Encyclopedia Gravity Gravity Seven Gaps Full Theory Ledger
ARTICLE 5 claims 5 theorems
Gravity Seven Gaps Full Theory Ledger
A machine-checked scoreboard for quantum gravity that refuses to declare victory until every promised result is actually proved.
The full-theory ledger
The full theory ledger is a formal, machine-checked record of progress toward a complete quantum theory of gravity. It works like a benchmark list: each item is a boolean flag that flips to true only when a specific target theorem has been verified by a proof-checking kernel, audited for hidden assumptions, and passed a separate review. The ledger's purpose is to make the difference between a claimed result and a proved result impossible to blur.
The ledger organizes the campaign into three pillars. The first pillar is classical recovery: deriving Einstein's gravity in the smooth four-dimensional limit from a discrete theory whose form was derived, not chosen. The second is a well-defined quantum amplitude: a bridge from the underlying substrate to geometry, a derived measure, and a continuum limit under mesh refinement. The third is a discriminating prediction: an observable where the theory differs from Einstein or LambdaCDM by a stated number of measurement sigma. The ledger also demands that no closer contain a free real constant.
In July 2026 the ledger's own criterion was audited and found wanting. Six defects shared one cause: the criterion checked that a statement had been proved, but never that the proved statement was the promised one. For example, pillar one never asked where the Regge discretization came from, and pillar two could have flipped on a complexity cutoff that is not a continuum limit. The repair is itself a proved theorem, strictly stronger than the old criterion against four decoy benchmark sets and a positive control.
The consequence is honest and precise: pillar one is open again. The three classical recovery strengths still hold, but the criterion now asks a question it previously did not. As of the ledger's record, pillars one and two are closed under the repaired criterion, pillar three remains open, and the discriminating-prediction gate is not confirmed. The ledger cannot drift from this state because the closure criterion is a definition, and the master theorem that the full theory is open remains provable until every flag flips.
In Recognition Science, this ledger is the campaign's memory. It does not claim to have built the theory; it claims to know exactly which parts are built, which are not, and what would count as building them.
THEOREM FullTheoryBenchmarks · IndisputableMonolith/Gravity/SevenGaps/FullTheoryLedger.lean
/-- The full-theory benchmark flags. Every field documents the exact target
theorem whose kernel-checked existence licenses flipping it. -/
structure FullTheoryBenchmarks where
/-- Phase 1 (pillar 2, part A): CLOSED 2026-07-22 under amended intent.
Closing theorems: `recognition_ratio_derived` (R5) +
`regge_deformation_signed_deficit_witness` including the N5 torus lift
(`regge_deformation_signed_deficit_witness_n5_torus_holds`,
`n5FaceDiagHingeDeficit_eq_faceDiagStarDeficit`) +
`gap1_hessian_join_closing_package` (sector-resolved join + counting
blocker + geometry-import firewall + weighted mesh join). Disclosed
scope: (1) geometry-import firewall —
`gap1_no_counting_weight_closure_holds` certifies the Euclidean hinge
measure import is not eliminable by counting weights; (2) derivation
carrier `H = Real` (`encodedFreudenthalLiftOpen` remains true upstream);
(3) `einsteinScaleJoinOpen` remains true (scale join not claimed). -/
gap1_bridge_derived : Bool
/-- Phase 2 (pillar 2, part B): the continuum limit on the simplicial class
together with a substrate-derived measure.
**No closing theorem is nominated, and none exists.** An earlier version of
this comment named `Z_RS_continuum_limit`, which is not a theorem anywhere in
the library; it is a status Boolean in `ZqPhaseStructure` and
`MeasureInvarianceNoGo`, both of which are themselves `false`. Naming a flag
as if it were a closer is how a truth source gets read wrong, so the honest
state is recorded instead.
What exists: the cap-shell bridge sub-premise is discharged below (P2.3).
What is missing for the convergence half is an `OscillatoryTail` witness for
a substrate-derived phase; the measure half is separately open.
**D5 correction (2026-07-26).** An earlier version of this comment said
`MeasureInvarianceNoGo` "proves counting weights cannot supply the measure".
It proves close to the opposite. Its headline
`invariance_admits_infinite_measure_family` exhibits infinitely many weights
satisfying relabeling invariance, positivity, the mass bound, and unit-on-
empty, and `muMeasure_satisfies` puts the counting weight `1 / |Aut K|`
itself among them. The result is that those four axioms *underdetermine* the
measure, which is why richer substrate structure is needed. Counting is not
excluded; it is exactly what `MeasureSubstrateBlocker` shows the gauge-
counting principle selects.
This flag is retained because other modules bind to it, and is now the
conjunction target of the two finer flags `gap2_measure_derived` and
`gap2_geometric_continuum_limit` below. Pillar 2 requires all three.
