Current focus — 2026-09-13
The owner asked to stop the proliferation of parallel analyses and choose one mainline after a repository-wide research review. This issue is the current allocation entrypoint. Preserve evidence and correction history; this change is about attention, not a promotion of scientific claims.
One active analytical deliverable: consolidate and independently audit the arbitrary-integer-period square-site matching-root theorem. Use the probability part of #735, read at 9d29d014df28af7c635e6859d98a95ffe2b34d06, as the working proof. Main is still eb89e9422791d9e3c3a78f0e65d56912b815a7bd (#705 merged); do not describe the later PR stack as integrated.
The single question
For the actual NN square-site model on Z^2/Lambda, with shortest nonzero Euclidean period ell(Lambda), does the root of M_Lambda=P2-P0 converge uniformly to the infinite square-site critical probability when ell→infinity, without aspect, area or shear restrictions?
The submitted proof compares the two rare-sector probabilities, not their absolute size. Its critical dependency is the oblique-band argument, yielding P2/P0 <= exp[-kappa(p) N/ell] at each fixed subcritical p, with the complementary bound above the threshold. No CFT label or fitted exponent is needed.
One acceptance package — return to #735, no parallel issue
Produce one self-contained theorem manuscript, with a lemma-indexed independent proof audit and a closest-prior-theorem comparison. The manuscript contains the finite rank dictionary, imported site sharpness and matching-critical relation, lattice reduction, local-arm/Harris lower bound, disjoint oblique-band upper bound, uniform ratio comparison, unique-root conclusion and one root-versus-full-law boundary example.
The independent audit must check: local event support and injectivity; last-entry/first-exit extraction for backtracking cycles; uniform entry-vertex counting at arbitrary tilt including a shortest vector nonprimitive in ambient Z^2; NN+NNN diagonal steps; independence only on disjoint site sets; constants uniform in area and shear; exact prior-art scope. Re-running the author's code or verifying a quotation is not a substitute for this audit.
A finite arithmetic form of the same proof is now in the owner handoff: with S=ell^2, B=4 ceil(sqrt(S)) and a rigorously justified arm bound a<=abar, (B abar)^4 < (1-abar)^S implies P2/P0 <= [(B abar)^4/(1-abar)^S]^(N/S)<1. This is a finite-root sign certificate, NOT an infinite-pc numerical enclosure. No near-critical arm bound has been computed here.
What is retained but not extended this round
Stop and completion conditions
The main theorem is an author-supplied proof with local controls, not yet a new independent publication-level acceptance. #732 audited the narrower rectangular #718 claim, not all of #735. If an oblique-band step fails, report the precise failed implication and retain the narrower valid result; do not evade it by opening another mechanism project. If prior art already proves the full claim, state the overlap and narrow the contribution rather than renaming it.
Do not add L^-4, original-U/Jordan identification, all-width spectral weights, a new numerical pc, or a full birth-law concentration theorem to this deliverable. #276's original task is already closed completed: do not reopen it as though the old proof is missing. #613 retains its own full-law scope.
No branches or raw data are deleted, no running machine job is interrupted, and no PR merge is authorized. Existing external retrievals may return; do not automatically generate another four-way production/peer-check round from each result. Completed results should reduce open claims, not generate new default queues.
Previous allocation, 2026-09-12 — preserved, superseded for new execution
Current allocation — 2026-09-12
Main now includes #702, #703 and #704. Latest integration commit: 6edf775. This replaces the old September 8 dispatch order under the owner's delegation. It is a resource decision, not a ban on unrelated useful exploration. Preserve raw data and correction history; merging is not a scientific claim upgrade.
Completed — do not commission again
#702, merged: correct symplectic orthogonality gives the all-honest-torus rank-one label map, allowed five-cell support and spiral set identity from the existing digital-Alexander theorem. D=r-1 and F=(1+M)/2 are structural. No extra census is needed merely to prove these statements. Degenerate short-period quotients stay outside the stated proof scope. Raw-p C3 and the alleged failure of the two Aff(1) actions to intertwine are corrected. P5's irreducibility/polygon-rank statements and #675's unrestricted operator no-go are corrected.
