The source-assisted complex word of #233 as one explicit numbered program (gcert/1): reference-checked, 7.547361·10⁻⁴ in the Lean-checked five-stage layout (no new κ)

[chafreaky]

The source-assisted complex word of #233 as one explicit numbered program (gcert/1): reference-checked, and 7.547361·10⁻⁴ in the Lean-checked five-stage layout (no new κ)

One self-contained package, research/gcert-program-233/, with its own workflow. No existing file is changed.

#194's contract records that for its flow word "a literal globally renumbered operation program is not exported". This package exports it — for #194's word and for #233's — in Jacob Sussman's certificate format gcert/1 (jacobalansussman/wht-power-saving-lean, tools/gx): 12,052 numbered registers (1,320 sources, 1,320 targets, 9,412 slots), 18,248 frames, every addition explicit, the star scatter as a rule. His reference checker gx.check1 (vendored unchanged) accepts both programs: nested frames of every register, block histogram, N = 262,944 unit moves, and the exact scalar identity (every target receives exactly its source; every source is restored).

program	blocks / invocation	N	gx.check1	five-stage saving (m = 110, W = 14,692)
#194's word (control; the circuit Sussman rebuilt from #193)	70,169 — equal to his published histogram in every class and rank	262,944	accepted	7474547/10¹⁰ (his Lean figure; his gxdry.py reproduces it on this file)
#233's word	69,683	262,944	accepted	7547/10⁷ with exact bounds here (7548/10⁷ rejected); 7547361/10¹⁰ by his mirror

Lean. With his generators unchanged (gxgen.py, gxrate.py) the #233 certificate yields 41 Lean modules; lake build of all of them passed (Lean 4.34.1, 9,229 jobs, exit 0, "declaration uses sorry" for the two challenge modules only), ending in

'OAI.PowerSaving.WHT.wht_main_block_B2Gp233x' depends on axioms: [propext, Classical.choice, Quot.sound]

i.e. the Walsh–Hadamard transform in O(n (log n)^(1 − 7547361/10¹⁰)) in his framework, against 1 − 7474547/10¹⁰ for the circuit of #193 (+0.97%). tools/Compare.lean and the Fourier seam are being run and are reported in jacobalansussman/wht-power-saving-lean#2 (both Compare.lean runs pass; the Fourier transform of every length at 1 − 7547360/10¹⁰ through a copy of his seam), not here; this package itself runs only his Python reference checker.

What this is and is not. #233's ledger is unchanged: the program's per-invocation histogram 3(x + y + s + c) + 2v·e₂ is exactly #233's certified child histogram, so this is the word #233 certifies through #184's lift and contract, now as one transcript that a third-party checker reads end to end. κ does not change (the bit supplier binds in every current assembly). The emitter (gcert_emit.py) has no proof of its own; it is validated by the control (it reproduces, class by class, a certificate rebuilt independently by Sussman from #168's and #193's data files) and by the ledger identity with #233.

Argument (PROOF.md)

The input is #184's tool chain on the aligned word: complex_frame_flow.py --witness (the flow DAG: one node per (phase, frame), the value channels on every edge, births, retirements, reads) and exact_complex_flow_lift.py (at every node an invertible completion as elementary row operations, and the coordinates of every read). The emitter numbers one slot per physical flow coordinate and, node by node at the node's frame, emits the source copies, the reads (side/deferred responses ±1/2 as in contract_v4.py; a centre read formed in place in a retiring input slot), the completion as single-target fan-outs (the lift stores the operations taking Q to I, replayed in reverse; a swap relabels, a scaling changes a slot's unit as his gxconv.py does), and names every pass-through coordinate as an extra register so that the block histogram is the flow's ledger. After phase 2 it applies #144's K blocks (1 − J/2 per parity class at the parity 3-space), reads each mixed source into its antipodal target at the target's cap frame, and undoes the K blocks — #194's contract read as a program.

