_SHA, 'Frozen source bytes') + raw = gzip.decompress(data) + need(hashlib.sha256(raw).hexdigest() == PAYLOAD_SHA, 'Frozen source payload') + return json.loads(raw) + + +def graph(payload, direction): + """Occurrence DAG; scalar indices omit climbs. No edge crosses a warp. + + 0..631 are persistent entrances; 632+i is scalar event i; a warp resets + its field to unconstrained node 632+N+i. All scalar contacts involving + owned C0 are released too. No helper or final boundary edges are used. + """ + c = payload['canonical'] + raw = [e for e in payload['programs'][direction] if e[0] != 'climb'] + need(len(c['start']) == len(c['final']) == 632, '632 independent persistent fields') + spaces = [span(b) for b in c['frames']] + need(all(len(b) == len(basis(b)) for b in c['frames']), 'Independent frame bases') + current = list(range(632)) + frames = dict(enumerate(c['start'])) + incoming = defaultdict(list) + edges = set() + targets = [] + warps = 0 + for i, event in enumerate(raw): + if event[0] == 'scalar': + gate, frame = event[1:] + refs = gate[1:3] if gate[0] in ('add', 'copy') else gate[1:2] + roles = [r[1] for r in refs if r[0] == 'L'] + node = 632 + i + frames[node] = frame + for r in roles: + a = current[r] + need(spaces[frames[a]] <= spaces[frame], 'Source monotone persistent edge') + edges.add((a, node)) + incoming[node].append(a) + current[r] = node + if frame != 0 and roles and any(r[0] == 'C' for r in refs): + need(len(roles) == 1, 'One persistent source at high owned contact') + targets.append({'event': i, 'node': node, 'role': roles[0], 'frame': frame}) + elif event[0] == 'warp': + need(event[1][0] == 'L', 'Native warp has persistent role') + node = 632 + len(raw) + i + frames[node] = event[4] + current[event[1][1]] = node + warps += 1 + centers = [(i, e) for i, e in enumerate(raw) if e[0] == 'center'] + need(len(targets) == len(centers) == 8, 'All eight owned lifetimes') + need([x['role'] for x in targets] == [92, 57, 81, 224, 11, 240, 9, 256], 'Actual owned sources') + for target, (i, center) in zip(targets, centers): + high = target['frame'] + need(len(c['frames'][high]) == 8, 'Source rank-eight high chart') + if direction == 'forward': + need(raw[target['event']][1] == ['copy', ['C', 0], ['L', target['role']]], 'Actual COPY') + need(target['event'] + 1 == i, 'COPY immediately before descending center') + need(raw[i - 2] == ['scalar', ['clear', ['C', 0]], high], 'Owned initialization') + need(center == ['center', 0, high, 0, 8], 'Actual descending center') + else: + need(raw[target['event']][1] == ['add', ['L', target['role']], ['C', 0], -1, 1], 'Actual dual output ADD') + need(i + 1 == target['event'], 'Ascending center immediately before output') + need(raw[i + 2] == ['scalar', ['clear', ['C', 0]], high], 'Owned final cleanup') + need(center == ['center', 0, 0, high, 8], 'Actual ascending center') + paid = Counter(e[5] for e in payload['programs'][direction] if e[0] == 'climb') + paid.update(e[4] for _, e in centers) + need(paid == Counter({1: 2201, 2: 412, 3: 510, 4: 127, 5: 40, 8: 8}), 'Complete baseline paid profile') + helpers = Counter(len(c['frames'][c['final'][r]]) - len(c['frames'][c['start'][r]]) for r in range(224, 632)) + need(helpers == Counter({4: 28, 7: 7, 8: 47, 9: 326}), 'All 408 independent helper targets') + return {'raw': raw, 'spaces': spaces, 'frames': frames, 'incoming': incoming, + 'edges': edges, 'targets': targets, 'warps': warps} + + +def witness_paths(payload, g, target): + """Shortest ancestor paths, greedily selecting independent entrance vectors.""" + dest = target['node'] + following = {dest: None} + queue = deque([dest]) + reached = [] + while queue: + node = queue.popleft() + if node < 224: + for v in payload['canonical']['frames'][g['frames'][node]]: + reached.append((node, v)) + for a in sorted(g['incoming'][node]): + if a not in following: + following[a] = node + queue.append(a) + witnesses, vectors = [], [] + for root, v in reached: + if len(basis(vectors + [v])) == len(vectors): + continue + path = [root] + while path[-1] != dest: + path.append(following[path[-1]]) + witnesses.append({'entrance_role': root, 