[EcmaXp]

Change and mathematical scope

This PR applies PR186's completed entrance banks to PR200's physical bit word and prices the result against the v4 source-assisted complex supplier, as composed in PR202. The new package is research/pr200-entrance-banks/.

κ = 6830611/10^10 ≈ 6.830611e-4. That is +0.913% over PR202 (6768823/10^10) and +2.342% over PR194. Without the finite leaf, κ = 6826211/10^10. The bit supplier still binds; the complex saving is 219037/312500000 ≈ 7.009184e-4.

Bit supplier, per group vertex	PR200 word	With completed banks
Live physical chains	17,114	17,114
Persistent stock W	20,634	56402/3
Rank mass	1,483,712	1,351,712
Deficit	1,936	1,936
Largest child	60	22
Coarse saving (10^-18 grid)	677773948354561/10^18	683528191056257/10^18

Construction:

• Packing: PR186's stage-private packing, with 18 × rank-4 entrance residuals or 3 × rank-24 completed residuals per width-72 bank and nine physical replicas. It removes the 2,200 rank-60 entrance exteriors. Per stage there are 1,100 entrance banks and 44,742 completed banks.
• Schedule: the round-8 BANK-SCHEDULE.md supplement.
• Sinks: PR200 deletes 34 terminal sinks, and a deleted sink has no register to bank. The live chains are 18,908 − 1,760 splices − 34 sinks = 17,114.
• Charts: exact integer charts for PR200's 220 entrance frames, built with PR197's inverse_integer. Every entry and denominator is at most 18. Charts for distinct slots of one bank differ by a nonzero integer matrix with entries below 2^80. So no prime q > 2^80 identifies two charts of one group, which discharges the round-8 prime exclusion for these charts.
• Pricing: PR186's paid moment, PR184's unchanged select() and 47-constraint assemble(), and PR185's 3-level finite leaf, composed as in PR199.

Separate commit: PR202's research/source-assisted-v4/certificate.json was written off Linux. Its gzip-dependent lift hashes therefore failed PR202's own workflow ("Canonical certificate does not reproduce"). Regenerated on amd64 Ubuntu 24.04 with Python 3.13, the hashes return to a8c8778's values and κ is unchanged. That commit also repins the single matching entry in PR200's SOURCE.json.

Stacking: this branch stacks on PR202, which stacks on PR194, so like those PRs it is not mergeable onto current main. PR200, PR202, PR197 and PR199 have no maintainer review yet.

Scope: a conditional finite witness. These stay inherited conditional contracts:

• from PR186 and the round-8 supplement: the bank routing, stage cover and low-residue streaming;
• from PR184: the weighted compiler, recovery, restored rows, fixed-tape routing and analytic transfer;
• the complex supplier keeps PR184's scope.

No optimality is claimed. NOTICE credits every borrowed piece. The package's files under references/ are byte-identical upstream copies, and their commits and blob ids are in references/manifest.json.

Validation

python3 -B research/pr200-entrance-banks/verify.py [--full] does the following:

• Literal word: reruns PR200's terminal prover on the literal sink-modified word. That covers all F2 and integer columns, both directions, with three mutation controls. It requires the result to equal PR200's certified profile.
• Banks: rebuilds the bank inventory and the exact charts, including factor replay to the identity and two-sided inverse checks.
• Endpoints: runs PR186's bank projector checks on 144 columns over F2 and Z, forward and reverse, rejecting omit and repeat. Also runs weighted endpoint checks over Z/9, Z/25 and Z/125, and the round-8 GL_2(Z/9) schedule diagnostic.
• Pricing: certifies the packed moment on the 10^-18 grid, with an independent base-two moment and the atom toll, then runs PR184's assembly with and without the leaf.
• Controls: reproduces PR202 (6768823/10^10) and PR199 (1693287/2500000000) from PR200's unpacked profile with the same code, and rejects five mutations.
• Provenance: recomputes every vendored file's git blob id, and checks the four ported PR186 functions are AST-identical to upstream.

Results:

• Passed with --full on amd64 Ubuntu 24.04 with Python 3.11, 3.13 and 3.14, and locally on macOS with Python 3.13.
• On the same Linux image, PR200's verify.py and v4's verify.py both pass after the certificate fix.
• The new workflow .github/workflows/pr200-entrance-banks.yml runs verify.py --full on that matrix and then git diff --exit-code.

These are finite certificate checks, not formal verification of the multiplication theorem.

🤖 Generated with Claude Code

[EcmaXp]

Closing this because #205 already covers the same construction: PR186's completed entrance banks applied to PR200's bit word, with the same packed profile and the same κ up to grid precision. #205 was opened first, so this PR is not needed.

🤖 Commented by Claude Code

[EcmaXp]

This branch stacks on #202 and conflicts with main, so this PR has no pull_request checks. The same workflows ran on the EcmaXp fork when 5cee197 was pushed, and all 4 passed on ubuntu-24.04:

• Verify research artifacts: 46 jobs, 14 groups on Python 3.11, 3.13, and 3.14, plus source-assisted and 3 formal jobs
• Verify completed entrance banks on the PR200 bit word: verify.py --full on Python 3.11, 3.13, and 3.14
• Verify source-assisted complex word on PR168 v4 modules: passes with the v4 certificate regenerated on Linux
• Verify finite bit leaf bootstrap

🤖 Commented by Claude Code