# 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](../../../../opportunities/040-queryable-permutation-framework/2026-10-09-v1.md).

## 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](../../../../checkpoints/manuscript-ledger-2026-10-09-v5.json), [finite controls](../../queryable-permutation-validation-2026-10-09-v1.json), [seed controls](../../permutation-entropy-validation-2026-10-09-v1.json), [source metadata](source.json). 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](../../../../opportunities/040-queryable-permutation-framework/2026-10-09-v2.md).

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](../../coordinate-contraction-review-2026-10-09-v1.json). 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](../../coordinate-contraction-review-2026-10-09-v2.json), [current dossier](../../../../opportunities/040-queryable-permutation-framework/2026-10-09-v3.md). No new manuscript count or proof acceptance is inferred.