Research: lower selected complex scalar primitives by 22–25% (no new kappa)

[thakrarsagar]

The selected CK and JP8 complex programs price every dyadic addition with cleared-work binary Horner. This research contribution replaces its leading clear/add pair with a copy and uses signed accumulation plus a work clear for unit coefficients. Both circuits preserve arbitrary private input and the complete scalar boundary.

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

Provider	Orientation	Original real primitives	Replacement	Saved
CK	Forward	224,938	169,618	55,320
CK	Backward	224,986	169,634	55,352
JP8	Forward	257,232	200,380	56,852
JP8	Backward	257,280	200,396	56,884

The 22.1–24.6% reduction covers scalar primitives, including source copies, coefficient preparation, signed accumulation and private clearing. Recursive calls, adapters and residual wrappers retain their existing costs. Scalar macro words, frames, paid profiles and κ are unchanged. No runtime speedup is claimed.

Only research/complex-dyadic-lowering/ is added. It contains the executable lowering, exact rational primitive interpreter, deterministic certificate, source pins, proof, local sprint claim and validation receipt. No selected emitter or certificate is changed.

Reproduce

python3 -B research/complex-dyadic-lowering/verify.py

Expected:

PASS_COMPLEX_DYADIC_LOWERING programs=4 columns=716 savings=55320,55352,56852,56884 controls=10

Python 3.11+, standard library, offline, no writes. Both receipt modes check the committed evidence. The verifier executes all 716 input columns of each selected program plus an arbitrary coefficient-work input. It checks all 686 distinct coefficients and proves finite prefix containment by exact per-register row membership in the reference Horner traces. Ten controls cover wrong signs, omitted copy/cleanup, coefficient and alias errors, cost inflation, and endpoint-neutral prefix growth.

Validation and scope

• Exact base: 66849e1475c930fd7732b1a0067ffee7e1e95f60; assignment seed 22, complex supplier track.
• Selected PR626 source: 660de893d27bb7abd1d5b01b1640207528a5c851, with the retained PR622 construction and Conditional κ = 0.001587467473762886: an E8 bit word with 420 helpers, c = 0.001653826988 (+4.18% over #510) #543 bit supplier. Consumed sources use exact or decompressed-payload SHA256 pins.
• Focused replay passes on Python 3.14.8 and Python 3.11.15 with -O. make selected-record-check passes. Additional scoped AI review found no remaining blocking issue.
• Final overlap check covered 513 open PRs through Research audit: signed block extraction and coefficient-alias controls #693. Related historical κ = 1.017629458064773e-3: exact target-prefix resynthesis on sequential206 #411 is credited for coefficient microcircuits. Consolidate six circuit PRs: 31.72% fewer bit ADDs and 22–25% fewer complex primitives #681 changes a factory scalar word; this lowers unchanged selected macros and does not depend on Consolidate six circuit PRs: 31.72% fewer bit ADDs and 22–25% fewer complex primitives #681.
• No pinned coordination issue exists, so the claim is recorded locally. The package includes attribution to the supplier lineage and disclosure of substantial OpenAI Codex assistance.

Repository-wide make verify, cold supplier regeneration, Linux CI and Lean were not run. The unchanged geometric/physical admission and uniform precision, compiler, hosting, tape and analytic contracts remain inherited. This is an exact local circuit result, not a formal proof of the multiplication theorem or production integration of a new selected supplier.