---

title: Research Lean gates — QC catalog ↔ kernel seals

audience: researchers_and_auditors

game: WIKI-RESEARCH-LEAN-GATES-001

updated: 2026-06-05

---

Research Lean gates — QC catalog ↔ kernel seals

Research contract: every QC math claim in gaiaftcl.qc_vm.research.v4 carries a named FirstRoars/*.lean artifact. Gate receipts are frozen in evidence/research/qc_vm_validation_latest.json and published on the mesh at /evidence/research/.

Frozen export: 2026-06-05T18:06:54Z · allLeanGatesCalorie: True · toolchain: leanprover/lean4:v4.12.0

→ Research-Publication — papers, datasets, findings

→ Lion-Math-Artifacts — full FirstRoars catalog (sorry/opaque/CALORIE)

---

Mesh evidence (downloadable JSON)

Artifact URL
QC VM validation + lean gates /evidence/research/qc_vm_validation_latest.json
ECDLP evaluation /evidence/research/ecdlp_evaluation_latest.json
QC-020 dual path /evidence/research/qc020_dual_path_latest.json
QC-020 improvement trend /evidence/research/qc020_improvement_trend_latest.json

---

QC catalog → Lean artifacts

QC ID Human name Lean artifact(s) Gate
QC-001 Shor period finding (RSA / mod-exp) ShorFactor15.lean, ShorFactorLarge.lean, ShorWitnessCertifier.lean CALORIE, CALORIE, CALORIE
QC-001-ECDLP Shor ECDLP period finding (secp256k1 lattice) ShorECDLP.lean CALORIE
QC-002 Grover search (hash / unstructured) GroverN4.lean CALORIE
QC-003 Quantum Fourier transform QFTN4.lean CALORIE
QC-004 Quantum phase estimation QPEN4.lean CALORIE
QC-005 HHL linear solver HHL2.lean CALORIE
QC-006 Deutsch–Jozsa DeutschJozsa2.lean CALORIE
QC-007 Bernstein–Vazirani BernsteinVazirani4.lean CALORIE
QC-008 Simon's algorithm Simon8.lean CALORIE
QC-009 Amplitude amplification AmpAmpN4.lean CALORIE
QC-010 Amplitude estimation AmplitudeEstimationMarked.lean CALORIE
QC-011 Phase kickback QSVT2.lean CALORIE
QC-012 Quantum walk CTQW2.lean CALORIE
QC-013 Variational quantum eigensolver VQE2.lean CALORIE
QC-014 QAOA QAOA1.lean CALORIE
QC-015 Quantum counting BosonSampling2.lean CALORIE
QC-016 Teleportation verifier GaussianBoson2.lean CALORIE
QC-017 Superdense coding verifier SteaneSyndrome.lean CALORIE
QC-018 Bell-state measurement SurfaceCodeD3.lean CALORIE
QC-019 Quantum random walk TopologicalFib.lean CALORIE
QC-020 Bitcoin preimage proof-of-work BTCPreimageN4.lean, BTCPreimageLarge.lean CALORIE, —
QC-021 Lean-validated communication MeaningInvariant.lean CALORIE

---

Lean gate roster (frozen leanGates NDJSON embedded in validation JSON)

Expected artifacts: 32 · Gated in export: 31

Artifact sorry opaque verdict checked (UTC)
AmpAmpN4.lean 0 0 CALORIE 2026-06-05T18:04:02Z
AmpAmpToGroverCoupling.lean 0 0 CALORIE 2026-06-05T18:04:03Z
AmplitudeEstimationMarked.lean 0 0 CALORIE 2026-06-05T18:04:03Z
BTCPreimageN4.lean 0 0 CALORIE 2026-06-05T18:04:04Z
BernsteinVazirani4.lean 0 0 CALORIE 2026-06-05T18:04:05Z
BosonSampling2.lean 0 0 CALORIE 2026-06-05T18:04:05Z
CTQW2.lean 0 0 CALORIE 2026-06-05T18:04:06Z
DeutschJozsa2.lean 0 0 CALORIE 2026-06-05T18:04:06Z
GaussianBoson2.lean 0 0 CALORIE 2026-06-05T18:04:06Z
GroverN4.lean 0 0 CALORIE 2026-06-05T18:04:07Z
GroverToPoWCoupling.lean 0 0 CALORIE 2026-06-05T18:04:07Z
HHL2.lean 0 0 CALORIE 2026-06-05T18:04:08Z
MeaningInvariant.lean 0 0 CALORIE 2026-06-05T18:04:08Z
QAOA1.lean 0 0 CALORIE 2026-06-05T18:04:09Z
QCFBennettUncompute.lean 0 0 CALORIE 2026-06-05T18:04:10Z
QCFOrthogonalCommute.lean 0 0 CALORIE 2026-06-05T18:04:10Z
QCFQualificationNonPerturbative.lean 0 0 CALORIE 2026-06-05T18:04:11Z
QFTN4.lean 0 0 CALORIE 2026-06-05T18:04:11Z
QFTToShorCoupling.lean 0 0 CALORIE 2026-06-05T18:04:11Z
QPEN4.lean 0 0 CALORIE 2026-06-05T18:04:12Z
QPEToShorCoupling.lean 0 0 CALORIE 2026-06-05T18:04:12Z
QSVT2.lean 0 0 CALORIE 2026-06-05T18:04:13Z
ShorECDLP.lean 0 0 CALORIE 2026-06-05T18:04:13Z
ShorFactor15.lean 0 0 CALORIE 2026-06-05T18:04:14Z
ShorFactorLarge.lean 0 0 CALORIE 2026-06-05T18:04:14Z
ShorWitnessCertifier.lean 0 0 CALORIE 2026-06-05T18:04:15Z
Simon8.lean 0 0 CALORIE 2026-06-05T18:04:15Z
SteaneSyndrome.lean 0 0 CALORIE 2026-06-05T18:04:16Z
SurfaceCodeD3.lean 0 0 CALORIE 2026-06-05T18:04:16Z
TopologicalFib.lean 0 0 CALORIE 2026-06-05T18:04:16Z
VQE2.lean 0 0 CALORIE 2026-06-05T18:04:17Z

Expected but not in leanGates export

---

Layer-2 coupling Lean edges (QCF-004)

Upstream Downstream Lean coupling Gate
QC-003 QC-001 QFTToShorCoupling.lean CALORIE
QC-004 QC-001 QPEToShorCoupling.lean CALORIE
QC-009 QC-002 AmpAmpToGroverCoupling.lean CALORIE
QC-002 QC-020-U GroverToPoWCoupling.lean CALORIE

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Verify locally

cells/xcode/scripts/peer_review_research_dataset.sh
cd proof/lean && lake build
proof/scripts/count_sorrys.sh | python3 -m json.tool --compact

*Regenerate this page: cells/xcode/scripts/export_research_lean_gates_wiki.py*

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