---
id: H01
title: Standardised secp256k1 parameters and GLV constants are exactly consistent
axis: A
kind: algebraic
statement: 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 libsecp256k1
  lattice basis satisfies a_i + b_i λ ≡ 0 (mod n) and has determinant n.
motivation: Every later result depends on these constants; an error here would invalidate the study.
assumptions: SEC 2 v2.0 parameter values; libsecp256k1 scalar_impl.h constants.
expected_contribution: Independent two-implementation verification (pure Python and PARI/GP).
related_work:
- certicom2010sec2
- gallant2001faster
- wuille2013libsecp256k1
possible_counterexamples: A transcription error in any constant; a wrong pairing of β with λ (β with λ² fails).
verification_strategy: 'experiments/baselines/secp256k1_facts.py: 14 named facts computed in Python and PARI/GP must agree.'
computational_budget: seconds
status: evaluated
classification: known_reproduced
evidence:
- results/baselines/secp256k1_facts.json
verdict: All 14 facts agree between Python and PARI/GP; (β, λ²) mismatch confirmed as expected.
commands:
- .venv/bin/python experiments/baselines/secp256k1_facts.py
---

# H01 — Standardised secp256k1 parameters and GLV constants are exactly consistent

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 libsecp256k1 lattice basis satisfies a_i + b_i λ ≡ 0 (mod n) and has determinant n.