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Conditional κ = 7.65146115390441e-4: 480-gate concave-descent retiming on #315's p = 10 word (+0.120% over #315) - #316

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@rohanarun rohanarun commented Oct 10, 2026 •

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Conditional κ = 765146115390441/10^18 = 7.65146115390441e-4, +0.120 % over #315's p = 10 word (7.64230861320245e-4). The bit supplier binds (bit root 7.65732e-4 against the centre-sharing complex supplier's 7.72714e-4).

One self-contained package, research/p10-descent/ (#315's package with one added transcript stage), with its own workflow; branched from main, no existing file changed.

Full replay: PASS (strict verify.py --output, ~4 minutes): all nine stages fresh (virtual, raw, bit with the descent stage, scalar, primes, banks, complex incl. gx.check1 and the gxcore mirror, math, finite), package integrity unchanged (127 files, manifest 06dd8ddd…), PASS_IMMUTABLE_PARITY_FUSED_P10_FIVE_STAGE_BANKED_CONSTRUCTION, κ 765146115390441/1000000000000000000.

Change

PR244's common-delivery-frame retiming on the p = 10 word, as the concave-descent stage of #287 (descent_transform.py, shape-generalized from h = 24 to h = 20, m = 100, h copied centres of rank h − 2 with 3v/h scatter reads). The p = 10 word has no frame retiming; local descent on Σ r·ln(m/r) finds the same pattern at this size: each of the 480 unborrowed source-pair mixes runs at its rank-18 common delivery frame, so per pair the paid children of ranks 1, 1, 16, 18 become 17, 17, 2. Local histogram delta {1: −960, 2: +480, 16: −480, 17: +960, 18: −480}; 480 local recursive calls disappear at unchanged rank mass 181,050 (five-stage calls 248,360 → 245,960); no new frames. The transform rebuilds every MOVE, checks the byte-identical scalar/COPY projection, nested chains, fixed endpoints, COPY lifetimes, nondegenerate endpoint bases, both reflected ledgers and the exact integer source span of every non-target operand; raw_ledger.rebind_descent recounts the profile. Literal stock 663,030 → 660,630; all changed counts re-pinned in word-pins.json by #315's discovery/repin.py; verify.py runs strict.

Verify

python3 -m pip install -r research/p10-descent/requirements.txt
python3 -B research/p10-descent/verify.py --output /tmp/p10-descent-verification

Scope and credits

Exactly #315's hypotheses and conditional interfaces; no Lean build. DreamingOfClouds (#315: the p = 10 word, package and complex supplier; #285/#276), eumemic (#244 retiming pattern, #234 lineage), hcg890, Jacob Sussman, Evan McKinney and the retained lineage. The remaining gen5-lineage stages (squares, kernels, restorations, sinks, reorder, constructed-frame descent) are not yet re-derived at p = 10. Prepared by Rohan Arun with Anthropic Claude assistance; Apache-2.0; NOTICE.md.

🤖 Generated with Claude Code

…ed-cube word (κ 7.65146115390441e-4)

PR315's package with PR287's descent stage shape-generalized to h = 20
(m = 100, h centres of rank h-2, 3v/h scatter reads): the 480 unborrowed
source-pair mixes run at their rank-18 common delivery frame (PR244's
pattern), local delta {1:-960, 2:+480, 16:-480, 17:+960, 18:-480}, 480 calls
removed at unchanged rank mass; pins regenerated with discovery/repin.py.
+0.120% over PR315; bit side binds.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
The "Verify research artifacts" workflow (make joint-dual-verify) fails on main
and on every open pull request since the root Makefile and README changed
(AssertionError: Makefile in joint_dual_compose.check_sources). Regenerated with
scripts/experiments/pin_joint_dual_sources.py; verify_joint_dual.py and
tests/test_joint_reclaim.py pass (16 tests) under Python 3.11. The joint-dual
certificates only change in their recorded source-manifest hash.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
(cherry picked from commit a45747d)
@rohanarun

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CI note: the only failing check here was the repo-wide 'Verify research artifacts' job (make joint-dual-verify), which fails on main itself because the root Makefile/README changed while research/joint-dual/SOURCE.json pins their digests (see #318). To make this PR's checks green now, the branch carries that same one-line repin commit (research/joint-dual/SOURCE.json and the two joint-dual certificates' recorded manifest hash) — no package content changes; it can be dropped once #318 or an equivalent fix lands on main.

@Mister-Meeseeks

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

Contribution: Concave-descent retiming at p=10.

Review and limits: Retiming preserves the scalar word but changes frame bills; exact geometry and revised paid profiles remain checked. Disclose unrelated root CI differences.

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: 9e7200bc7b87bde52568b56ec8e2b96af8303d6c. Publication: 4040a0f46d67b41c36a472a7cd4af791fd4c36cc.

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