On this page
Queryable permutation framework and randomness bridge
Family 238, source fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb. Revised selected-section assessment, 9 October 2026 Australia/Brisbane. Earlier editions remain preserved.
Current decision
Prototype sparse point/inverse replay and exact tiny-law controls. Defer a source-guaranteed short-seed data loader, universal production sweep count and cryptographic claims. Demand and profitability remain unvalidated. New dossier 040.
Reviewed finding and application boundary
The signed-tensor companion has logarithmic adaptive point access to a permutation, using shared independent fair switch bits. The trace companion separately proves an all-size full-law TV bound (1/2)n^-5 when 2v>=P for an existential absolute P. The selected CoordinateTrace interface covers that latter bound. No source-selected point-query compiler or numerical P is independently verified.
The source solution takes P=2u. TraceDecay chooses u=2m after taking m>=max(14/a,2/b), with a,b obtained from imported positive contraction bounds. Those a,b values were not numerically selected or validated here. The paper similarly uses large thresholds, finite-size powers and a bounded exponent product. No large-size practical sweep schedule has been measured.
The finite utility passed 176 switching/law controls and 21 seed-support controls. A one-sweep eight-slot law has uniform single-card marginals and full-law TV 283/315. Restricting the four-slot one-sweep law to three via cycle deletion gives TV 1/12 but biased marginals. Sparse replay supports a 63-bit domain without materializing its full table, provided the required bits exist; that deterministic replay proves no randomness law. Short-seed statistical TV cannot inherit the fair-bit theorem because support is at most 2^b. Fair-bit cache cost and seeded goals must be assessed separately.
Evidence extent
Signed-tensor preliminaries and section 03-spin lines 320–462; trace manuscript abstract/full introduction and proof lines 548–633; CoordinateTrace challenge selected prefix/endpoint and config; RegularTrace and TraceBound complete displayed modules; TraceDecay lines 65–180 were read. Imported contraction proofs, all companion manuscripts, full code/proof compilation and universal numerical constants remain pending.
Manuscript section ledger, finite controls, seed controls, source metadata. Six documentary controls add a fourteenth contract but verify no supplied evidence contents.
Next action
Quantify contraction constants, specify an immutable fair-bit provider and separately labeled seeded provider, and compare a realistic sparse query/restart workload with existing sampling methods. Preserve unknown global mixing and actual CPU/memory/latency costs. Do not call short probe count a practical speedup or infer joint uniformity from marginal checks.
Shared provider and imported contraction extension
A separate decimal-wire reference now implements a seeded keyed mapping and local locked append-only OS-bit assignment. 62 initial controls, 28 initial/repeated synthetic-workload controls and 11 hardening checks add 101 passed checks. Reordered local workers and restart/inverse behavior are tested, with model, damaged-store and capacity limits explicit. This is neither full SDK nor independent-bit statistical certification. The generated 256-slot JSON store loses a packed index-array storage comparison; compact storage and a realistic sparse task remain open. Revised dossier.
TraceModel's actual import is Harmonic.Main, not the parallel Casimir copy. Selected level/dimension contractions use eventual thresholds and finite positive minima. The finite gap is 1-mass/(2*2^exponent); its minorant chooses a positive convolution exponent classically and takes a full-group minimum. Numerical coefficients/P remain unselected. Four imported-module hashes and exact reading extents are preserved in the contraction record. This does not change the 25 manuscript-reading count or certify the import closure/proof. Continue quantitative spectral dependencies and independent finite palindrome calibration without generalizing a tiny case.
Explicit finite palindrome witness
The selected source recursion is child-before-root butterfly, and its physical-sweep inverse/adjoint bridge was read in InsertionPerm/BlockProduct. The exact two/four-slot reference passes 50 independent actual-card/law/transition controls. For four slots it constructs a minorant mass 3/4/exponent zero/gap 5/8, and provides a centered symmetric 24-by-24 matrix satisfying B^2=(1/4)B with rank two and a sharp eigenvector. Conservative norm/minorant schedules reach the finite target at 13/37 sweeps, while direct law TV already passes at six. None evaluates the source's classically selected minorant or selects universal P. Expanded hashed reading record, current dossier. No new manuscript count or proof acceptance is inferred.