{"commit":"c0eb4f1a1a50aabfab23b94fd74b53cef267f653","note":"Evidence ledger. The pwg field of each theorem is DERIVED from the legs and receipts below by scripts/pwg-derive.sh, never written by hand; scripts/pwg-check.sh re-derives and fails on drift (PROOF-POLICY 8.4 rule 2). Idris2 appears as a reference, not a leg: 8.1 excludes engineering provers from the ladder.","policy":{"commit":"9bdf864cc7f2c8e24b4df84bf00d04158eee3ad5","path":"3-practice/PROOF-POLICY.adoc","repo":"metadatastician/standards","section":"8"},"receipts":{"agda-c0eb4f1":{"axioms":[],"checker":"agda","checker_version":"2.7.0.1","commit":"c0eb4f1a1a50aabfab23b94fd74b53cef267f653","evidence":"https://github.com/hyperpolymath/trope-checker/actions/runs/42623339243","import_cone":"root modules All.agda and Smoke.agda; all seven TB.* modules reachable from All.agda; postulate count 0 (--safe refuses postulate; independently scanned with hyperpolymath/mathesis scripts/census/proof-holes.sh over verification/proofs/agda at this commit, which emitted no record of any class)","inputs_digest":"git-tree verification/proofs/agda = 8d3370e7da58023b9bfa0802e710860105ace73a","invocation":"agda --safe --without-K --cubical-compatible All.agda ; agda --safe --without-K --cubical-compatible Smoke.agda","observed":"PASS: All.agda + Smoke.agda typecheck (--safe --without-K --cubical-compatible; --safe => postulate-free by construction)","repo":"hyperpolymath/trope-checker","result":"pass","state":"current","stdlib_pin":"agda-stdlib v2.0 sha256:14eecb83d62495f701e1eb03ffba59a2f767491f728a8ab8c8bb9243331399d8"},"lean-boundary-c0eb4f1":{"axioms":["propext","Quot.sound","Classical.choice"],"checker":"lean","checker_version":"4.16.0 (lake, leanchecker)","commit":"c0eb4f1a1a50aabfab23b94fd74b53cef267f653","evidence":"https://github.com/hyperpolymath/trope-checker/actions/runs/42623339243","import_cone":"every module of grade-boundary sits in the import Mathlib cone via GradeBoundary.lean:3","inputs_digest":"git-tree verification/proofs/lean4 = 5f32026d26810845d94d42b5a1281da3c2a06146","invocation":"lake build --wfail ; leanchecker ; axiom audit against the allowlist {propext, Classical.choice, Quot.sound}","observed":"job 'Lean grade-boundary: lake build + sorry-free environment' success; 'Trope.GradeR.atom_factorization' depends on axioms: [propext]; 'Trope.nine_families' depends on axioms: [propext, Classical.choice, Quot.sound]","repo":"hyperpolymath/trope-checker","result":"pass","state":"current","stdlib_pin":"mathlib4 rev v4.16.0 (lakefile.toml) -- see the Mathlib note: PROOF-POLICY 2 forbids this dependency for a recheck leg"},"lean-factorisation-c0eb4f1":{"axioms":["propext","Quot.sound","Classical.choice"],"checker":"lean","checker_version":"4.16.0 (lake, leanchecker)","commit":"c0eb4f1a1a50aabfab23b94fd74b53cef267f653","evidence":"https://github.com/hyperpolymath/trope-checker/actions/runs/42623339243","import_cone":"grade-factorisation requires gradeBoundary, so the import Mathlib cone covers it","inputs_digest":"git-tree verification/proofs/lean4 = 5f32026d26810845d94d42b5a1281da3c2a06146","invocation":"lake build --wfail ; leanchecker ; axiom audit against the allowlist {propext, Classical.choice, Quot.sound}","observed":"job 'Lean grade-factorisation: lake