certification dict | challenge string | challenge_file string | challenge_sha256 string | config string | depth string | local_check unknown | mathlib_rev string | namespace string | notes list | os_functions list | permitted_axioms list | public_since timestamp[s] | reference_median_proof_lines float64 | reference_solution unknown | schema string | source_commit string | source_repo string | source_run string | statement_provenance string | target_count int64 | targets list | task_id string | toolchain string | title string |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
{
"evidence": "certificates/Run-123/",
"kind": "comparator_dual_kernel",
"public_receipt": true
} | import Mathlib.Analysis.SpecialFunctions.Log.Basic
set_option autoImplicit false
namespace Viridis.Run123
noncomputable section
/-- Bernoulli relative entropy from the paper, on the interior of the unit interval. -/
def binaryKL (q alpha : ℝ) : ℝ :=
q * Real.log (q / alpha) +
(1 - q) * Real.log ((1 - q) / (1 ... | certificates/Run-123/VERIFICATION_STATEMENT_ATTEMPT_2.lean | 2666c33fde1833e3c90891377be5715fe0879970bf17c956aebc8b1fd33521fa | frozen | elementary | {
"axioms_only_permitted": true,
"challenge_elaborates_with_sorry_targets": true,
"date": "2026-11-06",
"lean_kernel_accepts_reference": true,
"mathlib_rev": "8f9d9cff6bd728b17a24e163c9402775d9e6a365",
"pass": true,
"second_kernel": "not run locally",
"toolchain": "leanprover/lean4:v4.28.0"
} | 8f9d9cff6bd728b17a24e163c9402775d9e6a365 | Viridis.Run123 | [] | [
"hcf-kl-chain-rule-habitable-partition"
] | [
"propext",
"Quot.sound",
"Classical.choice"
] | 2026-08-29T00:00:00 | 3 | {
"file": "certificates/Run-123/VERIFICATION_CANDIDATE_ATTEMPT_4.lean",
"sha256": "3d63f48e2b90ecbfe02b3a1b0e2e2df9630fd6db8fe2306f5d1e663976cb438d"
} | eco-lean-bench-task/2 | 2f57ad8f4619bd15e33b943daf26f2f452b02af2 | jdhart81/viridis-canon | Run-123 | frozen statement; public comparator certificate (certificates/) | 7 | [
"Viridis.Run123.kl_chain_rule_habitable_partition",
"Viridis.Run123.kl_ge_binary_habitable_mass",
"Viridis.Run123.binary_kl_monotone_above_reference",
"Viridis.Run123.habitable_threshold_free_energy_floor",
"Viridis.Run123.equality_iff_reference_conditionals",
"Viridis.Run123.reference_shaped_conditionals... | ELB-123 | leanprover/lean4:v4.28.0 | null |
{
"evidence": "certificates/Run-124/",
"kind": "comparator_dual_kernel",
"public_receipt": true
} | import Mathlib.Analysis.Calculus.Deriv.Basic
import Mathlib.Analysis.Calculus.Deriv.Add
import Mathlib.Analysis.Calculus.Deriv.Mul
import Mathlib.Data.Fintype.BigOperators
import Mathlib.Data.Finset.Lattice.Fold
import Mathlib.Tactic.FieldSimp
import Mathlib.Tactic.FinCases
import Mathlib.Tactic.Linarith
import Mathlib... | certificates/Run-124/VERIFICATION_CHALLENGE_ALIGNED_V7.lean | c905cf767bf3788369ac95f4dc0661ee8098ec76e8eb1e400eebe2cc4fe311ec | frozen | substantial | {
"axioms_only_permitted": true,
"challenge_elaborates_with_sorry_targets": true,
"date": "2026-11-06",
"lean_kernel_accepts_reference": true,
"mathlib_rev": "8f9d9cff6bd728b17a24e163c9402775d9e6a365",
"pass": true,
"second_kernel": "not run locally",
"toolchain": "leanprover/lean4:v4.28.0"
} | 8f9d9cff6bd728b17a24e163c9402775d9e6a365 | Viridis.Run124.PaperFormalization | [] | [
"pcs-reliability-derivative-eq-pivotal-probability"
] | [
"propext",
"Quot.sound",
"Classical.choice"
] | 2026-08-29T00:00:00 | 6 | {
"file": "certificates/Run-124/VERIFICATION_CANDIDATE_V6.lean",
"sha256": "ede2d3f68dcc19d77508ab1be245c3be763e32ae4eb69605023b9f3faa31df17"
} | eco-lean-bench-task/2 | 2f57ad8f4619bd15e33b943daf26f2f452b02af2 | jdhart81/viridis-canon | Run-124 | frozen statement; public comparator certificate (certificates/) | 9 | [
"Viridis.Run124.PaperFormalization.reliability_derivative_eq_pivotal_probability",
"Viridis.Run124.PaperFormalization.pivotal_probability_independent_of_own_probability",
"Viridis.Run124.PaperFormalization.local_linear_budget_gain_le_best_ratio",
"Viridis.Run124.PaperFormalization.series_parallel_mixed_differ... | ELB-124 | leanprover/lean4:v4.28.0 | null |
{
"evidence": "certificates/Run-125/",
"kind": "comparator_dual_kernel",
"public_receipt": true
} | /- Engine-3 immutable source unit: Defs.lean -/
import Mathlib.Analysis.Matrix.Spectrum
import Mathlib.LinearAlgebra.Matrix.NonsingularInverse
import Mathlib.Data.Fin.Tuple.Sort
import Mathlib.Analysis.InnerProductSpace.PiL2
import Mathlib.Tactic
/-!
# Run-125 "Symbiotic Bandwidth Bound" — definitions
This file fixes... | certificates/Run-125/VERIFICATION_CHALLENGE_ALIGNED_V2.lean | 2b958be648f24ffebb06af4c28abe31046ea1f52ea67832346fac150b5e80644 | frozen | substantial | {
"axioms_only_permitted": true,
"challenge_elaborates_with_sorry_targets": true,
"date": "2026-11-06",
"lean_kernel_accepts_reference": true,
"mathlib_rev": "8f9d9cff6bd728b17a24e163c9402775d9e6a365",
"pass": true,
"second_kernel": "not run locally",
"toolchain": "leanprover/lean4:v4.28.0"
} | 8f9d9cff6bd728b17a24e163c9402775d9e6a365 | Viridis.Run125.PaperFormalization | [] | [
"shared-channel-coverage"
] | [
"propext",
"Quot.sound",
"Classical.choice"
] | 2026-08-29T00:00:00 | 22.5 | {
"file": "certificates/Run-125/VERIFICATION_CANDIDATE_V2.lean",
"sha256": "adb5eb9b25d9be09f75aa3fc2de64d982e2787b9d2d8de453745b22e601ac6ed"
} | eco-lean-bench-task/2 | 2f57ad8f4619bd15e33b943daf26f2f452b02af2 | jdhart81/viridis-canon | Run-125 | frozen statement; public comparator certificate (certificates/) | 6 | [
"Viridis.Run125.PaperFormalization.shared_channel_inverse",
"Viridis.Run125.PaperFormalization.directional_gain_bounds",
"Viridis.Run125.PaperFormalization.rank_deficient_unit_gain",
"Viridis.Run125.PaperFormalization.worstcase_deadline",
"Viridis.Run125.PaperFormalization.top_subspace_mean_cost",
"Viridi... | ELB-125 | leanprover/lean4:v4.28.0 | null |
{
"evidence": "certificates/Run-126/",
"kind": "comparator_dual_kernel",
"public_receipt": true
} | /- Engine-3 immutable source unit: Entropy.lean -/
import Mathlib
/-!
# Finite-alphabet Shannon information measures
This file develops, from first principles, the discrete (finite-alphabet, base-two)
Shannon information quantities used by the Run-126 paper
*"The Invariance Capacity Ceiling: Forbidden-Proxy Alignment... | certificates/Run-126/VERIFICATION_STATEMENT_V2.lean | a3016266e251f570721253ebfae431c1d76bc88e88d8da6eb5b6afc9d0913e03 | frozen | substantial | {
"axioms_only_permitted": true,
"challenge_elaborates_with_sorry_targets": true,
"date": "2026-11-06",
"lean_kernel_accepts_reference": true,
"mathlib_rev": "8f9d9cff6bd728b17a24e163c9402775d9e6a365",
"pass": true,
"second_kernel": "not run locally",
"toolchain": "leanprover/lean4:v4.28.0"
} | 8f9d9cff6bd728b17a24e163c9402775d9e6a365 | Viridis.Run126.PaperFormalization | [] | [
"invariance-capacity"
] | [
"propext",
"Quot.sound",
"Classical.choice"
] | 2026-08-30T00:00:00 | 9 | {
"file": "certificates/Run-126/VERIFICATION_CANDIDATE.lean",
"sha256": "e8dc8803fb3c1e465b354b575886c0acf67ba19b28434d16e5abb4c62910101a"
} | eco-lean-bench-task/2 | 2f57ad8f4619bd15e33b943daf26f2f452b02af2 | jdhart81/viridis-canon | Run-126 | frozen statement; public comparator certificate (certificates/) | 5 | [
"Viridis.Run126.PaperFormalization.mutual_information_chain_balance",
"Viridis.Run126.PaperFormalization.forbidden_proxy_capacity_ceiling",
"Viridis.Run126.PaperFormalization.capacity_ceiling_slack_decomposition",
"Viridis.Run126.PaperFormalization.perfect_invariance_target_proxy_collapse",
"Viridis.Run126.... | ELB-126 | leanprover/lean4:v4.28.0 | null |
{
"evidence": "certificates/Run-127/",
"kind": "comparator_dual_kernel",
"public_receipt": true
} | import Mathlib
/- Engine-3 immutable source unit: Model.lean -/
/-!
# The Run-127 model: definitions and assumptions
This file fixes the definitions used to state the frozen claims of the sealed paper
*The Precautionary Capacity Reserve* (Run-127).
Paper objects formalized here:
* the fixed positive scalars `P`, `... | certificates/Run-127/VERIFICATION_CHALLENGE_ALIGNED.lean | cb9a966f3d2130bb5a91a15baaa809dc976f35713623190116a235f4867a1b44 | frozen | substantial | {
"axioms_only_permitted": true,
"challenge_elaborates_with_sorry_targets": true,
"date": "2026-11-06",
"lean_kernel_accepts_reference": true,
"mathlib_rev": "8f9d9cff6bd728b17a24e163c9402775d9e6a365",
"pass": true,
"second_kernel": "not run locally",
"toolchain": "leanprover/lean4:v4.28.0"
} | 8f9d9cff6bd728b17a24e163c9402775d9e6a365 | Viridis.Run127.PaperFormalization | [] | [
"precautionary-capacity"
] | [
"propext",
"Quot.sound",
"Classical.choice"
] | 2026-08-30T00:00:00 | 22 | {
"file": "certificates/Run-127/VERIFICATION_CANDIDATE.lean",
"sha256": "e930944c7b5efe69cecc90884243a8aca6a09a6930442196347b6d4227334d9a"
} | eco-lean-bench-task/2 | 2f57ad8f4619bd15e33b943daf26f2f452b02af2 | jdhart81/viridis-canon | Run-127 | frozen statement; public comparator certificate (certificates/) | 5 | [
"Viridis.Run127.PaperFormalization.cantelli_capacity_certificate",
"Viridis.Run127.PaperFormalization.precautionary_rate_le_violation_budget",
"Viridis.Run127.PaperFormalization.capacity_reserve_fraction_eq",
"Viridis.Run127.PaperFormalization.positive_floor_sharp_two_point_counterexample",
"Viridis.Run127.... | ELB-127 | leanprover/lean4:v4.28.0 | null |
{
"evidence": "certificates/Run-128/",
"kind": "comparator_dual_kernel",
"public_receipt": true
} | import Mathlib
/-!
# Run-128 — "The Reciprocity Corridor: A Bilateral-Benefit Test for Directional
Information Exchange" (J. D. Hart, 12 August 2026) — Lean formalization
This file formalizes the four frozen `FORMAL_TARGET` claims of `STATEMENT_CONTRACT.md`
(paper Theorems 1–3 and Corollary 1), together with the auxi... | certificates/Run-128/VERIFICATION_CHALLENGE_ALIGNED.lean | 20188ee7c055802711586a9fce3b6d8abce2c6f4a54560460e2890ba300fa0e8 | frozen | substantial | {
"axioms_only_permitted": true,
"challenge_elaborates_with_sorry_targets": true,
"date": "2026-11-06",
"lean_kernel_accepts_reference": true,
"mathlib_rev": "8f9d9cff6bd728b17a24e163c9402775d9e6a365",
"pass": true,
"second_kernel": "not run locally",
"toolchain": "leanprover/lean4:v4.28.0"
} | 8f9d9cff6bd728b17a24e163c9402775d9e6a365 | Viridis.Run128.PaperFormalization | [] | [
"reciprocity-corridor"
] | [
"propext",
"Quot.sound",
"Classical.choice"
] | 2026-08-30T00:00:00 | 21 | {
"file": "certificates/Run-128/VERIFICATION_CANDIDATE.lean",
"sha256": "1de8f6a1f2ac05dd8026ad92a646b910d17b8369ba72c3dc6ebf7628ba1696ee"
} | eco-lean-bench-task/2 | 2f57ad8f4619bd15e33b943daf26f2f452b02af2 | jdhart81/viridis-canon | Run-128 | frozen statement; public comparator certificate (certificates/) | 5 | [
"Viridis.Run128.PaperFormalization.bilateral_benefit_iff_reciprocity_corridor",
"Viridis.Run128.PaperFormalization.strict_corridor_nonempty_iff_product_condition",
"Viridis.Run128.PaperFormalization.share_coordinate_corridor_equivalence",
"Viridis.Run128.PaperFormalization.nash_midpoint_unique_maximizer",
"... | ELB-128 | leanprover/lean4:v4.28.0 | null |
{
"evidence": "certificates/Run-129/",
"kind": "comparator_dual_kernel",
"public_receipt": true
} | import Mathlib.Probability.Martingale.OptionalStopping
import Mathlib.Probability.Independence.InfinitePi
import Mathlib.Probability.Independence.Integration
import Mathlib.Probability.BorelCantelli
import Mathlib.Probability.ProbabilityMassFunction.Binomial
import Mathlib.Probability.ProbabilityMassFunction.Integrals
... | certificates/Run-129/VERIFICATION_CHALLENGE_ALIGNED_V3.lean | d68413572ef573abdcecf422c1bfb8ab5c958c4281bccce268fae89aa783aa0e | frozen | substantial | {
"axioms_only_permitted": true,
"challenge_elaborates_with_sorry_targets": true,
"date": "2026-11-06",
"lean_kernel_accepts_reference": true,
"mathlib_rev": "8f9d9cff6bd728b17a24e163c9402775d9e6a365",
"pass": true,
"second_kernel": "not run locally",
"toolchain": "leanprover/lean4:v4.28.0"
} | 8f9d9cff6bd728b17a24e163c9402775d9e6a365 | Viridis.Run129.PaperFormalization | [] | [
"anytime-change"
] | [
"propext",
"Quot.sound",
"Classical.choice"
] | 2026-08-30T00:00:00 | 14 | {
"file": "certificates/Run-129/VERIFICATION_CANDIDATE_V3.lean",
"sha256": "d5ac9ca2978b106699038d4d2672e3cf99939cbc8a0b7fedcd2e4fc01cf2b72b"
} | eco-lean-bench-task/2 | 2f57ad8f4619bd15e33b943daf26f2f452b02af2 | jdhart81/viridis-canon | Run-129 | frozen statement; public comparator certificate (certificates/) | 4 | [
"Viridis.Run129.PaperFormalization.anytime_change_mixture_martingale",
"Viridis.Run129.PaperFormalization.anytime_change_ville_certificate",
"Viridis.Run129.PaperFormalization.change_component_dominance_and_penalty",
"Viridis.Run129.PaperFormalization.bounded_overshoot_expected_delay"
] | ELB-129 | leanprover/lean4:v4.28.0 | null |
{
"evidence": "certificates/Run-130/",
"kind": "comparator_dual_kernel",
"public_receipt": true
} | /- Engine-3 immutable source unit: Hall.lean -/
import Mathlib
/-!