#703, merged at d84fc48: covariance-support/PSD and saturated-df=0 inference repairs; full N580 covariance recovered from EXISTING delete-one shards, not simulation. Bare aspect is not rejected at the declared nominal 3-sigma cutoff in the retrospective pure-line test. Original frozen two-rung underpowered verdict unchanged. Full CI 34681074153 passed: 1626 tests, 3 existing skips, smoke/compile/C++ checks green. Test dependencies repaired; no tests removed to obtain a pass.
#704, merged at 6edf775: independently bounded rung-specific H8 ratios instead of an assumed common ratio. Seven nominated shape-plus-leakage images still miss one nominal 99.73% mean ellipsoid at B=1; bare aspect intersects at B=0. Executed C2 sensitivity, not new evidence or H8 measurement. Three new mathematical controls, all 24 fixed-bound fits, and threshold endpoints passed local 60-dps optimality checks. A full suite for this final six-file delta has not yet been observed; parent CI must not be presented as child CI. P3 correction addendum and current README are on main; the historical manuscript remains NOT submission-ready.
#575 closed completed: the original replay and subsequent existing-shard reader satisfy the recovery job. Cancel further N580 replay solely for cov(r2,r4).
#583 closed not planned: retire the standalone saturated three-angle pure-H8 acquisition. Any defensible replacement belongs to #589. Raw data, old designs, comments and branches remain preserved.
Two delegated analyses currently worth resources
1. #622 — CPU, existing data only. N145/290/725 same-observable square-site lineage, orientation-wise inverse CDF before spin0 combination, pooled anchored quantiles and aligned delete-one covariance. Report normalized reflection residual A, adjacent Delta Z/Delta A and uncertainty; no free exponent, no site/bond pseudo-ladder. One ordinary CPU machine, no new Monte Carlo or GPU; use the issue's first-delivery cap and measured runtime. Team assigns hardware. Use current main's support policy and the corrected #655 lineage code where needed, recording its source.
2. #681 — bounded primary retrieval/proof. Jacobsen 2015, Mertens–Ziff 2016, Jacobsen 2024 Reply. Give a typed finite-torus closure versus cylinder-spectrum dictionary, exact limit order, and the one missing hypothesis or restricted obstruction. No weighted transfer implementation, large enumeration or generic venue survey. This is the sole continuation channel for #321/#635/#658's bridge question. A missing paper statement is not an impossibility theorem.
Separate theory and reserve design
#275: original-U candidate-map problem remains live. Two named mechanisms must provide same-source normalized raw prediction columns; check represented coordinates and nuisance-profiled model images before another score or acquisition. N580 compatibility does not supply these columns.
#589: reserve design, not a purchase order. Find one identifiable angular/Smith contrast or an overdetermined angular closure test, with all nuisance columns explicit. Existing #205/#595/#596 calibration work is not to be repeated as new. Unanchored model cones both contain zero, so their minimum distance is zero: price source-anchored nonzero signal or fixed SNR, and disclose when a source range includes zero. N650/N1105/N2210 are candidate geometries, not automatic runs.
#636: uncommissioned until #681 provides a distinct scientific target for a restricted local transfer representation. The reason is information value, NOT the withdrawn #675 no-go.
#680/#673: genuinely remaining geometry statements can be pursued as proofs. Noncrossing does not itself imply equality of NN/NNN reachable state classes. Do not enumerate the next size simply to replace an argument.
Resource and interpretation limits
No GPU job or generic large-N campaign is justified by these next questions. Do not turn repeated views of one block into independent evidence. Do not infer a continuum field or pc law from a surviving finite shape, raw curvature sign, or a nominal confidence-region intersection. Hardware helpers, keys and power operations remain with the operators; do not alter credentials or interfere with other runs. Return a result/counterexample/precise missing input through the existing issue channels rather than opening duplicate tasks.