FLIPPED 2026-07-31 with the second finer flag: both finer flags are true,
so the roll-up is true. -/
gap2_continuum_and_measure : Bool
/-- Phase 3: the 4D Lorentzian lift (`CausalSimplex4D` +
`wick_action_continuation_4d_v2`). MODEL scope: three-pent one-hinge
(charts collapse to a single angle path; not a full multi-hinge complex).
V1 terminal `wick_action_continuation_4d` is retired
(`not_wick_action_continuation_4d`). Binding receipt:
`WickActionV2CloseStatus.gap6_lorentzian_action_bound_to_v2`. -/
gap6_lorentzian_action : Bool
/-- Phase 4 (pillar 1, operator strength):
`discrete_tt_spectrum_converges_curved` + `quasinormal_mode_spectrum`. -/
gap4_operator_recovery : Bool
/-- Phase 5 (pillar 1, constraint strength): CLOSED 2026-07-23.
`dirac_algebra_continuum_limit` + `hojman_pins_general_relativity`.
HKT half is the n=2 CanonicalMom ContDiff-2 point-split class with
disclosed kinetic intensivity normalization `hp = 2 cKin p`; conclusion
`hamDensity = cKin p² + cGrad · structureFunction · (b-a)² + V` with
`cMom = 4 cKin cGrad`. Kill tower cited as the scope certificate that no
stronger unconditioned n=2 statement is true. Binding receipt:
`Gap5ConstraintCloseStatus.gap5_constraint_recovery_bound_to_terminals`. -/
gap5_constraint_recovery : Bool
/-- Phase 6 (pillar 1, action strength): `edge_tt_decomposition` +
`S_RS_converges_EH_4d`. -/
gap_action_recovery : Bool
/-- Phase 7 (pillar 3, the theory-maker): a separately derived discriminating
observable together with a prospectively valid external pass.
**No closer is nominated.** An earlier version of this comment named
`bmv_entanglement_witness` or `seam_effective_count_derived`. Neither is the
live campaign. After the 2026-07-23 truth-repair the dynamic CPL bridge is not
the active closer either: its immutable gate
`plans/QG_Pillar3_CPL_Forecast_Gate_20260717.html` is formally `WAITING` with
reconstructed contours forbidden, and the retrospective DESI exclusion is
banked off-protocol. See the Pillar 3 entry in the cross-reference block below.
This flag is never flipped by a simulation and never by CPL materials. -/
discriminating_prediction_confirmed : Bool
/-- **D1 (added 2026-07-26, criterion repair).** Pillar 1, provenance
strength. The four recovery flags above certify that the Regge
discretization *recovers* Einstein gravity in the limit. None of them asks
where that discretization came from, so all four can be true while the
discrete theory was stipulated and then verified.
Open, with a written negative verdict:
`QG/papers/QG_Pillar1_Provenance_Verdict_20260726.html`. The geometric route
(O1-O5) is closed by `Gap1O2FaceMeasureExhaustion.no_geometric_rule_in_four_dimensions`
and `no_class_commensurate_rule`. The constraint-sector route is refuted by
`Gap5ChartFromLedgerMomentum.chart_not_forced_without_linearity` (the chart
`t = 2 arsinh (lam p)` is forced only after linearity of the momentum
observable is assumed, and linearity is not derived) together with
`event_cost_differs_from_state_cost`.
Sole surviving positive route (O15): derive that the momentum observable is
additive under ledger consolidation. `additive_continuous_balanced_is_imbalance`
already shows additivity plus continuity plus vanishing at balance forces the
imbalance coordinate, so additivity is the whole remaining obligation. The
Noether route is dead at the carrier: `Foundation.SigmaNoetherCharge.sigma_charge`
is identically zero on the analytic carrier, so its conservation proof is
vacuous.
**FLIPPED 2026-07-31 (Jon ruled D-A: `D-qg-da-adopted-20260731`).** Closed
at MODEL strength under the named adoptions, never derived. The O15
obligation (additivity of the momentum observable under ledger
consolidation) is a theorem about the adopted momentum:
`Gap5UnitIdentificationsAdopted.provenance_under_adoptions` composes
`additive_continuous_balanced_is_imbalance` with the adopted
identifications and forces the momentum observable to be the imbalance
coordinate, with the scale multiple pinned to `1` and the link channel
sharing the ground-state chart. The identifications themselves are
FOUNDATIONAL MODELs adopted by Jon: MODEL 1 (`physicalMomentum =
imbalance`, adopted 2026-07-31, `D-qg-eec-adopted-as-model-20260731`),
MODEL 1-L (`LinkChannelUnitIdentification`, adopted 2026-07-31, D-A), and
the SameLatticeUnitsPremise (`chi = 1`, adopted 2026-07-31, D-A); the
banked MODEL 2 stipulated chart relation (same 2026-07-31 EEC adoption)
supplies the `lam² = 1/4` the coherence conjunct needs. Every
derivation route for the identifications stays dead at kernel strength
exactly as recorded above and in `Gap5IncoherentConstraint`; what closed
the flag is Jon's adoption, not a derivation. Every claim resting on this
flag inherits MODEL strength. The flag name predates the ruling and is
retained so downstream modules stay sound. -/
gap1_provenance_derived : Bool
/-- **D6 (added 2026-07-26, criterion repair).** Pillar 2, measure half,
stated separately from the legacy roll-up flag because the roll-up cannot
express which half is open.
