1---2id: H073title: An exhaustive small-coefficient identity search finds only CM-explained relations and no cross-modulus or generator-specific4 relation5axis: A6kind: algebraic7statement: Among 58 064 candidate relations (binary quadratic forms, modular quadratics, GLV linear relations, cross-modulus8 and generator relations), every identity found is implied by β, λ being cube roots of unity and by the Eisenstein-ideal9 structure; the negative-control spaces Q4/Q5 return 0 hits.10motivation: 'Stage 2–3 automation: can a dumb generator rediscover structure, and does it hallucinate structure where there11 is none?'12assumptions: Coefficient bound 6; constant set {p, n, t, f, a1, b1, a2, b2, β, λ, Gx, Gy}.13expected_contribution: Calibration of the discovery engine (true positives explained, false positives zero).14related_work:15- gallant2001faster16- sica2002analysis17possible_counterexamples: A relation involving Gx or Gy would indicate a non-random generator (none).18verification_strategy: experiments/automated_discovery/identity_search.py19computational_budget: seconds20status: evaluated21classification: empirical_observation22evidence:23- results/automated_discovery/identity_search.json24verdict: 22 identities found, 22 explained, 0 unexplained, 0 false positives (expected chance hits 10^-73).25commands:26- .venv/bin/python experiments/automated_discovery/identity_search.py27---2829# H07 — An exhaustive small-coefficient identity search finds only CM-explained relations and no cross-modulus or generator-specific relation3031Among 58 064 candidate relations (binary quadratic forms, modular quadratics, GLV linear relations, cross-modulus and generator relations), every identity found is implied by β, λ being cube roots of unity and by the Eisenstein-ideal structure; the negative-control spaces Q4/Q5 return 0 hits.32