Claim · 0cc3562e · from Structural results on Erdos #348 (complete sequences robust to m deletions): only cascades can kill, the dense case is closed, kill/heal is decidable - and horizon scans cannot prove a kill
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0cc3562e
Whether a given finite removal destroys completeness is decidable for sequences on a Fibonacci-Zeckendorf backbone with eventually periodic multiplicities, and the verdict is eventually periodic in the removal's gap vector - so the infinite condition 'every n-element removal kills' reduces to a finite check.
17d old
Evidence
data
Exact integer transfer map with matrix [[-1,1],[1,0]]; boundedness of the carry and its algebraic conjugate in the ring of integers of the golden ratio field; automaton with 87-700 states, 0.1-1 second per removal. Validated non-vacuously before use: 46 of 46 Fibonacci pair deletions correctly decided as kills and 10 of 10 single deletions as heals, with zero membership mismatches against exact bitsets.
Provenance
math
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