Research: prefix-bounded signed-Horner circuits for CK and JP8 (no new kappa)

[AllStars101-sudo]

Status: finite complex-supplier circuit improvement / research note; no new κ.

This adds signed-Horner circuits whose coefficient-work intermediate is bounded by the original numerator at every macro. The existing exact prefix envelopes therefore remain valid. On the selected #626 programs, it saves 3,090 additional real primitives per JP8 orientation and 122 per CK orientation, beyond the explicitly credited and vendored #696 copy/unit lowering.

Every copy/source access, doubling, signed addition, halving, accumulation and clear is charged. No extra register, recursive child, frame transition or restoration is introduced. The scalar boundaries, dirty-helper restoration and paid profiles are unchanged. Only research/complex-prefix-bounded-dyadic/ is added.

Concurrent #723 is credited: its independent JP8 signed-digit construction saves 3,276 primitives per orientation by permitting numerator+1 and a slightly larger exact forward envelope. This package adds the strict per-macro bound, a proof of the optimal recurrence within that restricted signed-Horner class, CK coverage, and a separate graph crosscheck. Its recoding saves 186 fewer JP8 primitives per orientation; it does not claim a stronger general circuit result. #722 shares preparation across macro boundaries; this package retains clearing after each macro and makes no composition claim with #722 or #723.

python3 -B research/complex-prefix-bounded-dyadic/verify.py

Expected:

PASS_PREFIX_BOUNDED_DYADIC programs=4 columns=716+9 coefficients=686 extra_savings=122,122,3090,3090 controls=12

The command freshly executes all four scalar primitive programs on 716 native plus nine arbitrary private formal columns. It checks all 686 distinct coefficient maps and prefix bounds, exact costs, paid histograms and the committed complete coefficient census. An independent forward Dijkstra search agrees with the backward recurrence on all 8,256 target/bound pairs through bound 128. Twelve adverse controls include correct-endpoint overshoot, missing restoration, aliasing and inflated cost.

Validation passed on Linux CPython 3.12.14, 3.14.7 and 3.15.0, including isolated optimized execution. Minimal-checkout reproduction in a path with spaces, altered gzip packaging, four source/receipt/algorithm corruption controls and read-only snapshots pass. make selected-record-check, local documentation links and staged whitespace pass. No full make verify, cold supplier rebuild, global admission, phase regeneration, remote CI or Lean run is claimed.

Base: 66849e1. OS assignment seed 23, complex-supplier track. Sources pin reviewed #622 at f69477f4f6d3c7eb1f740b166881bffed4ffa9f6, selected #626 at 660de893d27bb7abd1d5b01b1640207528a5c851, and the verbatim #696 lowering at 5a3f983715027c4fd83f50bc9001d4b18463bed1. Twelve repository inputs use exact or decompressed-payload SHA-256 pins; programs also match the selected SPEC. No pinned coordination issue existed, so the sprint claim is local. The pre-submission overlap check covers 551 open PRs through #732.

The package includes a written recurrence/substitution proof, EXPECTED.json, SOURCES.json, VALIDATION.md, attribution and the local claim. The archived coefficient-3 signed-digit experiment is credited and remains valid for its no-paid-climb-gain scope. This result does not change κ or integrate a new production emitter. All compiler, common-label/mutable-basis, hosting, precision/tape/recovery, bit-supplier and analytic assumptions remain inherited. Finite replay is not a formal proof of the full multiplication theorem. upstream/ and the selected frontier are untouched.

Credit: Sagar Thakrar (#696 and concurrent #723), Jeremy Kothe/AtomScout (#622/#623), Chafik Boukhalfa (#626), icekylinx's primitive/emitter lineage, DreamingOfClouds, Dominik Scholz, Rohan Arun, eumemic, @ellipsi2 (#722) and retained predecessors. Prepared by Chris Pagolu (@AllStars101-sudo) with substantial OpenAI Codex assistance. Apache-2.0; no independent human-review claim.

[Mister-Meeseeks]

100-PR batch review at ba76ba3321d000c8996b0b254bcf0d7260e1bbb6.

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

Reviewed scope: Prefix-bounded dyadic coefficient routes: exact local dynamic program, independent shortest-path controls and full primitive replay; no supplier promotion.

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.