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"1", + "1", + "1", + "-1", + "1", + "1", + "1", + "1" + ] + ], + "kernel_basis": [], + "nullity": 0, + "response_rank": 2 + }, + { + "eligible_helpers": [ + 520, + 526, + 532 + ], + "frame": [ + [ + "1", + "1", + "1", + "1", + "-1", + "-1", + "1", + "-1" + ] + ], + "kernel_basis": [], + "nullity": 0, + "response_rank": 3 + }, + { + "eligible_helpers": [ + 590, + 596, + 602 + ], + "frame": [ + [ + "1", + "1", + "1", + "1", + "-1", + "1", + "-1", + "-1" + ] + ], + "kernel_basis": [], + "nullity": 0, + "response_rank": 3 + }, + { + "eligible_helpers": [ + 350, + 351, + 530, + 532, + 534 + ], + "frame": [ + [ + "1", + "1", + "1", + "1", + "0", + "0", + "0", + "0" + ] + ], + "kernel_basis": [], + "nullity": 0, + "response_rank": 5 + }, + { + "eligible_helpers": [ + 532 + ], + "frame": [ + [ + "1", + "1", + "1", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "1", + "-1", + "1" + ] + ], + "kernel_basis": [], + "nullity": 0, + "response_rank": 1 + }, + { + "eligible_helpers": [ + 644, + 650, + 656 + ], + "frame": [ + [ + "1", + "1", + "1", + "1", + "1", + "-1", + "1", + "1" + ] + ], + "kernel_basis": [], + "nullity": 0, + "response_rank": 3 + }, + { + "eligible_helpers": [ + 519, + 525, + 532 + ], + "frame": [ + [ + "1", + "1", + "1", + "1", + "1", + "1", + "-1", + "1" + ] + ], + "kernel_basis": [], + "nullity": 0, + "response_rank": 3 + }, + { + "eligible_helpers": [ + 578, + 584 + ], + "frame": [ + [ + "1", + "2", + "0", + "-1", + "0", + "-1", + "1", + "0" + ] + ], + "kernel_basis": [], + "nullity": 0, + "response_rank": 2 + }, + { + "eligible_helpers": [ + 609, + 615, + 621 + ], + "frame": [ + [ + "1", + "2", + "0", + "-1", + "0", + "1", + "-1", + "0" + ] + ], + "kernel_basis": [], + "nullity": 0, + "response_rank": 3 + }, + { + "eligible_helpers": [ + 608, + 614, + 620 + ], + "frame": [ + [ + "1", + "2", + "0", + "1", + "0", + "-1", + "-1", + "0" + ] + ], + "kernel_basis": [], + "nullity": 0, + "response_rank": 3 + }, + { + "eligible_helpers": [ + 521, + 524, + 530 + ], + "frame": [ + [ + "1", + "2", + "0", + "1", + "0", + "1", + "1", + "0" + ] + ], + "kernel_basis": [], + "nullity": 0, + "response_rank": 3 + } + ], + "closure_dimensions": { + "1": 213, + "2": 153 + }, + "distinct_plane_pairs": 11628, + "first_dimensions": { + "1": 286, + "2": 153 + }, + "first_frame_ids": 264, + "first_rowspaces": 264, + "helper_count": 439, + "initial_subspace_dimensions": { + "1": 111, + "2": 153 + }, + "intersecting_distinct_plane_pairs": 549, + "nullity_histogram": { + "0": 365, + "1": 1 + }, + "response_rows": 111 + }, + "controls": [ + "six-helper minimal kernel beyond sparse cutoff", + "one-response-bit mutation removes six-helper kernel", + "two absent input lines recovered as plane intersections", + "kernel alone does not imply a common entrance", + "dimension-three source fails closed", + "even-coordinate physical line is nonzero over Q" + ], + "new_kappa": false, + "raw_endpoint_columns": 661, + "schema_version": 1, + "scope": "binary response-null directions with arbitrary support and a nonzero rational common first-contact frame; fixed PR589 raw word", + "seed": 5 +} diff --git a/research/r439-kernel-entrance-closure/CLAIM.json b/research/r439-kernel-entrance-closure/CLAIM.json new file mode 100644 index 0000000000..9163a4168b --- /dev/null +++ b/research/r439-kernel-entrance-closure/CLAIM.json @@ -0,0 +1,42 @@ +{ + "worker": "astra_003", + "seed": 5, + "track": "bit supplier", + "base": "dd6403f774a0891093a006ae9716c02e371b1fdb", + "candidates": [ + "semantic D with nonzero entrances", + "larger-register abelian model", + "all-support response-kernel entrance classification" + ], + "scope": "R439 response-kernel entrance gauges over arbitrary support, exact eligible-helper kernel spaces for first-contact frame intersections", + "expected_deliverable": "source-bound all-support finite classification, exact controls, no new kappa", + "expected_finish": "2026-10-13T21:33:50Z", + "scope_status": "changed", + "os_draw": "secrets.randbelow(100), 2026-10-13T20:53:50.688826Z", + "no_pinned_coordination_issue": true, + "overlap": { + "open_pr_count": 843, + "read_full_bodies": true, + "discussions": [ + 1163, + 1166, + 1167, + 1233, + 1237, + 1210, + 1202 + ], + "closest_pr": 1179, + "closest_head": "a09f799fdb312e049a81f59b44f1339b5a053bbe", + "distinctness": "Complete linear-algebra classification for all binary supports, rather than sparse support<=4 enumeration. No imported construction." + }, + "result": "366 distinct nonzero rational subspaces; 365 zero kernels; unique remaining binary direction {444,470}", + "final_overlap": { + "checked_at_utc": "2026-10-13T21:06:56.906525+00:00", + "open_pr_count": 844, + "highest_open_pr": 1247, + "refreshed_default_head": "dadfea6e8a78ff6ba901705f87532a71c6f5bbb8", + "nearest_pr_1179_unchanged": true, + "new_overlap_found": false + } +} diff --git a/research/r439-kernel-entrance-closure/PROOF.md b/research/r439-kernel-entrance-closure/PROOF.md new file mode 100644 index 0000000000..b3d5e97620 --- /dev/null +++ b/research/r439-kernel-entrance-closure/PROOF.md @@ -0,0 +1,109 @@ +# Proof of the fixed first-contact classification + +## 1. Precisely delimited finite problem + +Let `K : F₂^439 → F₂^111` be the dirty-helper response of the frozen PR589 +A/scatter/B/C word. Physical helper labels run from 222 through 660. Its D +section has one target-only compensation matrix. The verifier independently +replays the raw word on 661 formal dirty columns and requires that its helper +response is exactly this D matrix; sources and helpers are restored and the +remaining target map is `y_i ↦ y_i+x_i`. + +For each helper `h`, let `F_h ≤ Q^8` be the span of the frame at its first A/B +contact. Every helper occurs, and every retained copied helper has an A contact +before the copy. Thus omission of scatter in the first-contact extraction does +not skip any earlier helper contact. Each `F_h` has dimension one or two. + +A **candidate direction** in this note is a nonzero binary vector `c` and a +nonzero rational subspace `U` such that + +1. `Kc=0`; +2. `U ⊆ F_h` for every `h ∈ supp(c)`. + +These are necessary conditions for the particular common-frame entrance +mechanism: an initial helper coordinate mapped into the raw helper bank as +column `c` is absent from D exactly when `Kc=0`; every helper carrying that +coordinate must admit the same entrance subspace before its first frozen raw +contact. We do not assert that these two conditions suffice for a physical +compiler, address realization or hosted execution. We do not assert their +necessity for differently timed or differently framed mechanisms. + +**Finite classification.