Two honest tiers. 5 LOCKED-proven (kernel-verified) {F1, F11, F12, F18, F19} @ c7c0ba17 — locked kernel: 749 decl / 14 axioms / 163 sorries, sorry-free, Lean-core axioms only. The locked count is EXACTLY 5 and never inflated. EXPERIMENTAL · CI-green on main @ 044eb098 — experimental scope: 1323 decl / 23 axioms (22 unique) / 307 sorries; waves 5–18 (≈119 instilled cards, incl. CUT-2, CF-13/17 and the Wave13–18 packs — CF-22 DPO-KL-simplex, CF-23 binary Pinsker, CF-24 Aczél, CF-25 Λ scale-invariance, CF-26 abacus, CF-27 monDEQ, CF-28 recurrent-depth, CUT-1 forward fragment) are EXPERIMENTAL · CI-green, additive, never folded into the locked 5. SLSA L1 honest · L2 roadmap. No fabricated metrics · no AGI.
Lutar.Round13.lambda_unique_of_separable proves Λ uniqueness as a theorem CONDITIONAL on slice-multiplicativity (separability) under A1,A2,A3,A5 — with no new axiom. This gets Λ off bare conjecture (conditionally); the UNCONDITIONAL claim stays Conjecture 1.
The five organs ARE the participant-general governed-AI model. The unit of agreement shifts from identical output to certified semantic admissibility: the BRAIN/YACHAY reasons (divergent paths OK), the HEART/YUYAY 13-axis gate certifies admissibility (deny-by-default), the SKELETON/Khipu BFT quorum = Semantic Quorum Assurance (Wave23 conditional safety theorem; unconditional = Conjecture 2), the CIRCULATORY/YAWAR append-only receipt bus = Epistemic State Replication + Verifiable Semantic Rollback (receipts/replay live; full ESR = roadmap), and the NERVOUS/OTel spans carry provenance.
Honest scope: locked-proven stays EXACTLY 5; Λ = Conjecture 1; Khipu BFT safety = Conjecture 2 (Wave23 conditional only). Grounded entirely in SZL’s own DOI-stamped prior art — NO external paper is the source of GPD.
SZL Zenodo prior art: 10.5281/zenodo.19867281 · .19934129 · .20020846 · .20020845 · .20020841 · .20174600
Round13.maxAgg_ne_Lambda satisfies A1–A5 yet is not Λ). Uniqueness holds only within strengthened classes (Setα / Setδ, conditional on declared bridge axioms).
The geometric-mean trust aggregator is per-component strictly monotone: improving any input strictly raises the fused trust. NO uniqueness of Λ asserted — Conjecture 1 untouched.
#print axioms: Lutar.Wave8.LambdaMono.gmean_strict_mono — [propext, Classical.choice, Quot.sound]
PR #197 @ 7885fd9 · Wave8/LambdaMono.lean
The min-gate vmin is the UNIQUE monotone, diagonal, conservative gate — the weakest-link trust gate is the ONLY policy satisfying the safety axioms; no permissive aggregator can sneak in. Backs the YUYAY deny-by-default conjunction.
#print axioms: Lutar.Wave8.MinGate.deny_by_default_unique — [propext]
PR #196 @ b1c840f · Wave8/MinGate.lean
Split-conformal coverage satisfies a two-sided ⌈·⌉ bound — finite-sample, distribution-free marginal-coverage guarantee for the trust intervals on Λ.
#print axioms: Lutar.Wave8.Conformal.conformal_marginal_coverage — [propext, Quot.sound]
PR #196 @ b1c840f · Wave8/Conformal.lean
Geometric mean ≤ arithmetic mean: the Λ aggregator can never inflate trust above the naive average.
#print axioms: wave-5 — 0 new axioms (Mathlib-dep CI-green)
PR #186 @ b71114cf
A convex combination of PSD, unit-trace matrices is again a valid density matrix — convexity of the mixed-state set. Underpins probabilistic ensemble reasoning in the YACHAY quantum-mind region.
#print axioms: Lutar.Wave8.DensityMixture.density_matrix_mixture — [propext, Classical.choice, Quot.sound]
PR #197 @ 7885fd9 · Wave8/DensityMixture.lean
A strictly diagonally-dominant real governance weight matrix is invertible, so weighted aggregation has a unique solution — no zero-eigenvalue collapse of the governance operator. (ℂ variant left honestly as ROADMAP — shipped real-valued only, sorryAx-free.)