Verify

python -m pip install numpy==2.3.5 scipy==1.17.0      # only for the pinned regeneration of #202's word
python3 -B research/gcert-program-233/verify.py        # about 95 s locally; -O refused

Checks every pin of SOURCE.json, rebuilds the 308 pinned files of #202 from the vendored #233 package, regenerates the aligned word, runs flow and lift for both layers, emits both programs, runs gx.check1, compares the histograms (control: his pr193-blocks.json; result: #233's certificate.json), certifies the five-stage moment at 7547/10⁷, and compares the regenerated certificates byte for byte with certificates/ and the run with certificate/expected.json. The workflow runs it on Python 3.11 and 3.13.

Scope and limits

• Python reference checker and mirror only, in this package; the Lean kernel run is reported above and will be filed in Sussman's repository (where his generators, not this package, produce the modules).
• No κ change; the complex cap of this lineage is unchanged at A stronger complex supplier: PR200's reuse pairing on the source-assisted v4 word, complex saving 7.0991·10⁻⁴ (+1.28% over #194; no new κ, bit binds) #233's 7.0991·10⁻⁴ in the three-stage assembly and 7.547·10⁻⁴ in the five-stage layout (The complex suppliers transfer to the exact DFT: θ = 1 − 7009/10⁷ (7.009·10⁻⁴) for the exact discrete Fourier transform (no new κ) #225 Proposition E, Compose terminal query retention into the five-stage complex supplier #250's ledger).
• The emitter supports the flows of Source-assisted v4 complex word with PR189's bit supplier: conditional κ = 6.674324e-4 #194 and A stronger complex supplier: PR200's reuse pairing on the source-assisted v4 word, complex saving 7.0991·10⁻⁴ (+1.28% over #194; no new κ, bit binds) #233 (no source-control vertices, no kernel reuse in these two words); other layers may need the source-control branch.

Credits

Prepared by Chafik Boukhalfa with substantial Anthropic Claude and OpenAI Codex assistance. Apache-2.0; full lineage in NOTICE and SOURCE.json. The certificate format, the reference checker (vendored unchanged, Apache-2.0, Copyright 2026 Jacob Sussman) and the five-stage layout are Jacob Sussman's; the flow, exact lift and contract are icekylinx's (#184) and ikeboy's (#191/#193/#194); the decoder and K blocks are #144's (icekylinx); the modules and frames are eumemic's (#168); the five-stage ledger statement used for the price is SovereignSteak's (#250) on hcg890's (#234) and rohanarun's (#209) layout; the moment bounds adapt eumemic/exact-dft-bounds. #202's baseline lineage as credited in #233's NOTICE.

[chafreaky]

Status of the Lean side (jacobalansussman/wht-power-saving-lean#2): beyond lake build and tools/Compare.lean, the official comparator (leanprover/comparator with its real landrun sandbox, Linux) now accepts both solutions: the Walsh–Hadamard theorem at 1 − 7547361/10¹⁰ and the exact DFT of every length at 1 − 7547360/10¹⁰. Nothing in this package changes.

[Mister-Meeseeks]

Thank you @chafreaky. This contribution is now retained on main in the scoped 100-PR review and contributor credits.

Contribution: Explicit numbered complex programs for source-assisted PR194/PR233.

Review and limits: Fresh full verifier passed: 308 pinned PR202 files regenerated, exact PR194 reference and PR233 numbered-program scalar/frame checks, canonical program payload and moment agreement. This closes a representational gap, not the all-size multiplier interfaces.

The complete original source, notices and relevant execution evidence are retained through the pinned source archive. The review distinguishes fresh local runs, source-bound historical Linux CI and prior exact-head review; it does not claim 100 fresh full mathematical audits. Closing this historical PR as reconciled. This preserves parallel and cumulative credit without replacing the selected frontier or promoting priced research targets to completed constructions.

Reviewed head: db3f75cdc5f03f3131d48fb220f6bf1958404ff3. Publication: 50d768818f579d4e165b4c257c6ee25bca300802.