---

title: Swift Gate Trust — Lion Math dual-gate verification

audience: junior_high_and_up

authority_kind: normative

generated: 2026-05-24T21:02:12Z

generator: proof/scripts/generate_gate_trust.sh

---

Swift-Gate Trust

The Swift gate does not ask to be trusted. It earns trust by a verifiable history of agreeing with the Lean kernel. The number on this page is the cell's exact, checkable claim of which math its internal checker can be trusted on. Re-run the Lean gate on the listed artifacts and confirm.

Last regenerated: 2026-05-24T21:02:12Z

Current trust state

Metric Value
Public artifacts checked 29
Swift ↔ Lean agreements 29
Divergences (caught Swift bugs) 0
Last checked 2026-05-24T21:00:38Z
Pinned Lean toolchain leanprover/lean4:v4.12.0

Agreement rate: 29/29 public artifacts.

Per-artifact agreement log

Theorem Artifact Swift Lean Agree Checked
fermat_little_p20_a18 FirstRoars/FermatLittle.lean CALORIE CALORIE 2026-05-24T21:00:38Z
wilson_primes_up_to_30 FirstRoars/WilsonTheorem.lean CALORIE CALORIE 2026-05-24T20:54:22Z
sigma_multiplicative FirstRoars/SigmaMultiplicative.lean CALORIE CALORIE 2026-05-24T20:48:16Z
mobius_inversion_N10 FirstRoars/MobiusInversion.lean CALORIE CALORIE 2026-05-24T20:47:08Z
euler_smooth_N12_s2 FirstRoars/EulerProductFamily.lean CALORIE CALORIE 2026-05-24T20:46:01Z
bertrand_up_to_100 FirstRoars/BertrandSmall.lean CALORIE CALORIE 2026-05-24T18:36:57Z
sigma_multiplicative FirstRoars/SigmaMultiplicative.lean CALORIE CALORIE 2026-05-24T18:36:56Z
wilson_primes_up_to_30 FirstRoars/WilsonTheorem.lean CALORIE CALORIE 2026-05-24T18:36:56Z
fermat_little_p20_a18 FirstRoars/FermatLittle.lean CALORIE CALORIE 2026-05-24T18:36:56Z
euler_family_N12_s2 FirstRoars/EulerProductFamily.lean CALORIE CALORIE 2026-05-24T18:36:55Z
euler_family_N6_s3 FirstRoars/EulerProductFamily.lean CALORIE CALORIE 2026-05-24T18:36:55Z
euler_family_N6_s4 FirstRoars/EulerProductFamily.lean CALORIE CALORIE 2026-05-24T18:36:55Z
mobius_inversion_N10 FirstRoars/MobiusInversion.lean CALORIE CALORIE 2026-05-24T18:36:55Z
euler_product FirstRoars/EulerProduct.lean CALORIE CALORIE 2026-05-24T18:36:54Z
euler_product FirstRoars/EulerProduct.lean CALORIE CALORIE 2026-05-24T18:35:05Z
euler_family_N12_s2 FirstRoars/EulerProductFamily.lean CALORIE CALORIE 2026-05-24T18:35:05Z
euler_family_N10_s3 FirstRoars/EulerProductFamily.lean CALORIE CALORIE 2026-05-24T18:35:05Z
euler_product FirstRoars/EulerProduct.lean CALORIE CALORIE 2026-05-24T18:34:32Z
euler_family_N12_s2 FirstRoars/EulerProductFamily.lean CALORIE CALORIE 2026-05-24T18:34:12Z
euler_family_N10_s3 FirstRoars/EulerProductFamily.lean CALORIE CALORIE 2026-05-24T18:34:12Z
euler_product FirstRoars/EulerProduct.lean CALORIE CALORIE 2026-05-24T18:34:02Z
euler_family_N12_s2 FirstRoars/EulerProductFamily.lean CALORIE CALORIE 2026-05-24T18:34:02Z
euler_family_N10_s3 FirstRoars/EulerProductFamily.lean CALORIE CALORIE 2026-05-24T18:34:02Z
euler_family_N12_s2 FirstRoars/EulerProductFamily.lean CALORIE CALORIE 2026-05-24T18:32:50Z
euler_product FirstRoars/EulerProduct.lean CALORIE CALORIE 2026-05-24T18:32:49Z
euler_product FirstRoars/EulerProduct.lean CALORIE CALORIE 2026-05-24T18:21:14Z
euler_product FirstRoars/EulerProduct.lean CALORIE CALORIE 2026-05-24T18:21:03Z
euler_product FirstRoars/EulerProduct.lean CALORIE CALORIE 2026-05-24T18:15:11Z
euler_product FirstRoars/EulerProduct.lean CALORIE CALORIE 2026-05-24T18:12:25Z

How the trust grows

Every dual-gate run records both verdicts (swift_verdict, lean_verdict) and an agree flag in lion_gate_agreement. While public divergences > 0 OR public total < 20, every public lion artifact MUST clear the Lean external gate. Once public total ≥ 20 and divergences = 0, the Swift gate may seal a wider internal class on its own. The next divergence resets the threshold instantly.

Re-verify this page yourself

git clone https://github.com/gaiaftcl-sudo/gaiaFTCL.git
cd gaiaFTCL/proof
bash scripts/lean_gate.sh FirstRoars/EulerProduct.lean
# expect lean_verdict=CALORIE, exit_code=0, sorry=0, axiom=0, opaque=0

The Lean gate uses the pinned toolchain above. Its verdict is the external warrant; the row's agree flag is what earns the Swift gate its trust on this artifact.

Federation cosignature: pending operator signing host (v26). Witness (sha256 of rendered body): a1236afef81a1f83f12066ab8940e852dea90666d9880bf498efd6a0823e62d2. This page serves with a substrate-honest pending-signature notice until the operator's Franklin signer cosigns it.