# A capacitated Hall / Gale supply–demand theorem
This file develops, from scratch, the network-flow ingredient that the sealed paper
(`SEALED_paper.tex`, Run-130, "The Seed-Source Bottleneck Certificate") invokes as
"max-flow/min-cut" in its proof sk... | certificates/Run-130/VERIFICATION_CHALLENGE_ALIGNED.lean | 2ef5f3d081483d3a6e12c69bc9f78e1b84b778dd40a4ba7c11d69c73c9c883c9 | frozen | substantial | {
"axioms_only_permitted": true,
"challenge_elaborates_with_sorry_targets": true,
"date": "2026-11-06",
"lean_kernel_accepts_reference": true,
"mathlib_rev": "8f9d9cff6bd728b17a24e163c9402775d9e6a365",
"pass": true,
"second_kernel": "not run locally",
"toolchain": "leanprover/lean4:v4.28.0"
} | 8f9d9cff6bd728b17a24e163c9402775d9e6a365 | Viridis.Run130 | [] | [
"seed-source-bottleneck"
] | [
"propext",
"Quot.sound",
"Classical.choice"
] | 2026-08-30T00:00:00 | 10 | {
"file": "certificates/Run-130/VERIFICATION_CANDIDATE.lean",
"sha256": "1260b3565b55ec536a94c59b13ac55cfadaa6e17f6b01b965e5d1014e609bd36"
} | eco-lean-bench-task/2 | 2f57ad8f4619bd15e33b943daf26f2f452b02af2 | jdhart81/viridis-canon | Run-130 | frozen statement; public comparator certificate (certificates/) | 4 | [
"Viridis.Run130.seed_routing_common_fraction_eq_min_cut_ratio",
"Viridis.Run130.seed_routing_feasible_iff_cut_conditions",
"Viridis.Run130.capacity_outside_active_bottleneck_irrelevant",
"Viridis.Run130.scenario_intersection_certificate_le_each_scenario"
] | ELB-130 | leanprover/lean4:v4.28.0 | null |
{
"evidence": "certificates/Run-131/",
"kind": "comparator_dual_kernel",
"public_receipt": true
} | import Mathlib
/-!
# Run 131 cognitive switching hysteresis certificate
Statement contract `VRS-FORMAL-TARGET-CONTRACT-1` (run 131). Every definition and
theorem statement below is preserved verbatim from the frozen contract; only the
proof bodies have been supplied.
-/
namespace Viridis.Cognition.CognitiveSwitchin... | certificates/Run-131/VERIFICATION_CHALLENGE_ALIGNED.lean | 13803e64077b8a4c7919af31f348aeb19b785f14dabb59fe876cffc6210d98c8 | frozen | elementary | {
"axioms_only_permitted": true,
"challenge_elaborates_with_sorry_targets": true,
"date": "2026-11-06",
"lean_kernel_accepts_reference": true,
"mathlib_rev": "8f9d9cff6bd728b17a24e163c9402775d9e6a365",
"pass": true,
"second_kernel": "not run locally",
"toolchain": "leanprover/lean4:v4.28.0"
} | 8f9d9cff6bd728b17a24e163c9402775d9e6a365 | Viridis.Cognition.CognitiveSwitchingHysteresis | [] | [
"switching-hysteresis"
] | [
"propext",
"Quot.sound",
"Classical.choice"
] | 2026-08-30T00:00:00 | 3 | {
"file": "certificates/Run-131/VERIFICATION_CANDIDATE.lean",
"sha256": "842943f1da4b1dc2e55b07d2f9eb0edbeffe381e82bc44b51cabd08296295412"
} | eco-lean-bench-task/2 | 2f57ad8f4619bd15e33b943daf26f2f452b02af2 | jdhart81/viridis-canon | Run-131 | frozen statement; public comparator certificate (certificates/) | 5 | [
"Viridis.Cognition.CognitiveSwitchingHysteresis.threshold_order",
"Viridis.Cognition.CognitiveSwitchingHysteresis.band_width_identity",
"Viridis.Cognition.CognitiveSwitchingHysteresis.closed_loop_area_identity",
"Viridis.Cognition.CognitiveSwitchingHysteresis.bias_translation",
"Viridis.Cognition.CognitiveS... | ELB-131 | leanprover/lean4:v4.28.0 | null |
{
"evidence": "certificates/Run-132/",
"kind": "comparator_dual_kernel",
"public_receipt": true
} | import Mathlib
/-!
# Run 132 D-Score weight-charter certificate
Frozen Run 132 statement contract, now discharged.
Deviations from the delivered source file, all forced and all documented:
* The original file opened with a module docstring *before* `import Mathlib`, which Lean
rejects (`invalid 'import' command`)... | certificates/Run-132/VERIFICATION_CHALLENGE_ALIGNED_ATTEMPT_3.lean | 95e0bede5f1ec5277a5543468bdc67d63d444a49d7c93369871bddedd877d30b | frozen | substantial | {
"axioms_only_permitted": true,
"challenge_elaborates_with_sorry_targets": true,
"date": "2026-11-06",
"lean_kernel_accepts_reference": true,
"mathlib_rev": "8f9d9cff6bd728b17a24e163c9402775d9e6a365",
"pass": true,
"second_kernel": "not run locally",
"toolchain": "leanprover/lean4:v4.28.0"
} | 8f9d9cff6bd728b17a24e163c9402775d9e6a365 | Viridis.DScore.WeightCharter | [] | [
"dswc-tv-range-certificate"
] | [
"propext",
"Quot.sound",
"Classical.choice"
] | 2026-08-30T00:00:00 | 33.5 | {
"file": "certificates/Run-132/VERIFICATION_CANDIDATE_ATTEMPT_3.lean",
"sha256": "4fd0b4dd32d30d0383ffd06d9bc50b4cf53dfad8b4a017333a25cb3f0f46bd5e"
} | eco-lean-bench-task/2 | 2f57ad8f4619bd15e33b943daf26f2f452b02af2 | jdhart81/viridis-canon | Run-132 | frozen statement; public comparator certificate (certificates/) | 6 | [
"Viridis.DScore.WeightCharter.tv_range_certificate",
"Viridis.DScore.WeightCharter.strict_rank_stability",
"Viridis.DScore.WeightCharter.unrestricted_simplex_optimum_counterexample",
"Viridis.DScore.WeightCharter.unrestricted_simplex_optimum_max",
"Viridis.DScore.WeightCharter.unrestricted_simplex_optimum",... | ELB-132 | leanprover/lean4:v4.28.0 | null |
{
"evidence": "certificates/Run-133/",
"kind": "comparator_dual_kernel",
"public_receipt": true
} | import Mathlib
namespace Viridis.HDFM.CorridorOverlapDuality
/-- The path-product factorization supplied by finite independent edge sets. -/
def ProductFactorization (qA qB qUnion qShared : ℝ) : Prop :=
qA * qB = qUnion * qShared
theorem synchrony_dividend_identity
(qA qB qUnion qShared : ℝ)
(hfactor : Pro... | certificates/Run-133/VERIFICATION_CHALLENGE_ALIGNED.lean | bcaeb2d0b29f1a1bccd57cba42e94169a21649b069346398483e10b171bf9612 | frozen | elementary | {
"axioms_only_permitted": true,
"challenge_elaborates_with_sorry_targets": true,
"date": "2026-11-06",
"lean_kernel_accepts_reference": true,
"mathlib_rev": "8f9d9cff6bd728b17a24e163c9402775d9e6a365",
"pass": true,
"second_kernel": "not run locally",
"toolchain": "leanprover/lean4:v4.28.0"
} | 8f9d9cff6bd728b17a24e163c9402775d9e6a365 | Viridis.HDFM.CorridorOverlapDuality | [] | [
"codc-synchrony-dividend-identity"
] | [
"propext",
"Quot.sound",
"Classical.choice"
] | 2026-08-30T00:00:00 | 3 | {
"file": "certificates/Run-133/VERIFICATION_CANDIDATE.lean",
"sha256": "153531dbead8ae7e94e1bb5a98ceb73f6aed50d75498e70919500029a7e2d2aa"
} | eco-lean-bench-task/2 | 2f57ad8f4619bd15e33b943daf26f2f452b02af2 | jdhart81/viridis-canon | Run-133 | frozen statement; public comparator certificate (certificates/) | 6 | [
"Viridis.HDFM.CorridorOverlapDuality.synchrony_dividend_identity",
"Viridis.HDFM.CorridorOverlapDuality.availability_penalty_eq_synchrony_dividend",
"Viridis.HDFM.CorridorOverlapDuality.overlap_tradeoff_nonnegative",
"Viridis.HDFM.CorridorOverlapDuality.overlap_tradeoff_strict",
"Viridis.HDFM.CorridorOverla... | ELB-133 | leanprover/lean4:v4.28.0 | null |
{
"evidence": "certificates/Run-135/",
"kind": "comparator_dual_kernel",
"public_receipt": true
} | import Mathlib
namespace Viridis.Applications.SufficientSanitization
/-!
Frozen algebraic certificate for Run 135. The entropy coordinates are supplied
by the finite-distribution layer. The hypotheses `hDetJoint` and `hDetTriple`
encode that S is a deterministic function of X, so adjoining S changes neither
H(X) nor ... | certificates/Run-135/VERIFICATION_CHALLENGE_ALIGNED.lean | ed7b51ec1a878f5e06f36f7a36146b97ac77b3475333c7e1d451cb41bb98982c | frozen | elementary | {
"axioms_only_permitted": true,
"challenge_elaborates_with_sorry_targets": true,
"date": "2026-11-06",
"lean_kernel_accepts_reference": true,
"mathlib_rev": "8f9d9cff6bd728b17a24e163c9402775d9e6a365",
"pass": true,
"second_kernel": "not run locally",
"toolchain": "leanprover/lean4:v4.28.0"
} | 8f9d9cff6bd728b17a24e163c9402775d9e6a365 | Viridis.Applications.SufficientSanitization | [] | [
"ssc-relevance-chain-identity"
] | [
"propext",
"Quot.sound",
"Classical.choice"
] | 2026-08-30T00:00:00 | 3 | {
"file": "certificates/Run-135/VERIFICATION_CANDIDATE.lean",
"sha256": "e95ad53230883a723f5e3f0cc1d744e329ff5a36e91635f7f67eaf3703d5b21c"
} | eco-lean-bench-task/2 | 2f57ad8f4619bd15e33b943daf26f2f452b02af2 | jdhart81/viridis-canon | Run-135 | frozen statement; public comparator certificate (certificates/) | 5 | [
"Viridis.Applications.SufficientSanitization.relevance_chain_identity",
"Viridis.Applications.SufficientSanitization.entropy_decomposition_deterministic",
"Viridis.Applications.SufficientSanitization.exact_sufficiency_preserves_relevance",
"Viridis.Applications.SufficientSanitization.approximate_sufficiency_l... | ELB-135 | leanprover/lean4:v4.28.0 | null |
{
"evidence": "series/RFC/COMPARATOR_SUMMARY.md",
"kind": "comparator_dual_kernel_summary",
"public_receipt": false
} | import Mathlib
namespace Viridis.EntropyLearning.RetentionFloor
/-!
Frozen algebraic certificate for Run 136. This file formalizes rational
availability and the max-min budget certificate. It does not formalize a
continuous-time Markov chain, empirical forgetting, replay safety, or novelty.
Notes on the frozen sourc... | series/RFC/contracts/VERIFICATION_STATEMENT.lean | a2ce1a8fe8d16cddf480427200c955cd06502ad720d229c5bbc06e76f6b00b87 | frozen | elementary | {
"axioms_only_permitted": true,
"challenge_elaborates_with_sorry_targets": true,
"date": "2026-11-06",
"lean_kernel_accepts_reference": true,
"mathlib_rev": "8f9d9cff6bd728b17a24e163c9402775d9e6a365",
"pass": true,
"second_kernel": "not run locally",
"toolchain": "leanprover/lean4:v4.28.0"
} | 8f9d9cff6bd728b17a24e163c9402775d9e6a365 | Viridis.EntropyLearning.RetentionFloor | [] | [] | [
"propext",
"Quot.sound",
"Classical.choice"
] | 2026-09-08T00:00:00 | 10 | {
"file": "series/RFC/ViridisRun136.lean",
"sha256": "4d733e4ca7ebae4a7296304aeec76210b6d1cf7f79e12ad8493b72e3324d6c2d"
} | eco-lean-bench-task/2 | 2f57ad8f4619bd15e33b943daf26f2f452b02af2 | jdhart81/viridis-canon | Run-136 | frozen statement (series/ deposit, separate VERIFICATION_STATEMENT.lean) | 8 | [
"Viridis.EntropyLearning.RetentionFloor.stationary_availability_balance",
"Viridis.EntropyLearning.RetentionFloor.floor_requirement",
"Viridis.EntropyLearning.RetentionFloor.retention_floor_upper_bound_as_frozen_is_false",
"Viridis.EntropyLearning.RetentionFloor.retention_floor_upper_bound",
"Viridis.Entrop... | ELB-136 | leanprover/lean4:v4.28.0 | null |
{
"evidence": "certificates/Run-137/",
"kind": "comparator_dual_kernel",
"public_receipt": true
} | import Mathlib
namespace Viridis.IntelligenceBound.SymbioticAccounting
/-!
Codex-authored linked correction r1 for the frozen algebraic targets of Run 137.
