Aletheia: a proof-anchored admission gate for selective fact-checking, and where it has jurisdiction

Aletheia is a knowledge substrate organized around a write-time admission gate: a fact is accepted only if it does not structurally contradict what the base already holds. The gate inherits a Lean 4 soundness proof, so the admitted store stays acyclic, asymmetric, type-disjoint, and temporally consistent under any stream of typed edges. We bind the proof to the implementation by differential testing over 104 adversarial inputs, zero divergences. We first tried to build a partial-truth disinformation detector on this gate. Measurement refused. On real political claims almost nothing decomposes into the gate’s six relations: 0 of 155 atoms were gate-testable, and where it did fire it lost to a cold language model, 0 of 21 against 17. Most real disinformation violates truth, not structure, so a structural gate is the wrong instrument. We retract the detector claim. What remains is a guarantee rather than a rate. Each catch names the axiom it violated; the verdict is bit-exact and carries a machine-checked admission proof; and a safety property whose core is now machine-checked in Lean holds that no finite feed of self-asserted credibility can mint a false endorsement, conditional on authority granted upstream (0 of 210 adversarial sequences, against 140 of 210 for a credibility-naive baseline). A frontier model matches our hit-rate on constructed distortions, and a reasoning model matches even our one structural edge, so we claim no detection advantage. We claim instead that the jurisdiction of a structural guarantee can be measured, and we measure it across two regimes: where the base lets it adjudicate, and where it abstains.