The exact obligation is `MeasureSubstrateBlocker.GaugeCountingPrinciple`,
which by `substrate_measure_blocker_certificate` holds exactly for
`1 / |Aut K|`. It must be *derived* from substrate structure richer than
counting, without reintroducing the automorphism group.
Open, and the record elsewhere in the library currently disagrees.
`GaugeHistoryMeasure.gap2_gauge_counting_from_history_discharged` is banked
as a discharge, and on its strength
`PathSumMeasure.pathSumMeasureStatus.substrate_measure_derived` and
`ExactShellGaugePreflight.gaugePreflightStatus.counting_principle_derived_from_ledger`
were flipped true. Audit 2026-07-26 finds that theorem contentless as a
derivation: `CanonicalHistory.equivUnderlying` proves the counted type
equivalent to the plain `BoundedComplex`, `HistoryRelabel.ofRelabel`
discharges every added posting condition by `rfl`, `GaugeHistoryEnrichment`
has no fields and `nuBuild` ignores it, `balancedZeroState` pins all ledger
data to zero, and both new counts are proved equal to the pre-existing
counts. The theorem is a true presentation result about the same ratio, and
survives replacing the ledger data by a constant, so no ledger information
selects the measure. Independently reached by a cross-family reader given
only the file and the question (2026-07-26), which named the failure
semantic rather than syntactic circularity: `Aut` is not written down, it is
reimported through an equivalent wrapper.
**The 2026-07-30 split (locked panel protocol, G1-signed).** The obligation
has two halves with separate gates. The base half asks why the counting
weight `1 / |Aut K|` rather than a rival (uniform-on-iso-classes is the
nearest): `Gap2LabelErasure.pushforward_labeledWeight_eq_gauge_divisor`
derives the divisor as the Jacobian of label erasure with `Aut` permitted in
the conclusion and forbidden on the hypothesis side (letterwise
`RelabelInvariant`; cross-family dependency-graph audit signed PASS), and
`no_local_additive_cost_realizes_log_aut` plus
`uniform_is_not_a_local_pushforward` discriminate by locality, since
`log |Aut|` is superextensive over disjoint doubling while local additive
costs are exactly extensive. The no-tilt half asks why the Boltzmann
numerator is one: numerator-first closure was killed the same day
(base-measure substitution; the chain is invariant under any base weight),
so the no-tilt half was routed through the C17 fugacity elimination.
**FLIPPED 2026-07-30 (gatekeeper-signed).** Both halves now hold, assembled
in `Gap2MeasureDerivation.gap2_gauge_counting_gibbsWeight` and
`gap2_gauge_counting_from_surface_and_kindTotals`. Load-bearing split, per
the gatekeeper review: the base closing rests on `blocker_iff_mu` plus the
C4 bridge (`mu_eq_gibbs_mul_erasePush_one`), all THEOREM; the no-tilt
closing rests on C17 `unit_fugacity_forced_by_surface_and_kindTotals` plus
the blocker iff, all THEOREM; the labeled-weight / erasure-pushforward
carrier is definitionally load-bearing (MODEL); the C16 fields
(`c16_cap3_uniform_measured`, `c16_cap4_uniform_derived_unformalized`,
`c16_rate_symmetry_balance`, `c16_ratio_half_under_uniform`) are process
discrimination only and are not cited by the closing proof terms. The
J-tilt is excluded from this flag by Jon's bookkeeping ruling
(`D-qg-c27-ruling-bookkeeping-20260730`) and routed to flag 9 as emergent
action. The gatekeeper's hostile probe discriminates: a wrong (uniform)
labeled weight fails `GaugeCountingPrinciple` kernel-side. -/
gap2_measure_derived : Bool
/-- **D2 (added 2026-07-26, criterion repair).** Pillar 2, continuum half,
at the geometric strength the pillar actually claims.
The legacy flag would flip on a complexity-cutoff limit, meaning convergence
of `Zcap` as the combinatorial complexity bound grows. That is not a
continuum limit: `gap2_metric_carrier_blocker_certified` shows the
combinatorial quotient forgets metric data, so a cutoff limit is compatible
with no metric refinement at all.
