Research: save 3,276 JP8 scalar primitives per orientation with signed digits

[thakrarsagar]

The selected JP8 supplier prepares every dyadic numerator with binary Horner. This finite local circuit improvement uses signed digits only when they reduce the complete primitive count, saving 3,276 real-component primitives per orientation. Status: research construction / finite circuit improvement; no new kappa.

JP8 orientation	Before	After	Saved
Forward	257,232	253,956	3,276
Backward	257,280	254,004	3,276

The 250 changed additions per orientation preserve the complete target/source/private-scratch boundary map. Every source read, doubling, signed accumulation, halving and scratch clear is charged. The original initial clear/add and unit circuits remain, so these savings exclude concurrent #696's copy and unit-coefficient work.

Signed digits can overshoot the numerator by one. The exact forward envelope increases by 34078712/34078711; the checker recomputes it rather than reusing the old receipt. Forward and backward bounds remain 64 and 101 bits, within the inherited 192-bit local allowance. Scalar macro words, frames, helpers, paid child profiles, adapters and restoration boundaries are unchanged.

Only research/complex-signed-digit/ is added. It contains the executable primitive recipe, written argument, independent rational interpreter, deterministic receipt, five source pins, local claim and validation record.

python3 -I -B research/complex-signed-digit/verify.py

Expected: PASS_COMPLEX_SIGNED_DIGIT jp8 additions=250+250 real_saved=3276+3276 columns=716 controls=9.

The offline standard-library check processes every event of both pinned JP8 programs, verifies all coefficient boundary maps, reconstructs the full 716-column scalar projection, recounts exact costs and prefix envelopes, and compares the committed receipt. Nine controls cover wrong signs, missing initialization/restoration/halving/accumulation, inadmissible coefficients, an undercharged scratch bound and an endpoint-neutral target excursion. Python 3.14.8 normal and isolated optimized runs pass; source/receipt corruption checks, make selected-record-check and staged whitespace checks pass.

Exact base: 66849e1475c930fd7732b1a0067ffee7e1e95f60. Selected #626 source: 660de893d27bb7abd1d5b01b1640207528a5c851, with #622 at f69477f4f6d3c7eb1f740b166881bffed4ffa9f6. All consumed source bytes have SHA-256 and Git-blob pins; gzip inputs also have payload pins.

OS seed 36, complex-supplier track. Three candidate tasks and the local claim are recorded. No pinned coordination issue exists. The overlap refresh covered 540 open PRs through #721 and refreshed #696, #681, #687 and #717. Numerator recoding adds a distinct incremental saving beyond #696; none of those pending PRs is an implementation dependency.

Concurrent #722, by @ellipsi2 at a0766ab0fab379e1997fadc3ca157578d57986c1, arrived between the final snapshot and submission and is now credited. It shares binary-Horner preparation across forward cleanup blocks. This contribution recodes individual numerators, preserves clearing after every macro, and also saves work backward, where #722 reports no eligible sharing runs. Its body and file inventory were inspected, but its implementation is neither imported nor independently verified here. No combined saving is claimed without a composed recount.

Credit to Jeremy Kothe and the #622 Claude Code contributors, Chafik Boukhalfa, icekylinx, DreamingOfClouds, Dugongue, eumemic and the retained predecessor notices. Prepared for Sagar Thakrar (@thakrarsagar) with substantial OpenAI Codex assistance, including a separately delegated mathematical/code cross-check. Apache-2.0; no independent human-review claim.

Full make verify, selected cold replay, global hosting/assembly, Linux CI and Lean were not run. All inherited compiler, physical hosting, precision/tape and analytic assumptions remain. This finite scalar check does not formalize the multiplication theorem or change the selected frontier. Integration must refresh the exact forward prefix receipt.

[Mister-Meeseeks]

100-PR batch review at d3bc41b87fc7d23f50d064a0f06f1a89e3ab02a7.

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

Reviewed scope: Signed-digit lowering with explicit overshoot/prefix bounds; finite coefficients and full local maps checked, no outer admission.

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.