# Three ranked contingent next experiments

None is presently admitted merely because prior coverage has a gap. The recommendation remains to close this campaign after final evidence review. These are reopening options with distinct triggers, not an automatic queue. No experiment below has been run by this document's author.

## 1. Adversarial differential check of the inverse period4 solver

**Scope:** Synthetic messages only, fixed AZ, sign+1, inverse top-down ragged columns, continuous source period4. Use lengths17 and23, widths3 and4, with disclosed subsets deliberately straddling source-block boundaries. Compare the complete feasible/infeasible result against literal exhaustive whole-column orders with key residues inferred independently. Generate inconsistent global bindings that pass every local-rowperiod placement test; require the solver to reject them. Include cases whose individual placements cover every source position but cannot form a use-once tiling.

**Prior-work delta:** Existing inverse-period4 controls already compare64 planted/random tiny instances and eight97-character plants. This targets two specific gaps in that validation distribution: locally consistent but globally contradictory key assignments, and full union support without a tiling. It is a regression audit, not new K4 coverage or an assertion that such controls have never been published. The inspected small-width inverse prior code does not independently validate our new position/column branch selection or memo implementation.

**First pilot and bound:** Preregister a deterministic generator and at most100 synthetic instances, with30seconds total on one local CPU and no canonical ciphertext. Retain only distinct failing fixtures and a compact outcome log. No solver changes unless a discrepancy is reproduced.

**Success/rejection gate:** A discrepancy is useful only after literal enumeration supplies a concrete counterexample and the declared model is checked. Correct the flaw before relying on affected negatives. Complete agreement supports these tested cases only; it does not independently certify every real proof leaf. Stop at the first discrepancy or the cap; timeouts remain unresolved.

**Reopen/admission trigger:** A substantive solver change, an audit finding about memo/branch completeness, or explicit authorization for stronger independent validation. Do not run solely to fill remaining time or repeat the already-passing fixtures.

## 2. One mechanism replay fixed by new primary evidence

**Scope:** One original97-character, all24-clue forward/decryption replay, using a complete method and parameter set independently specified by a newly available authentic source. Require the source to fix the route, alphabet convention, key schedule and key derivation before any K4 scoring. Permit at most four explicitly documented transcription/convention ambiguities; do not infer missing choices by language optimization. If the evidence cannot specify this bounded replay, it has not passed admission.

**Prior-work delta:** Current pinned public code leaves arbitrary-width18 inverse orders outside its exhaustive width≤7 scope, and our campaign closes only declared families. Those gaps alone justify no additional mechanism. The delta here must instead be newly sourced procedural evidence, absent from the current source register, that predicts one mechanism independently. A private archive's existence, an unsupported author quotation, or an already-inspected repository claim does not meet this condition.

**First pilot and bound:** Archive the admissible source and exact interpretation, then run one locked method plus no more than the four predeclared ambiguity variants, one CPU and60seconds total. No paid retrieval, private access, communications, or external compute without separately applicable authorization.

**Success/rejection gate:** Require exact original97-character round-trip and all24 clues, readable undisclosed text, and a source-derived route/key without post-hoc repair. Reject the declared interpretation on any mismatch. A match is still an independently reviewable candidate, not an automatic intended-solution claim; no broader method search follows a failed replay.

**Reopen/admission trigger:** New authenticated primary evidence supplies the bounded mechanism and the main reviewer admits its provenance and interpretation. No such new evidence is asserted to exist here.

## 3. Matched-budget null calibration of a future coherent candidate

**Scope:** Only if a future frozen candidate already passes exact arithmetic, all clues, coherent undisclosed text and independent key/method motivation. Compare the complete candidate-selection procedure with ciphertext permutations preserving its symbol multiset, under identical clue positions, model choices, search caps and stopping rules. Fix a language metric trained or selected independently of K4; specify treatment of clues, free columns, multiple model comparisons and censored searches before evaluation. Do not rearrange the current W31 witness to improve language.

**Prior-work delta:** The package documents a null protocol but has run no language scorer or matched-null simulation. The existing W31 witness has incoherent nonclue text and does not meet this trigger. Historical partial-clue scores in prior repositories are not a calibrated comparison to this campaign's adaptive selection procedure. A valid delta requires reproducing the full relevant selection opportunity, not comparing one fitted message with unoptimized random strings.

**First pilot and bound:** After separately reviewing the scorer and frozen protocol, use20 deterministic null replicates with at most10seconds each, one CPU and a five-minute total limit. Treat this as a calibration feasibility pilot, too small for a strong tail-probability claim. If the observed candidate required a larger search budget than the pilot can match, do not call the pilot matched; postpone admission or increase the authorized cap explicitly.

**Success/rejection gate:** Report every replicate, capped outcome and tie. Common comparable null fits reject evidentiary significance under the declared statistic; few or no fits motivate a separately preregistered larger calibration, not a claimed small p-value from this pilot. Failure to reproduce the selection budget invalidates the comparison. No scorer, p-value or significance result is claimed now.

**Reopen/admission trigger:** A new candidate clears the independent nonstatistical gates and an implementable matched selection protocol is approved. The present structural fit does not qualify.