The typed target is
`MetricRefinementCarrierBlocker
-- … truncated for the page; open the module for the rest.
THEOREM repaired_criterion_is_strictly_stronger · IndisputableMonolith/Gravity/SevenGaps/FullTheoryLedger.lean
/-- **The gate discriminates: strictness.** All four decoys close under the
pre-repair criterion and fail under the repaired one, each for its own defect,
while the positive control closes under both. A gate that rejected everything
would satisfy `repaired_criterion_implies_legacy` vacuously; the last conjunct
is what rules that out. -/
theorem repaired_criterion_is_strictly_stronger :
(LegacyFullTheoryClosed laundryBenchmarks ∧
¬ FullTheoryClosed laundryBenchmarks) ∧
(LegacyFullTheoryClosed cutoffOnlyBenchmarks ∧
¬ FullTheoryClosed cutoffOnlyBenchmarks) ∧
(LegacyFullTheoryClosed weakPredictionBenchmarks ∧
¬ FullTheoryClosed weakPredictionBenchmarks) ∧
(LegacyFullTheoryClosed freeConstantBenchmarks ∧
¬ FullTheoryClosed freeConstantBenchmarks) ∧
(LegacyFullTheoryClosed idealBenchmarks ∧
FullTheoryClosed idealBenchmarks) :=
⟨⟨laundry_closes_legacy, laundry_fails_repaired⟩,
⟨cutoffOnly_closes_legacy, cutoffOnly_fails_repaired⟩,
⟨weakPrediction_closes_legacy, weakPrediction_fails_repaired⟩,
⟨freeConstant_closes_legacy, freeConstant_fails_repaired⟩,
⟨ideal_closes_legacy, idealBenchmarks_closes⟩⟩
THEOREM full_theory_open_pillar3_alone · IndisputableMonolith/Gravity/SevenGaps/FullTheoryLedger.lean
/-- **MASTER THEOREM (the honest gate), replaced 2026-07-31 after the D-A
adoptions.** The full theory is NOT closed, and the obstruction is Pillar 3
alone: `discriminating_prediction_confirmed = false` and
`prediction_is_discriminating = false` (flag 11; its residual is E_lat and
the sky). The strength of every closed conjunct: flag 6
(`gap1_provenance_derived`) and flag 12 (`no_free_constants`) closed
2026-07-31 at MODEL strength under the named D-A adoptions (MODEL 1-L and
the SameLatticeUnitsPremise, on top of the already adopted MODEL 1 and
MODEL 2; never derived, the derivation routes kernel-proved dead), composed
in `Gap5UnitIdentificationsAdopted`; Pillar 2 closed 2026-07-31 with flag 9
at derived action shape plus MODEL super-critical strength
(D-qg-flag9-closes-at-model-strength-20260731) on top of the bridge and
measure flags at theorem strength; the four recovery flags of Pillar 1
stand at theorem strength. This theorem replaces `full_theory_not_yet_closed`,
retired the day pillars 1 and 2 closed because its recorded premise (two
pillars open) stopped being true; it fails to build unchanged the moment
flag 11 flips, so it cannot silently coexist with a closure claim. -/
theorem full_theory_open_pillar3_alone :
¬ FullTheoryClosed fullTheoryBenchmarks ∧
Pillar1Closed fullTheoryBenchmarks ∧
Pillar2Closed fullTheoryBenchmarks ∧
¬ Pillar3Closed fullTheoryBenchmarks := by
refine ⟨?_, ⟨rfl, rfl, rfl, rfl, rfl⟩, ⟨rfl, rfl, rfl, rfl⟩, fun h => ?_⟩
· intro h
have := h.2.2.1.1
simp [fullTheoryBenchmarks] at this
· have := h.1
simp [fullTheoryBenchmarks] at this
THEOREM classical_recovery_strengths_hold · IndisputableMonolith/Gravity/SevenGaps/FullTheoryLedger.lean
/-- The three classical recovery strengths of Pillar 1 are all still proved.
This is the content that the pre-repair Pillar 1 flag recorded, kept explicit
so that strengthening the criterion cannot be misread as retracting a
theorem. -/
theorem classical_recovery_strengths_hold :
LegacyPillar1Closed fullTheoryBenchmarks := by
simp [LegacyPillar1Closed, fullTheoryBenchmarks]
THEOREM pillar1_and_pillar2_closed_pillar3_open · IndisputableMonolith/Gravity/SevenGaps/FullTheoryLedger.lean
/-- **PILLARS 1 AND 2 CLOSED, Pillar 3 open, 2026-07-31 (the D-A day).**
Pillar 1 closed when `gap1_provenance_derived` flipped under Jon's D-A
ruling: its provenance conjunct holds at MODEL strength under the named
adoptions (never derived), on top of the four recovery strengths at theorem
strength (`classical_recovery_strengths_hold`). Pillar 2 closed the same
day (flag 9, at derived action shape plus MODEL super-critical strength).
