Outer retune of #2260: #1673 capped phase-cell fusion outer on the selective-borrowing supplier, conditional κ = 0.00168341258854…

[DreamingOfClouds]

Outer retune of #2260 (no new construction): conditional κ = 0.00168341258854260746233031974039993696…

What this is. #2260 (Dugongue) built a new finite complex supplier and assembled it with the retained balanced-prefix outer, whose final κ ≈ b/(1+b): 3361/2000000. #2220 (jeremykothe2) instead applied #1673's capped phase-cell fusion outer to its supplier, with strict slacks retuned to the fixed-grid maximum (#2180 / #2161). This package applies that same outer, with #2220's ledger code (formulas unchanged), to #2260's supplier. Nothing in the finite construction is new.

Result (research/selective-borrowing-outer-retune/):

• Supplier endpoint C, certified here to 10^-200 (Improve conditional κ to 0.0016805 with selective dirty borrowing and physical owner repacking #2260 itself certified only 8417/5000000):
  • native moment < 1 at C;
  • moment with Improve conditional κ to 0.0016805 with selective dirty borrowing and physical owner repacking #2260's retained conservative bad-residue surcharge < 1 at C;
  • conservative moment > 1 at C + 10^-200.
• Final conditional κ = C − 10^-246 − 10^-222 = 0.0016834125885426074623303197403999369605037…
  • That is about +0.1733% over Improve conditional κ to 0.0016805 with selective dirty borrowing and physical owner repacking #2260 (0.0016805) and about +0.2177% over Conditional κ = 0.001679754956125544521335670993920702576998311438502580295460327520162864548260325638826305656132844: recertified 1e-60000 supplier endpoint, fixed-grid-maximum kappa C - 1/F - B at 1e-60080 slacks (PR2180 / PR2161 retune)… #2220.
• Outer ledger: 54 strict rows. These are Conditional κ = 0.001679754956125544521335670993920702576998311438502580295460327520162864548260325638826305656132844: recertified 1e-60000 supplier endpoint, fixed-grid-maximum kappa C - 1/F - B at 1e-60080 slacks (PR2180 / PR2161 retune)… #2220's 63 rows, minus its 11 rows that compare with historical T74 κ values, plus improvement over Conditional κ = 0.001679754956125544521335670993920702576998311438502580295460327520162864548260325638826305656132844: recertified 1e-60000 supplier endpoint, fixed-grid-maximum kappa C - 1/F - B at 1e-60080 slacks (PR2180 / PR2161 retune)… #2220 and over Improve conditional κ to 0.0016805 with selective dirty borrowing and physical owner repacking #2260. 17 rejecting controls fire, and Conditional κ = 0.001679754956125544521335670993920702576998311438502580295460327520162864548260325638826305656132844: recertified 1e-60000 supplier endpoint, fixed-grid-maximum kappa C - 1/F - B at 1e-60080 slacks (PR2180 / PR2161 retune)… #2220's supplier-independent outer evidence is replayed (union schedule, structure, gauge-free, fine padding, Conditional kappa = 0.001677160151714381 via capped phase-cell fusion #1673's 19 exact replays).

Verify (≈75 s; assertions on; numpy and SymPy needed, as for #2220's outer evidence):

python3 -B research/selective-borrowing-outer-retune/verify.py

This replays #2260's supplier from scratch from a verbatim vendored copy at fde6b107, using #2260's own steps:

• native local words, owners, the independent family-factor audit, the finite invoice;
• Improve conditional κ to 0.0016805 with selective dirty borrowing and physical owner repacking #2260's own exact arithmetic and its 47-row outer.

It then binds #2260's recounted profile to the retune's SPEC, certifies the endpoint, and regenerates the outer ledger byte-identically.

Caveats

• Conditional. The claim is exactly as conditional as Improve conditional κ to 0.0016805 with selective dirty borrowing and physical owner repacking #2260 and Conditional κ = 0.001679754956125544521335670993920702576998311438502580295460327520162864548260325638826305656132844: recertified 1e-60000 supplier endpoint, fixed-grid-maximum kappa C - 1/F - B at 1e-60080 slacks (PR2180 / PR2161 retune)… #2220. It inherits Improve conditional κ to 0.0016805 with selective dirty borrowing and physical owner repacking #2260's supplier premises: the all-size compiler, physical fixed-tape realization, retained bit construction, exact recovery and analytic transfer. It also inherits every premise of Conditional kappa = 0.001677160151714381 via capped phase-cell fusion #1673's outer and of the Conditional κ = 0.001679754788150048 from fine source-prime padding #1786 / Conditional κ = 0.001679745508802299: gauge-free (fractional-shift) interiors, structured boundary solves and radix-distributed sparse-union schedule on PR1673's capped phase-cell fusion outer, pivot-566+554 T74 supplier #1758 / Conditional κ = 0.0016797549561255445213356709939207025769983114385025802954603275201628645482603256388263...: fixed-grid ceiling over PR2161 #2180 refinements in Conditional κ = 0.001679754956125544521335670993920702576998311438502580295460327520162864548260325638826305656132844: recertified 1e-60000 supplier endpoint, fixed-grid-maximum kappa C - 1/F - B at 1e-60080 slacks (PR2180 / PR2161 retune)… #2220's outer. Improve conditional κ to 0.0016805 with selective dirty borrowing and physical owner repacking #2260 is itself a recent, not-yet-reviewed PR, so this result is conditional on it as well.

