canonical-carriage: The Canonical Lane runtime for AI agents: plans, approvals, receipts, remainders, and stability preflight before side effects.

Canonical Lane is a manifold-constrained local-to-global theorem-program library.

This profile routes the public math surface through paired repositories: each problem has a canonical-lane closure package and a Mathlib formalization layer.

Latest checked results: q-Catalan bivariate n=6 replay checks all seven k slices over 132 312-avoiding permutations with zero mismatches; the all-n conjecture remains open. Finite q=7 permutation-polynomial replay checks all 115,248 admissible triples in F_49 with zero permutation polynomials; the general odd-q conjecture remains open. Bergeron Gaussian bound <=60 exhaustively checks 1,173 admissible quadruples and 613,167 coefficients with no negative coefficient; the unrestricted conjecture remains open. Misère escalation m=3 quotient gives the exact five-element quotient for the source game with moves {1,2,3}; the all-m finiteness conjecture remains open. Valley Delta area-two extension verifies the source-defined refined scaffold exchange exhaustively at (n,M)=(6,5) with zero asymmetric classes; the all-parameter Conjecture 8.2 remains open. Class-69 involution counterexample refutes the additional involution-restricted conjecture in arXiv:2606.14367v1 at S_3; the unrestricted Class-69 equidistribution question remains open. Almost Golomb Prefix Conjecture proves a_r(r)=G(r-1) for every r>=3; its separate Domination Lemma and full threshold law remain carried.

Latest replay note: Strong Sensitivity n=4 replay exhaustively checks all 65,536 four-variable Boolean functions with independent Python/Node replays. CRIM non-hook Conway-pair counterexample family remains available; the finite [3,3] and [4,4] replays independently reproduce pair (0,1). Dimension-3 Jacobian counterexample remains available with its Mathlib-backed Lean and SymPy replay. Latest finite counterexample: Goemans cost-conjecture counterexample gives an exact seven-vertex instance, exhaustively replayed in Python and Ruby with Lean 4.31.0 and a separate Mathlib-backed Lean replay; the general conjecture remains open. Book-graph n=5 finite replay gives exact rational Sturm counts with independent Python/Ruby, standalone Lean, and Mathlib-backed Lean replays; the all-n conjecture remains open. Extended 1–2–3 displayed-statement counterexample records the exact empty-set witness with standalone Lean and separately pinned Mathlib replays; the intended nonempty-set conjecture remains outside scope. Catch-Up {1,2} finite replay now includes standalone Lean and separately pinned Mathlib evaluators proving the initial position is a win; the all-N conjecture remains open. Continued-fraction k=1, N=3 replay verifies the source partial quotients (7,14) with independent rational-interval Python/Ruby replays; the all-k pattern remains open. Finite CRIM/Kotzig/Ringel batch includes the verified CRIM [2,2], Kotzig K17/K19/K21, and complete Ringel n=3 slices, each with independent Python/Ruby replays; the general conjectures remain open. Additional Kotzig/Ringel finite replays now include verified Kotzig K23/K9 and Ringel K9/K11/K13 slices with independent Python/Ruby replays; the general conjectures remain open. WOWII Conjecture 314 n≤5 replay checks 170 connected triangle-free graphs with no unequal minimal total-domination sizes; the unrestricted conjecture remains open. Public replay receipt audit has synchronized all file-hash manifests across the public packet surface; clean-clone replay remains the publication gate.

Independent domination n=4 finite replay checks all 41 isolate-free labeled simple graphs on four vertices against the source's parity-specific inequalities with independent Python/Ruby replays; the general conjectures remain open.

Catch-Up finite replay — the exact source evaluator gives a first-player win on S={1,2}, confirmed independently in Python and Ruby; the all-N conjecture remains open.

Catch-Up S={1,2,3} replay — the exact source evaluator gives a draw, confirmed in Python/Ruby and by standalone Lean plus Mathlib replays; the all-N conjecture remains open.

Erdős 624 H(4)=3 finite replay — the exact four-color powerset-covering slice is settled by an explicit construction and independent Python/Ruby replays; the asymptotic conjecture remains open.

Erdős 624 H(5)=3 finite replay — the exact five-color slice is settled by an explicit 32-entry table and independent Python/Ruby replays; the asymptotic conjecture remains open.

Erdős 624 H(6)=3 finite replay — the exact six-color slice is settled by an explicit 64-entry table and independent Python/Ruby replays; the asymptotic conjecture remains open.

Erdős 624 H(7) interval replay — an explicit table proves 3 <= H(7) <= 4; the m=3 case remains unresolved.

Mesh-pattern remaining-pairs scan — Classes 54, 69, and 71 have matching occurrence histograms through S_9 in independent Python/Ruby scans; the infinite conjectures remain open.

Strong Sensitivity n=4 replay — all 65,536 four-variable Boolean functions satisfy the source inequality in independent Python/Node enumerations; the general conjecture remains open.

Strong Sensitivity n=3 replay — all 256 three-variable Boolean functions satisfy the source inequality in independent Python/Ruby enumerations; the general conjecture remains open.