Pillar 3 stays open: both flag-11 conjuncts are `false`, with residual
E_lat and the sky. Nothing was un-proved to produce either closure, and no
Boolean was flipped down. Renamed from
`pillar1_and_pillar3_open_pillar2_closed` the day Pillar 1 closed. -/
theorem pillar1_and_pillar2_closed_pillar3_open :
Pillar1Closed fullTheoryBenchmarks ∧
Pillar2Closed fullTheoryBenchmarks ∧
¬ Pillar3Closed fullTheoryBenchmarks :=
full_theory_open_pillar3_alone.2
What this page does not claim
The full theory of quantum gravity is not claimed to be complete or closed. Pillar one is not claimed to be closed under the repaired criterion. The ledger does not claim that any discriminating prediction has been confirmed.
Verify this page
Every tagged claim above names its theorem. To check one yourself rather than trust this page, elaborate the source module with Lean 4 and audit its axiom basis:
$ lake env lean IndisputableMonolith/Gravity/SevenGaps/FullTheoryLedger.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)
A page whose claims cannot be reproduced this way does not ship. In production, every anchor links to the exact declaration in the public source release, and this block carries the build receipt for the page itself.
Derived articles
This page is generated by a question-recursion engine: the questions its answers raise become the next pages. The current agenda, with open targets marked red:
- What exactly does the derived substrate-to-geometry bridge look like?
- What observable could serve as the discriminating prediction for pillar three?
- How does the discrete theory recover the Einstein constraint algebra?
- What is the physical interpretation of the metric carrier blocker?
- How does the campaign plan to close the discriminating-prediction gate?
MACHINE LAYER · GROUNDED CLAIM TABLE · CLICK TO EXPAND
THEOREM FullTheoryBenchmarks · IndisputableMonolith/Gravity/SevenGaps/FullTheoryLedger.lean
/-- The full-theory benchmark flags. Every field documents the exact target theorem whose kernel-checked existence licenses flipping it. -/ structure FullTheoryBenchmarks where /-- Phase 1 (pillar 2, part A): CLOSED 2026-07-22 under amended intent. Closing theorems: `recognition_ratio_derived` (R5) + `regge_deformation_signed_deficit_witness` including the N5 torus lift (`regge_deformation_signed_deficit_witness_n5_torus_holds`, `n5FaceDiagHingeDeficit_eq_faceDiagStarDeficit`) + `gap1_hessian_join_closing_package` (sector-resolved join + counting blocker + geometry-import firewall + weighted mesh join). Disclosed scope: (1) geometry-import firewall — `gap1_no_counting_weight_closure_holds` certifies the Euclidean hinge measure import is not eliminable by counting weights; (2) derivation carrier `H = Real` (`encodedFreudenthalLiftOpen` remains true upstream); (3) `einsteinScaleJoinOpen` remains true (scale join not claimed). -/ gap1_bridge_derived : Bool /-- Phase 2 (pillar 2, part B): the continuum limit on the simplicial class together with a substrate-derived measure. **No closing theorem is nominated, and none exists.** An earlier version of this comment named `Z_RS_continuum_limit`, which is not a theorem anywhere in the library; it is a status Boolean in `ZqPhaseStructure` and `MeasureInvarianceNoGo`, both of which are themselves `false`. Naming a flag as if it were a closer is how a truth source gets read wrong, so the honest state is recorded instead. What exists: the cap-shell bridge sub-premise is discharged below (P2.3). What is missing for the convergence half is an `OscillatoryTail` witness for a substrate-derived phase; the measure half is separately open. **D5 correction (2026-07-26).** An earlier version of this comment said `MeasureInvarianceNoGo` "proves counting weights cannot supply the measure". It proves close to the opposite. Its headline `invariance_admits_infinite_measure_family` exhibits infinitely many weights satisfying relabeling invariance, positivity, the mass bound, and unit-on- empty, and `muMeasure_satisfies` puts the counting weight `1 / |Aut K|` itself among them. The result is that those four axioms *underdetermine* the measure, which is why richer substrate structure is needed. Counting is not excluded; it is exactly what `MeasureSubstrateBlocker` shows the gauge- counting principle selects. This flag is retained because other modules bind to it, and is now the conjunction target of the two finer flags `gap2_measure_derived` and `gap2_geometric_continuum_limit` below. Pillar 