Research: bind the selected complex event ledger to its height guard

[commdata2338]

Change and mathematical scope

PR #2327 leaves PR #2287's complete-program height ledger as an explicit premise. This package independently reads the actual selected R480/T16 event stream and supplies that finite source binding, followed by a written conditional induction and root-grid argument.

Per cover class it reconstructs 510,662 children with unnormalized rank mass 1,041,408, and a sufficient scalar-prefix charge 4,382,272, below the predecessor's conservative 21,194,688. It covers both 24,767-event local words, all 144 calls, the 482-event caller, 35,840 original idle deadlines and 7,526 positive idle remainders. All 6,088 stored local monomial records have the required invertible binary/quarter-phase shape.

Under explicit native-endpoint, depth-first dispatch, byte-preserving parking and elementary-kernel semantics, the actual ledger gives A(e)<=2Be, with s=1041408*Gamma, B=s+2^100000. It retains the existing <2^210000*d layer guard and proves both exact divisibility and the actual shift-extent conditions. Parked coefficients and unfinished-child prefixes are included; completed child endpoints improve the analysis without rounding their stored values.

This is a finite certificate plus a scoped conditional proof, not supplier admission. No change to the paid profile, selected frontier, production precision, or kappa. Native operator identities, hosting, physical interpreter correctness, row/tape/time admission and outer transfer remain separate obligations. No independent human review is claimed.

Package: research/selected-complex-height-ledger/.

Task and overlap

Base 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2; contribution commit 97d1b23a69c9488d0667a4e666fe3875d56113c3; main was rechecked unchanged at 07:19 UTC before submission.

The advance claim is in discussion #2253, comment 18942782, taking the released PR2327 complete-program handoff.

Task card:

• Task ID / scope key: independent-moment / c6f2494b197df3bc3591; refined selected-complex/R480-T16/PR2287-height-ledger-to-grid.
• Selection: nonce 3012c97dfee81c9485f5da37f5282030, track independent-verification, priority revision 4. The first suggestion was taken. formal-interface-lemma was passed over because generic recurrence and tensor lemmas already had nearby formal work, while this finite implication remained requested. No reroll.
• Base and exact predecessor heads: main 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2; PR2287 8c60765b5dea9d862b3b190d55da102a576031bf; PR2327 367a8539770166d3ccd555583b41e96097178a3e. Selected scientific baseline PR1094 is 0fc329d0bec93ca7cd288eaea1295172e8789810. The seven copied pending-source files retain exact Git blobs and SHA256 pins; no moving dependency.
• Concrete question: do the actual source scalar, child, idle and terminal operations satisfy PR2287 section 6's complete-prefix reserve and all executed division extents?
• Scope status: refined. The suggested card permits a changed supplier's missing source-bound implication; this takes a specific released handoff rather than another moment/root calculation.
• Exact implication audited: PR2327 assumes the complete-program height recurrence. This binds its finite premises to selected source operations while retaining the stated native/compiler semantics.
• Method / domain: independent exact event parsing and integer/rational arithmetic on both actual words and every caller event; a written all-width induction for e=73f+delta; symbolic complete cover multiplicity. No full-cover payload enumeration.
• Optimistic budget / observable advance: retain all child calls, E=2^100000, C0=2^210000 and the selected profile. Success is a correct source-to-height implication or an exact counterexample, not an exponent gain.
• Success / stop / cap: closed source alphabet, complete dispatch ledger, source and receipt binding, exact primitive-charge/recurrence proof and meaningful rejecting controls; stop on any unpriced operation or unjustified premise. One bounded 60-minute session, standard library, no unbounded search.
• Predecessor credit / artifact / command: Jose Manuel, AAAmirinu, Gareth Davidson and retained selected-supplier authors; research/selected-complex-height-ledger; registered command below.

Closest work: PR2287 owns the proposed construction; PR2327 owns the primitive proof and requests this binding. PR2284 advertises generic theorem APIs and PR2341 proves the generic tensor bridge; neither is used as a proof dependency here. The active physical-monomial refinement concerns an actual PR2250 interpreter and is complementary to this package's local shape check. This account's earlier PR1421 audits the binary PR589 paid-rank ledger, a different object.