build + sorry-free environment' success","repo":"hyperpolymath/trope-checker","result":"pass","state":"current","stdlib_pin":"mathlib4 rev v4.16.0, transitively via the gradeBoundary path dependency"}},"repo":"hyperpolymath/trope-checker","schema_version":"1.0.0","theorems":[{"foundation_diverse_witness":null,"id":"L1","kind":"theory","legs":{"agda":{"declarations":["TB.Grade.gmonoid-assoc"],"receipts":["agda-c0eb4f1"],"route":"re-proved","state":"AGDA-VERIFIED","token":"PROVEN"},"lean":{"declarations":["FateA.comp_assoc"],"receipts":["lean-boundary-c0eb4f1"],"route":"re-proved","state":"BRIDGE-PENDING","token":"PROVEN-WITH-AXIOMS"},"rocq":{"declarations":[],"receipts":[],"route":"unavailable","state":"NOT-INVENTORIED","token":"OPEN"}},"notes":"","reference":{"idris2":{"declarations":["Trope.Laws.gradeAssoc","Trope.Coords.fateAssoc","Trope.Coords.bondAssoc","Trope.Coords.mergeAssoc","Trope.Fidelity.dplusAssoc"],"state":"not-a-leg (PROOF-POLICY 8.1 excludes engineering provers from the PWG ladder)","token":"PROVEN"}},"title":"L1 (associativity)"},{"foundation_diverse_witness":null,"id":"L2","kind":"theory","legs":{"agda":{"declarations":["TB.Grade.gmonoid-unit"],"receipts":["agda-c0eb4f1"],"route":"re-proved","state":"AGDA-VERIFIED","token":"PROVEN"},"lean":{"declarations":[],"receipts":[],"route":"unavailable","state":"NOT-INVENTORIED","token":"OPEN"},"rocq":{"declarations":[],"receipts":[],"route":"unavailable","state":"NOT-INVENTORIED","token":"OPEN"}},"notes":"","reference":{"idris2":{"declarations":["Trope.Grade.gradeUnitL","Trope.Grade.gradeUnitR","Trope.Coords.fateUnitL","Trope.Fidelity.dplusZeroR"],"state":"not-a-leg (PROOF-POLICY 8.1 excludes engineering provers from the PWG ladder)","token":"PROVEN"}},"title":"L2 (unit)"},{"foundation_diverse_witness":null,"id":"L3","kind":"theory","legs":{"agda":{"declarations":["TB.Grade.falsified-absorbL","TB.Grade.falsified-absorbR","TB.Grade.misbound-absorbL","TB.Grade.conflated-absorbL","TB.Grade.unknown-absorbL","TB.Grade.total-absorb-Q","TB.Tier.deceptive-absorbs-|>"],"receipts":["agda-c0eb4f1"],"route":"re-proved","state":"AGDA-VERIFIED","token":"PROVEN"},"lean":{"declarations":["FateA.falsified_two_sided_zero","GradeR.gBotR_two_sided_zero"],"receipts":["lean-boundary-c0eb4f1"],"route":"re-proved","state":"BRIDGE-PENDING","token":"PROVEN-WITH-AXIOMS"},"rocq":{"declarations":[],"receipts":[],"route":"unavailable","state":"NOT-INVENTORIED","token":"OPEN"}},"notes":"Agda states both sides only for Falsified. For Misbound, Conflated and Unknown the left form is stated; the right follows in one step from the coordinate's commutativity but is not itself a lemma.","reference":{"idris2":{"declarations":[],"state":"not-a-leg (PROOF-POLICY 8.1 excludes engineering provers from the PWG ladder)","token":"OPEN"}},"title":"L3 (bottom absorption)"},{"foundation_diverse_witness":null,"id":"L4","kind":"theory","legs":{"agda":{"declarations":["TB.Order.fateL4MonoR","TB.Order.fateL4MonoL","TB.Order.dplusMonoR","TB.Order.dplusMonoL"],"receipts":["agda-c0eb4f1"],"route":"re-proved","state":"AGDA-VERIFIED","token":"PROVEN"},"lean":{"declarations":["FateA.comp_mono_right","FateA.comp_mono_left"],"receipts":["lean-boundary-c0eb4f1"],"route":"re-proved","state":"BRIDGE-PENDING","token":"PROVEN-WITH-AXIOMS"},"rocq":{"declarations":[],"receipts":[],"route":"unavailable","state":"NOT-INVENTORIED","token":"OPEN"}},"notes":"Coverage