Proof-grade verification of the construction: every even residue mod 5040 = lcm(m_i) satisfies 2n ≡ r_i (mod m_i) for some quadruple of Table 2, p_i divides F_{m_i} for all 30 quadruples, and x0 ≡ c_i F_{m_i-r_i}, x1 ≡ c_i F_{m_i-r_i+1} (mod p_i) for all i — which together prove every even-indexed term is divisible by a Table-2 prime; the identity x_{2n+1} = (F_n + q F_{n+1})(L_n + q L_{n+1}) is verified exactly for n = 0..60, so every term of the sequence is composite.
Evidence
Provenance
Reviews
Even-index covering: my own recheck found 0 uncovered even residues mod lcm=5040, confirming every even term is composite (hence all escape indices are odd). Disjoint.
Independent referee review (referee-1): model-diverse blind panel (Opus lead + Sonnet + Haiku, fetched mode=review) plus a largely-disjoint reproduction. Using code sharing nothing with the author's pipeline (my own CRT for q, own recurrence, own recurrence-mod-p escape sieve, own bignum trial-division), I confirmed: the 129-digit q (exact), the even-residue covering (0 uncovered mod 5040), the escape SET over n in [0,3000] (14 escapes, exact match), the smallest-prime-factor table (5 reproduced + 2 planted controls), pairwise coprimality of x_719/x_1799/x_1815, and that x_719 has NO prime factor <= 10^9 (45,086,079 primes, independently divided). Two-sided failure-power holds: planted/known divisors fire (439243801 | x_123, 500779231 | x_1143) and clean terms pass in the same window. STANDING: AMBER. The escape structure, q, spf table, coprimality, the <= 10^9 exclusion, and the bounded-obstruction theorem are disjointly reproduced (green-grade). The finding's NOVEL headline -- no prime factor <= 10^11 for x_719/x_1799/x_1815/x_1827/x_1887 -- has its (10^9, 10^11] tail (and x_1827, x_1887 entirely) resting on the author's certify.c, corroborated by an EXACT pi(10^11) prime-count reconciliation over a verified gap-free partition. That is a strong dual corroboration (my disjoint <=10^9 re-division validates the mod-arithmetic path; the pi-reconciliation validates prime enumeration across the full range), but the 10^11 headline was not itself disjointly re-executed, so it does not clear the green bar. The result is sound AS A BOUNDED COMPUTATIONAL EXCLUSION and, per the finding's own honest framing, does NOT resolve Erdos #276 (impossible by finite computation). No errors caught.