#print axioms: Lutar.Wave8.Gershgorin.governance_nonsingular_real — [propext, Classical.choice, Quot.sound]
PR #197 @ 7885fd9 · Wave8/Gershgorin.lean
A PAC-Bayes generalization envelope bounds true routing risk by empirical risk plus a KL complexity term — confidence on model routing.
#print axioms: wave-7 — 0 new axioms
PR #190 @ d6a232ba
For an injective hash step H, if any payload entry differs then the resulting head-hash differs — append-only hash chains are tamper-evident. The formal core behind receipt/audit-trail integrity.
#print axioms: Lutar.Wave8.HashChain.hashchain_tamper_evident — [propext]
PR #196 @ b1c840f · Wave8/HashChain.lean
Every hop in the governed loop leaves exactly one chained receipt — no silent drop or reorder.
#print axioms: agentic-loop — axiom-free core
PR #188 @ 2ede47a2
Erasure tolerance: data is recoverable IFF at least 6 of 10 shards survive — the resilience arithmetic for the receipt/payload encoding.
#print axioms: f18_* — [propext, Classical.choice, Quot.sound]
lutar-lean @ c7c0ba17
Replaying the SAME recorded log from the same initial state yields a BIT-IDENTICAL trace — no drift. Underpins the Khipu replay-hash gate.
#print axioms: f1_replay_fold_deterministic — [propext, Classical.choice, Quot.sound]
lutar-lean PuriqFormulaLean.lean @ c7c0ba17
Re-running a recorded run reproduces a byte-identical receipt chain.
#print axioms: P4 — PROVEN, axiom-free
PR #188 @ 2ede47a2
Fold-replay of an append-only reciprocity log conserves the balance invariant (Axelrod–Hamilton tit-for-tat parity).
#print axioms: f11_ayni_reciprocity_conservation — [propext, Classical.choice, Quot.sound]
lutar-lean PuriqFormulaLean.lean @ c7c0ba17
Any single-receipt mutation makes re-verify reject. AXIOM-GATED on hashFn_collision_resistant (NIST FIPS 180-4, disclosed).
#print axioms: P5 — AXIOM-GATED [hashFn_collision_resistant]
PR #188 @ 2ede47a2
For an injective hash step H, if any payload entry differs then the resulting head-hash differs — append-only hash chains are tamper-evident. The formal core behind receipt/audit-trail integrity.
#print axioms: Lutar.Wave8.HashChain.hashchain_tamper_evident — [propext]
PR #196 @ b1c840f · Wave8/HashChain.lean
Simplex/RTA run-time-assurance: a monitored switch to a verified recovery controller keeps the system in the safe set for ALL time. Backbone of fail-safe autonomy and the HUKLLA deadman reflex.
#print axioms: Lutar.Wave8.Simplex.simplex_safety_invariant — [propext]
PR #196 @ b1c840f · Wave8/Simplex.lean
The classic 3-node / 1-fault Byzantine impossibility — the formal n ≥ 3f+1 lower bound. Justifies consensus/quorum sizing in the shared mesh and rejects under-provisioned fault tolerance.
#print axioms: Lutar.Wave8.Byzantine.byzantine_impossibility_3_1 — does not depend on any axioms
PR #196 @ b1c840f · Wave8/Byzantine.lean
Re-running a recorded run reproduces a byte-identical receipt chain.
#print axioms: P4 — PROVEN, axiom-free
PR #188 @ 2ede47a2
Replaying the SAME recorded log from the same initial state yields a BIT-IDENTICAL trace — no drift. Underpins the Khipu replay-hash gate.
#print axioms: f1_replay_fold_deterministic — [propext, Classical.choice, Quot.sound]
lutar-lean PuriqFormulaLean.lean @ c7c0ba17
A strictly diagonally-dominant real governance weight matrix is invertible, so weighted aggregation has a unique solution — no zero-eigenvalue collapse of the governance operator. (ℂ variant left honestly as ROADMAP — shipped real-valued only, sorryAx-free.)
#print axioms: Lutar.Wave8.Gershgorin.governance_nonsingular_real — [propext, Classical.choice, Quot.sound]
PR #197 @ 7885fd9 · Wave8/Gershgorin.lean
Every hop in the governed loop leaves exactly one chained receipt — no silent drop or reorder.
#print axioms: agentic-loop — axiom-free core
PR #188 @ 2ede47a2
The axiom-disclosure gate is sound; locked_count_five proves there are EXACTLY 5 locked entries with kernel-only axioms (= by decide, no axioms). Mechanically enforces "no hidden axioms".
