R480 nonforest panel: 4,858 fewer Horner primitives beyond our forest baseline

[conorholds]

Change and mathematical scope

Finite scalar construction; no new κ. On the selected R480 word, a restored nonforest compensation network costs 14,076 Horner primitives, versus 18,934 for our same-input reimplementation of PR1080's alternating signed bi-forest method: 4,858 fewer primitives (25.7%).

The construction permits repeated donors, dyadic shears and scales beyond the single-parent forest restriction. Preparation and restoration are charged, arbitrary incoming helper values are restored, and no registers are added. The comparator runs our implementation of PR1080's method, not PR1080's published code. Neither baseline nor candidate is claimed optimal.

The matched comparison counts every scalar event in the complete local word under the same PR696 copy/unit tariff. Surrounding events are identical; recursive child work and physical Clifford/phase costs are excluded from this table:

Compensation panel / cleanup	Forward	Inverse transpose
Our forest / published PR1119 routine	67,874	67,890
Nonforest / published PR1119 routine	62,694	62,710
Our forest / package cleanup	65,378	65,394
Nonforest / package cleanup	60,198	60,214

The panel saves 5,180 copy/unit primitives with either cleanup, approximately 7.9% of the complete local word's scalar primitive count when holding the package cleanup fixed. This is a different tariff from the 4,858-primitives Horner result above.

The cleanup is an application of PR1119, not a new factorization algorithm. Its unmodified dimension-parameterized routines were also run on this input: seed 30, seventeen sequential trials, selecting the smallest cleanup Horner count. That bounded run reaches 36,482 Horner primitives, versus 33,368 for the package cleanup. All trial receipts are retained; this does not establish a method optimum.

Limits: the paid recursive profile, helper inventory, frame paths and selected κ are unchanged. The local compiler-allowance saving is non-binding. No integer-multiplication runtime improvement, supplier adoption or new multiplication bound is claimed. Only research/complex-compensation-network/ is added.

Task and overlap

• Scientific base: 0b1cccf86e2f5132ed286a26ef0a681a495740ea; immutable inputs retained.
• Integration/guidance checkpoint: 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2, priority revision 4.
• Original card: complex-new-helper-inventory.
• Actual scope: selected-R480-restored-dyadic-compensation-and-FULL-restoration-network.

Scope changed from a new recursive helper interface to a finite scalar rewrite. The original recursive-budget gate is not met; this supplies a cheaper component for possible interface work.

Nearest predecessors are the forest method #1080, cleanup method #1119, cleanup corridor result #1165, and same-word gauges #1161, #1214, #1259, #1263, #1353 and #1979. The gauge alternative is reconstructed and compared; its savings are not stacked with this network. Gauge/network composition remains unestablished.

The literal scalar word and cleanup synthesis held fixed in #1995/#2013 change here. The newer #2132 commuting-reorder/free-frame scope explicitly excludes coefficient-rescaling and compensation changes. No improvement to their recursive-budget or packing-ceiling conclusions is claimed.

TASK.json records the overlap snapshot and exact predecessor heads. SOURCES.json, COMPARISON-SOURCES.json and METHOD-BASELINES.json bind the inputs and comparisons. Metadata searches do not establish exhaustive novelty.

Validation

Python 3.12, standard library only, from the repository root:

python3.12 scripts/research_package.py --package research/complex-compensation-network --check-only
python3.12 scripts/research_package.py --package research/complex-compensation-network

Local macOS arm64 / Python 3.12.11: all four registered commands passed; the latest replay completed in 64.84 seconds. Coverage includes both native orientations on all 704 logical columns; 22 literal primitive programs on all 713 logical/private columns; helper restoration, private erasure, paid counts, source pins and rejecting corruption controls; and exact reproduction of all seventeen published-routine trials. Receipts are in CERTIFICATE.json and INDEPENDENT.json.

The separate arithmetic checker shares splicing conventions with the primary checker. Frame/adapter legality relies on the upstream native auditor. Both checkers share assisted authorship; no independent human review or proof-assistant formalization is claimed.

Not run: selected global cold replay, new physical Clifford/phase compilation, supplier/owner integration, regenerated SCALAR-FRAME-AUDIT.json, global hosted invoice, outer assembly or hosted CI. The legacy PR1119 full verifier binds its historical 728-register U8 archive and was not run; its synthesis routines and the resulting R480 operators are checked here.

Credit

Stephan Arrington's #1080/#1119 supply the inherited synthesis methods; Sagar Thakrar's #696 supplies the copy/unit tariff.

Restored-basis predecessors include Sricharan Vagvala, David Awad and Ross Richardson. Same-word gauge work is credited to woklerx, Hanson Sun, Sagar Thakrar, Philipp, Cinna Davis and George Lydakis. The README and retained notices describe their contributions and the native-compiler lineage, preserve PR1119's original Gemini disclosure, and retain Apache-2.0 licensing.

Open next questions

The smallest structural follow-up is to retain one specified helper shear across a boundary, conjugate the affected gates, and price the complete recursive profile. Frame chronology and supplier restoration must be resolved before scalar savings can support a recurrence claim.

Separately, test gauge composition on the rewritten event stream, charging every scale transition and checking restoration, frames and precision. The README and TASK.json give the detailed questions and blockers.