DONE / RELEASED: reachable-input cancellation in the upstream three-stage complex motif

[brianross93]

DONE / RELEASED: reachable-input cancellation in the upstream three-stage complex motif

Status / UTC update / priority revision: DONE / RELEASED / 2026-10-20 19:10 UTC / revision 7. The bounded local checkpoint is complete and this scope is released.

Outcome (LOCAL-ONLY): an exact clean-temporary cancellation reduces the older upstream centre gadget while preserving arbitrary dirty outputs, and the complete three-stage flow has a relation among its clean gathered increments. Exact small forward/reverse checks passed at h=4 and h=5. The selected construction already has a stronger clean-private-centre baseline; differing native frames and independent dirty offsets prevent treating the three-stage logical relation as a saved recursive call. No improved selected bound, fully charged native sharing construction, or general impossibility result was established. The report/checker remain local; no new PR or artifact upload, large search, or paid compute. This completion is not independent human review.

Question: starting from the complete known three-stage complex motif in upstream/build/sections/03-motifs.tex, can forward reachable-input relations among its centre gathers and backward demands at the final signed bank exchange remove expensive recursive producers? Analyze the actual source-changing middle shear, cross-stage cancellations, and all arbitrary dirty auxiliary outputs. Compare the unchanged full boundary with explicitly priced clean/cached alternatives; do not silently assume auxiliary inputs are zero or grant a free role/address change of basis.

Pin: canonical main 12fa8c5c844be21bfefb38a19503fbd867a11244. Exact primitive, tape, layout and guard contracts read in 00-introduction.tex, 02-streams.tex and 05-layers.tex. Start with symbolic equations for the existing full computation and one small exact instance, then at most two candidate identities or precise obstructions. Any candidate must name changed child histogram/weighted moment, acquisition, lifetime, restoration, address, precision and all-size obligations. No unchanged-invoice packing scan or generic symbolic-flow framework.

Overlap: bounded current centre/shared/joint/cross-stage searches and the latest twenty #1166 handoffs were checked. Related prior work includes the archived uniform scalar-oracle centre obstruction and PR3147 at 5cbc48b18cb05327a8dacab3f626412d3bc5e924; its active independent P112 sink/braid/circle audit is explicitly excluded. This scope concerns reachable relations of the upstream three-coordinate gather inputs and the changed native contract needed to exploit them, not another audit of those results, QQ16, GL3, or D4. No known active same-scope claim was found; search coverage is bounded, not a novelty guarantee. Please flag overlap.

Completed within the original 60-minute bound using small exact calculations only. The local checkpoint contains equations, the strongest relevant baseline, a preliminary cost comparison, limitations and the next conceptual decision. No work remains reserved by this claim.

Brian Ross proposed normalizing the complete known computation into a shared symbolic flow, propagating guaranteed input relations forward and required outputs backward to predict cross-branch cancellation before generating expensive terms. He provides conceptual research direction and oversight; implementation/analysis uses OpenAI Codex assistance. Prior authors' results will be credited, not recast as new discoveries.

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