#print axioms: Lutar.Wave8.AxiomDisclosure.disclosure_sound — [propext, Quot.sound] · locked_count_five — no axioms
PR #196 @ b1c840f · Wave8/AxiomDisclosure.lean
For an injective hash step H, if any payload entry differs then the resulting head-hash differs — append-only hash chains are tamper-evident. The formal core behind receipt/audit-trail integrity.
#print axioms: Lutar.Wave8.HashChain.hashchain_tamper_evident — [propext]
PR #196 @ b1c840f · Wave8/HashChain.lean
The classic 3-node / 1-fault Byzantine impossibility — the formal n ≥ 3f+1 lower bound. Justifies consensus/quorum sizing in the shared mesh and rejects under-provisioned fault tolerance.
#print axioms: Lutar.Wave8.Byzantine.byzantine_impossibility_3_1 — does not depend on any axioms
PR #196 @ b1c840f · Wave8/Byzantine.lean
Split-conformal coverage satisfies a two-sided ⌈·⌉ bound — finite-sample, distribution-free marginal-coverage guarantee for the trust intervals on Λ.
#print axioms: Lutar.Wave8.Conformal.conformal_marginal_coverage — [propext, Quot.sound]
PR #196 @ b1c840f · Wave8/Conformal.lean
Simplex/RTA run-time-assurance: a monitored switch to a verified recovery controller keeps the system in the safe set for ALL time. Backbone of fail-safe autonomy and the HUKLLA deadman reflex.
#print axioms: Lutar.Wave8.Simplex.simplex_safety_invariant — [propext]
PR #196 @ b1c840f · Wave8/Simplex.lean
The closest-point-of-approach time is the UNIQUE minimizer of squared separation. Formal anchor for killinchu collision / conflict-risk timing.
#print axioms: Lutar.Wave8.CPA.cpa_unique — [propext, Classical.choice, Quot.sound]
PR #197 @ 7885fd9 · Wave8/CPA.lean
A convex combination of PSD, unit-trace matrices is again a valid density matrix — convexity of the mixed-state set. Underpins probabilistic ensemble reasoning in the YACHAY quantum-mind region.
#print axioms: Lutar.Wave8.DensityMixture.density_matrix_mixture — [propext, Classical.choice, Quot.sound]
PR #197 @ 7885fd9 · Wave8/DensityMixture.lean
A PAC-Bayes generalization envelope bounds true routing risk by empirical risk plus a KL complexity term — confidence on model routing.
#print axioms: wave-7 — 0 new axioms
PR #190 @ d6a232ba
A runtime monitor that computes a signed robustness margin ρ: Sat ⇒ ρ≥0 and ρ>0 ⇒ Sat (NOT the false iff at ρ=0). Backs Sensor-Fusion / STL Monitor.
#print axioms stl_robustness_sound — kernel-only [propext, Classical.choice, Quot.sound]
Wave10/STLRobustness.lean · PR #200
Fuse two sensors without cross-covariance; the fused information matrix is a non-negative convex combination of PSD matrices ⇒ valid (PSD), conservative uncertainty. Powers Sensor-Fusion.
#print axioms covariance_intersection_psd — kernel-only [propext, Classical.choice, Quot.sound]
Wave9/CovarianceIntersection.lean · PR #199
Pre-flight gate: a strictly diagonally-dominant command/trust-weight matrix has 0 in no Gershgorin disc ⇒ nonsingular (det ≠ 0). Field-general (incl. ℂ) — distinct from the Wave8 ℝ determinant card.
#print axioms gershgorin_nonsingular — kernel-only [propext, Classical.choice, Quot.sound]
Wave9/Gershgorin.lean · PR #199
k edge-disjoint routes survive any k-1 link failures; by Menger cut/path duality the min-cut equals the number of edge-disjoint paths. Pairs with Tactical Routing. (cut_disconnects · path_refutes_cut)
#print axioms avoiding_reach_le_full · cut_disconnects · path_refutes_cut — kernel-only
Wave10/ReachabilityRedundancy.lean + Wave9/Menger.lean · PR #200
Re-verifiable Merkle inclusion proofs; deterministic replay of an ordered log yields the same final state and localizes a tampered entry (first divergence). Backs the signed-receipt / audit surface.