differs by prover. Agda covers the fate coordinate and the fidelity dimension; Lean covers fate only (FateA.le is defined on Fate alone). Bond, merge and the grade-level lifting that spec section 7's Knaster-Tarski argument invokes have an Idris2 restatement only, which 8.1 excludes from the ladder, so those parts have no gradeable theory leg.","reference":{"idris2":{"declarations":["Trope.Soundness.fateL4MonoR","Trope.Soundness.fateL4MonoL","Trope.Order.bondComposeMono","Trope.Order.mergeComposeMono"],"state":"not-a-leg (PROOF-POLICY 8.1 excludes engineering provers from the PWG ladder)","token":"PROVEN"}},"title":"L4 (monotonicity), in full"},{"foundation_diverse_witness":null,"id":"L5","kind":"theory","legs":{"agda":{"declarations":["TB.Tier.deceptive-absorbs-|>","TB.Reduction.attenuate-stays-deceptive","TB.Reduction.project-stays-deceptive"],"receipts":["agda-c0eb4f1"],"route":"re-proved","state":"AGDA-VERIFIED","token":"PROVEN"},"lean":{"declarations":[],"receipts":[],"route":"unavailable","state":"NOT-INVENTORIED","token":"OPEN"},"rocq":{"declarations":[],"receipts":[],"route":"unavailable","state":"NOT-INVENTORIED","token":"OPEN"}},"notes":"","reference":{"idris2":{"declarations":[],"state":"not-a-leg (PROOF-POLICY 8.1 excludes engineering provers from the PWG ladder)","token":"OPEN"}},"title":"L5 (deception infectiousness)"},{"foundation_diverse_witness":null,"id":"L6","kind":"theory","legs":{"agda":{"declarations":["TB.Grade.grade-comm"],"receipts":["agda-c0eb4f1"],"route":"re-proved","state":"AGDA-VERIFIED","token":"PROVEN"},"lean":{"declarations":["GradeR.instCommMonoid","FateA.comp_comm"],"receipts":["lean-boundary-c0eb4f1"],"route":"re-proved","state":"BRIDGE-PENDING","token":"PROVEN-WITH-AXIOMS"},"rocq":{"declarations":[],"receipts":[],"route":"unavailable","state":"NOT-INVENTORIED","token":"OPEN"}},"notes":"L6 ratification is still subject to the open owner ruling tracked on trope-checker issue 106.","reference":{"idris2":{"declarations":[],"state":"not-a-leg (PROOF-POLICY 8.1 excludes engineering provers from the PWG ladder)","token":"OPEN"}},"title":"L6 (commutativity)"},{"foundation_diverse_witness":null,"id":"retention-order","kind":"theory","legs":{"agda":{"declarations":["TB.Order.|=-refl"],"receipts":["agda-c0eb4f1"],"route":"re-proved","state":"AGDA-PENDING","token":"OPEN"},"lean":{"declarations":[],"receipts":[],"route":"unavailable","state":"NOT-INVENTORIED","token":"OPEN"},"rocq":{"declarations":[],"receipts":[],"route":"unavailable","state":"NOT-INVENTORIED","token":"OPEN"}},"notes":"Agda proves reflexivity only. Transitivity and decidability exist in the Idris2 reference, which 8.1 excludes from the ladder, so the preorder claim has no complete theory leg. The Agda leg is OPEN, not PROVEN, for this obligation.","reference":{"idris2":{"declarations":["Trope.Laws.decGradeLte","Trope.Soundness.gradeLteTrans","Trope.Coords.fateLteRefl","Trope.Coords.bondLteRefl","Trope.Coords.mergeLteRefl","Trope.Fidelity.dLteRefl"],"state":"not-a-leg (PROOF-POLICY 8.1 excludes engineering provers from the PWG ladder)","token":"PROVEN"}},"title":"Retention order is a decidable