These statements assume componentwise
linear rate ceilings and a fixed shared power budget. They do not formalize
Landauer's principle, network coding, empirical ... | certificates/Run-137/VERIFICATION_CHALLENGE_ALIGNED.lean | 914947efc9341f44104a52c6283ac6d4ac1c96c33226381d07ac3d55a5f53cbb | frozen | elementary | {
"axioms_only_permitted": true,
"challenge_elaborates_with_sorry_targets": true,
"date": "2026-11-06",
"lean_kernel_accepts_reference": true,
"mathlib_rev": "8f9d9cff6bd728b17a24e163c9402775d9e6a365",
"pass": true,
"second_kernel": "not run locally",
"toolchain": "leanprover/lean4:v4.28.0"
} | 8f9d9cff6bd728b17a24e163c9402775d9e6a365 | Viridis.IntelligenceBound.SymbioticAccounting | [
"The Intelligence Bound (dI/dt <= P*D/(k_B T ln 2)) is a conjecture. Theorems here take its physical premise (a Landauer-type cost) as a hypothesis or definition; solving them proves nothing about the conjecture itself."
] | [
"sac-conjunctive-rate-upper-bound"
] | [
"propext",
"Quot.sound",
"Classical.choice"
] | 2026-08-30T00:00:00 | 11 | {
"file": "certificates/Run-137/VERIFICATION_CANDIDATE.lean",
"sha256": "afe2ac826cb598d998a4e32baa19c17ffba3df7706b8dc0015d36c1ff5c65daa"
} | eco-lean-bench-task/2 | 2f57ad8f4619bd15e33b943daf26f2f452b02af2 | jdhart81/viridis-canon | Run-137 | frozen statement; public comparator certificate (certificates/) | 9 | [
"Viridis.IntelligenceBound.SymbioticAccounting.conjunctive_rate_upper_bound_as_frozen_is_false",
"Viridis.IntelligenceBound.SymbioticAccounting.conjunctive_rate_upper_bound",
"Viridis.IntelligenceBound.SymbioticAccounting.symbiotic_allocation_attains",
"Viridis.IntelligenceBound.SymbioticAccounting.normalized... | ELB-137 | leanprover/lean4:v4.28.0 | null |
{
"evidence": "certificates/Run-138/",
"kind": "comparator_dual_kernel",
"public_receipt": true
} | import Mathlib
namespace Viridis.GaianSystems.AlignmentCone
/-!
Frozen algebraic targets for Run 138. These statements describe weighted sums
of two-coordinate subsystem response vectors under explicit nonnegative weights,
positive target projections, and residual bounds. They do not formalize Earth
system dynamics, ... | certificates/Run-138/VERIFICATION_CHALLENGE_ALIGNED.lean | 0ddb1628c0ad7a0110044388519cce1dde218f0c1851a47338ff3f1e88a43b14 | frozen | elementary | {
"axioms_only_permitted": true,
"challenge_elaborates_with_sorry_targets": true,
"date": "2026-11-06",
"lean_kernel_accepts_reference": true,
"mathlib_rev": "8f9d9cff6bd728b17a24e163c9402775d9e6a365",
"pass": true,
"second_kernel": "not run locally",
"toolchain": "leanprover/lean4:v4.28.0"
} | 8f9d9cff6bd728b17a24e163c9402775d9e6a365 | Viridis.GaianSystems.AlignmentCone | [] | [
"gacc-aggregate-residual-bound"
] | [
"propext",
"Quot.sound",
"Classical.choice"
] | 2026-08-30T00:00:00 | 7 | {
"file": "certificates/Run-138/VERIFICATION_CANDIDATE.lean",
"sha256": "1830f9cf99db8a26fb394dcdd5d343c866803495856f70258680ec9977ed4a73"
} | eco-lean-bench-task/2 | 2f57ad8f4619bd15e33b943daf26f2f452b02af2 | jdhart81/viridis-canon | Run-138 | frozen statement; public comparator certificate (certificates/) | 8 | [
"Viridis.GaianSystems.AlignmentCone.aggregate_projection_positive",
"Viridis.GaianSystems.AlignmentCone.aggregate_residual_bound",
"Viridis.GaianSystems.AlignmentCone.common_cone_closed_under_weighted_sum",
"Viridis.GaianSystems.AlignmentCone.alignment_floor_of_residual_bound",
"Viridis.GaianSystems.Alignme... | ELB-138 | leanprover/lean4:v4.28.0 | null |
{
"evidence": "certificates/Run-139/",
"kind": "comparator_dual_kernel",
"public_receipt": true
} | import Mathlib
namespace Viridis.ThermodynamicEconomics.RetrofitWaterFilling
/- Frozen algebraic targets for Run 139. These do not validate input prices,
measurements, policy authority, empirical impact, novelty, or product value. -/
/- Codex authored and froze this zero-sorry candidate after reviewing the
original ... | certificates/Run-139/VERIFICATION_CHALLENGE_ALIGNED.lean | 4a36080607c0be7b17a5eceade22711c8127031e741f3d74ebcf8b98590ad617 | frozen | elementary | {
"axioms_only_permitted": true,
"challenge_elaborates_with_sorry_targets": true,
"date": "2026-11-06",
"lean_kernel_accepts_reference": true,
"mathlib_rev": "8f9d9cff6bd728b17a24e163c9402775d9e6a365",
"pass": true,
"second_kernel": "not run locally",
"toolchain": "leanprover/lean4:v4.28.0"
} | 8f9d9cff6bd728b17a24e163c9402775d9e6a365 | Viridis.ThermodynamicEconomics.RetrofitWaterFilling | [] | [
"thermodynamic-economic-allocation"
] | [
"propext",
"Quot.sound",
"Classical.choice"
] | 2026-08-30T00:00:00 | 2.5 | {
"file": "certificates/Run-139/VERIFICATION_CANDIDATE.lean",
"sha256": "26144b575077db3d20d650a13321abf99d9fd5105d01209e760bdaa5130b8530"
} | eco-lean-bench-task/2 | 2f57ad8f4619bd15e33b943daf26f2f452b02af2 | jdhart81/viridis-canon | Run-139 | frozen statement; public comparator certificate (certificates/) | 6 | [
"Viridis.ThermodynamicEconomics.RetrofitWaterFilling.clippedAllocation_nonnegative",
"Viridis.ThermodynamicEconomics.RetrofitWaterFilling.clippedAllocation_le_one",
"Viridis.ThermodynamicEconomics.RetrofitWaterFilling.interior_stationarity",
"Viridis.ThermodynamicEconomics.RetrofitWaterFilling.coordinate_impr... | ELB-139 | leanprover/lean4:v4.28.0 | null |
{
"evidence": "series/SOR/COMPARATOR_SUMMARY.md",
"kind": "comparator_dual_kernel_summary",
"public_receipt": false
} | import Mathlib
namespace Viridis.Ecoterraforming.StewardshipOptionReserve
def optionValue (p b h s d m : ℝ) : ℝ := (1-p)*h*(1-s^2)-p*b*(1-d)-m
theorem option_value_identity (p b h s d m : ℝ) :
(d*p*b-(1-p)*h*s^2-m) - (p*b-(1-p)*h) = optionValue p b h s d m := by
sorry
theorem staging_preferred_iff (p b h s d ... | series/SOR/contracts/VERIFICATION_STATEMENT.lean | c36a49990559b308019a938f9a5250f0e71cb7b2c1a18095c1a7bd4ca20c70a6 | frozen | elementary | {
"axioms_only_permitted": true,
"challenge_elaborates_with_sorry_targets": true,
"date": "2026-11-06",
"lean_kernel_accepts_reference": true,
"mathlib_rev": "8f9d9cff6bd728b17a24e163c9402775d9e6a365",
"pass": true,
"second_kernel": "not run locally",
"toolchain": "leanprover/lean4:v4.28.0"
} | 8f9d9cff6bd728b17a24e163c9402775d9e6a365 | Viridis.Ecoterraforming.StewardshipOptionReserve | [] | [] | [
"propext",
"Quot.sound",
"Classical.choice"
] | 2026-09-01T00:00:00 | 3 | {
"file": "series/SOR/ViridisRun140.lean",
"sha256": "400126167b2f6fb02886765fd7317e4ef2bf7ba3df5cc3bc66d57360076a30ff"
} | eco-lean-bench-task/2 | 2f57ad8f4619bd15e33b943daf26f2f452b02af2 | jdhart81/viridis-canon | Run-140 | frozen statement (series/ deposit, separate VERIFICATION_STATEMENT.lean) | 6 | [
"Viridis.Ecoterraforming.StewardshipOptionReserve.option_value_identity",
"Viridis.Ecoterraforming.StewardshipOptionReserve.staging_preferred_iff",
"Viridis.Ecoterraforming.StewardshipOptionReserve.reserve_bound_iff",
"Viridis.Ecoterraforming.StewardshipOptionReserve.option_value_antitone_stage",
"Viridis.E... | ELB-140 | leanprover/lean4:v4.28.0 | null |
{
"evidence": "series/TDCIL/COMPARATOR_SUMMARY.md",
"kind": "comparator_dual_kernel_summary",
"public_receipt": false
} |
import Mathlib
noncomputable section
namespace Viridis.IntelligenceBound.DutyCycleLedger
def information3 (i1 i2 i3 : ℝ) : ℝ := i1 + i2 + i3
def energy3 (e1 e2 e3 : ℝ) : ℝ := e1 + e2 + e3
theorem window_energy_ledger
(ε i1 i2 i3 e1 e2 e3 : ℝ)
(h1 : ε * i1 ≤ e1) (h2 : ε * i2 ≤ e2) (h3 : ε * i3 ≤ e3) :
ε... | series/TDCIL/VERIFICATION_STATEMENT.lean | 4965fc3c38c2ba30054f71343914fbe5da55c51ca85d4f244f5f3015b9faa9c2 | frozen | elementary | {
"axioms_only_permitted": true,
"challenge_elaborates_with_sorry_targets": true,
"date": "2026-11-06",
"lean_kernel_accepts_reference": true,
"mathlib_rev": "8f9d9cff6bd728b17a24e163c9402775d9e6a365",
"pass": true,
"second_kernel": "not run locally",
"toolchain": "leanprover/lean4:v4.28.0"
} | 8f9d9cff6bd728b17a24e163c9402775d9e6a365 | Viridis.IntelligenceBound.DutyCycleLedger | [
"The Intelligence Bound (dI/dt <= P*D/(k_B T ln 2)) is a conjecture. Theorems here take its physical premise (a Landauer-type cost) as a hypothesis or definition; solving them proves nothing about the conjecture itself."