2 requires all three. FLIPPED 2026-07-31 with the second finer flag: both finer flags are true, so the roll-up is true. -/ gap2_continuum_and_measure : Bool /-- Phase 3: the 4D Lorentzian lift (`CausalSimplex4D` + `wick_action_continuation_4d_v2`). MODEL scope: three-pent one-hinge (charts collapse to a single angle path; not a full multi-hinge complex). V1 terminal `wick_action_continuation_4d` is retired (`not_wick_action_continuation_4d`). Binding receipt: `WickActionV2CloseStatus.gap6_lorentzian_action_bound_to_v2`. -/ gap6_lorentzian_action : Bool /-- Phase 4 (pillar 1, operator strength): `discrete_tt_spectrum_converges_curved` + `quasinormal_mode_spectrum`. -/ gap4_operator_recovery : Bool /-- Phase 5 (pillar 1, constraint strength): CLOSED 2026-07-23. `dirac_algebra_continuum_limit` + `hojman_pins_general_relativity`. HKT half is the n=2 CanonicalMom ContDiff-2 point-split class with disclosed kinetic intensivity normalization `hp = 2 cKin p`; conclusion `hamDensity = cKin p² + cGrad · structureFunction · (b-a)² + V` with `cMom = 4 cKin cGrad`. Kill tower cited as the scope certificate that no stronger unconditioned n=2 statement is true. Binding receipt: `Gap5ConstraintCloseStatus.gap5_constraint_recovery_bound_to_terminals`. -/ gap5_constraint_recovery : Bool /-- Phase 6 (pillar 1, action strength): `edge_tt_decomposition` + `S_RS_converges_EH_4d`. -/ gap_action_recovery : Bool /-- Phase 7 (pillar 3, the theory-maker): a separately derived discriminating observable together with a prospectively valid external pass. **No closer is nominated.** An earlier version of this comment named `bmv_entanglement_witness` or `seam_effective_count_derived`. Neither is the live campaign. After the 2026-07-23 truth-repair the dynamic CPL bridge is not the active closer either: its immutable gate `plans/QG_Pillar3_CPL_Forecast_Gate_20260717.html` is formally `WAITING` with reconstructed contours forbidden, and the retrospective DESI exclusion is banked off-protocol. See the Pillar 3 entry in the cross-reference block below. This flag is never flipped by a simulation and never by CPL materials. -/ discriminating_prediction_confirmed : Bool /-- **D1 (added 2026-07-26, criterion repair).** Pillar 1, provenance strength. The four recovery flags above certify that the Regge discretization *recovers* Einstein gravity in the limit. None of them asks where that discretization came from, so all four can be true while the discrete theory was stipulated and then verified. Open, with a written negative verdict: `QG/papers/QG_Pillar1_Provenance_Verdict_20260726.html`. The geometric route (O1-O5) is closed by `Gap1O2FaceMeasureExhaustion.no_geometric_rule_in_four_dimensions` and `no_class_commensurate_rule`. The constraint-sector route is refuted by `Gap5ChartFromLedgerMomentum.chart_not_forced_without_linearity` (the chart `t = 2 arsinh (lam p)` is forced only after linearity of the momentum observable is assumed, and linearity is not derived) together with `event_cost_differs_from_state_cost`. Sole surviving positive route (O15): derive that the momentum observable is additive under ledger consolidation. `additive_continuous_balanced_is_imbalance` already shows additivity plus continuity plus vanishing at balance forces the imbalance coordinate, so additivity is the whole remaining obligation. The Noether route is dead at the carrier: `Foundation.SigmaNoetherCharge.sigma_charge` is identically zero on the analytic carrier, so its conservation proof is vacuous. **FLIPPED 2026-07-31 (Jon ruled D-A: `D-qg-da-adopted-20260731`).** Closed at MODEL strength under the named adoptions, never derived. The O15 obligation (additivity of the momentum observable under ledger consolidation) is a theorem about the adopted momentum: `Gap5UnitIdentificationsAdopted.provenance_under_adoptions` composes `additive_continuous_balanced_is_imbalance` with the adopted identifications and forces the momentum observable to be the imbalance coordinate, with the scale multiple pinned to `1` and the link channel sharing the ground-state chart. The identifications themselves are FOUNDATIONAL MODELs adopted by Jon: MODEL 1 (`physicalMomentum = imbalance`, adopted 2026-07-31, `D-qg-eec-adopted-as-model-20260731`), MODEL 1-L (`LinkChannelUnitIdentification`, adopted 2026-07-31, D-A), and the SameLatticeUnitsPremise (`chi = 1`, adopted 2026-07-31, D-A); the banked MODEL 2 stipulated chart relation (same 2026-07-31 EEC adoption) supplies the `lam² = 1/4` the coherence conjunct needs. Every derivation route for the identifications stays dead at kernel strength exactly as recorded above and in `Gap5IncoherentConstraint`; what closed the flag is Jon's adoption, not a derivation. Every claim resting on this flag inherits MODEL strength. The flag name predates the ruling and is retained so downstream modules stay sound. -/ gap1_provenance_derived : Bool /-- **D6 (added 2026-07-26, criterion repair).