1---2id: H013title: Standardised secp256k1 parameters and GLV constants are exactly consistent4axis: A5kind: algebraic6statement: p and n are prime, G ∈ E, [n]G = O, h = 1, β³ ≡ 1 (mod p), λ³ ≡ 1 (mod n), φ(G) = (βG_x, G_y) = [λ]G, the libsecp256k17 lattice basis satisfies a_i + b_i λ ≡ 0 (mod n) and has determinant n.8motivation: Every later result depends on these constants; an error here would invalidate the study.9assumptions: SEC 2 v2.0 parameter values; libsecp256k1 scalar_impl.h constants.10expected_contribution: Independent two-implementation verification (pure Python and PARI/GP).11related_work:12- certicom2010sec213- gallant2001faster14- wuille2013libsecp256k115possible_counterexamples: A transcription error in any constant; a wrong pairing of β with λ (β with λ² fails).16verification_strategy: 'experiments/baselines/secp256k1_facts.py: 14 named facts computed in Python and PARI/GP must agree.'17computational_budget: seconds18status: evaluated19classification: known_reproduced20evidence:21- results/baselines/secp256k1_facts.json22verdict: All 14 facts agree between Python and PARI/GP; (β, λ²) mismatch confirmed as expected.23commands:24- .venv/bin/python experiments/baselines/secp256k1_facts.py25---2627# H01 — Standardised secp256k1 parameters and GLV constants are exactly consistent2829p and n are prime, G ∈ E, [n]G = O, h = 1, β³ ≡ 1 (mod p), λ³ ≡ 1 (mod n), φ(G) = (βG_x, G_y) = [λ]G, the libsecp256k1 lattice basis satisfies a_i + b_i λ ≡ 0 (mod n) and has determinant n.30