Withdrawn claim of a Bean proof against a repeating key plus transposition (see E-S-28)

This run claimed that the Bean constraints rule out a repeating-key cipher followed by any transposition at most periods. The claim does not hold: E-S-28 found the check proved nothing (it was true by construction), and the related 'universal period proof' (E-FRAC-35) was retracted on 2026-08-24. Kept for the record only.

In plain English: This run claimed that the Bean constraints rule out a repeating-key cipher followed by any transposition at most periods.

NOISE

How to read this record

Verdict – ELIMINATED (ruled out within the tested scope), NOISE (nothing beyond what chance produces for a search of this size; also shown when a record stored no verdict of its own), INCONCLUSIVE (the test left candidates or options standing, or could not decide, so it does not rule the method out), INTERESTING (slightly above random, almost certainly coincidence), SIGNAL (statistically unusual, warrants investigation), or FULL MATCH (all 24 known letters correct).
Confidence Tier – Tier 1 = mathematical proof, valid while its stated assumptions hold. Tier 2 = every possibility within the stated scope tested. Tier 3 = partially tested or sampled. Tier 4 = not yet properly tested.
Configs Tested – How many different key/parameter combinations were tried.
Best Score – How many of the 24 known plaintext letters the best attempt matched (out of 24). N/A means no such score could be read from this record.
Keystream Consistency (Bean) – Whether the key values at different positions are mathematically consistent with each other. The check only holds when the known letters stay in their carved positions (no letters rearranged or removed), and the full set used here assumes the standard A to Z alphabet.
Scope Limitations – What this elimination does not rule out.

Configs Tested: N/A
Best Score: N/A
Confidence: Not classified.
Script: scripts/_uncategorized/e_s_27_bean_algebraic_proof.py

Reproduce

PYTHONPATH=src python3 -u scripts/_uncategorized/e_s_27_bean_algebraic_proof.py

Requires the kryptos repo, Python 3.11+, PYTHONPATH=src. Some recent scripts may not be in the public repository yet.

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