CLEARED EXCERPT (2 of 3) — "A correction"
Source: a real design-session transcript. Session-ids, repo names, and internal
paths removed; the shape is kept, the sequence is not. This is the system telling
the operator his own proposal was wrong — and showing the arithmetic instead of
asserting it.

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  Your sketch failed on shape, not size.

  A three-empty box admits 3! = 6 arrangements, so a free guess-and-check
  cracks it in six tries. Under a 2s / 3s / +1s penalty schedule, five wrong
  guesses cost ten seconds — search beats deduction outright. No constants
  fix that, because arithmetic escalation cannot catch a factorial.

  Replaced with a geometric ×3 penalty after a free first strike:
  0 / 5s / 15s / 45s / 135s / 405s. Cracking that box now costs 3m20s against
  about 60s of deduction — and an honest misread still costs nothing.

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Why this is a receipt: honesty over validation is the house rule. The operator
proposed a fix; the system proved it couldn't work — not with an opinion, with
a factorial — and then proposed one that does. Agreement for the sake of
agreement is a defection here, not a courtesy.