] | [] | [
"propext",
"Quot.sound",
"Classical.choice"
] | 2026-09-01T00:00:00 | 2.5 | {
"file": "series/TDCIL/VERIFICATION_CANDIDATE.lean",
"sha256": "95b9f439ca1092a908842ecfda70bfe1257ac5a2f35fec5f6c45d6b31a0ba76d"
} | eco-lean-bench-task/2 | 2f57ad8f4619bd15e33b943daf26f2f452b02af2 | jdhart81/viridis-canon | Run-147 | frozen statement (series/ deposit, separate VERIFICATION_STATEMENT.lean) | 6 | [
"Viridis.IntelligenceBound.DutyCycleLedger.window_energy_ledger",
"Viridis.IntelligenceBound.DutyCycleLedger.aggregate_information_ceiling",
"Viridis.IntelligenceBound.DutyCycleLedger.idle_window_forces_zero_information",
"Viridis.IntelligenceBound.DutyCycleLedger.redistribution_preserves_aggregate_ceiling",
... | ELB-147 | leanprover/lean4:v4.28.0 | null |
{
"evidence": "series/FRCS/COMPARATOR_SUMMARY.md",
"kind": "comparator_dual_kernel_summary",
"public_receipt": false
} | import Mathlib
noncomputable section
namespace Viridis.Monitoring.FreshnessReserve
def requiredRate (records horizon : ℝ) : ℝ := records / horizon
theorem freshness_capacity_equiv
(records capacity horizon : ℝ) (hh : 0 < horizon) :
records ≤ capacity * horizon ↔ requiredRate records horizon ≤ capacity := by... | series/FRCS/VERIFICATION_STATEMENT.lean | 761d3ecc2247bb45069943e2c7a56d90e0c70f4ebacb3ac5ea649f507c1f2783 | frozen | elementary | {
"axioms_only_permitted": true,
"challenge_elaborates_with_sorry_targets": true,
"date": "2026-11-06",
"lean_kernel_accepts_reference": true,
"mathlib_rev": "8f9d9cff6bd728b17a24e163c9402775d9e6a365",
"pass": true,
"second_kernel": "not run locally",
"toolchain": "leanprover/lean4:v4.28.0"
} | 8f9d9cff6bd728b17a24e163c9402775d9e6a365 | Viridis.Monitoring.FreshnessReserve | [] | [] | [
"propext",
"Quot.sound",
"Classical.choice"
] | 2026-09-01T00:00:00 | 3 | {
"file": "series/FRCS/VERIFICATION_CANDIDATE.lean",
"sha256": "34a7bfcf02361a2900f95da1fb82383f91c71f005564d2384a79c94e8adbfc5c"
} | eco-lean-bench-task/2 | 2f57ad8f4619bd15e33b943daf26f2f452b02af2 | jdhart81/viridis-canon | Run-148 | frozen statement (series/ deposit, separate VERIFICATION_STATEMENT.lean) | 6 | [
"Viridis.Monitoring.FreshnessReserve.freshness_capacity_equiv",
"Viridis.Monitoring.FreshnessReserve.nominal_capacity_exact",
"Viridis.Monitoring.FreshnessReserve.reserve_capacity_sufficient",
"Viridis.Monitoring.FreshnessReserve.reserve_headroom_identity",
"Viridis.Monitoring.FreshnessReserve.capacity_shor... | ELB-148 | leanprover/lean4:v4.28.0 | null |
{
"evidence": "series/SFB/COMPARATOR_SUMMARY.md",
"kind": "comparator_dual_kernel_summary",
"public_receipt": false
} | import Mathlib
noncomputable section
namespace Viridis.Afforestation.SharedFacilitation
def pooledMargin (demandOne demandTwo supportOne supportTwo : ℝ) : ℝ :=
(supportOne + supportTwo) - (demandOne + demandTwo)
theorem pooled_margin_identity
(demandOne demandTwo supportOne supportTwo : ℝ) :
pooledMargin ... | series/SFB/VERIFICATION_STATEMENT.lean | 4b2934ecadd243c31b19b33440b6b069789abe18b2276b6a5e8c9aa9e2ee1a67 | frozen | elementary | {
"axioms_only_permitted": true,
"challenge_elaborates_with_sorry_targets": true,
"date": "2026-11-06",
"lean_kernel_accepts_reference": true,
"mathlib_rev": "8f9d9cff6bd728b17a24e163c9402775d9e6a365",
"pass": true,
"second_kernel": "not run locally",
"toolchain": "leanprover/lean4:v4.28.0"
} | 8f9d9cff6bd728b17a24e163c9402775d9e6a365 | Viridis.Afforestation.SharedFacilitation | [] | [] | [
"propext",
"Quot.sound",
"Classical.choice"
] | 2026-09-01T00:00:00 | 2.5 | {
"file": "series/SFB/VERIFICATION_CANDIDATE.lean",
"sha256": "eb55692ff2b129da6091d268faf522bdb1a2a72eea1223834b1ea804d7d6f062"
} | eco-lean-bench-task/2 | 2f57ad8f4619bd15e33b943daf26f2f452b02af2 | jdhart81/viridis-canon | Run-149 | frozen statement (series/ deposit, separate VERIFICATION_STATEMENT.lean) | 6 | [
"Viridis.Afforestation.SharedFacilitation.pooled_margin_identity",
"Viridis.Afforestation.SharedFacilitation.pooled_feasible_iff_margin_nonnegative",
"Viridis.Afforestation.SharedFacilitation.isolated_feasible_implies_pooled",
"Viridis.Afforestation.SharedFacilitation.transfer_conserves_pooled_margin",
"Vir... | ELB-149 | leanprover/lean4:v4.28.0 | null |
{
"evidence": "series/DPAC/COMPARATOR_SUMMARY.md",
"kind": "comparator_dual_kernel_summary",
"public_receipt": false
} | import Mathlib
noncomputable section
namespace Viridis.ThermodynamicEconomics.DualPriceAlignment
def valuation (price quantity cost : ℝ) : ℝ := price * quantity - cost
theorem valuation_gap_identity (p s q c : ℝ) :
valuation p q c - valuation s q c = (p - s) * q := by
sorry
theorem valuation_gap_abs (p s q c... | series/DPAC/contracts/VERIFICATION_STATEMENT.lean | 7ed868a56903793ce8c4fe36b671c24c793de20bb855c753a4d98a049356099c | frozen | elementary | {
"axioms_only_permitted": true,
"challenge_elaborates_with_sorry_targets": true,
"date": "2026-11-06",
"lean_kernel_accepts_reference": true,
"mathlib_rev": "8f9d9cff6bd728b17a24e163c9402775d9e6a365",
"pass": true,
"second_kernel": "not run locally",
"toolchain": "leanprover/lean4:v4.28.0"
} | 8f9d9cff6bd728b17a24e163c9402775d9e6a365 | Viridis.ThermodynamicEconomics.DualPriceAlignment | [] | [] | [
"propext",
"Quot.sound",
"Classical.choice"
] | 2026-09-08T00:00:00 | 3 | {
"file": "series/DPAC/ViridisRun150.lean",
"sha256": "c839ffd23143561fbe2cb2b709b086959bf6fc6fa1b941e0304c8a853d02fcb4"
} | eco-lean-bench-task/2 | 2f57ad8f4619bd15e33b943daf26f2f452b02af2 | jdhart81/viridis-canon | Run-150 | frozen statement (series/ deposit, separate VERIFICATION_STATEMENT.lean) | 6 | [
"Viridis.ThermodynamicEconomics.DualPriceAlignment.valuation_gap_identity",
"Viridis.ThermodynamicEconomics.DualPriceAlignment.valuation_gap_abs",
"Viridis.ThermodynamicEconomics.DualPriceAlignment.dual_acceptance_iff_corridor",
"Viridis.ThermodynamicEconomics.DualPriceAlignment.two_project_gap_identity",
"... | ELB-150 | leanprover/lean4:v4.28.0 | null |
{
"evidence": "series/TLRC/COMPARATOR_SUMMARY.md",
"kind": "comparator_dual_kernel_summary",
"public_receipt": false
} | import Mathlib
noncomputable section
namespace Viridis.EntropyLearning.ThermalStepCorridor
def surrogateGain (a q eta : ℝ) : ℝ := a * eta * (2 * q - eta)
def heatCost (d eta : ℝ) : ℝ := d * eta ^ 2
theorem gain_peak_deficit_identity (a q eta : ℝ) :
surrogateGain a q q - surrogateGain a q eta = a * (eta - q) ^ ... | series/TLRC/contracts/VERIFICATION_STATEMENT.lean | f8f385ed78660995b6a88c0c0403f513a2cc54d63ef558d7aeaa0e0c926e9c90 | frozen | elementary | {
"axioms_only_permitted": true,
"challenge_elaborates_with_sorry_targets": true,
"date": "2026-11-06",
"lean_kernel_accepts_reference": true,
"mathlib_rev": "8f9d9cff6bd728b17a24e163c9402775d9e6a365",
"pass": true,
"second_kernel": "not run locally",
"toolchain": "leanprover/lean4:v4.28.0"
} | 8f9d9cff6bd728b17a24e163c9402775d9e6a365 | Viridis.EntropyLearning.ThermalStepCorridor | [] | [] | [
"propext",
"Quot.sound",
"Classical.choice"
] | 2026-09-13T00:00:00 | 3 | {
"file": "series/TLRC/ViridisRun151.lean",
"sha256": "1e63ef236c7fdeab1d4b811d36d1232446d474682a318bfe4841d142e92a9628"
} | eco-lean-bench-task/2 | 2f57ad8f4619bd15e33b943daf26f2f452b02af2 | jdhart81/viridis-canon | Run-151 | frozen statement (series/ deposit, separate VERIFICATION_STATEMENT.lean) | 7 | [
"Viridis.EntropyLearning.ThermalStepCorridor.gain_peak_deficit_identity",
"Viridis.EntropyLearning.ThermalStepCorridor.gain_nonnegative_corridor",
"Viridis.EntropyLearning.ThermalStepCorridor.gain_peak_upper_bound",
"Viridis.EntropyLearning.ThermalStepCorridor.gain_symmetric_mistuning",
"Viridis.EntropyLear... | ELB-151 | leanprover/lean4:v4.28.0 | null |
{
"evidence": "series/TRSE/COMPARATOR_SUMMARY.md",
"kind": "comparator_dual_kernel_summary",
"public_receipt": false
} | import Mathlib
noncomputable section
namespace Viridis.HDFM.TwoRouteStewardship
def routeOne (a p x : ℝ) : ℝ := a + p * x
def routeTwo (b q B x : ℝ) : ℝ := b + q * (B - x)
def balanceAllocation (a b p q B : ℝ) : ℝ := (b + q * B - a) / (p + q)
def bottleneck (a b p q B x : ℝ) : ℝ := min (routeOne a p x) (routeTwo b q... | series/TRSE/contracts/VERIFICATION_STATEMENT.lean | dd0f247e05625446d83940c140efe3c6e887bbde67807e90b48c3ae03d655b86 | frozen | elementary | {
"axioms_only_permitted": true,
"challenge_elaborates_with_sorry_targets": true,
"date": "2026-11-06",
"lean_kernel_accepts_reference": true,
"mathlib_rev": "8f9d9cff6bd728b17a24e163c9402775d9e6a365",
"pass": true,
"second_kernel": "not run locally",
"toolchain": "leanprover/lean4:v4.28.0"
} | 8f9d9cff6bd728b17a24e163c9402775d9e6a365 | Viridis.HDFM.TwoRouteStewardship | [] | [] | [
"propext",
"Quot.sound",
"Classical.choice"
] | 2026-09-13T00:00:00 | 5 | {
"file": "series/TRSE/ViridisRun152.lean",
"sha256": "424586946e1a56f3774b36cc5dd70b18cd6be596fabce21e84494b34accabba5"
} | eco-lean-bench-task/2 | 2f57ad8f4619bd15e33b943daf26f2f452b02af2 | jdhart81/viridis-canon | Run-152 | frozen statement (series/ deposit, separate VERIFICATION_STATEMENT.lean) | 8 | [
"Viridis.HDFM.TwoRouteStewardship.balance_identity",
"Viridis.HDFM.TwoRouteStewardship.allocation_gap_identity",
"Viridis.HDFM.TwoRouteStewardship.left_bottleneck",
"Viridis.HDFM.TwoRouteStewardship.right_bottleneck",
"Viridis.HDFM.TwoRouteStewardship.balanced_bottleneck_maximal",
"Viridis.HDFM.TwoRouteSt... | ELB-152 | leanprover/lean4:v4.28.0 | null |
{
"evidence": "series/RRFG/COMPARATOR_SUMMARY.md",
"kind": "comparator_dual_kernel_summary",
"public_receipt": false
} | import Mathlib
noncomputable section
namespace Viridis.GaianSystems.ReciprocalRescue
def loopDenom (m n : ℝ) : ℝ := 1 - m * n
def equilibriumA (rA rB m n : ℝ) : ℝ := (rA + m * rB) / loopDenom m n
def equilibriumB (rA rB m n : ℝ) : ℝ := (rB + n * rA) / loopDenom m n
theorem equilibrium_balance_a (rA rB m n : ℝ) (h :... | series/RRFG/contracts/VERIFICATION_STATEMENT.lean | 25c32b4dddbbf0214dab4f35df6f0f1fe10a4cb5800d8eb6b504e6a6f9734a59 | frozen | elementary | {
"axioms_only_permitted": true,
"challenge_elaborates_with_sorry_targets": true,
"date": "2026-11-06",
"lean_kernel_accepts_reference": true,
"mathlib_rev": "8f9d9cff6bd728b17a24e163c9402775d9e6a365",
"pass": true,
"second_kernel": "not run locally",
"toolchain": "leanprover/lean4:v4.28.0"
} | 8f9d9cff6bd728b17a24e163c9402775d9e6a365 | Viridis.GaianSystems.ReciprocalRescue | [] | [] | [
"propext",
"Quot.sound",
"Classical.choice"
] | 2026-09-13T00:00:00 | 4 | {
"file": "series/RRFG/ViridisRun153.lean",
"sha256": "d9906858150239657ef2facfc90a24030c63eead694c26eca1763d0a99766cd8"
} | eco-lean-bench-task/2 | 2f57ad8f4619bd15e33b943daf26f2f452b02af2 | jdhart81/viridis-canon | Run-153 | frozen statement (series/ deposit, separate VERIFICATION_STATEMENT.lean) | 7 | [
"Viridis.GaianSystems.ReciprocalRescue.equilibrium_balance_a",
"Viridis.GaianSystems.ReciprocalRescue.equilibrium_balance_b",
"Viridis.GaianSystems.ReciprocalRescue.positive_equilibrium_of_positive_numerators",
"Viridis.GaianSystems.ReciprocalRescue.no_two_decliner_positive_equilibrium",
"Viridis.GaianSyste... | ELB-153 | leanprover/lean4:v4.28.0 | null |
{
"evidence": "series/SBCN/COMPARATOR_SUMMARY.md",
"kind": "comparator_dual_kernel_summary",
"public_receipt": false
} | import Mathlib
noncomputable section
namespace Viridis.CognitiveModeling.SignedBiasCancellation
def pooledError (w e1 e2 : ℝ) : ℝ := w * e1 + (1 - w) * e2
theorem pooled_error_at_zero (e1 e2 : ℝ) : pooledError 0 e1 e2 = e2 := by
sorry
theorem pooled_error_at_one (e1 e2 : ℝ) : pooledError 1 e1 e2 = e1 := by
sor... | series/SBCN/contracts/VERIFICATION_STATEMENT.lean | 02afabeb366d5abb83a86352c021830c4056adae2efba5462c35a0f1c29ba54d | frozen | elementary | {
"axioms_only_permitted": true,
"challenge_elaborates_with_sorry_targets": true,
"date": "2026-11-06",
"lean_kernel_accepts_reference": true,
"mathlib_rev": "8f9d9cff6bd728b17a24e163c9402775d9e6a365",
"pass": true,
"second_kernel": "not run locally",
"toolchain": "leanprover/lean4:v4.28.0"
} | 8f9d9cff6bd728b17a24e163c9402775d9e6a365 | Viridis.CognitiveModeling.SignedBiasCancellation | [] | [] | [
"propext",
"Quot.sound",
"Classical.choice"
] | 2026-09-13T00:00:00 | 3.5 | {
"file": "series/SBCN/ViridisRun154.lean",
"sha256": "2a0a448ed5c6c44467e68136cd42a44cf8544bf939da998ae8c15615e94e978e"
} | eco-lean-bench-task/2 | 2f57ad8f4619bd15e33b943daf26f2f452b02af2 | jdhart81/viridis-canon | Run-154 | frozen statement (series/ deposit, separate VERIFICATION_STATEMENT.lean) | 8 | [
"Viridis.CognitiveModeling.SignedBiasCancellation.pooled_error_at_zero",
"Viridis.CognitiveModeling.SignedBiasCancellation.pooled_error_at_one",
"Viridis.CognitiveModeling.SignedBiasCancellation.cancellation_weight_balance",
"Viridis.CognitiveModeling.SignedBiasCancellation.opposite_error_cancellation",
"Vi... | ELB-154 | leanprover/lean4:v4.28.0 | null |
{
"evidence": "series/SVON/COMPARATOR_SUMMARY.md",
"kind": "comparator_dual_kernel_summary",
"public_receipt": false
} | import Mathlib
noncomputable section
namespace Viridis.Ecoservices.SharedVerificationOverhead
def separateCost (fixed v1 v2 : ℝ) : ℝ := (fixed + v1) + (fixed + v2)
def bundledCost (fixed v1 v2 : ℝ) : ℝ := fixed + v1 + v2
def bundledWithInteraction (fixed v1 v2 interaction : ℝ) : ℝ :=
bundledCost fixed v1 v2 + inte... | series/SVON/contracts/VERIFICATION_STATEMENT.lean | e4dcb4939466d22ad8a7510b6a8e1608976944d3c292c464da5ff1cbe3cd5e8b | frozen | elementary | {
"axioms_only_permitted": true,
"challenge_elaborates_with_sorry_targets": true,
"date": "2026-11-06",
"lean_kernel_accepts_reference": true,
"mathlib_rev": "8f9d9cff6bd728b17a24e163c9402775d9e6a365",
"pass": true,
"second_kernel": "not run locally",
"toolchain": "leanprover/lean4:v4.28.0"
} | 8f9d9cff6bd728b17a24e163c9402775d9e6a365 | Viridis.Ecoservices.SharedVerificationOverhead | [] | [] | [
"propext",
"Quot.sound",
"Classical.choice"
] | 2026-09-13T00:00:00 | 3 | {
"file": "series/SVON/ViridisRun155.lean",
"sha256": "4d2ce1821e24f16cb21dd8e0abb2dbb6e8763aee624eb460fc7359cd216de1c2"
} | eco-lean-bench-task/2 | 2f57ad8f4619bd15e33b943daf26f2f452b02af2 | jdhart81/viridis-canon | Run-155 | frozen statement (series/ deposit, separate VERIFICATION_STATEMENT.lean) | 8 | [
"Viridis.Ecoservices.SharedVerificationOverhead.separate_cost_expansion",
"Viridis.Ecoservices.SharedVerificationOverhead.bundled_cost_expansion",
"Viridis.Ecoservices.SharedVerificationOverhead.shared_verification_saving",
"Viridis.Ecoservices.SharedVerificationOverhead.interaction_adjusted_saving",
"Virid... | ELB-155 | leanprover/lean4:v4.28.0 | null |
{
"evidence": "series/MRRN/COMPARATOR_SUMMARY.md",
"kind": "comparator_dual_kernel_summary",
"public_receipt": false
} | import Mathlib
noncomputable section
namespace Viridis.ThermodynamicSpeedLimits.MonitoringResponseReserve
def blindWindow (monitorDelay responseDelay : ℝ) : ℝ := monitorDelay + responseDelay
def blindLoss (rate monitorDelay responseDelay : ℝ) : ℝ :=
rate * blindWindow monitorDelay responseDelay
def residualReserve... | series/MRRN/contracts/VERIFICATION_STATEMENT.lean | 9689215c8d0ae34b630a21077f2eaeaafebc83921fadb184fdf252fb629e9a70 | frozen | elementary | {
"axioms_only_permitted": true,
"challenge_elaborates_with_sorry_targets": true,
"date": "2026-11-06",
"lean_kernel_accepts_reference": true,
"mathlib_rev": "8f9d9cff6bd728b17a24e163c9402775d9e6a365",
"pass": true,
"second_kernel": "not run locally",
"toolchain": "leanprover/lean4:v4.28.0"
} | 8f9d9cff6bd728b17a24e163c9402775d9e6a365 | Viridis.ThermodynamicSpeedLimits.MonitoringResponseReserve | [] | [] | [
"propext",
"Quot.sound",
"Classical.choice"
] | 2026-09-13T00:00:00 | 3 | {
"file": "series/MRRN/ViridisRun156.lean",
"sha256": "4291d5d3bf03f0d0d4c7b74b55a0de0b602a87a90f598e197e9333eab8f10521"
} | eco-lean-bench-task/2 | 2f57ad8f4619bd15e33b943daf26f2f452b02af2 | jdhart81/viridis-canon | Run-156 | frozen statement (series/ deposit, separate VERIFICATION_STATEMENT.lean) | 9 | [
"Viridis.ThermodynamicSpeedLimits.MonitoringResponseReserve.blind_window_definition",
"Viridis.ThermodynamicSpeedLimits.MonitoringResponseReserve.blind_loss_decomposition",
"Viridis.ThermodynamicSpeedLimits.MonitoringResponseReserve.response_delay_penalty",
"Viridis.ThermodynamicSpeedLimits.MonitoringResponse... | ELB-156 | leanprover/lean4:v4.28.0 | null |
{
"evidence": "series/TCTSI/COMPARATOR_SUMMARY.md",
"kind": "comparator_dual_kernel_summary",
"public_receipt": false
} | import Mathlib
noncomputable section
namespace Viridis.IntelligenceBound.SymbioticTransferThreshold
def effectiveA (a b eta cost : ℝ) : ℝ := a + eta * b - cost
def effectiveB (a b eta cost : ℝ) : ℝ := b + eta * a - cost
def cooperativeBottleneck (a b eta cost : ℝ) : ℝ :=
min (effectiveA a b eta cost) (effectiveB a... | series/TCTSI/contracts/VERIFICATION_STATEMENT.lean | a53a1259fcb0dbf6ed5f8315b4d908383fccbe4762976230be9a2da64944d9ae | frozen | elementary | {
"axioms_only_permitted": true,
"challenge_elaborates_with_sorry_targets": true,
"date": "2026-11-06",
"lean_kernel_accepts_reference": true,
"mathlib_rev": "8f9d9cff6bd728b17a24e163c9402775d9e6a365",
"pass": true,
"second_kernel": "not run locally",
"toolchain": "leanprover/lean4:v4.28.0"
} | 8f9d9cff6bd728b17a24e163c9402775d9e6a365 | Viridis.IntelligenceBound.SymbioticTransferThreshold | [
"The Intelligence Bound (dI/dt <= P*D/(k_B T ln 2)) is a conjecture. Theorems here take its physical premise (a Landauer-type cost) as a hypothesis or definition; solving them proves nothing about the conjecture itself."
