Audit: independent recount confirms #696's 22–25% primitive saving (no new kappa)

[Rohansguliani]

Independent audit of #696 by Sagar Thakrar (thakrarsagar) at head 5a3f983715027c4fd83f50bc9001d4b18463bed1. Verdict: the 22–25% primitive claim is confirmed exactly. It does not change κ.

Exact base: 66849e1475c930fd7732b1a0067ffee7e1e95f60 (current main, also the base of #696). Only research/community-pr696-audit/ is added. Credit for the construction belongs to #696.

Reproduce

python3 -B research/community-pr696-audit/recount.py

Expected:

PASS_PR696_INDEPENDENT_RECOUNT savings=55320,55352,56852,56884 percent=22.10-24.60 kappa_inputs_unchanged=True

The recount uses the standard library, runs offline, writes nothing and takes about 3 minutes. It imports no #696 code.

Findings

Program	Old	New	Saved	%
CK forward	224,938	169,618	55,320	24.59
CK backward	224,986	169,634	55,352	24.60
JP8 forward	257,232	200,380	56,852	22.10
JP8 backward	257,280	200,396	56,884	22.11

• The re-derived Horner baseline equals each emitter's real_component_primitive_bound. The re-implemented copy-init and unit rules match every Research: lower selected complex scalar primitives by 22–25% (no new kappa) #696 count. The saving equals 2·(additions + units) in every program.
• A separate randomized replay checks every complete program twice per real component, with dirty private work. After every macro the old and new states are equal, and W = 0 after each addition. Every value the new word writes to a register also occurs in that register in the old trace.
• κ: the selected assembly (complex-k492-owner-repair/code/assemble.py) computes κ from the paid profile, m = 73, live, the deficit and the PR543 bit profile. Scalar primitives enter only the finite per-vertex invoice and its pass/fail inequalities, which already pass. Over the 72 selected calls, the lowering saves 4,082,112 of 18,263,888 scalar primitives, or 8.7·10⁻¹⁰ of the per-vertex allowance. This cannot feed a κ gain in the current model.

Limits

make verify, the cold selected replay and Lean were not run. The inherited geometric, compiler, hosting, precision and tape contracts were not audited. Open #681, which consolidates #696, was not audited.

Rohan Guliani (@Rohansguliani), with substantial AI assistance. New files are under the repository's Apache-2.0 license.

[Mister-Meeseeks]

100-PR batch review at e3576811d416f91dc80b995ce4b8bc8a6144509e.

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

Reviewed scope: Independent PR696 coefficient recount and local primitive checks; no new exponent or complete supplier proof.

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.