ALIGNMENT SENSITIVITY — NECESSARY SCREENS, NOT FULL CIPHER SAT

Model M001 permits any fixed base permutation, any independent starting decks,
and an unconstrained plaintext alphabet. The only plaintext assumptions in this
experiment are selected links E4[68+k] = W4[71+k], k=0..29.

All83 top-orbit lengths completed. The algorithm learns sound contradiction
cores from the outside-coordinate screen, top-orbit propagation, and direct
short-return/nonreturn constraints including trailing nonreturns. An exact
minimum hitting set of these cores proposes deleted links. Once that proposal
escapes all screens, the hitting-set lower bound and the surviving set together
certify the optimum for this collection of necessary screens. A surviving set
does not prove the existence of a common base, deck, key or decipherment.

Deleting one of the30 links can escape the current screens, but only for L=1
and only by deleting offset0 or22. Both are repeated-pattern anchors.

Retaining all repeated-symbol backbone positions
  [0,1,5,9,16,18,22,26,27,29]
leaves only L=7,8,10 unresolved when all singleton assumptions are discarded.
The minimum singleton-link deletions from the full context are:
  L7: 4; example dropped offsets [3,6,11,25]
  L8: 4; example dropped offsets [2,4,6,7]
  L10:5; example dropped offsets [4,6,8,15,28]
All other L are already excluded using the backbone alone. Therefore keeping
the ten backbone links and deleting at most three singleton links still
excludes the entire M001 family under these necessary screens. Four deletions
can escape the relaxation, but actual cipher feasibility remains unknown.

The repeated-symbol backbone is a description of the ciphertext motif, not
proof that those plaintext positions agree. This test measures sensitivity
within the explicit equal-plaintext hypothesis.

NEW SHORT CERTIFICATE (found while inspecting this run; exploratory)
Offset0 alone, a repeated anchor, excludes every L>=12:
  E4[56]=E4[68]=79, with no79 at57..67: first return after12steps.
  W4[59]=68, no68 at60..71, and W4[71]=63: no return after12steps.
For a top orbit of length L>=12, the first forces p_E4[68]=R^12(0),
while the second forbids p_W4[71]=R^12(0). The assumed equality of those two
plaintext symbols contradicts this. The argument remains valid at L=12,
when the forced selected position is0. It requires no shared initial state.
The older propagation code tracked intervals that ended in another observed
return, overlooking trailing nonreturn constraints. The direct screen closes
that algorithmic gap without changing any ciphertext or old evidence.

The prior sprint's main17-step certificate remains valid. This strengthens it
and uses a repeated anchor instead of a singleton alignment position. The old
proof files were left untouched as required by the protocol.

Validation:45 planted full-deck ciphers (L1..15) with independent initial decks
were never excluded. Empty alignment sets were accepted by all83 screens;
the full context was excluded in all83. All922 saved contradiction cores and
every saved surviving set were rerun. Saved cardinality checks show UNSAT one
deletion below each recorded optimum. Independent review is still required.