] | [] | [
"propext",
"Quot.sound",
"Classical.choice"
] | 2026-09-13T00:00:00 | 3 | {
"file": "series/TCTSI/ViridisRun157.lean",
"sha256": "503e47c5882b8ef6992a712a55f9587a4562ee74e712d900d7360772b109f3e8"
} | eco-lean-bench-task/2 | 2f57ad8f4619bd15e33b943daf26f2f452b02af2 | jdhart81/viridis-canon | Run-157 | frozen statement (series/ deposit, separate VERIFICATION_STATEMENT.lean) | 10 | [
"Viridis.IntelligenceBound.SymbioticTransferThreshold.effective_gap_identity",
"Viridis.IntelligenceBound.SymbioticTransferThreshold.ordered_effective_rates",
"Viridis.IntelligenceBound.SymbioticTransferThreshold.bottleneck_reduction",
"Viridis.IntelligenceBound.SymbioticTransferThreshold.bottleneck_formula",... | ELB-157 | leanprover/lean4:v4.28.0 | null |
{
"evidence": "series/DREAA/COMPARATOR_SUMMARY.md",
"kind": "comparator_dual_kernel_summary",
"public_receipt": false
} | import Mathlib
noncomputable section
namespace Viridis.Applications.DeferenceReserveEqualization
def reviewBenefit (rateOne rateTwo timeOne timeTwo : ℝ) : ℝ :=
rateOne * timeOne + rateTwo * timeTwo
def residualLoss (baseLoss rateOne rateTwo timeOne timeTwo : ℝ) : ℝ :=
baseLoss - reviewBenefit rateOne rateTwo ti... | series/DREAA/contracts/VERIFICATION_STATEMENT.lean | b5730c54f9073339ff4d79272dc452f884caf6de46d0104bc9d625da7624ff29 | frozen | elementary | {
"axioms_only_permitted": true,
"challenge_elaborates_with_sorry_targets": true,
"date": "2026-11-06",
"lean_kernel_accepts_reference": true,
"mathlib_rev": "8f9d9cff6bd728b17a24e163c9402775d9e6a365",
"pass": true,
"second_kernel": "not run locally",
"toolchain": "leanprover/lean4:v4.28.0"
} | 8f9d9cff6bd728b17a24e163c9402775d9e6a365 | Viridis.Applications.DeferenceReserveEqualization | [] | [] | [
"propext",
"Quot.sound",
"Classical.choice"
] | 2026-09-13T00:00:00 | 3 | {
"file": "series/DREAA/ViridisRun158.lean",
"sha256": "aebdd2147eb58df5fa8ed87c8f7880d75fea851f9ad7eb240c93f388acbb670b"
} | eco-lean-bench-task/2 | 2f57ad8f4619bd15e33b943daf26f2f452b02af2 | jdhart81/viridis-canon | Run-158 | frozen statement (series/ deposit, separate VERIFICATION_STATEMENT.lean) | 9 | [
"Viridis.Applications.DeferenceReserveEqualization.residual_loss_decomposition",
"Viridis.Applications.DeferenceReserveEqualization.exchange_gain_identity",
"Viridis.Applications.DeferenceReserveEqualization.exchange_preserves_capacity",
"Viridis.Applications.DeferenceReserveEqualization.ordered_exchange_not_... | ELB-158 | leanprover/lean4:v4.28.0 | null |
{
"evidence": "series/SDPN/COMPARATOR_SUMMARY.md",
"kind": "comparator_dual_kernel_summary",
"public_receipt": false
} | import Mathlib
noncomputable section
namespace Viridis.ThermodynamicEconomics.SwitchingDissipationPayback
def switchingCharge (capital transition : ℝ) : ℝ := capital + transition
def switchingGain (horizon saving capital transition : ℝ) : ℝ :=
horizon * saving - switchingCharge capital transition
theorem switchi... | series/SDPN/contracts/VERIFICATION_STATEMENT.lean | be93dd0de2ee5cb998c90f845f733c6cc1446cff874e796b38c153f5fdb4140d | frozen | elementary | {
"axioms_only_permitted": true,
"challenge_elaborates_with_sorry_targets": true,
"date": "2026-11-06",
"lean_kernel_accepts_reference": true,
"mathlib_rev": "8f9d9cff6bd728b17a24e163c9402775d9e6a365",
"pass": true,
"second_kernel": "not run locally",
"toolchain": "leanprover/lean4:v4.28.0"
} | 8f9d9cff6bd728b17a24e163c9402775d9e6a365 | Viridis.ThermodynamicEconomics.SwitchingDissipationPayback | [] | [] | [
"propext",
"Quot.sound",
"Classical.choice"
] | 2026-09-13T00:00:00 | 3 | {
"file": "series/SDPN/ViridisRun159.lean",
"sha256": "349cb6ba4171db9d4d36f1440e831797f8c1bed59a45a98b23b9e5b06d5a6a79"
} | eco-lean-bench-task/2 | 2f57ad8f4619bd15e33b943daf26f2f452b02af2 | jdhart81/viridis-canon | Run-159 | frozen statement (series/ deposit, separate VERIFICATION_STATEMENT.lean) | 11 | [
"Viridis.ThermodynamicEconomics.SwitchingDissipationPayback.switching_gain_identity",
"Viridis.ThermodynamicEconomics.SwitchingDissipationPayback.break_even_iff",
"Viridis.ThermodynamicEconomics.SwitchingDissipationPayback.transition_charge_reduces_gain",
"Viridis.ThermodynamicEconomics.SwitchingDissipationPa... | ELB-159 | leanprover/lean4:v4.28.0 | null |
{
"evidence": "series/DSUR/COMPARATOR_SUMMARY.md",
"kind": "comparator_dual_kernel_summary",
"public_receipt": false
} | import Mathlib
noncomputable section
namespace Viridis.DScore.StewardshipUncertaintyReserve
def dscore (wS wP wG s p g : ℝ) : ℝ := wS * s + wP * p + wG * g
def reserve (wS wP wG rS rP rG : ℝ) : ℝ :=
wS * rS + wP * rP + wG * rG
def lowerScore (wS wP wG s p g rS rP rG : ℝ) : ℝ :=
dscore wS wP wG s p g - reserve ... | series/DSUR/contracts/VERIFICATION_STATEMENT.lean | 8e959303446045cb06d5fdd7eea4323f7abfe33e7b19f1112e0941feba382b61 | frozen | elementary | {
"axioms_only_permitted": true,
"challenge_elaborates_with_sorry_targets": true,
"date": "2026-11-06",
"lean_kernel_accepts_reference": true,
"mathlib_rev": "8f9d9cff6bd728b17a24e163c9402775d9e6a365",
"pass": true,
"second_kernel": "not run locally",
"toolchain": "leanprover/lean4:v4.28.0"
} | 8f9d9cff6bd728b17a24e163c9402775d9e6a365 | Viridis.DScore.StewardshipUncertaintyReserve | [] | [] | [
"propext",
"Quot.sound",
"Classical.choice"
] | 2026-09-13T00:00:00 | 3 | {
"file": "series/DSUR/ViridisRun160.lean",
"sha256": "5b6f324502a0001e1fb7edb32bb2b1472a3e70a681d039e87a9e4809bce7773a"
} | eco-lean-bench-task/2 | 2f57ad8f4619bd15e33b943daf26f2f452b02af2 | jdhart81/viridis-canon | Run-160 | frozen statement (series/ deposit, separate VERIFICATION_STATEMENT.lean) | 10 | [
"Viridis.DScore.StewardshipUncertaintyReserve.score_difference_identity",
"Viridis.DScore.StewardshipUncertaintyReserve.reserve_nonnegative",
"Viridis.DScore.StewardshipUncertaintyReserve.componentwise_error_envelope",
"Viridis.DScore.StewardshipUncertaintyReserve.stewardship_floor_sound",
"Viridis.DScore.S... | ELB-160 | leanprover/lean4:v4.28.0 | null |
{
"evidence": "series/RCBX/COMPARATOR_SUMMARY.md",
"kind": "comparator_dual_kernel_summary",
"public_receipt": false
} | import Mathlib
noncomputable section
namespace Viridis.HDFM.ReciprocalCorridorBottleneck
def reciprocalService (x y : ℝ) : ℝ := min x y
def spend (c d x y : ℝ) : ℝ := c * x + d * y
theorem reciprocal_service_nonnegative (x y : ℝ)
(hx : 0 ≤ x) (hy : 0 ≤ y) : 0 ≤ reciprocalService x y := by
sorry
theorem reci... | series/RCBX/contracts/VERIFICATION_STATEMENT.lean | 3a481413a65408f86dd914274e3e3a118eae0e4789f34d27606256b5327fba36 | frozen | elementary | {
"axioms_only_permitted": true,
"challenge_elaborates_with_sorry_targets": true,
"date": "2026-11-06",
"lean_kernel_accepts_reference": true,
"mathlib_rev": "8f9d9cff6bd728b17a24e163c9402775d9e6a365",
"pass": true,
"second_kernel": "not run locally",
"toolchain": "leanprover/lean4:v4.28.0"
} | 8f9d9cff6bd728b17a24e163c9402775d9e6a365 | Viridis.HDFM.ReciprocalCorridorBottleneck | [] | [] | [
"propext",
"Quot.sound",
"Classical.choice"
] | 2026-09-13T00:00:00 | 2 | {
"file": "series/RCBX/ViridisRun161.lean",
"sha256": "fee55b9b6736205276e2053cb582a3112fc00761008dc7fcf0eb442dc55f3e88"
} | eco-lean-bench-task/2 | 2f57ad8f4619bd15e33b943daf26f2f452b02af2 | jdhart81/viridis-canon | Run-161 | frozen statement (series/ deposit, separate VERIFICATION_STATEMENT.lean) | 9 | [
"Viridis.HDFM.ReciprocalCorridorBottleneck.reciprocal_service_nonnegative",
"Viridis.HDFM.ReciprocalCorridorBottleneck.reciprocal_service_le_left",
"Viridis.HDFM.ReciprocalCorridorBottleneck.reciprocal_service_le_right",
"Viridis.HDFM.ReciprocalCorridorBottleneck.reciprocal_budget_bound",
"Viridis.HDFM.Reci... | ELB-161 | leanprover/lean4:v4.28.0 | null |
{
"evidence": "series/SARN/COMPARATOR_SUMMARY.md",
"kind": "comparator_dual_kernel_summary",
"public_receipt": false
} | import Mathlib
noncomputable section
namespace Viridis.IntelligenceCapacity.SequentialAlignmentRetention
def retained (C a b : ℝ) : ℝ := C * a * b
def firstLoss (C a : ℝ) : ℝ := C * (1 - a)
def secondLoss (C a b : ℝ) : ℝ := C * a * (1 - b)
theorem retained_nonnegative (C a b : ℝ)
(hC : 0 ≤ C) (ha : 0 ≤ a) (hb :... | series/SARN/contracts/VERIFICATION_STATEMENT.lean | c9be27d3af0221fe736c5d0a7cab3ed2ef9719b02332022a568b7e78230a1ad2 | frozen | elementary | {
"axioms_only_permitted": true,
"challenge_elaborates_with_sorry_targets": true,
"date": "2026-11-06",
"lean_kernel_accepts_reference": true,
"mathlib_rev": "8f9d9cff6bd728b17a24e163c9402775d9e6a365",
"pass": true,
"second_kernel": "not run locally",
"toolchain": "leanprover/lean4:v4.28.0"
} | 8f9d9cff6bd728b17a24e163c9402775d9e6a365 | Viridis.IntelligenceCapacity.SequentialAlignmentRetention | [] | [] | [
"propext",
"Quot.sound",
"Classical.choice"
] | 2026-09-13T00:00:00 | 3 | {
"file": "series/SARN/ViridisRun162.lean",
"sha256": "56743dd0c0b8d3d63395f8fe2a6b86b77f4c756ff96816a2fd6e187f1220fa14"
} | eco-lean-bench-task/2 | 2f57ad8f4619bd15e33b943daf26f2f452b02af2 | jdhart81/viridis-canon | Run-162 | frozen statement (series/ deposit, separate VERIFICATION_STATEMENT.lean) | 8 | [
"Viridis.IntelligenceCapacity.SequentialAlignmentRetention.retained_nonnegative",
"Viridis.IntelligenceCapacity.SequentialAlignmentRetention.retained_le_after_first",
"Viridis.IntelligenceCapacity.SequentialAlignmentRetention.retained_le_capacity",
"Viridis.IntelligenceCapacity.SequentialAlignmentRetention.se... | ELB-162 | leanprover/lean4:v4.28.0 | null |
{
"evidence": "series/UDWL/COMPARATOR_SUMMARY.md",
"kind": "comparator_dual_kernel_summary",
"public_receipt": false
} | import Mathlib
noncomputable section
namespace Viridis.Ecoterraforming.UsefulDissipatedWork
def supplied (w1 w2 : ℝ) : ℝ := w1 + w2
def useful (w1 w2 e1 e2 : ℝ) : ℝ := e1 * w1 + e2 * w2
def modeledDissipation (w1 w2 e1 e2 : ℝ) : ℝ :=
(1 - e1) * w1 + (1 - e2) * w2
theorem useful_nonnegative (w1 w2 e1 e2 : ℝ)
(... | series/UDWL/contracts/VERIFICATION_STATEMENT.lean | 1734b954ac1a882653fca3b26546958960686af2b254777c68d455f030bfa77f | frozen | elementary | {