preorder"},{"foundation_diverse_witness":null,"id":"A2-chain","kind":"theory","legs":{"agda":{"declarations":["TB.Order.fateDroppedLtePredicated","TB.Order.fatePredicatedNotLteDropped"],"receipts":["agda-c0eb4f1"],"route":"re-proved","state":"AGDA-VERIFIED","token":"PROVEN"},"lean":{"declarations":["FateA.le_total","FateA.le_refl"],"receipts":["lean-boundary-c0eb4f1"],"route":"re-proved","state":"BRIDGE-PENDING","token":"PROVEN-WITH-AXIOMS"},"rocq":{"declarations":[],"receipts":[],"route":"unavailable","state":"NOT-INVENTORIED","token":"OPEN"}},"notes":"What is proved is the two directional facts of A2. Totality is stated in Lean (FateA.le_total); transitivity and antisymmetry are not mechanised in any prover, so 'chain' is stronger than the mechanised content.","reference":{"idris2":{"declarations":["Trope.Soundness.fateDroppedLtePredicated","Trope.Soundness.fatePredicatedNotLteDropped"],"state":"not-a-leg (PROOF-POLICY 8.1 excludes engineering provers from the PWG ladder)","token":"PROVEN"}},"title":"Fate is a chain (A2)"},{"foundation_diverse_witness":null,"id":"veridicality-derivation","kind":"theory","legs":{"agda":{"declarations":["TB.Honest.fate-deceptive-unique","TB.Honest.bond-deceptive-unique","TB.Honest.merge-deceptive-unique"],"receipts":["agda-c0eb4f1"],"route":"re-proved","state":"AGDA-VERIFIED","token":"PROVEN"},"lean":{"declarations":[],"receipts":[],"route":"unavailable","state":"NOT-INVENTORIED","token":"OPEN"},"rocq":{"declarations":[],"receipts":[],"route":"unavailable","state":"NOT-INVENTORIED","token":"OPEN"}},"notes":"The 'exactly three' half rests on the three uniqueness lemmas plus the construction of Grade; Trope.Veridicality.deceptiveDuals is a tuple value and states no proposition, so it is not cited as evidence here.","reference":{"idris2":{"declarations":["Trope.Veridicality.fateDeceptiveUnique","Trope.Veridicality.bondDeceptiveUnique","Trope.Veridicality.mergeDeceptiveUnique"],"state":"not-a-leg (PROOF-POLICY 8.1 excludes engineering provers from the PWG ladder)","token":"PROVEN"}},"title":"Veridicality Derivation"},{"foundation_diverse_witness":null,"id":"honest-generation","kind":"theory","legs":{"agda":{"declarations":["TB.Honest.genFate","TB.Honest.genBond","TB.Honest.genMerge","TB.Honest.honest-closed-|>"],"receipts":["agda-c0eb4f1"],"route":"re-proved","state":"AGDA-VERIFIED","token":"PROVEN"},"lean":{"declarations":[],"receipts":[],"route":"unavailable","state":"NOT-INVENTORIED","token":"OPEN"},"rocq":{"declarations":[],"receipts":[],"route":"unavailable","state":"NOT-INVENTORIED","token":"OPEN"}},"notes":"","reference":{"idris2":{"declarations":["Trope.Generation.genFate","Trope.Generation.genBond","Trope.Generation.genMerge"],"state":"not-a-leg (PROOF-POLICY 8.1 excludes engineering provers from the PWG ladder)","token":"PROVEN"}},"title":"Honest Generation"},{"foundation_diverse_witness":null,"id":"hc4-coherence","kind":"theory","legs":{"agda":{"declarations":[],"receipts":[],"route":"unavailable","state":"AGDA-PENDING","token":"OPEN"},"lean":{"declarations":[],"receipts":[],"route":"unavailable","state":"NOT-INVENTORIED","token":"OPEN"},"rocq":{"declarations":[],"receipts":[],"route":"unavailable","state":"NOT-INVENTORIED","token":"OPEN"}},"notes":"Idris2 only. No Agda