• Supplier-generic outer. Conditional kappa = 0.001677160151714381 via capped phase-cell fusion #1673's theorem is "parameterized by the effective supplier rate". It was first stated on the T8 selected supplier and substituted with T74. The substitution needs only:

  • a fixed native dimension and maximum child rank (73, and 48);
  • restoration of arbitrary dirty helpers and spectators under the same normalized transform;
  • the retained interfaces with C_1 = 1. Improve conditional κ to 0.0016805 with selective dirty borrowing and physical owner repacking #2260 states it uses the same interfaces.

  Whole-role hosting is checked, not assumed: Improve conditional κ to 0.0016805 with selective dirty borrowing and physical owner repacking #2260 has one owner row per (call, helper) with contiguous axes.

  The README gives the argument. An independent check of this point is welcome.

• The gain is the outer. Improve conditional κ to 0.0016805 with selective dirty borrowing and physical owner repacking #2260's own above_balance control tests the balanced-prefix outer's margin; 3361/2e6 is the floor of that margin on Improve conditional κ to 0.0016805 with selective dirty borrowing and physical owner repacking #2260's 1e-7 grid (about 8e-8 below the margin), so the gain comes from the different outer, not from Improve conditional κ to 0.0016805 with selective dirty borrowing and physical owner repacking #2260 having claimed loosely.

• One verifier deviation, stated. Improve conditional κ to 0.0016805 with selective dirty borrowing and physical owner repacking #2260's independent receipt pins the SHA-256 of gzip.compress(payload, mtime=0) bytes, and those bytes depend on the zlib build (CPython 3.9–3.14 here do not reproduce Improve conditional κ to 0.0016805 with selective dirty borrowing and physical owner repacking #2260's recorded hash). Every other receipt key matches Improve conditional κ to 0.0016805 with selective dirty borrowing and physical owner repacking #2260's EXPECTED.json verbatim. The payload hash is a reproducibility pin from this package (the uncompressed payload, identical across CPython 3.11, 3.12 and 3.14 here), because the published compressed hash is not reproducible across zlib builds.

• If Improve conditional κ to 0.0016805 with selective dirty borrowing and physical owner repacking #2260's supplier is withdrawn or corrected, this retune falls with it.

• There is no new finite construction, no Lean proof and no independent human review.

Credits

• Improve conditional κ to 0.0016805 with selective dirty borrowing and physical owner repacking #2260 (Dugongue): the supplier, selective 44-alias borrowing, and the new physical owner packing.
• Research: 80-helper anticipatory borrowing component and exact price rejection (no new kappa) #2226 (Cinna Davis): the anticipatory borrowing architecture.
• Conditional κ = 0.001679754956125544521335670993920702576998311438502580295460327520162864548260325638826305656132844: recertified 1e-60000 supplier endpoint, fixed-grid-maximum kappa C - 1/F - B at 1e-60080 slacks (PR2180 / PR2161 retune)… #2220 (jeremykothe2): the retune method, outer ledger and evidence package.
• Conditional kappa = 0.001677160151714381 via capped phase-cell fusion #1673 (Vlado Vojdanovski): the capped phase-cell fusion outer.
• Conditional κ = 0.0016797549561255445213356709939207025769983114385025802954603275201628645482603256388263...: fixed-grid ceiling over PR2161 #2180 / Conditional κ = 0.00167975495612554452133567099392070257699831143850258029546032752016286454826032563882630565613284: tighter free epsilon over PR2044 #2161 (dataisfire): the fixed-grid maximum.
• Conditional κ = 0.001679754788150048 from fine source-prime padding #1786 (Chafik Boukhalfa): fine prime padding.
• Conditional κ = 0.001679745508802299: gauge-free (fractional-shift) interiors, structured boundary solves and radix-distributed sparse-union schedule on PR1673's capped phase-cell fusion outer, pivot-566+554 T74 supplier #1758 and Conditional κ = 0.001677641731343354: classical matrix boundary with signed554 T74 #1699: the gauge-free interiors and the classical boundary.
• All upstream notices are retained.

