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Research note: price a width-9 spectral split with dirty restoration - #665
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Thank you @Mister-Meeseeks. This contribution is now retained on main in the scoped 100-PR review and contributor credits. Contribution: A fully priced spectral split with dirty restoration. Review and limits: The explicit encoded interface differs from the rejected direct-sum routing proposal, but its complete boundary bill loses. This is a negative result for that implementation, not every encoding. 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: |
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Change and mathematical scope
Research note and scoped negative cost result; no new κ. This adds one standalone package investigating whether a width-9 complex residual can be hosted across width-4 and width-5 owners by changing the recursive interface.
For every integer
f >= 1, exact eigenspace counts admit an explicit encoder intoC_(4f) direct-sum C_(5f). Its complementary workspace action is a known diagonal phase, so one additional phase pass restores arbitrary dirty inputs. This changes the hypotheses of #451's routing/similarity obstruction; it does not contradict that obstruction or validate #448's original priced word.The complete boundary bill rejects this particular implementation as an improvement. The literal profile is
2 C_(9f) + 3 C_(4f) + 3 C_(5f), with moment ratio at least 5 relative to one residual. Granting both owner calls for free still leaves ratio at least 4. Collapsing the host sandwiches leaves two width-9f transforms; collapsing the entire operator recovers the original single call. Routing, source access, workspace, normalization, phase restoration, preparation and precision are explicitly included. This is a scoped result for the stated encoder, not a lower bound for all encoded hosting.Base:
66849e1475c930fd7732b1a0067ffee7e1e95f60. Assignment seed 51, recursive interfaces;4 = 1 + (51 mod 8)selects the split. The accepted #626/#543 record remains51110230636731/31250000000000000. No existing file orupstream/byte changes.Research note, exact certificate, source pins, and completed local claim.
No pinned coordination issue existed at either check. The pre-submission refresh covered 484 open PRs. New #663 audits #628's nonlinear dirty commutator and leaf count; this note studies the distinct linear spectral encoding above. #661/#662/#664 concern fixed-order bit frames, Clifford verification speed, and entrance promotions. No matching claimed scope was found.
The note credits Sreekanth Nair / higherbeing's #448, Chafik Boukhalfa's #451, hipotures / RaD's single-stream audit, icekylinx's exact frame interface, the selected Kothe/Boukhalfa/eumemic construction lineage, and the earlier Fourier-boundary diagnostic. Prepared by Douglas R. Colkitt with substantial OpenAI Codex assistance, under Apache-2.0.
Validation
Expected:
PASS_EXACT_DILATION_AND_UNFAVORABLE_BOUNDARY_BUDGET.f=1,...,32. A separate written averaging argument proves the capacity inequality for allf; finite enumeration is not described as its proof.-I -O.make selected-record-check, artifact hashes, local links, staged whitespace and preservation checks pass. The replay takes approximately four seconds on macOS / Python 3.14.6, standard library only.No full repository suite, cold supplier replay, Linux CI or Lean pass is claimed. No ownership schedule, all-size tape compiler, numerical rounding theorem, or multiplication theorem is supplied by this local interface. These remain explicit scope limits.