'vector': v, 'path': path}) + vectors.append(v) + need(len(vectors) == 8, 'Eight independent main entrance ancestors') + return {**target, 'lower_dimension': 8, 'witnesses': witnesses} + + +def check_witnesses(payload, g, rows): + need(len(rows) == len(g['targets']), 'Complete target list') + links = 0 + for row, target in zip(rows, g['targets']): + need(all(row[k] == v for k, v in target.items()), 'Actual target binding') + vectors = [] + need(len(row['witnesses']) == row['lower_dimension'] == 8, 'Eight witness vectors') + for w in row['witnesses']: + root, v, path = w['entrance_role'], w['vector'], w['path'] + need(0 <= root < 224, 'Seed is a fixed main entrance') + need(v != 0 and v in g['spaces'][payload['canonical']['start'][root]], 'Actual fixed entrance vector') + need(path[0] == root and path[-1] == target['node'], 'Path endpoints') + need(len(path) == len(set(path)), 'Acyclic witness path') + for a, b in zip(path, path[1:]): + need((a, b) in g['edges'], 'Actual monotone chronological edge') + links += 1 + need(v in g['spaces'][target['frame']], 'Source attains witness containment') + vectors.append(v) + need(len(basis(vectors)) == 8, 'Independent witness vectors') + need(span(vectors) == g['spaces'][target['frame']], 'Sharp original high frame') + return links + + +def rejection_controls(payload, g, rows): + def rejects(mutant): + try: + check_witnesses(payload, g, mutant) + except ValueError: + return + raise ValueError('Corruption control accepted') + bad = deepcopy(rows); bad.pop(); rejects(bad) + bad = deepcopy(rows); bad[0]['role'] ^= 1; rejects(bad) + bad = deepcopy(rows); bad[0]['witnesses'][1] = deepcopy(bad[0]['witnesses'][0]); rejects(bad) + bad = deepcopy(rows); bad[0]['witnesses'][0]['entrance_role'] = 224; rejects(bad) + bad = deepcopy(rows); bad[0]['witnesses'][0]['vector'] = 0; rejects(bad) + bad = deepcopy(rows); bad[0]['witnesses'][0]['path'][-1] -= 1; rejects(bad) + bad = deepcopy(rows) + path = bad[0]['witnesses'][0]['path'] + need(len(path) > 2, 'Nontrivial path control') + bad[0]['witnesses'][0]['path'] = [path[0], path[-1]]; rejects(bad) + for row in rows: + vectors = [w['vector'] for w in row['witnesses']] + for omitted in range(8): + smaller = span(vectors[:omitted] + vectors[omitted + 1:]) + need(len(smaller) == 128 and not all(v in smaller for v in vectors), 'Rank-seven hyperplane control') + for i, e in enumerate(g['raw']): + if e[0] == 'warp': + out = 632 + len(g['raw']) + i + need(not g['incoming'][out], 'Every warp relation cut') + return 7 + 8 * len(rows) + 1 + + +def produce(payload): + out = {'source_sha256': SOURCE_SHA, 'payload_sha256': PAYLOAD_SHA, + 'scope': 'FIXED_SCALAR_WORD_MONOTONE_CONTACT_FLOOR_ONLY', 'directions': {}} + for direction in ('forward', 'backward'): + g = graph(payload, direction) + rows = [witness_paths(payload, g, t) for t in g['targets']] + links = check_witnesses(payload, g, rows) + out['directions'][direction] = {'cut_native_events': g['warps'], + 'monotone_edges': len(g['edges']), 'targets': rows, 'path_links': links} + return out + + +def main(): + ap = argparse.ArgumentParser() + ap.add_argument('--write', action='store_true', help='Regenerate deterministic witnesses') + args = ap.parse_args() + payload = load_source() + result = produce(payload) + path = HERE / 'WITNESSES.json' + if args.write: + path.write_text(json.dumps(result, indent=2, sort_keys=True) + '\n') + saved = json.loads(path.read_text()) + need(saved == result, 'Deterministic source-bound witness artifact') + controls = 0 + for direction in ('forward', 'backward'): + g = graph(payload, direction) + rows = saved['directions'][direction]['targets'] + check_witnesses(payload, g, rows) + controls += rejection_controls(payload, g, rows) + print(json.dumps({'status': 'PASS_MONOTONE_OWNED_CENTRE_FLOOR', 'directions': 2, + 'centers_per_direction': 8, 'minimum_each_high_dimension': 8, + 'minimum_center_rank_mass_with_opposite_zero': 64, + 'path_links': {d: result['directions'][d]['path_links'] for d in result['directions']}, + 'controls': controls, 'new_kappa': False}, sort_keys=True)) + + +if __name__ == '__main__': + main()