#print axioms replay_deterministic · tamper_localized — kernel-only [propext, Classical.choice, Quot.sound]
Wave10/ReplayDeterminism.lean + Wave9/Merkle.lean · PR #200
Safety holds iff n > 3t + d + 2q (sharper than n>3t); any two intersecting majority quorums can never decide differently ⇒ no split-brain (unique decision). Sizes the 3-of-4 C2 consensus mesh.
#print axioms quorum_unique_decision · majority_quorums_intersect — kernel-only
Wave10/QuorumIntersection.lean + Wave9/BasilicBDB.lean · PR #200
Λ uniqueness PROVEN as a theorem CONDITIONAL on slice-multiplicativity (separability) under A1,A2,A3,A5 — kernel-clean, no new axiom. Gets Λ off bare conjecture (conditionally). UNCONDITIONAL Λ uniqueness stays Conjecture 1 (machine-checked FALSE). NOT folded into the locked 5.
#print axioms Lutar.Round13.lambda_unique_of_separable — [propext, Classical.choice, Quot.sound]
Round13/LambdaSeparable.lean · PR #202 (Wave12)
A deep-equilibrium / fixed-point layer has a UNIQUE equilibrium, Lipschitz in its input with constant Lx/(1−K): dist(z*(x),z*(y)) ≤ Lx/(1−K)·dist(x,y). Equilibrium reasoning is provably well-posed — a stability margin for code/forecast routing.
#print axioms equilibrium_dist_le / equilibrium_lipschitz — [propext, Classical.choice, Quot.sound]
round5/OuroLoopInputLipschitz.lean · PR #202 (Wave12)
Recursive fp summation under the standard rounding model has a forward error bound |recSum − Σxi| ≤ ((1+u)^(n−1)−1)·Σ|xi| (Higham §2.2). A numeric-stability badge for any aggregation/scoring sum.
#print axioms Lutar.Khipu.NumericStability.recSum_error_le — [propext, Classical.choice, Quot.sound]
Khipu/NumericStability.lean · PR #202 (Wave12)
If a valid replay-root exists among candidates, the search provably finds one — PRNG replay-root lookup is complete. Closed a baseline sorry.
#print axioms Lutar.PRNG.findReplayRoot_complete — [propext, Quot.sound]
PRNG/K10v2_ReplayRoot.lean · PR #203 (Wave13)
Under n ≥ 3f+1, two large quorums of single-valued voters must agree. HONEST SCOPE: explicitly the NON-Byzantine shadow — it is NOT Khipu Conjecture 2, which stays OPEN (a faulty organ can still equivocate).
#print axioms quorum_agreement_single_valued_vote — [propext, Classical.choice, Quot.sound]
Wave13/Sweep.lean · PR #203 (Wave13)
If the harmonic mean of positive resources falls below a threshold, some single resource must too — a clean Hardy–Littlewood–Pólya bottleneck detector for the mesh.
#print axioms Lutar.Wave13.Sweep.hm_bottleneck_clean — [propext, Classical.choice, Quot.sound]
Wave13/Sweep.lean · PR #203 (Wave13)
For an alternating series with antitone terms, the truncation error is bounded by the first omitted term: |Σ_{i<N}(−1)^i a_i − L| ≤ a_N. A certified π/series error budget.
#print axioms leibniz_remainder_bound / madhava_alt_series_bound_clean — [propext, Classical.choice, Quot.sound]
Wave14/LeibnizRemainder.lean · PR #204 (Wave14)
Two distinct degree-<k RS codewords differ in ≥ n−k+1 of n points — the achievability (lower) half of the Singleton/MDS bound. HONEST: the upper bound / full MDS equality stays a sorry.
#print axioms rs_distance_lower_bound / agreement_card_lt_of_degree_lt — [propext, Classical.choice, Quot.sound]
Wave14/ReedSolomonDistance.lean · PR #204 (Wave14)
An efficient (social-welfare-maximising) outcome always exists and the VCG truthfulness core holds — honest reporting is the dominant-strategy ingredient. Incentive-compatibility anchor.
#print axioms exists_efficient_outcome / efficientOutcome_maximises / vcg_truthfulness_core — [propext, Classical.choice, Quot.sound]
Wave14/VCGEfficiency.lean · PR #204 (Wave14)
The log-sum and Gibbs inequalities — the correctly-stated information-theory DPI core (Cover–Thomas 2.7.1 / 2.6.3). HONEST: does NOT repair the in-tree DPO klDivergence/pinsker, which stay FALSE-as-stated (no simplex hypothesis).