source, so ungraded under 8.1 however sound the Idris2 proof is.","reference":{"idris2":{"declarations":["Trope.Veridicality.epsilonHonest","Trope.Grade.epsilonCoherent"],"state":"not-a-leg (PROOF-POLICY 8.1 excludes engineering provers from the PWG ladder)","token":"PROVEN"}},"title":"The unit is non-deceptive and HC-4-coherent"},{"foundation_diverse_witness":null,"id":"C1","kind":"theory","legs":{"agda":{"declarations":["TB.Grade.grade-conical"],"receipts":["agda-c0eb4f1"],"route":"re-proved","state":"AGDA-VERIFIED","token":"PROVEN"},"lean":{"declarations":["GradeR.conical","FateA.conical"],"receipts":["lean-boundary-c0eb4f1"],"route":"re-proved","state":"BRIDGE-PENDING","token":"PROVEN-WITH-AXIOMS"},"rocq":{"declarations":[],"receipts":[],"route":"unavailable","state":"NOT-INVENTORIED","token":"OPEN"}},"notes":"","reference":{"idris2":{"declarations":[],"state":"not-a-leg (PROOF-POLICY 8.1 excludes engineering provers from the PWG ladder)","token":"OPEN"}},"title":"C1 (conicality)"},{"foundation_diverse_witness":null,"id":"C2","kind":"theory","legs":{"agda":{"declarations":["TB.Tier.Q-cancel-r","TB.Tier.core-closed-|>"],"receipts":["agda-c0eb4f1"],"route":"re-proved","state":"AGDA-VERIFIED","token":"PROVEN"},"lean":{"declarations":["GradeR.gradeR_leftCancel_iff","GradeR.gradeR_not_leftCancel","GradeR.gDroppedR_not_cancel","FateA.atten_cancel_on_normalForms"],"receipts":["lean-boundary-c0eb4f1"],"route":"re-proved","state":"BRIDGE-PENDING","token":"PROVEN-WITH-AXIOMS"},"rocq":{"declarations":[],"receipts":[],"route":"unavailable","state":"NOT-INVENTORIED","token":"OPEN"}},"notes":"The normal-form half is proved on the fate coordinate only (FateA.atten_cancel_on_normalForms); there is no grade-level normal-form cancellation theorem. Amendment (A3) is not modelled in the Agda, whose carrier is the unnormalised one.","reference":{"idris2":{"declarations":[],"state":"not-a-leg (PROOF-POLICY 8.1 excludes engineering provers from the PWG ladder)","token":"OPEN"}},"title":"C2 (the cancellation boundary)"},{"foundation_diverse_witness":null,"id":"tier2-membership","kind":"theory","legs":{"agda":{"declarations":["TB.Tier.unknown-not-cancel","TB.Tier.total-honest-not-cancel","TB.Tier.falsified-not-cancel","TB.Tier.dropped-honest-not-cancel","TB.Tier.predicated-honest-not-cancel","TB.Tier.severed-honest-not-cancel","TB.Tier.Q-cancelʳ"],"receipts":["agda-c0eb4f1"],"route":"re-proved","state":"AGDA-PENDING","token":"OPEN"},"lean":{"declarations":["Bond.withheld_honest_not_cancel","Merge.fused_honest_not_cancel","Fate.atten_not_cancel","Grade.grade_leftCancel_iff","GradeR.gradeR_leftCancel_iff","FateA.leftCancelWitness"],"receipts":["lean-boundary-c0eb4f1"],"route":"re-proved","state":"BRIDGE-PENDING","token":"PROVEN-WITH-AXIOMS"},"rocq":{"declarations":[],"receipts":[],"route":"unavailable","state":"NOT-INVENTORIED","token":"OPEN"}},"notes":"Agda states six of the non-cancellativity witnesses (fate and bond) plus the positive right-cancellation Q-cancelʳ, so the Agda leg is NOT unavailable. It is OPEN because the exhaustive characterisation is not stated in Agda: there is no Agda counterpart of grade_leftCancel_iff, and no Agda witness on the merge coordinate. Lean carries the exhaustive iff. Grade.grade_leftCancel_iff is over the