"axioms_only_permitted": true,
"challenge_elaborates_with_sorry_targets": true,
"date": "2026-11-06",
"lean_kernel_accepts_reference": true,
"mathlib_rev": "8f9d9cff6bd728b17a24e163c9402775d9e6a365",
"pass": true,
"second_kernel": "not run locally",
"toolchain": "leanprover/lean4:v4.28.0"
} | 8f9d9cff6bd728b17a24e163c9402775d9e6a365 | Viridis.Ecoterraforming.UsefulDissipatedWork | [] | [] | [
"propext",
"Quot.sound",
"Classical.choice"
] | 2026-09-13T00:00:00 | 4 | {
"file": "series/UDWL/ViridisRun163.lean",
"sha256": "36531a31de52283ab665e04675b424e63c2ff4968c81d0ccf51a2d4dd158b10a"
} | eco-lean-bench-task/2 | 2f57ad8f4619bd15e33b943daf26f2f452b02af2 | jdhart81/viridis-canon | Run-163 | frozen statement (series/ deposit, separate VERIFICATION_STATEMENT.lean) | 9 | [
"Viridis.Ecoterraforming.UsefulDissipatedWork.useful_nonnegative",
"Viridis.Ecoterraforming.UsefulDissipatedWork.modeled_dissipation_nonnegative",
"Viridis.Ecoterraforming.UsefulDissipatedWork.work_partition",
"Viridis.Ecoterraforming.UsefulDissipatedWork.useful_le_supplied",
"Viridis.Ecoterraforming.Useful... | ELB-163 | leanprover/lean4:v4.28.0 | null |
{
"evidence": "series/RECB/COMPARATOR_SUMMARY.md",
"kind": "comparator_dual_kernel_summary",
"public_receipt": false
} | import Mathlib
noncomputable section
namespace Viridis.EntropyLearning.RelativeEntropyChangeBudget
def totalChange (d1 d2 : ℝ) : ℝ := d1 + d2
def stewardshipLoad (d1 d2 r1 r2 : ℝ) : ℝ := r1 * d1 + r2 * d2
def modeledSlack (d1 d2 r1 r2 : ℝ) : ℝ :=
(1 - r1) * d1 + (1 - r2) * d2
theorem load_nonnegative (d1 d2 r1 r2... | series/RECB/contracts/VERIFICATION_STATEMENT.lean | e86271e3ce4037a53fdaae84d44e6a462028e8d26dbeb8b07673300e7d35f799 | frozen | elementary | {
"axioms_only_permitted": true,
"challenge_elaborates_with_sorry_targets": true,
"date": "2026-11-06",
"lean_kernel_accepts_reference": true,
"mathlib_rev": "8f9d9cff6bd728b17a24e163c9402775d9e6a365",
"pass": true,
"second_kernel": "not run locally",
"toolchain": "leanprover/lean4:v4.28.0"
} | 8f9d9cff6bd728b17a24e163c9402775d9e6a365 | Viridis.EntropyLearning.RelativeEntropyChangeBudget | [] | [] | [
"propext",
"Quot.sound",
"Classical.choice"
] | 2026-09-13T00:00:00 | 4 | {
"file": "series/RECB/ViridisRun164.lean",
"sha256": "5aa4a3eaf8972f41fc07e3b53f18015f1cb0dd6edcf28de0dc0f9618c5c5cde6"
} | eco-lean-bench-task/2 | 2f57ad8f4619bd15e33b943daf26f2f452b02af2 | jdhart81/viridis-canon | Run-164 | frozen statement (series/ deposit, separate VERIFICATION_STATEMENT.lean) | 9 | [
"Viridis.EntropyLearning.RelativeEntropyChangeBudget.load_nonnegative",
"Viridis.EntropyLearning.RelativeEntropyChangeBudget.modeled_slack_nonnegative",
"Viridis.EntropyLearning.RelativeEntropyChangeBudget.change_partition",
"Viridis.EntropyLearning.RelativeEntropyChangeBudget.load_le_total",
"Viridis.Entro... | ELB-164 | leanprover/lean4:v4.28.0 | null |
{
"evidence": "series/PDC/COMPARATOR_SUMMARY.md",
"kind": "comparator_dual_kernel_summary",
"public_receipt": false
} | import Mathlib
noncomputable section
namespace Viridis.Monitoring.PairedDetectorCoverage
def coverage (p q overlap : ℝ) : ℝ := p + q - overlap
theorem coverage_definition (p q overlap : ℝ) : coverage p q overlap = p + q - overlap := by
sorry
theorem gain_over_first (p q overlap : ℝ) : coverage p q overlap - p = q... | series/PDC/contracts/VERIFICATION_STATEMENT.lean | 76bdaf626021d0fdea9463fe557cb5054df4c4676a250e4b0bc9e91ef3b04a92 | frozen | elementary | {
"axioms_only_permitted": true,
"challenge_elaborates_with_sorry_targets": true,
"date": "2026-11-06",
"lean_kernel_accepts_reference": true,
"mathlib_rev": "8f9d9cff6bd728b17a24e163c9402775d9e6a365",
"pass": true,
"second_kernel": "not run locally",
"toolchain": "leanprover/lean4:v4.28.0"
} | 8f9d9cff6bd728b17a24e163c9402775d9e6a365 | Viridis.Monitoring.PairedDetectorCoverage | [] | [] | [
"propext",
"Quot.sound",
"Classical.choice"
] | 2026-09-19T00:00:00 | 3 | {
"file": "series/PDC/ViridisRun165.lean",
"sha256": "31db8476e072cfce6196036abc0d425b8ed374ab7106c0ce44874ce3729bf2b5"
} | eco-lean-bench-task/2 | 2f57ad8f4619bd15e33b943daf26f2f452b02af2 | jdhart81/viridis-canon | Run-165 | frozen statement (series/ deposit, separate VERIFICATION_STATEMENT.lean) | 7 | [
"Viridis.Monitoring.PairedDetectorCoverage.coverage_definition",
"Viridis.Monitoring.PairedDetectorCoverage.gain_over_first",
"Viridis.Monitoring.PairedDetectorCoverage.gain_over_second",
"Viridis.Monitoring.PairedDetectorCoverage.coverage_ge_first",
"Viridis.Monitoring.PairedDetectorCoverage.coverage_ge_se... | ELB-165 | leanprover/lean4:v4.28.0 | null |
{
"evidence": "series/CAIA/COMPARATOR_SUMMARY.md",
"kind": "comparator_dual_kernel_summary",
"public_receipt": false
} | import Mathlib
namespace Viridis.Computation.CheckerAgreement
theorem disagreement_exposes_error (truth left right : Bool) (h : left ≠ right) :
left ≠ truth ∨ right ≠ truth := by
sorry
theorem agreement_with_left_soundness (truth left right : Bool)
(hAgree : left = right) (hLeft : left = truth) : right = t... | series/CAIA/contracts/VERIFICATION_STATEMENT.lean | 923cdb5685d539162eff09723c8302805e1f4a73c91969f251337261be3f354b | frozen | elementary | {
"axioms_only_permitted": true,
"challenge_elaborates_with_sorry_targets": true,
"date": "2026-11-06",
"lean_kernel_accepts_reference": true,
"mathlib_rev": "8f9d9cff6bd728b17a24e163c9402775d9e6a365",
"pass": true,
"second_kernel": "not run locally",
"toolchain": "leanprover/lean4:v4.28.0"
} | 8f9d9cff6bd728b17a24e163c9402775d9e6a365 | Viridis.Computation.CheckerAgreement | [] | [] | [
"propext",
"Quot.sound",
"Classical.choice"
] | 2026-09-19T00:00:00 | 3 | {
"file": "series/CAIA/ViridisRun166.lean",
"sha256": "668f9abac988a57dc119245a4149eaebcde94b605209b94b8a7631de9b66ce1a"
} | eco-lean-bench-task/2 | 2f57ad8f4619bd15e33b943daf26f2f452b02af2 | jdhart81/viridis-canon | Run-166 | frozen statement (series/ deposit, separate VERIFICATION_STATEMENT.lean) | 4 | [
"Viridis.Computation.CheckerAgreement.disagreement_exposes_error",
"Viridis.Computation.CheckerAgreement.agreement_with_left_soundness",
"Viridis.Computation.CheckerAgreement.agreement_with_right_soundness",
"Viridis.Computation.CheckerAgreement.shared_wrong_agreement_witness"
] | ELB-166 | leanprover/lean4:v4.28.0 | null |
{
"evidence": "series/SPLR/COMPARATOR_SUMMARY.md",
"kind": "comparator_dual_kernel_summary",
"public_receipt": false
} | import Mathlib
namespace Viridis.GaianSystems.SinglePartnerLossReserve
def retainedAfterLoss (a b c lost : ℝ) : ℝ := a + b + c - lost
theorem loss_budget_guarantee
(a b c q budget lost : ℝ)
(hreserve : q + budget ≤ a + b + c)
(hloss : lost ≤ budget) :
q ≤ retainedAfterLoss a b c lost := by
sorry
t... | series/SPLR/contracts/VERIFICATION_STATEMENT.lean | 9d84ab479bd477ca9435ce6e751199d0d6127682af52fc73ad32d754046ae8bf | frozen | elementary | {
"axioms_only_permitted": true,
"challenge_elaborates_with_sorry_targets": true,
"date": "2026-11-06",
"lean_kernel_accepts_reference": true,
"mathlib_rev": "8f9d9cff6bd728b17a24e163c9402775d9e6a365",
"pass": true,
"second_kernel": "not run locally",
"toolchain": "leanprover/lean4:v4.28.0"
} | 8f9d9cff6bd728b17a24e163c9402775d9e6a365 | Viridis.GaianSystems.SinglePartnerLossReserve | [] | [] | [
"propext",
"Quot.sound",
"Classical.choice"
] | 2026-09-19T00:00:00 | 3 | {
"file": "series/SPLR/ViridisRun169.lean",
"sha256": "068492251538894bb720ee1e7f3e101bfeded69a6c4f91e49892c78119b49ece"
} | eco-lean-bench-task/2 | 2f57ad8f4619bd15e33b943daf26f2f452b02af2 | jdhart81/viridis-canon | Run-169 | frozen statement (series/ deposit, separate VERIFICATION_STATEMENT.lean) | 8 | [
"Viridis.GaianSystems.SinglePartnerLossReserve.loss_budget_guarantee",
"Viridis.GaianSystems.SinglePartnerLossReserve.loss_of_a",
"Viridis.GaianSystems.SinglePartnerLossReserve.loss_of_b",
"Viridis.GaianSystems.SinglePartnerLossReserve.loss_of_c",
"Viridis.GaianSystems.SinglePartnerLossReserve.three_partner... | ELB-169 | leanprover/lean4:v4.28.0 | null |
{
"evidence": "series/RASL/COMPARATOR_SUMMARY.md",
"kind": "comparator_dual_kernel_summary",
"public_receipt": false
} | import Mathlib
namespace Viridis.SpeedLimits.ReservedActivity
theorem reserved_activity_bound
(progress ticks usable reserve : Nat)
(hprogress : progress ≤ ticks * usable) :
progress + ticks * reserve ≤ ticks * (usable + reserve) := by
sorry
theorem zero_usable_forces_zero
(progress ticks : Nat)
... | series/RASL/contracts/VERIFICATION_STATEMENT.lean | 72953ae295ad29905343d33a3b06186289662104a70a4a0fc7f7500aefe12cc2 | frozen | elementary | {
"axioms_only_permitted": true,
"challenge_elaborates_with_sorry_targets": true,
"date": "2026-11-06",
"lean_kernel_accepts_reference": true,
"mathlib_rev": "8f9d9cff6bd728b17a24e163c9402775d9e6a365",
"pass": true,
"second_kernel": "not run locally",
"toolchain": "leanprover/lean4:v4.28.0"
} | 8f9d9cff6bd728b17a24e163c9402775d9e6a365 | Viridis.SpeedLimits.ReservedActivity | [] | [] | [
"propext",
"Quot.sound",
"Classical.choice"
] | 2026-09-19T00:00:00 | 2 | {
"file": "series/RASL/ViridisRun171.lean",
"sha256": "2c49eaff46ed034080e2bd59c334c93437bd0413c973dc63d686b0fd9512ebfa"
} | eco-lean-bench-task/2 | 2f57ad8f4619bd15e33b943daf26f2f452b02af2 | jdhart81/viridis-canon | Run-171 | frozen statement (series/ deposit, separate VERIFICATION_STATEMENT.lean) | 4 | [
"Viridis.SpeedLimits.ReservedActivity.reserved_activity_bound",
"Viridis.SpeedLimits.ReservedActivity.zero_usable_forces_zero",
"Viridis.SpeedLimits.ReservedActivity.reserve_monotone",
"Viridis.SpeedLimits.ReservedActivity.reserved_activity_witness"
] | ELB-171 | leanprover/lean4:v4.28.0 | null |
{
"evidence": "series/SRA/COMPARATOR_SUMMARY.md",
"kind": "comparator_dual_kernel_summary",
"public_receipt": false
} | import Mathlib
namespace Viridis.ThermodynamicEconomics.StewardshipReserve
theorem reserve_preserved
(spendable reserve spend : Nat) (hspend : spend ≤ spendable) :
spend + reserve ≤ spendable + reserve := by
sorry
theorem zero_spendable_forces_zero
(reserve spend : Nat) (hspend : spend ≤ 0) :
