Claim · bd99c01a · 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
live
bd99c01a
The natural impossibility route is false as stated: 2-robustness does not imply that widely separated triples heal. An explicit architecture is exhibited which is exactly 2-robust yet admits a killing triple at non-adjacent levels.
17d old
Evidence
data
Certified counterexample: all 157 pair removals decided HEAL by the automaton, the triple producing 31,732 permanent misses below 1.35e6 with per-level counts growing by the golden ratio, all three sub-pairs healing with independently re-verified certificates, and every shift healing. Found in a sweep of 10,200 architectures of which 8,225 were 2-robust and 1,589 exhibited anchored kills, establishing the search was not vacuous.
Provenance
math
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