** Pillar 2, measure half, stated separately from the legacy roll-up flag because the roll-up cannot express which half is open. The exact obligation is `MeasureSubstrateBlocker.GaugeCountingPrinciple`, which by `substrate_measure_blocker_certificate` holds exactly for `1 / |Aut K|`. It must be *derived* from substrate structure richer than counting, without reintroducing the automorphism group. Open, and the record elsewhere in the library currently disagrees. `GaugeHistoryMeasure.gap2_gauge_counting_from_history_discharged` is banked as a discharge, and on its strength `PathSumMeasure.pathSumMeasureStatus.substrate_measure_derived` and `ExactShellGaugePreflight.gaugePreflightStatus.counting_principle_derived_from_ledger` were flipped true. Audit 2026-07-26 finds that theorem contentless as a derivation: `CanonicalHistory.equivUnderlying` proves the counted type equivalent to the plain `BoundedComplex`, `HistoryRelabel.ofRelabel` discharges every added posting condition by `rfl`, `GaugeHistoryEnrichment` has no fields and `nuBuild` ignores it, `balancedZeroState` pins all ledger data to zero, and both new counts are proved equal to the pre-existing counts. The theorem is a true presentation result about the same ratio, and survives replacing the ledger data by a constant, so no ledger information selects the measure. Independently reached by a cross-family reader given only the file and the question (2026-07-26), which named the failure semantic rather than syntactic circularity: `Aut` is not written down, it is reimported through an equivalent wrapper. **The 2026-07-30 split (locked panel protocol, G1-signed).** The obligation has two halves with separate gates. The base half asks why the counting weight `1 / |Aut K|` rather than a rival (uniform-on-iso-classes is the nearest): `Gap2LabelErasure.pushforward_labeledWeight_eq_gauge_divisor` derives the divisor as the Jacobian of label erasure with `Aut` permitted in the conclusion and forbidden on the hypothesis side (letterwise `RelabelInvariant`; cross-family dependency-graph audit signed PASS), and `no_local_additive_cost_realizes_log_aut` plus `uniform_is_not_a_local_pushforward` discriminate by locality, since `log |Aut|` is superextensive over disjoint doubling while local additive costs are exactly extensive. The no-tilt half asks why the Boltzmann numerator is one: numerator-first closure was killed the same day (base-measure substitution; the chain is invariant under any base weight), so the no-tilt half was routed through the C17 fugacity elimination. **FLIPPED 2026-07-30 (gatekeeper-signed).** Both halves now hold, assembled in `Gap2MeasureDerivation.gap2_gauge_counting_gibbsWeight` and `gap2_gauge_counting_from_surface_and_kindTotals`. Load-bearing split, per the gatekeeper review: the base closing rests on `blocker_iff_mu` plus the C4 bridge (`mu_eq_gibbs_mul_erasePush_one`), all THEOREM; the no-tilt closing rests on C17 `unit_fugacity_forced_by_surface_and_kindTotals` plus the blocker iff, all THEOREM; the labeled-weight / erasure-pushforward carrier is definitionally load-bearing (MODEL); the C16 fields (`c16_cap3_uniform_measured`, `c16_cap4_uniform_derived_unformalized`, `c16_rate_symmetry_balance`, `c16_ratio_half_under_uniform`) are process discrimination only and are not cited by the closing proof terms. The J-tilt is excluded from this flag by Jon's bookkeeping ruling (`D-qg-c27-ruling-bookkeeping-20260730`) and routed to flag 9 as emergent action. The gatekeeper's hostile probe discriminates: a wrong (uniform) labeled weight fails `GaugeCountingPrinciple` kernel-side. -/ gap2_measure_derived : Bool /-- **D2 (added 2026-07-26, criterion repair).** Pillar 2, continuum half, at the geometric strength the pillar actually claims. The legacy flag would flip on a complexity-cutoff limit, meaning convergence of `Zcap` as the combinatorial complexity bound grows. That is not a continuum limit: `gap2_metric_carrier_blocker_certified` shows the combinatorial quotient forgets metric data, so a cutoff limit is compatible with no metric refinement at all. The typed target is `MetricRefinementCarrierBlocker -- … truncated for the page; open the module for the rest.the full theory ledger is a formal, machine-checked record of progress toward a complete quantum theory of gravity FullTheoryBenchmarks · IndisputableMonolith/Gravity/SevenGaps/FullTheoryLedger.leanTHEOREM repaired_criterion_is_strictly_stronger · IndisputableMonolith/Gravity/SevenGaps/FullTheoryLedger.lean