Current focus — 2026-09-13
The owner asked to stop the proliferation of parallel analyses and choose one mainline after a repository-wide research review. This issue is the current allocation entrypoint. Preserve evidence and correction history; this change is about attention, not a promotion of scientific claims.
One active analytical deliverable: consolidate and independently audit the arbitrary-integer-period square-site matching-root theorem. Use the probability part of #735, read at
9d29d014df28af7c635e6859d98a95ffe2b34d06, as the working proof. Main is stilleb89e9422791d9e3c3a78f0e65d56912b815a7bd(#705 merged); do not describe the later PR stack as integrated.The single question
For the actual NN square-site model on
Z^2/Lambda, with shortest nonzero Euclidean periodell(Lambda), does the root ofM_Lambda=P2-P0converge uniformly to the infinite square-site critical probability whenell→infinity, without aspect, area or shear restrictions?The submitted proof compares the two rare-sector probabilities, not their absolute size. Its critical dependency is the oblique-band argument, yielding
P2/P0 <= exp[-kappa(p) N/ell]at each fixed subcritical p, with the complementary bound above the threshold. No CFT label or fitted exponent is needed.One acceptance package — return to #735, no parallel issue
Produce one self-contained theorem manuscript, with a lemma-indexed independent proof audit and a closest-prior-theorem comparison. The manuscript contains the finite rank dictionary, imported site sharpness and matching-critical relation, lattice reduction, local-arm/Harris lower bound, disjoint oblique-band upper bound, uniform ratio comparison, unique-root conclusion and one root-versus-full-law boundary example.
The independent audit must check: local event support and injectivity; last-entry/first-exit extraction for backtracking cycles; uniform entry-vertex counting at arbitrary tilt including a shortest vector nonprimitive in ambient Z^2; NN+NNN diagonal steps; independence only on disjoint site sets; constants uniform in area and shear; exact prior-art scope. Re-running the author's code or verifying a quotation is not a substitute for this audit.
A finite arithmetic form of the same proof is now in the owner handoff: with
S=ell^2,B=4 ceil(sqrt(S))and a rigorously justified arm bounda<=abar,(B abar)^4 < (1-abar)^SimpliesP2/P0 <= [(B abar)^4/(1-abar)^S]^(N/S)<1. This is a finite-root sign certificate, NOT an infinite-pc numerical enclosure. No near-critical arm bound has been computed here.What is retained but not extended this round
Stop and completion conditions
The main theorem is an author-supplied proof with local controls, not yet a new independent publication-level acceptance. #732 audited the narrower rectangular #718 claim, not all of #735. If an oblique-band step fails, report the precise failed implication and retain the narrower valid result; do not evade it by opening another mechanism project. If prior art already proves the full claim, state the overlap and narrow the contribution rather than renaming it.
Do not add
L^-4, original-U/Jordan identification, all-width spectral weights, a new numerical pc, or a full birth-law concentration theorem to this deliverable. #276's original task is already closed completed: do not reopen it as though the old proof is missing. #613 retains its own full-law scope.No branches or raw data are deleted, no running machine job is interrupted, and no PR merge is authorized. Existing external retrievals may return; do not automatically generate another four-way production/peer-check round from each result. Completed results should reduce open claims, not generate new default queues.
Previous allocation, 2026-09-12 — preserved, superseded for new execution
Current allocation — 2026-09-12
Main now includes #702, #703 and #704. Latest integration commit: 6edf775. This replaces the old September 8 dispatch order under the owner's delegation. It is a resource decision, not a ban on unrelated useful exploration. Preserve raw data and correction history; merging is not a scientific claim upgrade.
Completed — do not commission again
#702, merged: correct symplectic orthogonality gives the all-honest-torus rank-one label map, allowed five-cell support and spiral set identity from the existing digital-Alexander theorem. D=r-1 and F=(1+M)/2 are structural. No extra census is needed merely to prove these statements. Degenerate short-period quotients stay outside the stated proof scope. Raw-p C3 and the alleged failure of the two Aff(1) actions to intertwine are corrected. P5's irreducibility/polygon-rank statements and #675's unrestricted operator no-go are corrected.