Final cached overlap covered 583 open PRs at 2026-10-15T06:55:23.240869+00:00 and 1,111 Discussion records at 2026-10-15T06:57:32.010338+00:00, both with complete pagination. Expected offline warnings remain; arbitrary code diffs are excluded, so this is not a novelty guarantee. Canonical main and both dependency heads were fetched again at approximately 07:02 UTC, unchanged. The local branch retains the exact original base.

Validation

CPython 3.12.3, standard library only, from the repository root:

python3 -I -B scripts/research_package.py --package research/selected-complex-height-ledger
python3 -I -B scripts/research_package.py --package research/selected-complex-height-ledger --check-only

The registered replay passes normal and optimized execution and all eight focused tests. Its marker is:

PASS_SELECTED_COMPLEX_HEIGHT_LEDGER local_events=3566448 children=510662 rank_mass=1041408 scalar_height=4382272 controls=10 conditional_no_new_kappa

It compares the complete immutable receipt, verifies exact reserve inequalities, and checks 1,009 finite width consequences (the quantified proof is in PROOF.md). All 332 actual distinct coefficients are checked through 2,324 signed dyadic SCALE and 6,972 ADD fixtures, inspecting every allocated arithmetic temporary against exact rational semantics. Ten rejection controls address missing events/idle children, native rank and dispatch changes, unknown operations, unpriced padding, non-quarter phases, nondyadic coefficients and accidental time normalization. The focused tests additionally cover singular adapters, changed bridge coefficients, missing idle dispatch, changed pending source bytes and typed receipt changes.

The independent ledger does not import the producer's charge, profile or schedule functions. Pinned source arithmetic is executed as the subject of the finite oracle checks. All seven copied predecessor files were separately compared with their exact Git blobs. Metadata/source checks and git diff --cached --check pass. A JSON key-order serialization bug found during the first registered run was fixed before the final passing replay; count types remain strict.

Not run: selected supplier cold replay, the full O(73,2) payload, Lean, physical compiler execution, hosted CI, or outer multiplication validation. These checks establish only the stated finite source binding and support the written conditional proof.

The registered replay was run again on the final package bytes before submission, under an 8 GiB memory cap: it passed in about 40 seconds and left the worktree unchanged. The seven copied PR #2287 and PR #2327 files match those heads by Git blob. The ledger's rank mass, 1,041,408, is the constant in PR #2287's recurrence A(e) <= A(48 floor(e/73)) + 1041408*Gamma*floor(e/73) + E.

Credit

Jose Manuel (@jmbarrancoml) supplied PR2287's proposed construction, arithmetic and precision allowance. AAAmirinu supplied PR2327's primitive audit and requested this complete-program binding. Gareth Davidson (@bitplane) supplied PR1282's earlier prefix/Horner analysis. The selected sources retain Rohan Arun, Jeremy Kothe, Hao Yan, DreamingOfClouds/eumemic and the full lineage recorded in the selected review and copied NOTICE. No original technique or construction is reattributed here. Exact copied sources and Apache-2.0 notices are unchanged.

Prepared for commdata2338 (@commdata2338), with substantial OpenAI Codex assistance.

AI assistance: submitted by @commdata2338 with substantial AI assistance. OpenAI Codex (GPT-6 Astra) did the derivation, the implementation, the checking and the writing; it was packaged and submitted with Claude Code. No independent human review is claimed.

Open next questions

The README and TASK contain structured handoffs. The next useful step is to bind one actual selected rank-one child, its monomial adapters, coefficient scratch, spectators and parking return to the semantic hypotheses in PROOF section 1, coordinating with the active monomial refinement. A larger integer guard does not substitute for this physical implementation obligation.

A later per-family height analysis could refine the coarse global maximum, but no smaller production guard or exponent improvement follows from the present result.

Workflow feedback (optional)

The released handoff made the missing implication concrete. The main orientation cost was tracing a proof premise across pending packages and a nested selected archive. A short list mapping each remaining implication to its exact source input and acceptance test would make subsequent audits easier to route.

🤖 Generated with Claude Code

https://claude.ai/code/session_01X86sCSXdoDd61SDFfC1PKG