Prepared by DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code; Apache-2.0.
🤖 Generated with Claude Code

[Mister-Meeseeks]

Maintainer progress at 49ce38fee91f33edb54645724e7be9530f5631f6: the full registered replay passes (48.655 seconds here), including the supplier replay with the stated canonical-payload comparison, the 200-digit endpoint, 54 outer rows/17 rejection controls, and the 19 inherited finite evidence replays. All 70 vendored supplier files match #2260 exactly; the independently published decompressed-factor hash also matches our separate reconstruction. This is finite evidence, not completion of the shared analytic/tape proof review.

One concrete packaging correction: outer/FINE-PADDING-COMPOSITION.md says that vendor/pr1786/FINE-PRIME-PADDING.md is vendored verbatim and uses it as the proof of the prime/precision/locality statements, but that path is absent from this package (and its manifest). The source is available in #2220 at fc09a70baf7d6bcff935df226f6fc9e6c6c0131d:research/capped-fusion-t74-k554/vendor/pr1786/FINE-PRIME-PADDING.md, SHA256 47d1b1b4df28aadda3cd6bdeb1fbc47290595e9208cd09c1a1f338520d33fdce; it matches #1786's c52345caa318fc6b1b6e2659c57d746317a72823:research/fine-prime-padding/FINE-PRIME-PADDING.md exactly. Please include the proof and its retained notice with manifest coverage, or replace the nonexistent local link with a precise pinned external dependency and accurately describe what is bundled.

The shared accretive-circuit statement also needs the scale qualification described in the #1758 review. This appears repairable for the normalized Gaussian application; it is not a rejection of that application.

The shared #1673/#1758/#1786 all-size analytic and fixed-tape composition is still under review. No selected-frontier change follows from this replay. Credit for the supplier and outer refinements remains as recorded in your package.

[DreamingOfClouds]

Thanks for the replay and for both corrections, and apologies for the oversight: the package cited a vendored proof that it didn't actually contain. Both are fixed at 6b09c565887c400ca01fafb067bc9d855f1ef9fc (one commit on top of 49ce38fe).

1. Packaging (vendored, not an external pin)

• research/selective-borrowing-outer-retune/vendor/pr1786/FINE-PRIME-PADDING.md, SHA-256 47d1b1b4df28aadda3cd6bdeb1fbc47290595e9208cd09c1a1f338520d33fdce. It is copied verbatim from Conditional κ = 0.001679754956125544521335670993920702576998311438502580295460327520162864548260325638826305656132844: recertified 1e-60000 supplier endpoint, fixed-grid-maximum kappa C - 1/F - B at 1e-60080 slacks (PR2180 / PR2161 retune)… #2220 fc09a70baf7d6bcff935df226f6fc9e6c6c0131d:research/capped-fusion-t74-k554/vendor/pr1786/FINE-PRIME-PADDING.md and is byte-identical to Conditional κ = 0.001679754788150048 from fine source-prime padding #1786 c52345caa318fc6b1b6e2659c57d746317a72823:research/fine-prime-padding/FINE-PRIME-PADDING.md.
• vendor/pr1786/NOTICE.md, SHA-256 dcc1adb2461aa93ca62b6a912dbd8b215599e6af8053dfbacb7423b544dd659a. This is Conditional κ = 0.001679754956125544521335670993920702576998311438502580295460327520162864548260325638826305656132844: recertified 1e-60000 supplier endpoint, fixed-grid-maximum kappa C - 1/F - B at 1e-60080 slacks (PR2180 / PR2161 retune)… #2220's retained notice, also verbatim. The outer/check_fine_padding.py it mentions is byte-identical to Conditional κ = 0.001679754956125544521335670993920702576998311438502580295460327520162864548260325638826305656132844: recertified 1e-60000 supplier endpoint, fixed-grid-maximum kappa C - 1/F - B at 1e-60080 slacks (PR2180 / PR2161 retune)… #2220's (a0ae6912…).
• Both files are now covered by MANIFEST.json (new SHA-256 9d43e9620e7b32fc1b18eb8d4f27679fdcb4ca29cf9952fe71f28d3b7d33e7a6, 285 entries). README step 6 states what is bundled and where it comes from.

