[JosieElliston]

Summary

No new κ. The selected PR6030 record (κ = 0.003125804) has 54 strict and 4 functional outer checks. #6109 tied 24 of the strict checks to written sources. This PR ties the other 30 and all 4 functional checks to written sources. Each row's formula is restated from its written statement and evaluated with exact rationals at PR6030's parameter point. The result matches RESULT.json exactly, and all 34 values are strictly positive.

Package: research/p104-6030-outer-row-binding/. The stdlib verifier imports no repository code: not endpoint.py, pricing.py or any outer ledger. Run it with python3 -I -B research/p104-6030-outer-row-binding/verify.py. It takes under 0.1 s and passes on CPython 3.10–3.14, with and without -O. python3.12 scripts/research_package.py --package research/p104-6030-outer-row-binding passes. So does check_research_commit.py --check-source-history --check-modes. CI was not monitored.

What is bound to what

• Stopped-supplier rows (11). These are the λ, λ′, leaf, internal and stop rows. They map to the hypotheses of the stopped-recursion layer theorem in notes/batched-complex-rows.tex, which is a selected proof supplement (SHA equal to the selected pin):

  • max{τ,σ,χ} < λ < λ′ < 1
  • max{σ+β(1−σ), 1−c, 0} < λ′

  Here β = stop, σ = 1−b, τ = 1−a, χ = τ+(1−β)max{σ−τ,0}, λ′ = 1−q and λ = (τ+λ′)/2.

• The other 19 strict rows and 4 functional rows. These cover effective savings, halo/locality, logarithmic guards, record geometry and BIT stock. Each maps to a written sentence or constant in one of:

  • PR4359's OUTER-TRANSFER-AUDIT.md and ENDPOINT.md
  • PR1673's SUPPLIER-SUPPORT-AUDIT.md and phase_fusion_note.tex
  • PR1786's FINE-PRIME-PADDING.md

  Each of these files is byte-identical to a file in certificates/frontier6030-source.json. The verifier checks this, along with 41 verbatim fragments.

• Status counts. Of the 34 rows, 11 are theorem hypotheses, 16 are inequalities a written sentence asserts and 3 are fixed constants. 2 are implied by a stronger written margin that carries r0. 1 substitutes PR6030's current atom 1/250 into the written stock rule group_beta*(1-0.003) > 0. 1 is a reporting check (improvement_over_user_baseline, which ENDPOINT.md itself labels as reporting).

Findings (none changes κ)

1. One theorem hypothesis has no ledger row. The 1−c < λ′ term uses the compact-control exponent K ≥ d^c/2. With the selected K = 128G = Θ(log p), no fixed c > 0 satisfies that, so the supplement's theorem cannot be instantiated as written. The chain's replacement is PR1673 SUPPLIER-SUPPORT-AUDIT.md §4–6. It charges exposure at O(V h^(1−a) polylog p) with h_(j+1) ≤ h_j/16, so the condition needed becomes τ < λ′, which the λ rows imply. PR1673 records this itself. The point is only that the replacement is in the source manifest but is not a selected proof supplement. The bridge is my reading and is not verified: the verifier checks only τ < λ′. This is a citation suggestion, not a claimed gap. The theorem's moment hypothesis Ψ_c(σ) < 1 is also not checked here; its PR6030 counterpart is the complex supplier's saving, which is Bind PR6030 uniform compiler and nine outer rows to written theorems; j=47005 is first passing grid point (no new κ) #6109's compiler scope.
2. One ledger row is stronger than the theorem. leaf_saving_above_effective, (1−β)b > a, is stronger than the theorem's leaf condition (1−β)b > q. It comes from PR1673's note ("a strict leaf saving above a_eff and q"). At β = d/b the theorem's checked order hypotheses hold but this row rejects.
3. ENDPOINT.md's stated premises do not hold at PR6030. Its family proof assumes q < 0.002306 and BIT 0.0027. PR6030 has q ≈ 0.0031258 and admitted BIT 17/5000. Its closed-form gaps still hold as identities, and PR6030 lies inside Nick Petalas's Prove the exact κ region of the selected outer ledger: min(U, B, 1/32) (no new κ) #5984 region OLD < κ < min(U, B, 1/32), which covers the general case.
4. Some rows repeat each other. Several rows are the same expression in the free parameters, so the 54 strict checks contain fewer distinct inequalities than rows. For example, q_below_leaf = lambda_prime_above_leaf, and group_key_fits_record = group_below_dimension. The verifier lists every group.

With #6109, all 54 strict and 4 functional outer predicates of PR6030 are now tied to written sources by code outside the PR4359 ledger lineage.

Controls

Each control below is rejected:

• β = 0
• β = 1−q/b
• q = a
• BIT 0.0027
• β = d/b, which passes the theorem's checked order hypotheses but fails the ledger's leaf ordering
• a RESULT.json row perturbed by 10⁻³⁰
• halo exponent 43 and core exponent 50, both through the row evaluator

The verifier also fails if any pinned byte, statement fragment or selected-manifest copy is missing or changed.

Scope

This is source binding and independent evaluation. It does not re-prove the written statements, PR1673's support-local replacement, PR1786's locality bounds or the analytic outer decomposition. The formulas were transcribed by hand, and the sources and ledger share authors. The five framework assumptions are unchanged. This is an agent check, not human or proof-kernel review. It changes no selected record.

Task and overlap

The chooser drew independent-verification / independent-moment (seed ddb1a4fe3fc592ca90b11f62e4a57c66), with a changed scope. This PR answers open question 1 of #6109. Base: canonical main 721c03822, priority revision 8. Before starting, I refreshed find_overlap.py and listed open PRs, and repeated both before submission. #5984 and #6062 treat the outer ledger as parameter feasibility and do not bind rows to the theorems they encode. research/complex-stopped-recursion-cost audits #4100's COMPLEX.md, which is a different object.

Open next questions

The package lists three, each with a relevance note, first step and blocker:

• Cite the PR1673 replacement for the 1−c hypothesis in the selected review.
• Audit SUPPLIER-SUPPORT-AUDIT.md §6 itself.
• Controller batches against the compiler's §4 premises, carried over from Bind PR6030 uniform compiler and nine outer rows to written theorems; j=47005 is first passing grid point (no new κ) #6109.

Credit

• DreamingOfClouds: PR6030, PR5907.
• zxv: the PR4359 outer ledger, ENDPOINT.md and OUTER-TRANSFER-AUDIT.md.
• Vlado Vojdanovski: PR1673 support-local supplier.
• Chafik Boukhalfa: PR1786 fine-prime padding and halo/core powers.
• icekylinx: stopped product-ring exponents.
• The compact-control and stopped-recursion authors in notes/.
• Nick Petalas: Prove the exact κ region of the selected outer ledger: min(U, B, 1/32) (no new κ) #5984, cited rather than repeated.
• Douglas Colkitt with OpenAI Codex: the PR6030 application review.
• Bind PR6030 uniform compiler and nine outer rows to written theorems; j=47005 is first passing grid point (no new κ) #6109 (JosieElliston).

Prepared for JosieElliston with Claude Opus 5.5 (Anthropic) via Claude Code, in an unattended donated session. Codex (OpenAI) gave a read-only adversarial review. Apache-2.0.

🤖 Generated with Claude Code