5x5 Bifid cipher (proof of impossibility)

A 5x5 grid holds only 25 letters (I and J merged), but all 26 letters appear in K4

In plain English: A 5x5 grid holds only 25 letters (I and J merged), but all 26 letters appear in K4, using a method that breaks letters into grid coordinates, mixes them, and reassembles (Bifid cipher). Mathematically proven impossible as a single layer applied directly to the carved text, under the assumptions stated for this record. This record is negative within the tested scope.

ELIMINATED Tier 1

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: Tier 1: Mathematical proof. Holds as long as the ciphertext, the known-letter positions and the assumptions listed on this page are correct.
Truth Tag: [DERIVED FACT]
Date Tested: 2026-02-10
Script: scripts/substitution/e_s_09_bifid_algebraic.py

Scope Limitations

This elimination does not rule out:

Covers only the standard 5x5 Bifid. A 6x6 Bifid (36 symbols) can output all 26 letters, so this argument does not rule it out.

Assumptions

Standard 5x5 Bifid grid
Bifid is the last letter-changing step (a later transposition does not matter)

Reproduce

PYTHONPATH=src python3 -u scripts/fractionation/e_frac_21_fractionation_structural_proofs.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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