2. Scale qualification of the accretive circuit theorem

• New file outer/ACCRETIVE-SCALE.md (8b449cbd…) is our own text. It states the corrected theorem and carries it through.
  • General form (Thm 4.1'): log(max prefix / suffix / inverse-prefix norm) = O(log N · log(2 + Λ + 1/μ) + log N). The precision statement becomes p + O(log N · log(2 + Λ + 1/μ)) bits. This is the absolute-scale guard of the vendored SHALLOW-TOEPLITZ §9.
  • Proof change: step (d) uses the pair (Λ′, 1/μ) instead of the ratio Λ′/μ, and log(2 + Λ′ + 1/μ) = O(log(2 + Λ + 1/μ)).
  • Ratio form for unit-diagonal kernels (Cor 4.1''): h₀ = 1 gives Λ ≥ |h₀| = 1 and μ ≤ Re⟨He₀, e₀⟩ = 1. So Λ + 1/μ ≤ 2Λ/μ, because 2Λ/μ − Λ − 1/μ = (Λ−1)/μ + Λ(1−μ)/μ ≥ 0.
  • Descendants and shears: the hypothesis is needed only at the root kernel. The descendant and shear bounds are stated in root quantities, and on a unit diagonal they satisfy Λ′ + 1/μ ≤ 3(Λ/μ)², 1/μ ≤ Λ/μ and shears ≤ Λ/μ. So each per-node log factor is ≤ 2·log(2 + Λ/μ) + log 4.
  • Truncated/rounded kernels (Cor 4.2): band truncation and rounding leave the diagonal at exactly 1. There is also a near-unit fallback with constant 7/2 for |h₀ − 1| ≤ 1/2.
  • Boundary pivots (Cor 4.3): the pivot bounds are absolute and stay true. Where they feed a guard, they convert to the ratio form in the same way.
• Why our application satisfies the restricted form: both circuits apply the normalised kernel G′ₛ(u) = exp(−γu² + 2γsu), whose diagonal is G′ₛ(0) = 1. The narrow block has N_ii = 1. The chirps and the e^{γs²} constants sit outside the circuit. With Λ ≤ 3 + √(2π/γ) and μ ≥ p^{−O(1)}, we get log(2 + Λ + 1/μ) ≤ log 2 + log(2 + Λ/μ) = O(log p), so the guard is O(log N log p) bits per axis, as stated before.
• New script outer/check_accretive_scale.py (ec6e7bee…) runs 188 exact checks using Fractions/SymPy, and outer/run_outer.py now calls it. It covers:
  • the N = 2, H = tI counterexample;
  • the inequalities above, as polynomials with nonnegative coefficients;
  • G′ₛ(0) = 1 and N_ii = 1, checked symbolically;
  • exact rational truncated/rounded sections (γ ∈ {1/2, 2, 20}, s ∈ {0, 1/4, ±0.499}, n ∈ {2, 4, 8}): unit diagonal, e₀*He₀ = 1, ‖He₀‖² ≥ 1, and a positive-definite Hermitian part by exact LDLᵀ.
• Inherited texts are not edited. outer/GAUGEFREE-INTERIORS.md gets a pointer note at the top, following Conditional κ = 0.001679754956125544521335670993920702576998311438502580295460327520162864548260325638826305656132844: recertified 1e-60000 supplier endpoint, fixed-grid-maximum kappa C - 1/F - B at 1e-60080 slacks (PR2180 / PR2161 retune)… #2220's existing package-note precedent; the body is byte-for-byte unchanged, including its CRLF line endings. outer/FINE-PADDING-COMPOSITION.md and vendor/pr1786/FINE-PRIME-PADDING.md §3 still cite the uncorrected form verbatim. ACCRETIVE-SCALE.md lists them and says this package relies on the corrected form wherever they cite the theorem.

Effect on numbers: none. The circuit guard enters the ledger only as an additive g·polylog(p) bit term. check_ledger.py and independent_check.py take no Λ or μ input, and the binding inequality β + 2ξ − ε ≤ 1 − r − ζ is unchanged. LEDGER.json and INDEPENDENT.json still regenerate byte-identically, and κ is unchanged. The theorem form the package relies on is now the restricted one. This addresses only the scale issue; the shared #1673/#1758/#1786 analytic and fixed-tape review stays open as before.

Verify: I ran python3 -B verify.py from a fresh git archive export of 6b09c565 under nice 10, in 59 s. Every step passed: PASS_MANIFEST 285, the PR2260 supplier replay and binding, PASS_ENDPOINT, PASS_ACCRETIVE_SCALE 188, PASS_EXACT_REPLAY 19, PASS_OUTER and PASS_COMPLETE. κ = 0.00168341258854260746233031974039993696050370972245… is identical to the 49ce38fe run.

Prepared by DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code; Apache-2.0.