** In this precise problem, every candidate has +`c=e_444+e_470` and +`U=span_Q(0,1,0,-1,1,0,1,0)`. Consequently there is only one independent binary +candidate direction, even without a support-size bound. + +## 2. A finite closure covers all rational entrances + +Let `L` be the nonzero intersection closure of the distinct `F_h`. Because all +generators have dimension at most two, its elements are exactly: + +- the distinct original lines and planes; +- every nonzero intersection of two distinct original planes. + +Indeed, an intersection involving a line is either that line or zero. An +intersection involving only planes is one plane if all are equal; otherwise +choose two unequal ones. Their intersection has dimension at most one, and +further intersections can only preserve that line or make it zero. This proves +closure and completeness without sampling vectors or bounding their rational +numerators or denominators. + +For any candidate with support `S`, let `V=∩_{h∈S} F_h`. Then `U⊆V`, so `V≠0` +and `V∈L`. Define the eligible set + +`I(V)={h : V⊆F_h}`. + +All of S lies in I(V). Thus c belongs to the kernel of the column restriction +`K|_{I(V)}`. It suffices to compute these finitely many kernels. Testing the +maximal intersection V is enough even when U is an arbitrary subline of a +plane: V contains the whole support's common subspace and still has every +support helper in its eligible set. No possible candidate is discarded by +using V rather than listing infinitely many sublines U. + +## 3. Exact finite certificate + +The certificate has 264 original rowspaces (111 lines and 153 planes). All +`153 choose 2 = 11628` distinct plane pairs are checked. Of those, 549 have a +one-dimensional intersection. After identifying equal rational subspaces the +closure consists of 213 lines and 153 planes, or 366 elements. + +For each V, `CERTIFICATE.json` lists a rational RREF basis of V, the entire +I(V), rank of its response matrix and a complete binary nullbasis. Column +Gaussian elimination retains each input column's binary combination mask. +A newly dependent column produces one null vector with a distinct highest +input position. Those dependency vectors are independent and their count is +`|I(V)|−rank(K|I(V))`; hence they form the full kernel, not a sparse sample. + +The separately implemented checker converts source spaces and certificate +spaces to exact orthogonal Gram projectors, so equality is equality of rational +subspaces rather than coordinate representatives. For two different planes +A and B, it forms the residuals of A's two basis vectors after projection onto +B. A nonzero linear combination in the joint kernel exists exactly when those +two residual columns are dependent. It obtains that line from one nonzero +residual coordinate and checks every residual coordinate. This yields exactly +the same closure. Eligibility is checked by exact projection. Binary row +elimination of all target equations independently recovers every rank and +nullbasis. + +There are 365 zero kernels. The remaining space is the line U₀ stated above, +with `I(U₀)={390,391,444,470,578,580,582}`. Its response rank is six and its +kernel is spanned by `e_444+e_470`. Over F₂ that one-dimensional kernel has only +one nonzero vector. The intersection `F_444 ∩ F_470` is exactly U₀ (checked +by both engines' source geometry). Therefore every nonzero U admitted by the +candidate pair is U₀ itself. This proves the finite classification. + +## 4. What the result does and does not bound + +For any invertible binary helper-basis matrix in this same common-first-contact +model, independent dormant coordinates would have independent response-null +columns. There is only one allowable nonzero column direction, so the model +cannot provide two independent dormant coordinates. A single direction also +has only a one-dimensional common entrance. This is an algebraic limitation +on the stated boundary, not a global bound on gate counts or recursive moments. + +PR1179 constructs this direction by a restored pair shear; its finite word and +physical costs are not re-executed here. New helpers, changed first contacts, +nonuniform timing, later cuts, raw-word changes, changed target interfaces and +broader address maps are outside this proof. Finite exact checking of this +source word does not establish any inherited all-size, realization, hosting, +precision/tape or analytic implication, or the integer-multiplication theorem. diff --git a/research/r439-kernel-entrance-closure/README.md b/research/r439-kernel-entrance-closure/README.md new file mode 100644 index 0000000000..97a4518eba --- /dev/null +++ b/research/r439-kernel-entrance-closure/README.md @@ -0,0 +1,148 @@ +# R439: all-support common-frame kernel entrance classification + +**Scoped negative result in the bit-supplier track; no new κ.