κ = 7.93392809671713586967588e-4: complete native admission for #346/#348

[eumemic]

κ = 7.93392809671713586967588e-4

Exact κ: 198348202417928396741897/250000000000000000000000000.

This completes the native bank, changed-projector, geometry and finite-invoice obligations left open for #346's Design T/twin bit word, combines it with #348's fully regenerated pointwise complex supplier, and applies eight finite bootstrap levels. The numerical increment over #348 is 3.80022586967588e-13; the main contribution is the complete source-bound admission chain. All prior published PR heads and claims remain frozen.

Draft #350 appeared during final validation with a higher numerical claim from retiming the complex program. This PR retains its frozen #348 supplier and completes the native admission; it does not claim to exceed #350. New structural improvements will be separate PRs.

The bit pipeline freshly verifies pinned #325 and reproduces its complete word, states and frames in two byte-exact exports before rerunning #346's construction. It removes exactly 480 FULL/FULL helpers that occur in no event, with inverse relabeling reproducing every original event byte. The compacted word has 405,188 events, 358,128 additions and 7,620 dirty helpers. Its hash is 05df0a39669bb077a9a2fa527904023a5a9da18cf644e06429d44f2a7ea92603.

Native admission recomputes both reflected frame ledgers, all 11,460 F2 formal columns, COPY immutability and dirty restoration, 320 new frames, 1,776 changed projectors, 26,410 minor witnesses, and all 11,430,000 helper/replica/stage assignments. At T=300, the literal bank stock is 3,142,800; the exact selector charge is 1,808,510,397,000 and the complete finite coefficient is 120,582,915,658,909,001.

Every full replay runs #348's unmodified module/spec/flow/lift/contract regeneration, requires the emitted complex program to match byte for byte, then independently checks its scalar words, both reflected splices, dirty restoration, row guard and both moment engines with full fallback. This admits b = 794022782431403/10^18 from complex program ff2d7307b09aceb8776654f21099b10a68be547b562b7f4a7fc918f6c5f51112.

Validation: two complete immutable 21-stage replays on Python 3.11 and 3.12, identical mathematical certificates apart from receipt hashes, a distinct literal-word/bank/minor/closed-form audit, all 47 strict outer constraints, and rejection of the adjacent κ grid point. The full package manifest and every committed blob are checked before publication. Replay instructions and limitations are in research/w3-p10-pointwise-native/README.md; receipt summaries are in the companion audit directory.

This remains a conditional sufficient construction under the inherited compiler, selector/chart, routing, prime-supply, precision/recovery, symbolic-complex and analytic interfaces. The operator replay is over F2; the signed elementary-shear inverse and integer decoder/recovery semantics remain inherited. No unconditional or new Lean theorem is claimed.

Credits and AI disclosure: Design T/twins originate with utcorvusvolat-dotcom's #310; Louis Harrison/Anthropic Claude supplied #346's h=20 port and module combination; Chafik Boukhalfa/Anthropic Claude supplied #348's pointwise complex program. DreamingOfClouds/Anthropic Claude supplied #325 and #327. All upstream licenses/notices and the #266/#315/#321/#202/#200/#194/Sussman checker lineage are preserved. This integration, compaction, native admission and finite-bootstrap binding were prepared with substantial OpenAI Codex assistance; see NOTICE.md.

[Mister-Meeseeks]

Thank you @eumemic. This contribution is now retained on main in the scoped 100-PR review and contributor credits.

Contribution: Native admission of the w3/pointwise composition.

Review and limits: Completes finite integration obligations left by PR346/348, with unchanged all-size assumptions. Verification work is credited separately from the supplier discoveries.

The complete original source, notices and relevant execution evidence are retained through the pinned source archive. The review distinguishes fresh local runs, source-bound historical Linux CI and prior exact-head review; it does not claim 100 fresh full mathematical audits. Closing this historical PR as reconciled. This preserves parallel and cumulative credit without replacing the selected frontier or promoting priced research targets to completed constructions.

Reviewed head: c0f9f480440a25f89a8a00e1b2076467cf484754. Publication: 4040a0f46d67b41c36a472a7cd4af791fd4c36cc.