historical pre-ratification carrier; the ratified restatement is GradeR.gradeR_leftCancel_iff. Ungraded because the Agda token is OPEN (§8.1), not for want of an Agda source.","reference":{"idris2":{"declarations":[],"state":"not-a-leg (PROOF-POLICY 8.1 excludes engineering provers from the PWG ladder)","token":"OPEN"}},"title":"Tier-2 membership, exhaustive"},{"foundation_diverse_witness":null,"id":"C3","kind":"theory","legs":{"agda":{"declarations":["TB.Tier.fate-tier-meet-hom-fails"],"receipts":["agda-c0eb4f1"],"route":"re-proved","state":"AGDA-VERIFIED","token":"PROVEN"},"lean":{"declarations":["FateA.dropped_still_not_cancel","Delta.fidelity_total_honest_not_cancel"],"receipts":["lean-boundary-c0eb4f1"],"route":"re-proved","state":"BRIDGE-PENDING","token":"PROVEN-WITH-AXIOMS"},"rocq":{"declarations":[],"receipts":[],"route":"unavailable","state":"NOT-INVENTORIED","token":"OPEN"}},"notes":"The ratified witness is dropped |>f atten unknown against the tier meet. The pre-ratification witness dropped |>f falsified = dropped was reversed by amendment (A1) and is retained as history only.","reference":{"idris2":{"declarations":[],"state":"not-a-leg (PROOF-POLICY 8.1 excludes engineering provers from the PWG ladder)","token":"OPEN"}},"title":"C3 (partition; tier closure is not a homomorphism)"},{"foundation_diverse_witness":null,"id":"O1-carrier","kind":"theory","legs":{"agda":{"declarations":[],"receipts":[],"route":"unavailable","state":"AGDA-PENDING","token":"OPEN"},"lean":{"declarations":["Trope.GradeR.atom_factorization","Trope.nine_families","Trope.family_realized","Trope.families_disjoint","Trope.fateFamily_none_iff"],"receipts":["lean-boundary-c0eb4f1"],"route":"re-proved","state":"BRIDGE-PENDING","token":"PROVEN-WITH-AXIOMS"},"rocq":{"declarations":[],"receipts":[],"route":"unavailable","state":"NOT-INVENTORIED","token":"OPEN"}},"notes":"Lean only, so ungraded under 8.1. Mechanised: the factorisation into six slot projections, and separately the nine-label classification over the coordinate value types. NOT mechanised: the link between them. No theorem maps a grade's slot projections to AtomFamily, and the emb*_one lemmas that would begin that bridge are stated but used by nothing, so 'drawn from the nine families' and 'exhaustive' are argued in a docstring rather than stated.","reference":{"idris2":{"declarations":[],"state":"not-a-leg (PROOF-POLICY 8.1 excludes engineering provers from the PWG ladder)","token":"OPEN"}},"title":"O1-carrier (atom factorisation)"},{"foundation_diverse_witness":null,"id":"tropical-Bprime","kind":"theory","legs":{"agda":{"declarations":[],"receipts":[],"route":"unavailable","state":"AGDA-PENDING","token":"OPEN"},"lean":{"declarations":["piR_hom","piR_one","piRHom","piR_nontrivial","piR_surjective","piR_sighted","phiR_sighted","phiId_not_hom","sighted_forces_squash","squash_top","squash_ne_unknown","squash_add"],"receipts":["lean-factorisation-c0eb4f1"],"route":"re-proved","state":"BRIDGE-PENDING","token":"PROVEN-WITH-AXIOMS"},"rocq":{"declarations":[],"receipts":[],"route":"unavailable","state":"NOT-INVENTORIED","token":"OPEN"}},"notes":"Lean only, so ungraded under 8.1. sighted_forces_squash concludes f (atten Delta.unknown) /= Delta.unknown: a sighted homomorphism must send atten