** For the fixed +PR589 R439 word, the only nonzero binary response-null direction whose entire +support shares a nonzero rational first-contact frame is + +``` +e_444 + e_470, +U = span_Q(0, 1, 0, -1, 1, 0, 1, 0). +``` + +This is the same pair already constructed by Adam Gall in [PR1179](https://github.com/CrocSwap/integer-mult-bounds/pull/1179). +The new result removes that package's support-at-most-four restriction: +**arbitrary binary support sizes among all 439 helpers are covered**. There is +no second independent null direction in this fixed common-entrance model. +This does not exclude changed raw words, later chronological cuts, changed +first-contact frames, differently timed basis changes or different physical +interfaces. + +## Concrete evidence + +The selected record at base `dd6403f774a0891093a006ae9716c02e371b1fdb` +selects #1094, conditional κ `0.001672660197076918`, with the unchanged #589 +bit supplier. Its actual source manifest binds the word used here. The complex +supplier binds. The selected record, `upstream/` and predecessors are unchanged. + +| Object | Exact result | +|---|---:| +| Original dirty helper columns | 439 | +| Distinct first-contact rowspaces | 264: 111 lines and 153 planes | +| Helper counts by first-contact dimension | 286 at rank one; 153 at rank two | +| Distinct plane pairs checked | 11,628 | +| Pairs meeting in a line | 549 | +| Complete nonzero intersection closure | 366: 213 lines and 153 planes | +| Restricted response spaces with zero nullity | 365 | +| Restricted response spaces with nullity one | 1 | +| Helpers eligible at the unique surviving line | 390, 391, 444, 470, 578, 580, 582 | +| Complete nullbasis there | `{444,470}` | + +The full [certificate](CERTIFICATE.json) records every subspace, every eligible +helper set, its exact binary rank and a complete nullbasis. `verify.py` also +rederives the raw A/scatter/B/C operator and checks equality with compensation D +on all 661 dirty columns. COPY values are snapshots of the retained helpers; +this finite scalar endpoint check is not a native COPY/ERASE or physical audit. + +The [proof](PROOF.md) explains why the finite closure covers every rational +common entrance and every support size. The main engine uses rational RREF, +orthogonal complements and binary column elimination. A separately written +engine uses exact Gram projectors, two-column residual equations, and binary +row elimination. They compare all 366 spaces and all 366 restricted response +matrices, rather than just agreeing on final counts. Neither engine imports the +other or PR1179's implementation. + +## Reproduce + +Python 3.10 or newer, standard library only, from the repository root: + +```sh +python3 -I -B research/r439-kernel-entrance-closure/verify.py +python3 -I -B research/r439-kernel-entrance-closure/independent.py +python3 -I -O -B research/r439-kernel-entrance-closure/test_package.py -v +``` + +The first two commands print `PASS_R439_KERNEL_ENTRANCE_CLOSURE` and +`PASS_R439_KERNEL_ENTRANCE_INDEPENDENT`, with 366 classes and the unique +`444+470` direction. The test command checks all 4,096 binary 3×4 response +matrices against all 16 support masks, a minimal six-helper dependency beyond +the old cutoff, rational geometry controls, source/receipt corruptions and a +relocated optimized replay. See [VALIDATION.json](VALIDATION.json) for the +executed environment and results. + +The package also opts into the bounded registered replay: + +```sh +python3.12 scripts/research_package.py --package research/r439-kernel-entrance-closure +``` + +The registered wrapper specifically requires Python 3.12. The standalone commands +also pass on Python 3.14. Exact source bytes and the base commit are pinned in [SOURCES.json](SOURCES.json). +The selected record and catalogue are historical Git provenance, not moving +runtime inputs. This package does not rerun the selected hosted construction, +PR1179's complete candidate, native compilation, all-size interfaces or the +multiplication theorem. + +## Scope and paid-cost implication + +The question is whether a new binary helper direction `c` can satisfy `Kc=0` +while every helper in its support can receive the **same nonzero rational +entrance subspace before its original first raw contact**. The raw word and +its first-contact frames are frozen; no helper/source/target replacements, +free frame descent, reassigned frame paths or later-cut borrowing are allowed. +Geometry is over Q; response coefficients are over F₂. An algebraic direction +is necessary, not sufficient, for a compiled and hosted entrance gauge. + +PR1179 already supplies the known direction's finite entry/exit shear witness. +Its inherited complete local bill is 24,252 ADDs versus 24,305, with rank mass +5,128 versus 5,129; those construction claims are credited, **not re-executed +here**. Its old width-eight host needs an additional rank-one idle child when +hosting the width-seven residual, cancelling the local one-rank gain before +adapters. Even granting free entry/exit synthesis cannot create another algebraic direction. +This package supplies no new gate saving, physical invoice, hosted +supplier, precision improvement or exponent saving. It closes only the hope +that larger supports alone produce another direction under the same boundary. + +## Task, overlap and stopping rule + +OS assignment seed **5**, drawn with `secrets.randbelow(100)`, selects the bit +supplier track in the user's assignment. The alternatives and local claim are +in [CLAIM.json](CLAIM.json). The catalogue card is declared **changed** in +[TASK.json](TASK.json): this investigates a nonzero-entrance necessary condition, +not a replacement H2/K proof for frame-zero helper mixing. PR1194 already covers +that narrower semantic-D task. + +Live open-PR and discussion checks preceded the experiment and submission; +there was no pinned coordination issue, so the authorized local-claim fallback +was used. The experiment stops after the complete intersection closure and all +restricted kernels, with independent verification. It is not an enlarged +random sparse-support