Research: JP8 additive coefficient routes save 2,784 beyond rescaling (no new kappa)

[Ryan-Haines]

The #626 JP8 forward cleanup has adjacent coefficients with different odd numerators that cannot share private work through power-of-two rescaling alone. A positive unit source read between dyadic shifts makes 269 of those transitions profitable while retaining the original target order and full frame.

Status: finite circuit construction / research result; no new kappa. The complete forward scalar projection falls from 257,232 to 224,422 real-component primitives: 32,810 total saving, including 2,784 beyond the independently reconstructed #739 power-only comparator. Backward remains 257,280 and still binds the conservative local invoice, which remains 11,334,342,462,720.

Only research/jp8-additive-coefficient-routes/ is added, on exact base 66849e1475c930fd7732b1a0067ffee7e1e95f60. Every read, shift, signed target update, preparation and clear is paid. Helpers, paid children, frames, wrappers and the selected frontier are unchanged.

Reproduce with standard-library Python 3.11+:

python3 -I -B research/jp8-additive-coefficient-routes/verify.py

Expected final line:

PASS_JP8_ADDITIVE_ROUTES extra_saved=2784 total_saved=32810 columns=725 orientations=2 controls=12

Validation:

• Literal primitive replay of both complete scalar projections on 716 native plus nine arbitrary private input columns; exact shear endpoints, dirty-helper restoration, private clearing, costs, paid profiles and unchanged 64/101-bit positive prefix bounds.
• Separate integer-only implementation exhausts 849,420 exponent pairs for 780 distinct coefficient pairs and checks all 1,091 replacement blocks on 6,776 local input columns. It imports no construction code.
• Twelve construction controls, four independent matrix/prefix controls and 25 inherited native frame/wrapper controls reject mutations.
• Windows Python 3.14 and Linux Python 3.12 pass. Four packaging tests cover optimized Python, a relocated minimal source tree, equivalent recompression, read-only execution and corrupted inputs/certificates/receipts. Ruff and selected-record integrity pass.

The search is complete only for positive one-read transitions with exponents in [-16,16], plus power-only reuse/reset, in consecutive same-source nonunit cleanup additions. Signed transitions, multiple reads, reordering and other phases are outside scope. Production private-work contract integration and global admission remain open, as do inherited all-size, compiler, hosting, precision/tape and analytic assumptions. Finite replay is not a formal proof of the multiplication theorem; no full repository suite, cold global rebuild, Lean or remote CI pass is claimed.

Credit Jeremy Kothe's #622/#623 construction, Chafik Boukhalfa's #626 owner allocation, the retained emitter/auditor lineage, @ellipsi2's #722 equal-magnitude reuse and Jeffrey Cox (@namredips)'s #739 power-of-two reuse. #793 changes compensation order, #769 handles CK power-of-two ladders, and #807 uses restored CK helper pairs; these are distinct mechanisms and no additive savings with their pending work are asserted. Source/comparison heads and payload hashes are recorded. OS seed 31 and the local coordination fallback are in CLAIM.md; no pinned sprint issue was available.

Prepared and submitted by Ryan Haines (@Ryan-Haines), with substantial OpenAI Codex assistance in research, implementation, verification and writing. Apache-2.0; no independent human review is claimed.

Main advanced during submission to #741/#589 at conditional kappa 0.001661202643272239. This result retains its historical #626 scope and now pins the immutable #626 assembly rather than the moving selected-result pointer. No saving is asserted for #741.

[Mister-Meeseeks]

100-PR batch review at b5c244c916dd0b30957332edad7ae7ae22b0eb9d.

Merged to main, preserving the original contributor commits and package attribution.

Reviewed scope: Additive coefficient routes beyond rescaling: 2,784 forward primitives saved; backward invoice remains binding, no new κ.

The pinned scoped command passed; the batch ledger contains its command, input hashes, environment and log. This incorporates the research/tooling contribution and does not change the selected κ or discharge the inherited multiplication-theorem assumptions.

Batch review, attribution and evidence. Thank you for the contribution.