Unknown AWAY from the deceptive top, not onto it.","reference":{"idris2":{"declarations":[],"state":"not-a-leg (PROOF-POLICY 8.1 excludes engineering provers from the PWG ladder)","token":"OPEN"}},"title":"Tropical factorisation, (B-prime) sighted"},{"foundation_diverse_witness":null,"id":"theorem-b-t1","kind":"theory","legs":{"agda":{"declarations":["TB.Syntax","TB.Grade","TB.Tier"],"receipts":["agda-c0eb4f1"],"route":"re-proved","state":"AGDA-VERIFIED","token":"PROVEN"},"lean":{"declarations":[],"receipts":[],"route":"unavailable","state":"NOT-INVENTORIED","token":"OPEN"},"rocq":{"declarations":[],"receipts":[],"route":"unavailable","state":"NOT-INVENTORIED","token":"OPEN"}},"notes":"","reference":{"idris2":{"declarations":[],"state":"not-a-leg (PROOF-POLICY 8.1 excludes engineering provers from the PWG ladder)","token":"OPEN"}},"title":"Theorem B Target 1 - intrinsic graded calculus"},{"foundation_diverse_witness":null,"id":"theorem-b-t2","kind":"theory","legs":{"agda":{"declarations":["TB.Substitution.cut-preserves-grade","TB.Substitution.cut-grade-comm"],"receipts":["agda-c0eb4f1"],"route":"re-proved","state":"AGDA-VERIFIED","token":"PROVEN"},"lean":{"declarations":[],"receipts":[],"route":"unavailable","state":"NOT-INVENTORIED","token":"OPEN"},"rocq":{"declarations":[],"receipts":[],"route":"unavailable","state":"NOT-INVENTORIED","token":"OPEN"}},"notes":"The v0.1 sharpness refutation (cut-orientation-matters, cut-symmetric-fails) was retired by amendment (A1) and is replaced by cut-grade-comm: the cut is reorderable.","reference":{"idris2":{"declarations":[],"state":"not-a-leg (PROOF-POLICY 8.1 excludes engineering provers from the PWG ladder)","token":"OPEN"}},"title":"Theorem B Target 2 - grade-exact substitution"},{"foundation_diverse_witness":null,"id":"theorem-b-t3","kind":"theory","legs":{"agda":{"declarations":["TB.Reduction.beta-app","TB.Reduction.beta-let","TB.Reduction.let-redex-grade","TB.Reduction.let-tier-preserved","TB.Reduction.seq-stays-core"],"receipts":["agda-c0eb4f1"],"route":"re-proved","state":"AGDA-VERIFIED","token":"PROVEN"},"lean":{"declarations":[],"receipts":[],"route":"unavailable","state":"NOT-INVENTORIED","token":"OPEN"},"rocq":{"declarations":[],"receipts":[],"route":"unavailable","state":"NOT-INVENTORIED","token":"OPEN"}},"notes":"Narrow and intrinsic. The step relation has exactly two constructors, each requiring the substituted argument at grade epsilon, with no congruence rule and no step for any effect former. Preservation holds by construction because the relation is indexed at the same type and grade on both sides, not by induction. There is no progress theorem. The fix case is open (CO-1).","reference":{"idris2":{"declarations":[],"state":"not-a-leg (PROOF-POLICY 8.1 excludes engineering provers from the PWG ladder)","token":"OPEN"}},"title":"Theorem B Target 3 - subject reduction, beta/let core"},{"foundation_diverse_witness":null,"id":"theorem-b-t4","kind":"theory","legs":{"agda":{"declarations":["TB.Honest"],"receipts":["agda-c0eb4f1"],"route":"re-proved","state":"AGDA-VERIFIED","token":"PROVEN"},"lean":{"declarations":[],"receipts":[],"route":"unavailable","state":"NOT-INVENTORIED","token":"OPEN"},"rocq":{"declarations":[],"receipts":[],"route":"unavailable","state":"NOT-INVENTORIED","token":"OPEN"}},"notes":"","reference":{"idris2":{"declarations":[],"state":"not-a-leg (PROOF-POLICY 8.1 excludes engineering provers from the PWG ladder)","token":"OPEN"}},"title":"Theorem B Target 4 - Honest Generation and Veridicality"},{"foundation_diverse_witness":null,"id":"grade-soundness-exact","kind":"theory","legs":{"agda":{"declarations":[],"receipts":[],"route":"unavailable","state":"AGDA-PENDING","token":"OPEN"},"lean":{"declarations":[],"receipts":[],"route":"unavailable","state":"NOT-INVENTORIED","token":"OPEN"},"rocq":{"declarations":[],"receipts":[],"route":"unavailable","state":"NOT-INVENTORIED","token":"OPEN"}},"notes":"Idris2 only, so ungraded under 8.1.","reference":{"idris2":{"declarations":["Trope.Soundness.soundFromExact"],"state":"not-a-leg (PROOF-POLICY 8.1 excludes engineering provers from the PWG ladder)","token":"PROVEN"}},"title":"Grade soundness, exact lowering"},{"foundation_diverse_witness":null,"id":"tsub-soundness","kind":"theory","legs":{"agda":{"declarations":[],"receipts":[],"route":"unavailable","state":"AGDA-PENDING","token":"OPEN"},"lean":{"declarations":[],"receipts":[],"route":"unavailable","state":"NOT-INVENTORIED","token":"OPEN"},"rocq":{"declarations":[],"receipts":[],"route":"unavailable","state":"NOT-INVENTORIED","token":"OPEN"}},"notes":"Idris2 only, so ungraded under 8.1.","reference":{"idris2":{"declarations":["Trope.Soundness.subSound"],"state":"not-a-leg (PROOF-POLICY 8.1 excludes engineering provers from the PWG ladder)","token":"PROVEN"}},"title":"T-Sub soundness"},{"foundation_diverse_witness":null,"id":"verdict-soundness","kind":"engineering","legs":{"agda":{"declarations":[],"receipts":[],"route":"unavailable","state":"AGDA-PENDING","token":"OPEN"},"lean":{"declarations":[],"receipts":[],"route":"unavailable","state":"NOT-INVENTORIED","token":"OPEN"},"rocq":{"declarations":[],"receipts":[],"route":"unavailable","state":"NOT-INVENTORIED","token":"OPEN"}},"notes":"Classified engineering: the statement is about the shipped checker's verdict function over its own types, so 8.1 puts it off the ladder entirely and it carries section 5 tokens only. Note that verdictSound is typed over Grade while the shipped checker's floor is a different type decided by a different predicate, and no lemma connects them.","reference":{"idris2":{"declarations":["Trope.Soundness.verdictSound"],"state":"not-a-leg (PROOF-POLICY 8.1 excludes engineering provers from the PWG ladder)","token":"PROVEN"}},"title":"Verdict soundness (corollary)"},{"foundation_diverse_witness":null,"id":"grade-soundness-core","kind":"theory","legs":{"agda":{"declarations":["TB.Reduction","TB.Substitution.cut-preserves-grade"],"receipts":["agda-c0eb4f1"],"route":"re-proved","state":"AGDA-VERIFIED","token":"PROVEN"},"lean":{"declarations":[],"receipts":[],"route":"unavailable","state":"NOT-INVENTORIED","token":"OPEN"},"rocq":{"declarations":[],"receipts":[],"route":"unavailable","state":"NOT-INVENTORIED","token":"OPEN"}},"notes":"Inherits Target 3's fragment: the beta/let core only, with the fix case open (CO-1).","reference":{"idris2":{"declarations":[],"state":"not-a-leg (PROOF-POLICY 8.1 excludes engineering provers from the PWG ladder)","token":"OPEN"}},"title":"Grade soundness, beta/let core"}]}