search. All support sizes are handled by exact nullspace +algebra. Scope exclusions remain material. + +## Open next questions + +The full fixed-first-contact common-frame question is closed by this result. +A useful distinct next step is to choose one later chronological cut and +recompute both the remaining response and actual current frames, then price +all transport and restoration. Such a cut may change this necessary condition; +the blocker is a complete, legal entry/exit and hosting contract. No wider +search under the same frozen first-contact rule is warranted. + +## Credit and AI disclosure + +Prepared for **mightyOil** with substantial **OpenAI Codex, GPT-6 Astra** +assistance in research, proof, implementation, verification and writing. +The two algorithms were written by the same AI-assisted contributor; no +independent human review or proof-assistant verification is implied. + +Adam Gall's #1179, pinned at `a09f799fdb312e049a81f59b44f1339b5a053bbe`, +provides the sparse-support first-contact formulation and the known pair's +construction. This package independently corroborates that pair and completes +its support domain; it makes no priority claim for the gauge mechanism. +Dugongue's #254 (`9ce32efb421132420242cfdb91ddd9eabe2c3795`) and +Chafik Boukhalfa's #382 (`536329e6cddd37d70a6b52cbe2c2604ea18c5e83`) +are earlier kernel-entrance precedents. DreamingOfClouds' #589 +(`a5afc8c6169ea61ba7c51dfd3cade02cc7b13b46`) supplies the tuned word on +eumemic's #555/#543 construction. Their original notices and license remain +unchanged. Ali Romman's #1128 and #1043, Hanson Sun's #1079, and the broader +kernel/retiming lineage are related work, not imported dependencies. New work +is under the repository's Apache-2.0 license. diff --git a/research/r439-kernel-entrance-closure/SOURCES.json b/research/r439-kernel-entrance-closure/SOURCES.json new file mode 100644 index 0000000000..6386ec50d1 --- /dev/null +++ b/research/r439-kernel-entrance-closure/SOURCES.json @@ -0,0 +1,24 @@ +{ + "schema_version": 1, + "base_commit": "dd6403f774a0891093a006ae9716c02e371b1fdb", + "files": [ + { + "path": "certificates/selected-result.json", + "usage": "provenance", + "git_blob": "ae6a99f28aa468649eb66a361e764d769363bf11", + "sha256": "10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32" + }, + { + "path": "docs/research/agent-task-catalog.json", + "usage": "provenance", + "git_blob": "c05fafaa25ba95b2d5af86b1800427198e3d20eb", + "sha256": "89b5928bc92c81e2647b6d702a7ad85a6795b8f44e2eb267b2ff3145d8f2b2ce" + }, + { + "path": "research/e8-bit-p111-tuned/tune/bitE8mut-p111-tuned.json.gz", + "usage": "input", + "git_blob": "85a4499bf9e4911a705d50567a2c2ef6cf23739a", + "sha256": "e3e301e62bc2b41dbf1ceac0acf3d35824ebeab1848c5a2142d4577b109da52f" + } + ] +} diff --git a/research/r439-kernel-entrance-closure/TASK.json b/research/r439-kernel-entrance-closure/TASK.json new file mode 100644 index 0000000000..d83ed315db --- /dev/null +++ b/research/r439-kernel-entrance-closure/TASK.json @@ -0,0 +1,60 @@ +{ + "schema_version": 1, + "task_id": "bit-helper-contract", + "priority_revision": 2, + "base_commit": "dd6403f774a0891093a006ae9716c02e371b1fdb", + "original_card": { + "id": "bit-helper-contract", + "question": "Can one precisely specified helper-mixing word satisfy a replacement for the inherited H2/K interface?", + "starting_points": [ + "research/r439-bsection-stars-seed01/README.md", + "research/r439-copy-path-sharing-barrier/README.md" + ], + "methods": [ + "Derive a replacement interface lemma and price its implementation.", + "Seek an exact dirty-input or chronological-cut counterexample to the proposed replacement." + ], + "acceptance_gate": "A full boundary contract and paid profile; unchanged scalar counts alone are insufficient.", + "first_step": { + "command": [ + "python3", + "-B", + "research/r439-bsection-stars-seed01/verify.py" + ], + "expected": "PASS_R439_BSECTION_STARS", + "inspect": "Compare the two false H2/K flags with the unchanged paid profile in its README.", + "scope": "Positive control / source-bound orientation only; this is not a new construction or full cold replay." + }, + "first_experiment": "Write one replacement H2/K implication for a single helper-star operation, then try to falsify it on dirty inputs.", + "bottleneck_link": "A legitimate replacement could admit a cheaper bit circuit; scalar savings alone do not alter the selected moment.", + "allowed_variations": [ + "Choose one helper-star or quartet instance; narrow to one boundary implication." + ], + "scope_change_triggers": [ + "Changing only source count or scalar addition count without an interface argument." + ], + "overlap_terms": [ + "H2_D_frame0_targets_from_helpers", + "K_equals_D", + "helper-star" + ] + }, + "scope_status": "changed", + "actual_scope": "All-support binary response-kernel classification under fixed PR589 common first-contact rational entrance frames", + "scope_change_reason": "The user assigned the bit-supplier track. PR1194 already treats the catalogue card's frame-zero semantic D contract; this contribution instead closes the arbitrary-support nonzero-entrance necessary condition beyond PR1179's support<=4 census.", + "bottleneck_link": "No new direction means larger supports alone do not provide another dormant helper coordinate in this frozen boundary; no kappa or hosted gain follows.", + "budget_minutes": 40, + "stop_rule": "Complete all distinct first-frame intersections and all restricted binary kernels, then independently compare the full finite certificate.", + "outcome": "negative-result", + "evidence": "CERTIFICATE.json, PROOF.md, verify.py, independent.py and test_package.py", + "author": "mightyOil, with substantial OpenAI Codex (GPT-6 Astra) assistance", + "ai_assistance": "Substantial OpenAI Codex GPT-6 Astra assistance in all research, mathematics, code, verification and writing; same