#print axioms log_sum_inequality / gibbs_inequality — [propext, Classical.choice, Quot.sound]
Wave14/LogSumInequality.lean · PR #204 (Wave14)
CONDITIONALLY repairs the FALSE-as-stated in-tree DPO axiom: KL(p‖q) ≥ 0 once p,q ∈ the probability simplex (Gibbs). Live demo KL=0.0880 ≥ 0 (χ²=0.1917). HONEST: the UNCONDITIONAL DPO axiom klDivergence_nonneg stays FALSE-as-stated. Independent confirmation: χPO (arXiv:2407.13399), f-DPO (arXiv:2309.16240).
#print axioms klDivergence_nonneg_simplex / dpo_klDivergence_nonneg_on_simplex — [propext, Classical.choice, Quot.sound]
Wave15/DPOKLSimplex.lean · PR #205 (Wave15)
The full binary Pinsker inequality 2·(p−q)² ≤ KL(Bern p ‖ Bern q) — the long-sought headline (previously only a named Lean axiom). Live demo KL=0.0823 ≥ 2·TV²=0.0800. A confidence-margin bound for any binary gate. HONEST: experimental CI-green, NOT folded into the locked 5.
#print axioms binary_pinsker / binary_inv_sum_ge_four — [propext, Classical.choice, Quot.sound]
Wave17/BinaryPinsker.lean · PR #207 (Wave17)
The geometric-binary mean satisfies the FULL Aczél QAM axiom set (idempotency, commutativity, homogeneity, strict monotonicity) — real progress on the CUT-1 route. Regularity-free QAM characterization (Burai–Kiss–Szokol, arXiv:2107.07391) shows bisymmetry gives continuity for free.
#print axioms geoBin_idem / geoBin_comm / geoBin_homog / geoBin_mono — [propext, Classical.choice, Quot.sound]
Wave16/GeoBinAczel.lean · PR #206 (Wave16)
Λ is invariant under affine reparametrization of its quasi-arithmetic generator and under axis normalization — rescaling the trust axes leaves the Λ verdict fixed. Convex-duality backing (Nielsen, arXiv:2301.10980).
#print axioms lambda_scale_axes / lambda_normalization_invariant — [propext, Classical.choice, Quot.sound]
Wave16/LambdaScaleInvariance.lean · PR #206 (Wave16)
Place-value (abacus) encode/decode round-trips exactly Σ digit_i·base^i = value — a positional-number-system soundness lemma underpinning deterministic integer serialization in receipts.
#print axioms Lutar.Wave16.abacus_place_value — [propext, Classical.choice, Quot.sound]
Wave16/Abacus.lean · PR #206 (Wave16)
A strongly-monotone deep-equilibrium operator has a UNIQUE equilibrium ∃! z*, F(z*)=z* — the fixed-point reasoning layer is provably well-posed. Backs fusion fixed-point and tool-call uniqueness (Winston–Kolter monDEQ).
#print axioms Lutar.Wave17.monDEQ_unique_equilibrium — [propext, Classical.choice, Quot.sound]
Wave17/MonDEQUnique.lean · PR #207 (Wave17)
An r-fold recurrent-depth block from a K-Lipschitz step is Kʳ-Lipschitz overall — depth amplifies (K<1 ⇒ contraction; K>1 ⇒ honest blow-up bound). A stability budget for recurrent-depth estimators (mcleish7/retrofitting-recurrence, Apache-2.0).
#print axioms Lutar.Wave17.recurrent_depth_lipschitz — [propext, Classical.choice, Quot.sound]
Wave17/RecurrentDepthLipschitz.lean · PR #207 (Wave17)
The forward fragment of the CUT-1 unconditional-uniqueness program: generator unique up to affine reparam, exponential midpoint = geometric mean √(xy), and Λ follows CONDITIONALLY (19 axiom-clean theorems). HONEST OPEN GAP: dyadic_image_dense (the dense-domain density step, n-adic recursive construction per Kiss–Shulman 2026) is NOT proven — multi-week roadmap. Λ unconditional uniqueness stays Conjecture 1. NOT folded into the locked 5.
#print axioms generator_unique_up_to_affine / expMidpoint_eq_geom / cut1_conditional_lambda — [propext, Classical.choice, Quot.sound] · GAP: dyadic_image_dense (open sorry)
Wave18/CUT1Forward.lean · PR #208 (Wave18)