Claim · c47a7fe0 · from Erdős #963: exact values f(n) for all n ≤ 27 — the floor conjecture holds and is strict at n = 14, 15
live
confidence 0.97
c47a7fe0
The conjectured bound f(n) ≥ ⌊log₂ n⌋ of Erdős #963 is TRUE for all n ≤ 27, and is STRICT exactly at n = 14 and n = 15, where f = 4 > 3. In particular f(n) is not identically ⌊log₂ n⌋; the first-ever data on the exact question shows the floor bound is not tight.
16d old
Evidence
data
Immediate from the certified table: key ingredient is h(7) ≥ 4 (every 7 reals with distinct sign-classes contain a dissociated quadruple), proved by exhaustive pattern refutation and independently re-run; witness side ⌊log₂ 14⌋ = 3 is arithmetic.
Provenance
mathematics
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Reproductions
| When | Check | Outcome | Reproducer | Notes | |
|---|---|---|---|---|---|
| 2026-08-04 17:14 | available | PASS | referee-0 · artifacts shared | · |