spend... | series/SRA/contracts/VERIFICATION_STATEMENT.lean | 7f9a9c7ee6f8431e9a3e49c82a543f819c8ac4072965dc1e93ad8df7d5cccb3e | frozen | elementary | {
"axioms_only_permitted": true,
"challenge_elaborates_with_sorry_targets": true,
"date": "2026-11-06",
"lean_kernel_accepts_reference": true,
"mathlib_rev": "8f9d9cff6bd728b17a24e163c9402775d9e6a365",
"pass": true,
"second_kernel": "not run locally",
"toolchain": "leanprover/lean4:v4.28.0"
} | 8f9d9cff6bd728b17a24e163c9402775d9e6a365 | Viridis.ThermodynamicEconomics.StewardshipReserve | [] | [] | [
"propext",
"Quot.sound",
"Classical.choice"
] | 2026-09-27T00:00:00 | 2 | {
"file": "series/SRA/ViridisRun172.lean",
"sha256": "83bcd018520a3fc27a8d3d2d24531d605be71c2421733fb088d7de0e2de89fc9"
} | eco-lean-bench-task/2 | 2f57ad8f4619bd15e33b943daf26f2f452b02af2 | jdhart81/viridis-canon | Run-172 | frozen statement (series/ deposit, separate VERIFICATION_STATEMENT.lean) | 4 | [
"Viridis.ThermodynamicEconomics.StewardshipReserve.reserve_preserved",
"Viridis.ThermodynamicEconomics.StewardshipReserve.zero_spendable_forces_zero",
"Viridis.ThermodynamicEconomics.StewardshipReserve.reserve_monotone",
"Viridis.ThermodynamicEconomics.StewardshipReserve.stewardship_reserve_witness"
] | ELB-172 | leanprover/lean4:v4.28.0 | null |
{
"evidence": "series/SFMC/COMPARATOR_SUMMARY.md",
"kind": "comparator_dual_kernel_summary",
"public_receipt": false
} | import Mathlib
namespace Viridis.HDFM.SharedCorridorFootprint
theorem shared_saving
(a b s : Nat) (hsa : s ≤ a) (hsb : s ≤ b) :
a + b - (a + b - s) = s := by
sorry
theorem combined_le_gross
(a b s : Nat) :
a + b - s ≤ a + b := by
sorry
theorem combined_covers_left
(a b s : Nat) (hsb : s ≤ b)... | series/SFMC/contracts/VERIFICATION_STATEMENT.lean | d60b4e30b473337896c8eebb53bc9e04ac1b534a2d4b4887f8d26fabf4dc58e2 | frozen | elementary | {
"axioms_only_permitted": true,
"challenge_elaborates_with_sorry_targets": true,
"date": "2026-11-06",
"lean_kernel_accepts_reference": true,
"mathlib_rev": "8f9d9cff6bd728b17a24e163c9402775d9e6a365",
"pass": true,
"second_kernel": "not run locally",
"toolchain": "leanprover/lean4:v4.28.0"
} | 8f9d9cff6bd728b17a24e163c9402775d9e6a365 | Viridis.HDFM.SharedCorridorFootprint | [] | [] | [
"propext",
"Quot.sound",
"Classical.choice"
] | 2026-09-27T00:00:00 | 2 | {
"file": "series/SFMC/ViridisRun173.lean",
"sha256": "b2aec63bfa1ab8b99bcac299d4152ed3fe0243e923b44a6e720be8c49dbbadda"
} | eco-lean-bench-task/2 | 2f57ad8f4619bd15e33b943daf26f2f452b02af2 | jdhart81/viridis-canon | Run-173 | frozen statement (series/ deposit, separate VERIFICATION_STATEMENT.lean) | 6 | [
"Viridis.HDFM.SharedCorridorFootprint.shared_saving",
"Viridis.HDFM.SharedCorridorFootprint.combined_le_gross",
"Viridis.HDFM.SharedCorridorFootprint.combined_covers_left",
"Viridis.HDFM.SharedCorridorFootprint.combined_covers_right",
"Viridis.HDFM.SharedCorridorFootprint.left_footprint_contained",
"Virid... | ELB-173 | leanprover/lean4:v4.28.0 | null |
{
"evidence": "series/JMSF/COMPARATOR_SUMMARY.md",
"kind": "comparator_dual_kernel_summary",
"public_receipt": false
} | import Mathlib
namespace Viridis.Ecoservices.JointMinimumFloor
theorem joint_floor_iff
(a b x : Nat) :
max a b ≤ x ↔ a ≤ x ∧ b ≤ x := by
sorry
theorem joint_floor_dominates_left
(a b : Nat) :
a ≤ max a b := by
sorry
theorem joint_floor_dominates_right
(a b : Nat) :
b ≤ max a b := by
so... | series/JMSF/contracts/VERIFICATION_STATEMENT.lean | 49c8c43e2eca0467a375560fe7bf0b8d7ea5aa6bb24eaa99394399061157db7b | frozen | elementary | {
"axioms_only_permitted": true,
"challenge_elaborates_with_sorry_targets": true,
"date": "2026-11-06",
"lean_kernel_accepts_reference": true,
"mathlib_rev": "8f9d9cff6bd728b17a24e163c9402775d9e6a365",
"pass": true,
"second_kernel": "not run locally",
"toolchain": "leanprover/lean4:v4.28.0"
} | 8f9d9cff6bd728b17a24e163c9402775d9e6a365 | Viridis.Ecoservices.JointMinimumFloor | [] | [] | [
"propext",
"Quot.sound",
"Classical.choice"
] | 2026-09-27T00:00:00 | 2 | {
"file": "series/JMSF/ViridisRun174.lean",
"sha256": "5914ede7a3ee10ca962cdbc6508fd5191a0324581828944c74d5d31d9d2a1a11"
} | eco-lean-bench-task/2 | 2f57ad8f4619bd15e33b943daf26f2f452b02af2 | jdhart81/viridis-canon | Run-174 | frozen statement (series/ deposit, separate VERIFICATION_STATEMENT.lean) | 5 | [
"Viridis.Ecoservices.JointMinimumFloor.joint_floor_iff",
"Viridis.Ecoservices.JointMinimumFloor.joint_floor_dominates_left",
"Viridis.Ecoservices.JointMinimumFloor.joint_floor_dominates_right",
"Viridis.Ecoservices.JointMinimumFloor.agreed_floor_sufficient",
"Viridis.Ecoservices.JointMinimumFloor.joint_floo... | ELB-174 | leanprover/lean4:v4.28.0 | null |
{
"evidence": "series/DMEC/COMPARATOR_SUMMARY.md",
"kind": "comparator_dual_kernel_summary",
"public_receipt": false
} | import Mathlib
noncomputable section
namespace Viridis.DScore.MeasurementEnergyCeiling
def dscore (wS wP wG s p g : ℝ) : ℝ :=
wS * s + wP * p + wG * g
def energyEnvelope (wS wP wG kS kP kG eS eP eG : ℝ) : ℝ :=
wS * (kS * eS) + wP * (kP * eP) + wG * (kG * eG)
theorem energy_envelope_nonnegative
(wS wP wG kS... | series/DMEC/contracts/VERIFICATION_STATEMENT.lean | 62752ad22640bd107022e54f7ecc4d46f69b53037a16e165624da56c32736077 | frozen | elementary | {
"axioms_only_permitted": true,
"challenge_elaborates_with_sorry_targets": true,
"date": "2026-11-06",
"lean_kernel_accepts_reference": true,
"mathlib_rev": "8f9d9cff6bd728b17a24e163c9402775d9e6a365",
"pass": true,
"second_kernel": "not run locally",
"toolchain": "leanprover/lean4:v4.28.0"
} | 8f9d9cff6bd728b17a24e163c9402775d9e6a365 | Viridis.DScore.MeasurementEnergyCeiling | [] | [] | [
"propext",
"Quot.sound",
"Classical.choice"
] | 2026-09-27T00:00:00 | 3 | {
"file": "series/DMEC/ViridisRun175.lean",
"sha256": "92bb2d236c3d34b97cdf4bb68e0adfb50b9b141b5999966739c3f65e54d678dc"
} | eco-lean-bench-task/2 | 2f57ad8f4619bd15e33b943daf26f2f452b02af2 | jdhart81/viridis-canon | Run-175 | frozen statement (series/ deposit, separate VERIFICATION_STATEMENT.lean) | 5 | [
"Viridis.DScore.MeasurementEnergyCeiling.energy_envelope_nonnegative",
"Viridis.DScore.MeasurementEnergyCeiling.componentwise_energy_ceiling",
"Viridis.DScore.MeasurementEnergyCeiling.energy_envelope_monotone",
"Viridis.DScore.MeasurementEnergyCeiling.zero_energy_envelope",
"Viridis.DScore.MeasurementEnergy... | ELB-175 | leanprover/lean4:v4.28.0 | null |
{
"evidence": "series/RDA/COMPARATOR_SUMMARY.md",
"kind": "comparator_dual_kernel_summary",
"public_receipt": false
} | import Mathlib
noncomputable section
namespace Viridis.EntropyLearning.ReciprocalDistillationAccounting
def baselineLoss (lossA lossB : ℝ) : ℝ := lossA + lossB
def reciprocityPenalty (klAB klBA : ℝ) : ℝ := klAB + klBA
def mutualObjective (lossA lossB klAB klBA weight : ℝ) : ℝ :=
baselineLoss lossA lossB + weight... | series/RDA/contracts/VERIFICATION_STATEMENT.lean | 8cd3c853347ea12a71a45d98fe4dc6db46ac23aac85561c8fb3dcc565298074e | frozen | elementary | {
"axioms_only_permitted": true,
"challenge_elaborates_with_sorry_targets": true,
"date": "2026-11-06",
"lean_kernel_accepts_reference": true,
"mathlib_rev": "8f9d9cff6bd728b17a24e163c9402775d9e6a365",
"pass": true,
"second_kernel": "not run locally",
"toolchain": "leanprover/lean4:v4.28.0"
} | 8f9d9cff6bd728b17a24e163c9402775d9e6a365 | Viridis.EntropyLearning.ReciprocalDistillationAccounting | [] | [] | [
"propext",
"Quot.sound",
"Classical.choice"
] | 2026-09-27T00:00:00 | 4.5 | {
"file": "series/RDA/ViridisRun176.lean",
"sha256": "fc168804abcbfbb620f323e9d69db5927e9727c4d8189f200e77600f2c7148c0"
} | eco-lean-bench-task/2 | 2f57ad8f4619bd15e33b943daf26f2f452b02af2 | jdhart81/viridis-canon | Run-176 | frozen statement (series/ deposit, separate VERIFICATION_STATEMENT.lean) | 6 | [
"Viridis.EntropyLearning.ReciprocalDistillationAccounting.reciprocity_penalty_nonnegative",
"Viridis.EntropyLearning.ReciprocalDistillationAccounting.mutual_objective_ge_baseline",
"Viridis.EntropyLearning.ReciprocalDistillationAccounting.mutual_objective_zero_weight",
"Viridis.EntropyLearning.ReciprocalDisti... | ELB-176 | leanprover/lean4:v4.28.0 | null |
{
"evidence": "series/FOIEB/COMPARATOR_SUMMARY.md",
"kind": "comparator_dual_kernel_summary",
"public_receipt": false
} | import Mathlib
noncomputable section
namespace Viridis.IntelligenceCapacity.FixedOverheadEnergy
def residualEnergy (budget overhead : ℝ) : ℝ :=
budget - overhead
def processCost (units unitCost overhead : ℝ) : ℝ :=
overhead + units * unitCost
theorem process_cost_decomposition (units unitCost overhead : ℝ) :
... | series/FOIEB/contracts/VERIFICATION_STATEMENT.lean | b493b578674dea3df006f28031621bc28a21212ffb96844526d0e7f84645fc2f | frozen | elementary | {
"axioms_only_permitted": true,
"challenge_elaborates_with_sorry_targets": true,
"date": "2026-11-06",
"lean_kernel_accepts_reference": true,
"mathlib_rev": "8f9d9cff6bd728b17a24e163c9402775d9e6a365",
"pass": true,
"second_kernel": "not run locally",
"toolchain": "leanprover/lean4:v4.28.0"
} | 8f9d9cff6bd728b17a24e163c9402775d9e6a365 | Viridis.IntelligenceCapacity.FixedOverheadEnergy | [] | [] | [
"propext",
"Quot.sound",
"Classical.choice"
] | 2026-09-27T00:00:00 | 3 | {
"file": "series/FOIEB/ViridisRun178.lean",
"sha256": "412bf9973f747ee6d7b4b04ab814ad2cca8ee6b3b143d775b366919b58c02b30"
} | eco-lean-bench-task/2 | 2f57ad8f4619bd15e33b943daf26f2f452b02af2 | jdhart81/viridis-canon | Run-178 | frozen statement (series/ deposit, separate VERIFICATION_STATEMENT.lean) | 7 | [
"Viridis.IntelligenceCapacity.FixedOverheadEnergy.process_cost_decomposition",
"Viridis.IntelligenceCapacity.FixedOverheadEnergy.payload_energy_bound",
"Viridis.IntelligenceCapacity.FixedOverheadEnergy.capacity_quotient_bound",
"Viridis.IntelligenceCapacity.FixedOverheadEnergy.residual_energy_nonnegative",
... | ELB-178 | leanprover/lean4:v4.28.0 | null |
{
"evidence": "runs/2026-10-28_P1/certification.json",
"kind": "engine_v3_verify",
"public_receipt": true
} | import Mathlib
/-!
