Research: compose R420 circuits with 16,704 fewer hosted instructions (no new kappa)

[aliromman]

This composes yongjae321's #670 block-3 circuit and x0hu's #674 block-5 circuit in eumemic's #543 R420 word. The circuit improvements belong to those authors. This contribution adds their checked composition, fresh C++ multistage replay, and complete nine-stage whole-owner and finite-invoice replay. Status: finite bit-circuit construction / independent integration evidence; no new κ.

The combined word saves 58 scalar ADDs per local invocation (26,916 → 26,858). Its 288-invocation physical program saves 16,704 emitted instructions (8,603,712 → 8,587,008). Every register frame path, all 120,960 whole helper invocations, zero-bank allocation, recursive profile and bit exponent remain unchanged. The raw global prefix and coefficient bounds decrease from 189 to 188 bits; the charged prefix remains 192 bits.

Base: 66849e1475c930fd7732b1a0067ffee7e1e95f60.
Source pins: #543 2065fe4f72a914d907f1046603f5a36f17018535, #670 2e31fcad7f9ecc8b97039ecb2333e581fd725fa1, #674 1b01fd8b135fb2c458554fbbbab4338336bf366d.
Only research/r420-two-block-composition/ is added. Original certificates and attribution are retained byte for byte; SOURCES.json pins all consumed research inputs. Neither predecessor verifier is imported. Single-block reconstructed words must first match their authors' canonical hashes.

python3 -B research/r420-two-block-composition/verify.py --hosted

Requires NumPy, SciPy, SymPy, C++17 and Boost. Set CXX and BOOST_INCLUDE if needed. Expected final line:

PASS_R420_TWO_BLOCK_COMPOSITION local_additions=26916->26858 saved=58 kappa=unchanged

Passed locally on macOS, Python 3.14.7, GCC 16.2.0 and Boost 1.92:

• Exact 4,096-input truth tables per block, forward/reverse nonnegative transfer domination, all 660 dirty-input columns, all 672 frames and H1–H5.
• Fresh C++ replay on 900 / 1,380 / 1,620 formal columns at five / nine / eleven stages for both words; all 6 / 18 / 24 omitted-bridge controls per word.
• Fresh physical templates, independent owner audits, 17 parent and 16 hosted mutation controls per word, both exact moment engines and finite invoices. The bit saving stays 0.001653826988146798944268.
• Composition-specific stale-offset failure, corrupted block maps with correct cleanup, missing cleanup and unpaid-frame controls. Old cleanup is correctly classified as scalar-valid but outside literal-reversal H4.
• Selected-record binding, final-source native receipt comparison, source/certificate hashes and staged whitespace checks.

CERTIFICATE.json and VALIDATION.json retain the exact evidence. Repository-wide make verify is not a pass: it ran once, completed community/producer/partial-gauge/three-stage-cover/paired-cube groups, then was stopped during recycled-bit verification when free disk space fell to about 2.2 GiB. No mathematical check failure was observed before interruption. No remote CI result is claimed.

The final overlap refresh through #686 found no competing composition. #686 changes frame-zero D compensation and its interface; this contribution changes two phase-B blocks under the original H1–H5 interface. Its D mechanism is not imported or combined here. Both predecessor PRs explicitly omit C++ multistage and hosted replay; this adds that coverage for their combined word. Assignment seed 15 originally selected block 5; a weaker local 37-gate candidate was archived after #674 arrived. The local claim records this single scope pivot. No pinned coordination issue existed.

All-size compiler, common-label/mutable-basis realization, whole-owner hosting, precision/tape and analytic-transfer assumptions remain. No complex construction, new selected outer assembly, Lean multiplication proof, optimality or measured runtime speedup is claimed. upstream/ and the selected frontier are unchanged.

Prepared by Ali Romman with substantial OpenAI Codex assistance. Apache-2.0. Credit is retained for the two circuit authors and the complete supplier, exporter, checker, hosting and pricing lineage in the README. No independent human review is claimed.