#703, merged at d84fc48: covariance-support/PSD and saturated-df=0 inference repairs; full N580 covariance recovered from EXISTING delete-one shards, not simulation. Bare aspect is not rejected at the declared nominal 3-sigma cutoff in the retrospective pure-line test. Original frozen two-rung underpowered verdict unchanged. Full CI 34681074153 passed: 1626 tests, 3 existing skips, smoke/compile/C++ checks green. Test dependencies repaired; no tests removed to obtain a pass.
#704, merged at 6edf775: independently bounded rung-specific H8 ratios instead of an assumed common ratio. Seven nominated shape-plus-leakage images still miss one nominal 99.73% mean ellipsoid at B=1; bare aspect intersects at B=0. Executed C2 sensitivity, not new evidence or H8 measurement. Three new mathematical controls, all 24 fixed-bound fits, and threshold endpoints passed local 60-dps optimality checks. A full suite for this final six-file delta has not yet been observed; parent CI must not be presented as child CI. P3 correction addendum and current README are on main; the historical manuscript remains NOT submission-ready.
#575 closed completed: the original replay and subsequent existing-shard reader satisfy the recovery job. Cancel further N580 replay solely for cov(r2,r4).
#583 closed not planned: retire the standalone saturated three-angle pure-H8 acquisition. Any defensible replacement belongs to #589. Raw data, old designs, comments and branches remain preserved.
Two delegated analyses currently worth resources
1. #622 — CPU, existing data only. N145/290/725 same-observable square-site lineage, orientation-wise inverse CDF before spin0 combination, pooled anchored quantiles and aligned delete-one covariance. Report normalized reflection residual A, adjacent Delta Z/Delta A and uncertainty; no free exponent, no site/bond pseudo-ladder. One ordinary CPU machine, no new Monte Carlo or GPU; use the issue's first-delivery cap and measured runtime. Team assigns hardware. Use current main's support policy and the corrected #655 lineage code where needed, recording its source.
2. #681 — bounded primary retrieval/proof. Jacobsen 2015, Mertens–Ziff 2016, Jacobsen 2024 Reply. Give a typed finite-torus closure versus cylinder-spectrum dictionary, exact limit order, and the one missing hypothesis or restricted obstruction. No weighted transfer implementation, large enumeration or generic venue survey. This is the sole continuation channel for #321/#635/#658's bridge question. A missing paper statement is not an impossibility theorem.
Separate theory and reserve design
#275: original-U candidate-map problem remains live. Two named mechanisms must provide same-source normalized raw prediction columns; check represented coordinates and nuisance-profiled model images before another score or acquisition. N580 compatibility does not supply these columns.
#589: reserve design, not a purchase order. Find one identifiable angular/Smith contrast or an overdetermined angular closure test, with all nuisance columns explicit. Existing #205/#595/#596 calibration work is not to be repeated as new. Unanchored model cones both contain zero, so their minimum distance is zero: price source-anchored nonzero signal or fixed SNR, and disclose when a source range includes zero. N650/N1105/N2210 are candidate geometries, not automatic runs.
#636: uncommissioned until #681 provides a distinct scientific target for a restricted local transfer representation. The reason is information value, NOT the withdrawn #675 no-go.
#680/#673: genuinely remaining geometry statements can be pursued as proofs. Noncrossing does not itself imply equality of NN/NNN reachable state classes. Do not enumerate the next size simply to replace an argument.
Resource and interpretation limits
No GPU job or generic large-N campaign is justified by these next questions. Do not turn repeated views of one block into independent evidence. Do not infer a continuum field or pc law from a surviving finite shape, raw curvature sign, or a nominal confidence-region intersection. Hardware helpers, keys and power operations remain with the operators; do not alter credentials or interfere with other runs. Return a result/counterexample/precise missing input through the existing issue channels rather than opening duplicate tasks.