AI-assisted contributor wrote both algorithms; no independent human review.", + "open_questions": [ + { + "question": "Can one named later chronological cut yield a new kernel entrance?", + "why_it_matters": "A later cut changes both the remaining response matrix and actual current frames, outside this closed class.", + "first_step": "Choose one cut, derive its remaining helper response and live frame state, then price a complete entry/exit construction.", + "blocked_by": "A valid physical compiler, transport/restoration and owner/window contract; no candidate has been established here." + } + ] +} diff --git a/research/r439-kernel-entrance-closure/VALIDATION.json b/research/r439-kernel-entrance-closure/VALIDATION.json new file mode 100644 index 0000000000..680f6a5460 --- /dev/null +++ b/research/r439-kernel-entrance-closure/VALIDATION.json @@ -0,0 +1,34 @@ +{ + "status": "passed", + "tested_utc": "2026-10-13T21:06:56.906838+00:00", + "base_commit": "dd6403f774a0891093a006ae9716c02e371b1fdb", + "refreshed_default_head": "dadfea6e8a78ff6ba901705f87532a71c6f5bbb8", + "platform": "macOS-27.0.1-arm64-arm-64bit-Mach-O", + "interpreters": [ + "CPython 3.14.7", + "CPython 3.12.14" + ], + "registered_replay": "Python 3.12.14: verify.py, independent.py and optimized test_package.py passed", + "standalone_replay": "Python 3.14.7: main and independent verifiers passed; optimized package tests and relocated replay passed", + "mathematical_controls": 6, + "package_tests": 10, + "actual_raw_boundary_mutations": 3, + "binary_matrix_oracle": { + "matrices": 4096, + "support_masks_per_matrix": 16 + }, + "repository_tests": { + "test_finite_bit_contract.py": 9, + "test_selected_result.py": 5 + }, + "certificate_sha256": "f08b9de12089687fe6c0c6b2eb985d0e6a883b72fa4f08ded11d34d875f48909", + "unrun": [ + "selected complete cold replay", + "PR1179 complete finite construction replay", + "native compiler", + "physical hosting", + "all-size/precision/tape/analytic obligations", + "remote CI" + ], + "ai_disclosure": "Substantial OpenAI Codex GPT-6 Astra assistance; algorithmic independence within one AI-assisted contribution, no independent human review." +} diff --git a/research/r439-kernel-entrance-closure/VERIFY.json b/research/r439-kernel-entrance-closure/VERIFY.json new file mode 100644 index 0000000000..5099ad5fba --- /dev/null +++ b/research/r439-kernel-entrance-closure/VERIFY.json @@ -0,0 +1,42 @@ +{ + "schema_version": 1, + "status": "ready", + "python": "3.12", + "requirements": [], + "inputs": [ + "research/e8-bit-p111-tuned/tune/bitE8mut-p111-tuned.json.gz" + ], + "commands": [ + { + "argv": [ + "{python}", + "-I", + "-B", + "{package}/verify.py" + ], + "timeout_seconds": 120, + "checks": "Exact all-support certificate, raw dirty-column response and six mathematical controls" + }, + { + "argv": [ + "{python}", + "-I", + "-B", + "{package}/independent.py" + ], + "timeout_seconds": 120, + "checks": "Independent Gram projector closure and row-matrix kernel comparison" + }, + { + "argv": [ + "{python}", + "-I", + "-O", + "-B", + "{package}/test_package.py" + ], + "timeout_seconds": 180, + "checks": "Complete small binary matrix oracle, source/receipt corruption and relocated optimized replay" + } + ] +} diff --git a/research/r439-kernel-entrance-closure/independent.py b/research/r439-kernel-entrance-closure/independent.py new file mode 100644 index 0000000000..c8961ddd4f --- /dev/null +++ b/research/r439-kernel-entrance-closure/independent.py @@ -0,0 +1,155 @@ +#!/usr/bin/env python3 +"""Independent exact Gram-projector and row-matrix check; Apache-2.0. + +No imports from verify.py or the predecessor implementation. Same researcher +with AI assistance; algorithmic independence does not imply human review. +""" +from fractions import Fraction as F +from itertools import combinations +import gzip +import hashlib +import json +from pathlib import Path + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] + + +def check(ok, message): + if not ok: + raise ValueError(message) + + +def dot(x, y): + return sum(a*b for a,b in zip(x,y)) + + +def basis(rows): + out = [] + for raw in rows: + v = tuple(map(F, raw)) + rem = tuple(v[i]-project(v, out)[i] for i in range(8)) if out else v + if any(rem): + out.append(v) + check(len(out) <= 2, 'independent rank exceeds two') + check(out, 'zero first-contact frame') + return tuple(out) + + +def project(v, b): + if len(b) == 1: + c = dot(v,b[0])/dot(b[0],b[0]) + return tuple(c*x for x in b[0]) + x,y = b + a,c,d = dot(x,x),dot(x,y),dot(y,y) + denominator = a*d-c*c + check(denominator > 0, 'positive Gram determinant') + s,t = dot(v,x),dot(v,y) + u,z = (d*s-c*t)/denominator,(a*t-c*s)/denominator + return tuple(u*x[i]+z*y[i] for i in range(8)) + + +def key(b): + return tuple(project(tuple(F(i == j) for i in range(8)), b) for j in range(8)) + + +def meet(a, b): + """Intersect distinct planes by a 2-column residual dependence, no elimination.""" + check(len(a) == len(b) == 2, 'plane pair') + ra = tuple(x-y for x,y in zip(a[0], project(a[0],b))) + rb = tuple(x-y for x,y in zip(a[1], project(a[1],b))) + coordinate = next((j for j in range(8) if ra[j] or rb[j]), None) + check(coordinate is not None, 'distinct planes') + s,t = rb[coordinate],-ra[coordinate] + if any(s*ra[j]+t*rb[j] for j in range(8)): + return None + v = tuple(s*a[0][j]+t*a[1][j] for j in range(8)) + check(any(v) and project(v,a) == project(v,b) == v, 'intersection vector') + return (v,) + + +def nullrows(rows, n): + """F2 elimination on target rows, opposite orientation to main checker.""" + matrix = [list(row) for row in rows] + pivots = [] + k = 0 + for col in range(n): + selected = next((j for j in range(k,len(matrix)) if matrix[j][col]), None) + if selected is None: + continue + matrix[k],matrix[selected] = matrix[selected],matrix[k] + for j in range(len(matrix)): + if j != k and matrix[j][col]: + matrix[j] = [x^y for