Odd-q permutation-polynomial q=5 replay — all 15,000 admissible F_25 triples produce zero permutation polynomials in independent Python/Ruby replays; the general odd-q conjecture remains open.

Stack-sort/Motzkin n=11 replay — the source-defined exhaustive slice counts 5,798 of 39,916,800 permutations, matching M_11; the all-n conjecture remains open.

1. 新时代英烈精神传承弘扬智慧平台
2. Private Clients: access-controlled client surface for private implementation, onboarding, and review.
3. Canonical Lane Mathlib: Mathlib-backed Canonical Lane projection and carriage core for Lean 4 theorem packages.

Public mathematical packets are published directly to main under a single, auditable workflow:

1. Verify the pinned source, exact scope, and claim boundary.
2. Require independent replay routes or a checked proof/certificate.
3. Stage only the intended packet and index files.
4. Commit directly to main with the subject Canon.
5. Push main, then verify the public endpoint and a clean-clone replay.

Publication branches and pull requests are not used for this workflow. Source-mismatched, speculative, incomplete, or uncertified results remain UNKNOWN and are not published.

• Commentary: source-bound mathematical commentary, counterexample certificates, and replay scripts.
• formal-record: machine-readable source identities, bounded outcomes, and replay routes for Commentary packets.

Current source-bound OpenConjecture proof and counterexample packets are linked below.

The theorem-program library follows through the lane and Mathlib repository pairs below.

Private client access is handled by invitation through the access-controlled repository.

• Lane: the theorem-facing closure package with admissible-class formulation, projection gates, local-to-global bridge, and carried remainder.
• Mathlib: the source-derived formalization layer for proof-boundary checking and package translation.
• Scope: each row points to the public object to inspect; each repository carries its own claim boundary, citation notice, and remainder surface.

Commentary is the public shelf for source-bound notes, counterexample certificates, and replay records.

This page indexes 87 paired math surfaces generated from live GitHub repository names.

For readers coming from Objectivist epistemology, the bridge is:

Objectivism:
A = A

Canonical Lane:
Π(A) = A ⇔ lawful coherence under projection

identity as asserted fixity → identity as achieved invariance under projection
law → idempotent projection from flux into invariance
freedom → lawful variation inside admissible scope
rationality → fixed-point coherence under projection

A is A is preserved, but strengthened: Π(A) = A expresses identity as achieved invariance under lawful projection.

This layer is intentionally redacted from the public library surface.

The full Moral Tensor Dialectic is available only through the private WeChat archive:

HautevilleHouse

| Kotzig 13-edge T-tree cyclic K27 slice | Twenty-seven shifts partition K27; one finite tree only, general Kotzig remains open. | | Kotzig 12-edge T-tree cyclic K25 slice | Twenty-five shifts partition K25; one finite tree only, general Kotzig remains open. | | Kotzig 11-edge T-tree cyclic K23 slice | Twenty-three shifts partition K23; one finite tree only, general Kotzig remains open. | | Kotzig 10-edge T-tree cyclic K21 slice | Twenty-one shifts partition K21; one finite tree only, general Kotzig remains open. | | Kotzig 9-edge T-tree cyclic K19 slice | Nineteen shifts partition K19; one finite tree only, general Kotzig remains open. | | Kotzig 8-edge T-tree cyclic K17 slice | Seventeen shifts partition K17; one finite tree only, general Kotzig remains open. | | Kotzig 6-edge T-tree cyclic K13 slice | Thirteen shifts partition K13; one finite tree only, general Kotzig remains open. | | Kotzig 5-edge T-tree cyclic K11 slice | Eleven shifts partition K11; one finite tree only, general Kotzig remains open. | | Kotzig T-tree cyclic K9 slice | Nine shifts partition K9; one finite tree only, general Kotzig remains open. | | Formal Conjectures curling-number length-3 replay | 39-case bounded replay; 27 immediate, 12 after one append; unrestricted conjecture remains open. |

This page is a routing surface. The mathematical claim boundary lives inside the individual lane repositories, their formalization layers, and their carried-remainder records. The P3-in-K5, P4-in-K7, P5-in-K9, K1,3-in-K7, K1,4-in-K9, P6-in-K11, P7-in-K13, K1,6-in-K13, P8-in-K15, P9-in-K17, P10-in-K19, K1,10-in-K21, and K1,11-in-K23 Ringel slices now have standalone Lean and separately pinned Mathlib finite replays in their public packets.

All Rights Reserved - No License Granted. Viewing these repositories through GitHub grants read access only. Reuse, redistribution, derivative forks, or implementation of patent-covered material require separate written permission. Cite the relevant repository when discussing, reviewing, comparing, or referencing the work. | Ringel bounded decompositions | Independently replayable slices: P3 in K5, P4 in K7, K1,3 in K7, P5 in K9, K1,4 in K9, P6 in K11, P7 in K13, K1,6 in K13, P8 in K15, K1,7 in K15, P9 in K17, K1,8 in K17, P10 in K19, K1,9 in K19, K1,10 in K21, K1,11 in K23, K1,12 in K25, and K1,13 in K27. Each is bounded only; general Ringel remains open. |