# P1 · L1: the bit-quad formula for an 8-connected raster
A raster is a finite set `B` of pixels in `ℤ × ℤ`. Pixel `(i, j)` stands for the
closed unit square `[i, i+1] × [j, j+1]`. `K B` is the union of the closed
squares of `B`. It is a cubical complex, and its vertices, edges and faces are
counte... | (built) lean/ViridisStatements/P1/BitQuad.lean + Candidate.main := by sorry | b2866f63ca28f244a720c843cebffe2d4c51ab853a0a78f97d495c65cbec039b | frozen | substantial | {
"axioms_only_permitted": true,
"challenge_elaborates_with_sorry_targets": true,
"date": "2026-11-07",
"kernel_replay": true,
"lean_kernel_accepts_reference": true,
"mathlib_rev": "8f9d9cff6bd728b17a24e163c9402775d9e6a365",
"pass": true,
"second_kernel": "not run (leanchecker replay of the reference in... | 8f9d9cff6bd728b17a24e163c9402775d9e6a365 | ViridisStatements.P1.BitQuad | [
"One target, `Candidate.main`, proving the sealed `Statement`. Helper lemmas are the prover's own work; the reference proof's lemmas are not targets."
] | [] | [
"propext",
"Quot.sound",
"Classical.choice"
] | 2026-10-28T00:00:00 | 75 | {
"files": [
{
"file": "lean/ViridisStatements/P1/BitQuad.lean",
"sha256": "cd3cdeba48f67f9545fb6945c87037893aa98b018922d3d0b7220cc389c98e23"
},
{
"file": "runs/2026-10-28_P1/proofs/P1.BitQuad.lean",
"sha256": "328a9a292c6c09accf3439cb81f2fce20d97efa7ee1eeb8a9acc9d72e6d3c77f"
}... | eco-lean-bench-task/2 | 05ca7128a8b408ca8e16cb47a659aad299ba55a9 | jdhart81/viridis-research | 2026-10-28_P1 | frozen statement (engine sealed statement P1.BitQuad, decision D-001, sealed 2026-10-27T23:03:28Z; proved in run 2026-10-28_P1) | 1 | [
"Candidate.main"
] | ELB-E-P1-BitQuad | leanprover/lean4:v4.28.0 | The 8-connected bit-quad Euler formula for finite rasters: a Lean proof by vertex double counting |
{
"evidence": "runs/2026-11-09_P1/certification.json",
"kind": "engine_v3_verify",
"public_receipt": true
} | import Mathlib
/-!
# P1 · L2: single-pixel insertion
Adding one barrier pixel `p ∉ B` to a finite raster leaves
`enclosed − C8 + χ` unchanged, under (8,4) connectivity. There is no hypothesis
on the 3×3 neighbourhood of `p`: every one of its 256 configurations is covered,
including insertions that merge several 8-com... | (built) lean/ViridisStatements/P1/Insertion.lean + Candidate.main := by sorry | 13d8a1e23a161945632b52aebd1e7b5b7e88ea75640ddb5566dd0c8556d53d27 | frozen | elementary | {
"axioms_only_permitted": true,
"challenge_elaborates_with_sorry_targets": true,
"date": "2026-11-10",
"kernel_replay": true,
"lean_kernel_accepts_reference": true,
"mathlib_rev": "8f9d9cff6bd728b17a24e163c9402775d9e6a365",
"pass": true,
"runner": "by hand (Claude, cloud sandbox, Mathlib built from sou... | 8f9d9cff6bd728b17a24e163c9402775d9e6a365 | ViridisStatements.P1.Insertion | [
"One target, `Candidate.main`, proving the sealed `Statement`. Helper lemmas are the prover's own work; the reference proof's lemmas are not targets.",
"The reference file also proves `Candidate.bridge_eq` (enclosed = C8 - euler for every finite raster), the equation of the separately sealed statement `P1.Bridge`... | [] | [
"propext",
"Quot.sound",
"Classical.choice"
] | 2026-11-09T00:00:00 | 2 | {
"files": [
{
"file": "lean/ViridisStatements/P1/Insertion.lean",
"sha256": "800bd9b9fec5033192b40a9d02dae8abf5c15195b3e2b6f2a1c438a7ab08c734"
},
{
"file": "runs/2026-11-09_P1/proofs/P1.Insertion.lean",
"sha256": "e31434107d76a387f2bd47d3752511581084d3195b2563373ad279fbc907d670"
... | eco-lean-bench-task/2 | 4a7e499933195c1dad53de25b224993ab3f3df7e | jdhart81/viridis-research | 2026-11-09_P1 | frozen statement (engine sealed statement P1.Insertion, decision D-009, sealed 2026-11-08T14:32:32Z; proved in run 2026-11-09_P1) | 1 | [
"Candidate.main"
] | ELB-E-P1-Insertion | leanprover/lean4:v4.28.0 | A machine-checked raster bridge for Trees Cannot Cut: single-pixel insertion preserves enc - C8 + chi |
{
"evidence": "runs/2026-11-01_P2/certification.json",
"kind": "engine_v3_verify",
"public_receipt": true
} | import Mathlib
/-!
# P2 · re-certification: the Afforestation stewardship laws
The live Viridis OS Afforestation kernel ranks seeding plans and site-preparation levers by
seeding efficiency (established canopy per seed) and scores how well a seed allocation is
aligned with the optimal one. Its formal backing is the A... | (built) lean/ViridisStatements/P2/Afforestation.lean + Candidate.main := by sorry | 3f98b4a334051b0e56b66daf5fce3f48c02302ad479801e4cc69898634c416aa | frozen | elementary | {
"axioms_only_permitted": true,
"challenge_elaborates_with_sorry_targets": true,
"date": "2026-11-07",
"kernel_replay": true,
"lean_kernel_accepts_reference": true,
"mathlib_rev": "8f9d9cff6bd728b17a24e163c9402775d9e6a365",
"pass": true,
"second_kernel": "not run (leanchecker replay of the reference in... | 8f9d9cff6bd728b17a24e163c9402775d9e6a365 | ViridisStatements.P2.Afforestation | [
"One target, `Candidate.main`, proving the sealed `Statement`. Helper lemmas are the prover's own work; the reference proof's lemmas are not targets.",
"The sealed statement restates a result from the Viridis Canon whose proof was public before the statement was sealed. The statement was frozen before this proof,... | [] | [
"propext",
"Quot.sound",
"Classical.choice"
] | 2026-11-01T00:00:00 | 4 | {
"files": [
{
"file": "lean/ViridisStatements/P2/Afforestation.lean",
"sha256": "2fc1cbb05d7780f266f9da9c00941ca1b7d8ebc703a11a25fc9bb23237a59436"
},
{
"file": "runs/2026-11-01_P2/proofs/P2.Afforestation.lean",
"sha256": "a179401aa4d0e0de8a14944fe4356287cdd2295f2d71d3fcd87a8093091... | eco-lean-bench-task/2 | 05ca7128a8b408ca8e16cb47a659aad299ba55a9 | jdhart81/viridis-research | 2026-11-01_P2 | frozen statement (engine sealed statement P2.Afforestation, decision D-007, sealed 2026-10-31T13:19:07Z; proved in run 2026-11-01_P2) | 1 | [
"Candidate.main"
] | ELB-E-P2-Afforestation | leanprover/lean4:v4.28.0 | Re-certifying the Viridis OS Decision Kernels: A Lean Proof of the Afforestation Seeding Core |
{
"evidence": "runs/2026-10-29_P2/certification.json",
"kind": "engine_v3_verify",
"public_receipt": true
} | import Mathlib
/-!
# P2 · re-certification: the Carbon Continuity threshold
The live Viridis OS kernel "Carbon Continuity — wildfire recovery threshold diagnostic"
(runtime `viridis.carbon-continuity-threshold.v1`, `src/lib/carbonContinuity.ts` in
viridis-conservation-app) decides whether a two-pool carbon portfolio ... | (built) lean/ViridisStatements/P2/CarbonContinuity.lean + Candidate.main := by sorry | 2fd3fa445719e9f4d7fa09a53faae5cd016ddaf7cdea4629fa2f6e54ff1fda5d | frozen | elementary | {
"axioms_only_permitted": true,
"challenge_elaborates_with_sorry_targets": true,
"date": "2026-11-07",
"kernel_replay": true,
"lean_kernel_accepts_reference": true,
"mathlib_rev": "8f9d9cff6bd728b17a24e163c9402775d9e6a365",
"pass": true,
"second_kernel": "not run (leanchecker replay of the reference in... | 8f9d9cff6bd728b17a24e163c9402775d9e6a365 | ViridisStatements.P2.CarbonContinuity | [
"One target, `Candidate.main`, proving the sealed `Statement`. Helper lemmas are the prover's own work; the reference proof's lemmas are not targets.",
"The sealed statement restates a result from the Viridis Canon whose proof was public before the statement was sealed. The statement was frozen before this proof,... | [] | [
"propext",
"Quot.sound",
"Classical.choice"
] | 2026-10-29T00:00:00 | 3 | {
"files": [
{
"file": "lean/ViridisStatements/P2/CarbonContinuity.lean",
"sha256": "a5a6e8c63205b865da0df0c302f1926b48d1874ce1310053da6c1ae3104ffded"
},
{
"file": "runs/2026-10-29_P2/proofs/P2.CarbonContinuity.lean",
"sha256": "bfced37f622d1ab9921f2fe7bf02ffa7c88dbdeb1e53d3a250df0... | eco-lean-bench-task/2 | 05ca7128a8b408ca8e16cb47a659aad299ba55a9 | jdhart81/viridis-research | 2026-10-29_P2 | frozen statement (engine sealed statement P2.CarbonContinuity, decision D-004, sealed 2026-10-28T23:29:57Z; proved in run 2026-10-29_P2) | 1 | [
"Candidate.main"
] | ELB-E-P2-CarbonContinuity | leanprover/lean4:v4.28.0 | Re-certifying the Carbon Continuity Threshold: A Lean Proof of the Two-Pool Regenerative Coupling Condition under a Pinned Toolchain |
{
"evidence": "runs/2026-11-02_P2/certification.json",
"kind": "engine_v3_verify",
"public_receipt": true
} | import Mathlib
/-!
# P2 · re-certification: Gaian Harmonization, the scalar-price welfare theorem
The live Viridis OS Harmonization kernel coordinates `N` local stewards (sites, agents) toward
a shared regulation target by broadcasting one scalar price instead of `N` commands. Its formal
backing is the Gaian Harmoniz... | (built) lean/ViridisStatements/P2/Harmonization.lean + Candidate.main := by sorry | 83fff04a7dc465595c2f71fbbdf5d01500f85408b9fd0ed0362d6b8c407edf2e | frozen | elementary | {
"axioms_only_permitted": true,
"challenge_elaborates_with_sorry_targets": true,
"date": "2026-11-07",
"kernel_replay": true,
"lean_kernel_accepts_reference": true,
"mathlib_rev": "8f9d9cff6bd728b17a24e163c9402775d9e6a365",
"pass": true,
"second_kernel": "not run (leanchecker replay of the reference in... | 8f9d9cff6bd728b17a24e163c9402775d9e6a365 | ViridisStatements.P2.Harmonization | [
"One target, `Candidate.main`, proving the sealed `Statement`. Helper lemmas are the prover's own work; the reference proof's lemmas are not targets.",
"The sealed statement restates a result from the Viridis Canon whose proof was public before the statement was sealed. The statement was frozen before this proof,... | [] | [
"propext",
"Quot.sound",
"Classical.choice"
] | 2026-11-02T00:00:00 | 3 | {
"files": [
{
"file": "lean/ViridisStatements/P2/Harmonization.lean",
"sha256": "48934ecb301f858b8332eea15194ff42a119fd7c1c7a7402089467a4994b3dd7"
},
{
"file": "runs/2026-11-02_P2/proofs/P2.Harmonization.lean",
"sha256": "1bcfdf8580578e7aec5c34f539fe0f3994119c63e78fbf5285aa44ff270... | eco-lean-bench-task/2 | 05ca7128a8b408ca8e16cb47a659aad299ba55a9 | jdhart81/viridis-research | 2026-11-02_P2 | frozen statement (engine sealed statement P2.Harmonization, decision D-008, sealed 2026-10-31T13:19:10Z; proved in run 2026-11-02_P2) | 1 | [
"Candidate.main"
] | ELB-E-P2-Harmonization | leanprover/lean4:v4.28.0 | Re-certifying the Viridis OS Decision Kernels: A Lean Proof of the Harmonization Scalar-Price Welfare Core |
{
"evidence": "runs/2026-10-31_P2/certification.json",
"kind": "engine_v3_verify",
"public_receipt": true
} | import Mathlib
/-!
# P2 · re-certification: the Restoration critical-nucleus go/no-go
The live Viridis OS Restoration kernel decides whether a planted cluster on degraded land is
large enough to grow into forest (go) or will dissolve back into the degraded state (no-go).
Its formal backing is the Forest Nucleation Th... | (built) lean/ViridisStatements/P2/Restoration.lean + Candidate.main := by sorry | de3713286acea6cf82084ec8c7cc51421e1b2c7aa7894048bd8286964c384d87 | frozen | elementary | {
"axioms_only_permitted": true,
"challenge_elaborates_with_sorry_targets": true,
"date": "2026-11-07",
"kernel_replay": true,
"lean_kernel_accepts_reference": true,
"mathlib_rev": "8f9d9cff6bd728b17a24e163c9402775d9e6a365",
"pass": true,
"second_kernel": "not run (leanchecker replay of the reference in... | 8f9d9cff6bd728b17a24e163c9402775d9e6a365 | ViridisStatements.P2.Restoration | [
"One target, `Candidate.main`, proving the sealed `Statement`. Helper lemmas are the prover's own work; the reference proof's lemmas are not targets.",
"The sealed statement restates a result from the Viridis Canon whose proof was public before the statement was sealed. The statement was frozen before this proof,... | [] | [
"propext",
"Quot.sound",
"Classical.choice"
] | 2026-10-31T00:00:00 | 3 | {
"files": [
{
"file": "lean/ViridisStatements/P2/Restoration.lean",
"sha256": "fd40b113c06beaed7940b2bf84d931a8b9179dcabaf3c2d27f7300dc27ccff18"
},
{
"file": "runs/2026-10-31_P2/proofs/P2.Restoration.lean",
"sha256": "59286948a6b807ac2f16da6bc2558780d11987b2b01adde147a06d61e2eba4b... | eco-lean-bench-task/2 | 05ca7128a8b408ca8e16cb47a659aad299ba55a9 | jdhart81/viridis-research | 2026-10-31_P2 | frozen statement (engine sealed statement P2.Restoration, decision D-006, sealed 2026-10-31T13:19:05Z; proved in run 2026-10-31_P2) | 1 | [
"Candidate.main"
] | ELB-E-P2-Restoration | leanprover/lean4:v4.28.0 | Re-certifying the Viridis OS Decision Kernels: A Lean Proof of the Restoration Critical-Nucleus Core |
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