x,y in zip(matrix[j],matrix[k])] + pivots.append(col) + k += 1 + vectors = [] + for j in range(n): + if j not in pivots: + v = [int(i == j) for i in range(n)] + for pivot,equation in zip(pivots,matrix): + v[pivot] = equation[j] + vectors.append(v) + return k,vectors + + +def run(): + pins = json.loads((HERE/'SOURCES.json').read_text()) + inputs = [r for r in pins['files'] if r['usage'] == 'input'] + check(len(inputs) == 1, 'one pinned word input') + data = (ROOT/inputs[0]['path']).read_bytes() + check(hashlib.sha256(data).hexdigest() == inputs[0]['sha256'], 'independent source hash') + word = json.loads(gzip.decompress(data)) + check((word['v'],word['R']) == (111,439), 'dimensions') + contacts = {} + for section in ['A','B']: + for frame,destination,sources in word[section]: + for helper in [destination,*sources]: + if helper >= 222 and helper not in contacts: + contacts[helper] = frame + check(sorted(contacts) == list(range(222,661)), 'complete helper contacts') + original = {f:basis([word['lines'][i] for i in word['frames'][f]]) for f in set(contacts.values())} + all_spaces = {key(b):b for b in original.values()} + planes = [b for b in all_spaces.values() if len(b)==2] + for a,b in combinations(planes,2): + intersection = meet(a,b) + if intersection: + all_spaces[key(intersection)] = intersection + check(len(all_spaces)==366, 'complete independent closure') + response = [[0]*439 for _ in range(111)] + for frame,target,sources in word['D']: + check(frame==0 and 111<=target<222,'independent D shape') + for source in sources: + check(222<=source<661,'independent source role') + response[target-111][source-222] ^= 1 + receipt = json.loads((HERE/'CERTIFICATE.json').read_text()) + classes = receipt['classification']['classes'] + recorded = {} + for row in classes: + b = basis(row['frame']) + k = key(b) + check(k not in recorded,'duplicate certificate frame') + recorded[k] = row + check(set(recorded)==set(all_spaces),'exact closure equals certificate') + live = [] + for k,b in all_spaces.items(): + row = recorded[k] + eligible_frames = {f for f,v in original.items() if all(project(x,v)==x for x in b)} + helpers = sorted(h for h in contacts if contacts[h] in eligible_frames) + check(helpers == row['eligible_helpers'],'independent eligibility') + matrix = [[r[h-222] for h in helpers] for r in response] + rank,vectors = nullrows(matrix,len(helpers)) + check(rank==row['response_rank'] and len(vectors)==row['nullity'],'independent nullity') + supports = [[h for h,value in zip(helpers,v) if value] for v in vectors] + # Only the zero space or a one-dimensional nullspace occurs in this input. + check(supports==row['kernel_basis'],'independent kernel basis') + if supports: + live.extend(supports) + check(live==[[444,470]],'unique independent nonzero direction') + fixture = [[int((c>>r)&1) for c in [1,2,4,8,16,31]] for r in range(5)] + check(nullrows(fixture,6)==(5,[[1]*6]),'independent long-support control') + print('PASS_R439_KERNEL_ENTRANCE_INDEPENDENT projectors=366 all_response_matrices=366 unique_kernel=444+470 no_new_kappa') + + +if __name__ == '__main__': + run() diff --git a/research/r439-kernel-entrance-closure/test_package.py b/research/r439-kernel-entrance-closure/test_package.py new file mode 100644 index 0000000000..4f3d7269aa --- /dev/null +++ b/research/r439-kernel-entrance-closure/test_package.py @@ -0,0 +1,140 @@ +#!/usr/bin/env python3 +"""Admission and mathematical mutation controls, standard-library only.""" +import copy +import gzip +import json +from pathlib import Path +import runpy +import shutil +import subprocess +import sys +import tempfile +import unittest + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] +V = runpy.run_path(str(HERE/'verify.py')) +I = runpy.run_path(str(HERE/'independent.py')) + + +class MathematicalTests(unittest.TestCase): + def test_complete_small_binary_matrices(self): + # All 4096 binary 3x4 response matrices and all 16 possible support masks. + for entries in range(1 << 12): + columns = [(entries >> (3*j)) & 7 for j in range(4)] + rank, basis = V['kernel'](columns, list(range(4)), offset=0) + masks = [sum(1 << x for x in b) for b in basis] + generated = {0} + for mask in masks: + generated |= {x^mask for x in tuple(generated)} + brute = set() + for mask in range(16): + response = 0 + for j,c in enumerate(columns): + if mask >> j & 1: + response ^= c + if response == 0: + brute.add(mask) + self.assertEqual(generated, brute) + self.assertEqual(1 << (4-rank), len(brute)) + rows = [[c >> bit & 1 for c in columns] for bit in range(3)] + second_rank, second_basis = I['nullrows'](rows,4) + self.assertEqual(second_rank, rank) + self.assertEqual(len(second_basis),len(basis)) + + def test_scoped_geometry_controls(self): + self.assertEqual(len(V['controls']()),6) + + def test_equal_weight_responses_remain_distinct(self): + # A zero-response direction must vanish, not merely have equal popcount. + columns = [0b001,0b010,0b100] + self.assertEqual(V['kernel'](columns,[0,1,2],offset=0),(3,[])) + + + def test_actual_raw_boundary_mutations(self): + word = json.loads(gzip.decompress((ROOT/V['WORD']).read_bytes())) + V['extract'](word) + bad = copy.deepcopy(word) + bad['D'][0][2].pop() + with self.assertRaisesRegex(ValueError, 'raw response/compensation equality'): + V['extract'](bad) + bad = copy.deepcopy(word) + bad['C'].pop() + with self.assertRaisesRegex(ValueError, 'raw response/compensation equality'): + V['extract'](bad) + bad = copy.deepcopy(word) + bad['scatter'][0].append(0) + with self.assertRaisesRegex(ValueError, 'raw response/compensation equality'): + V['extract'](bad) + + +class PackageTests(unittest.TestCase): + def setUp(self): + self.tmp = tempfile.TemporaryDirectory(prefix='r439 closure test ') + self.root = Path(self.tmp.name) + self.package = self.root/'research'/HERE.name + shutil.copytree(HERE,self.package,ignore=shutil.ignore_patterns('__pycache__')) + source = V['WORD'] + destination = self.root/source + destination.parent.mkdir(parents=True) + shutil.copyfile(ROOT/source,destination) + + def tearDown(self): + self.tmp.cleanup() + + def execute(self, script): + return subprocess.run([sys.executable,'-I','-O','-B',str(self.package/script)], + cwd=self.root, text=True, capture_output=True, timeout=120) + + def test_relocated_optimized_replay(self): + for script in ['verify.py','independent.py']: + result = self.execute(script) + self.assertEqual(result.returncode,0,result.stdout+result.stderr) + self.assertIn('PASS_R439_KERNEL_ENTRANCE',result.stdout) + + def test_source_mutation_rejected_by_both(self): + p = self.root/V['WORD'] + p.write_bytes(p.read_bytes()+b'changed') + for script in ['verify.py','independent.py']: + result = self.execute(script) + self.assertNotEqual(result.returncode,0) + self.assertIn('source',result.stderr) + + def test_missing_intersection_rejected(self): + p = self.package/'CERTIFICATE.json' + data = json.loads(p.read_text()) + data['classification']['classes'].pop() + p.write_text(json.dumps(data)) + result = self.execute('independent.py') + self.assertNotEqual(result.returncode,0) + self.assertIn('exact closure equals certificate',result.stderr) + + def test_wrong_kernel_rejected(self): + p = self.package/'CERTIFICATE.json' + data = json.loads(p.read_text()) + row = next(r for r in data['classification']['classes'] if r['nullity']) + row['kernel_basis'] = [[444,469]] + p.write_text(json.dumps(data)) + result = self.execute('independent.py') + self.assertNotEqual(result.returncode,0) + self.assertIn('independent kernel basis',result.stderr) + + def test_wrong_eligible_helper_rejected(self): + p = self.package/'CERTIFICATE.json' + data = json.loads(p.read_text()) + data['classification']['classes'][0]['eligible_helpers'].append(222) + p.write_text(json.dumps(data)) + result = self.execute('independent.py') + self.assertNotEqual(result.returncode,0) + self.assertIn('independent eligibility',result.stderr) + + def test_receipt_overwrite_refused(self): + result = subprocess.run([sys.executable,'-I','-O','-B',str(self.package/'verify.py'), + '--write',str(self.package/'CERTIFICATE.json')], + cwd=self.root,text=True,capture_output=True,timeout=120) + self.assertNotEqual(result.returncode,0) + self.assertIn('FileExistsError',result.stderr) + + +if __name__ == '__main__': + unittest.main() diff --git a/research/r439-kernel-entrance-closure/verify.py b/research/r439-kernel-entrance-closure/verify.py new file mode 100644 index 0000000000..2a5be67077 --- /dev/null +++ b/research/r439-kernel-entrance-closure/verify.py @@ -0,0 +1,236 @@ +#!/usr/bin/env python3 +"""All-support R439 common-frame kernel closure; Apache-2.0. + +Prepared for mightyOil with substantial OpenAI Codex assistance. +This finite classifier does not admit a physical supplier or change kappa. +""" +import argparse +from collections import Counter +from fractions import Fraction as Q +import gzip +import hashlib +from itertools import combinations +import json +from pathlib import Path + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] +WORD = 'research/e8-bit-p111-tuned/tune/bitE8mut-p111-tuned.json.gz' + + +def require(condition, message): + if not condition: + raise ValueError(message) + + +def canonical(value): + return json.dumps(value, sort_keys=True, separators=(',', ':')).encode() + + +def rref(rows, width=8): + """Canonical rational rowspace; no physical coordinates reduced mod 2.""" + a = [list(map(Q, row)) for row in rows] + require(all(len(row) == width for row in a), 'row width') + k = 0 + for col in range(width): + p = next((i for i in range(k, len(a)) if a[i][col]), None) + if p is None: + continue + a[k], a[p] = a[p], a[k] + divisor = a[k][col] + a[k] = [x / divisor for x in a[k]] + for i in range(len(a)): + if i != k and a[i][col]: + multiplier = a[i][col] + a[i] = [x - multiplier*y for x, y in zip(a[i], a[k])] + k += 1 + return tuple(tuple(row) for row in a[:k]) + + +def orthogonal(rows, width=8): + reduced = rref(rows, width) + pivots = [next(i for i, x in enumerate(row) if x) for row in reduced] + out = [] + for free in range(width): + if free not in pivots: + row = [Q(int(i == free)) for i in range(width)] + for p, equation in zip(pivots, reduced): + row[p] = -equation[free] + out.append(row) + return rref(out, width) + + +def subspace(a, b): + return len(rref(a + b)) == len(b) + + +def geometry_closure(frames): + """Complete nonzero intersection closure when every generator has dim <= 2.""" + require(all(1 <= len(f) <= 2 for f in frames), 'first-contact dimension outside theorem') + planes = sorted(f for f in frames if len(f) == 2) + result = set(frames) + normals = {f: orthogonal(f) for f in planes} + intersecting = 0 + for a, b in combinations(planes, 2): + joined_rank = len(rref(a + b)) + require(joined_rank in (3, 4), 'distinct plane rank') + if joined_rank == 3: + result.add(orthogonal(normals[a] + normals[b])) + intersecting += 1 + return sorted(result), intersecting + + +def extract(word): + require((word['v'], word['R']) == (111, 439), 'fixed R439 dimensions') + offset = 2*word['v'] + columns = [0]*word['R'] + for f, target, sources in word['D']: + require(f == 0 and word['v'] <= target < offset, 'original D shape') + for source in sources: + require(offset <= source < offset+word['R'], 'D source is helper') + columns[source-offset] ^= 1 << (target-word['v']) + first = {} + for f, target, sources in word['A'] + word['B']: + for role in [target] + sources: + if role >= offset: + require(role < offset+word['R'], 'raw helper range') + first.setdefault(role, f) + require(set(first) == set(range(offset, offset+word['R'])), 'all helpers contacted') + spaces = {f: rref([word['lines'][i] for i in word['frames'][f]]) for f in set(first.values())} + # The claimed response is rederived from the raw chronological A/scatter/B/C + # program, independently of the compensation list D used to form columns. + rows = [1 << i for i in range(offset+word['R'])] + a_helpers = {r for _, t, ss in word['A'] for r in [t]+ss if r >= offset} + require(set(word['ret']) <= a_helpers, 'retained copies have preceding A contact') + for phase in ('A', 'scatter', 'B', 'C'): + if phase == 'scatter': + copied = [rows[h] for h in word['ret']] + for i, terms in enumerate(word['scatter']): + for term in terms: + rows[word['v']+i] ^= copied[term] + else: + for _, target, sources in word[phase]: + for source in sources: + rows[target] ^= rows[source] + for role, actual in enumerate(rows): + expected = 1 << role + if word['v'] <= role < offset: + target = role-word['v'] + expected ^= 1 << target + for j, col in enumerate(columns): + if col >> target & 1: + expected ^= 1 << (j+offset) + require(actual == expected, 'raw response/compensation equality on every dirty column') + return columns, first, spaces + + +def kernel(columns, helpers, offset=222): + """Column elimination retaining dependency masks, hence a full F2 nullbasis.""" + basis = {} + dependencies = [] + for helper in sorted(helpers): + response, mask = columns[helper-offset], 1 << helper + while response: + pivot = response.bit_length()-1 + if pivot not in basis: + basis[pivot] = (response, mask) + break + old_response, old_mask = basis[pivot] + response ^= old_response + mask ^= old_mask + if not response: + dependencies.append([h for h in sorted(helpers) if (mask >> h) & 1]) + return len(basis), dependencies + + +def classify(word): + columns, first, frames = extract(word) + closure, pairs = geometry_closure(set(frames.values())) + rows = [] + for frame in closure: + allowed = [h for h in sorted(first) if subspace(frame, frames[first[h]])] + rank, nullbasis = kernel(columns, allowed) + rows.append(dict(frame=[[str(x) for x in row] for row in frame], + eligible_helpers=allowed, response_rank=rank, + nullity=len(allowed)-rank, kernel_basis=nullbasis)) + require(len(nullbasis) == len(allowed)-rank, 'nullity identity') + return dict(helper_count=len(first), response_rows=word['v'], + first_frame_ids=len(frames), first_rowspaces=len(set(frames.values())), + first_dimensions=dict(sorted(Counter(len(frames[first[h]]) for h in first).items())), + initial_subspace_dimensions=dict(sorted(Counter(map(len, set(frames.values()))).items())), + distinct_plane_pairs=sum(1 for _ in combinations([f for f in set(frames.values()) if len(f)==2], 2)), + intersecting_distinct_plane_pairs=pairs, + closure_dimensions=dict(sorted(Counter(map(len, closure)).items())), + nullity_histogram=dict(sorted(Counter(row['nullity'] for row in rows).items())), + classes=rows) + + +def controls(): + tested = [] + # No support cutoff: unique dependency requires six helpers, beyond PR1179's four. + e = tuple(Q(int(i == 0)) for i in range(8)) + columns = [1, 2, 4, 8, 16, 31] + rank, deps = kernel(columns, list(range(6)), offset=0) + require((rank, deps) == (5, [[0, 1, 2, 3, 4, 5]]), 'six-support fixture') + tested.append('six-helper minimal kernel beyond sparse cutoff') + rank, deps = kernel([1, 2, 4, 8, 16, 63], list(range(6)), offset=0) + require((rank, deps) == (6, []), 'response mutation escapes kernel') + tested.append('one-response-bit mutation removes six-helper kernel') + basis = [tuple(Q(int(i == j)) for i in range(8)) for j in range(4)] + plane_a = rref([basis[0], basis[1]]) + plane_b = rref([basis[0], basis[2]]) + plane_c = rref([basis[2], basis[3]]) + closure, count = geometry_closure({plane_a, plane_b, plane_c}) + require(rref([basis[0]]) in closure and rref([basis[2]]) in closure and count == 2, 'generated lines') + tested.append('two absent input lines recovered as plane intersections') + require(not subspace(rref([basis[1]]), plane_b), 'incompatible entrance rejected') + tested.append('kernel alone does not imply a common entrance') + try: + geometry_closure({rref(basis[:3])}) + except ValueError: + tested.append('dimension-three source fails closed') + else: + raise ValueError('dimension-three source incorrectly admitted') + require(rref([tuple(2*x for x in e)]) == rref([e]), 'rational geometry retained') + tested.append('even-coordinate physical line is nonzero over Q') + return tested + + +def sources(): + manifest = json.loads((HERE/'SOURCES.json').read_text()) + for row in manifest['files']: + if row['usage'] == 'input': + require(hashlib.sha256((ROOT/row['path']).read_bytes()).hexdigest() == row['sha256'], 'source pin: '+row['path']) + return manifest + + +def run(): + manifest = sources() + word = json.loads(gzip.decompress((ROOT/WORD).read_bytes())) + census = classify(word) + live = [row for row in census['classes'] if row['nullity']] + require(len(live) == 1 and live[0]['kernel_basis'] == [[444, 470]], 'unique all-support kernel') + require(live[0]['frame'] == [['0','1','0','-1','1','0','1','0']], 'unique entrance line') + require(live[0]['eligible_helpers'] == [390,391,444,470,578,580,582], 'eligible set') + return dict(schema_version=1, base_commit=manifest['base_commit'], seed=5, + classification=census, raw_endpoint_columns=661, controls=controls(), new_kappa=False, + scope='binary response-null directions with arbitrary support and a nonzero rational common first-contact frame; fixed PR589 raw word') + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--write', type=Path, help='write a new receipt; refuses overwrite') + args = parser.parse_args() + result = run() + if args.write: + with args.write.open('x') as handle: + json.dump(result, handle, sort_keys=True, indent=2) + handle.write('\n') + else: + expected = json.loads((HERE/'CERTIFICATE.json').read_text()) + require(canonical(result) == canonical(expected), 'certificate mismatch') + print('PASS_R439_KERNEL_ENTRANCE_CLOSURE classes=366 zero_nullity=365 unique_kernel=444+470 controls=6 no_new_kappa') + + +if __name__ == '__main__': + main()