/-- **The gate discriminates: strictness.** All four decoys close under the pre-repair criterion and fail under the repaired one, each for its own defect, while the positive control closes under both. A gate that rejected everything would satisfy `repaired_criterion_implies_legacy` vacuously; the last conjunct is what rules that out. -/ theorem repaired_criterion_is_strictly_stronger : (LegacyFullTheoryClosed laundryBenchmarks ∧ ¬ FullTheoryClosed laundryBenchmarks) ∧ (LegacyFullTheoryClosed cutoffOnlyBenchmarks ∧ ¬ FullTheoryClosed cutoffOnlyBenchmarks) ∧ (LegacyFullTheoryClosed weakPredictionBenchmarks ∧ ¬ FullTheoryClosed weakPredictionBenchmarks) ∧ (LegacyFullTheoryClosed freeConstantBenchmarks ∧ ¬ FullTheoryClosed freeConstantBenchmarks) ∧ (LegacyFullTheoryClosed idealBenchmarks ∧ FullTheoryClosed idealBenchmarks) := ⟨⟨laundry_closes_legacy, laundry_fails_repaired⟩, ⟨cutoffOnly_closes_legacy, cutoffOnly_fails_repaired⟩, ⟨weakPrediction_closes_legacy, weakPrediction_fails_repaired⟩, ⟨freeConstant_closes_legacy, freeConstant_fails_repaired⟩, ⟨ideal_closes_legacy, idealBenchmarks_closes⟩⟩the ledger's own criterion was audited and found wanting repaired_criterion_is_strictly_stronger · IndisputableMonolith/Gravity/SevenGaps/FullTheoryLedger.leanTHEOREM full_theory_open_pillar3_alone · IndisputableMonolith/Gravity/SevenGaps/FullTheoryLedger.lean
/-- **MASTER THEOREM (the honest gate), replaced 2026-07-31 after the D-A adoptions.** The full theory is NOT closed, and the obstruction is Pillar 3 alone: `discriminating_prediction_confirmed = false` and `prediction_is_discriminating = false` (flag 11; its residual is E_lat and the sky). The strength of every closed conjunct: flag 6 (`gap1_provenance_derived`) and flag 12 (`no_free_constants`) closed 2026-07-31 at MODEL strength under the named D-A adoptions (MODEL 1-L and the SameLatticeUnitsPremise, on top of the already adopted MODEL 1 and MODEL 2; never derived, the derivation routes kernel-proved dead), composed in `Gap5UnitIdentificationsAdopted`; Pillar 2 closed 2026-07-31 with flag 9 at derived action shape plus MODEL super-critical strength (D-qg-flag9-closes-at-model-strength-20260731) on top of the bridge and measure flags at theorem strength; the four recovery flags of Pillar 1 stand at theorem strength. This theorem replaces `full_theory_not_yet_closed`, retired the day pillars 1 and 2 closed because its recorded premise (two pillars open) stopped being true; it fails to build unchanged the moment flag 11 flips, so it cannot silently coexist with a closure claim. -/ theorem full_theory_open_pillar3_alone : ¬ FullTheoryClosed fullTheoryBenchmarks ∧ Pillar1Closed fullTheoryBenchmarks ∧ Pillar2Closed fullTheoryBenchmarks ∧ ¬ Pillar3Closed fullTheoryBenchmarks := by refine ⟨?_, ⟨rfl, rfl, rfl, rfl, rfl⟩, ⟨rfl, rfl, rfl, rfl⟩, fun h => ?_⟩ · intro h have := h.2.2.1.1 simp [fullTheoryBenchmarks] at this · have := h.1 simp [fullTheoryBenchmarks] at thispillar one is open again full_theory_open_pillar3_alone · IndisputableMonolith/Gravity/SevenGaps/FullTheoryLedger.leanTHEOREM classical_recovery_strengths_hold · IndisputableMonolith/Gravity/SevenGaps/FullTheoryLedger.lean
/-- The three classical recovery strengths of Pillar 1 are all still proved. This is the content that the pre-repair Pillar 1 flag recorded, kept explicit so that strengthening the criterion cannot be misread as retracting a theorem. -/ theorem classical_recovery_strengths_hold : LegacyPillar1Closed fullTheoryBenchmarks := by simp [LegacyPillar1Closed, fullTheoryBenchmarks]the three classical recovery strengths still hold classical_recovery_strengths_hold · IndisputableMonolith/Gravity/SevenGaps/FullTheoryLedger.leanTHEOREM pillar1_and_pillar2_closed_pillar3_open · IndisputableMonolith/Gravity/SevenGaps/FullTheoryLedger.lean
/-- **PILLARS 1 AND 2 CLOSED, Pillar 3 open, 2026-07-31 (the D-A day).** Pillar 1 closed when `gap1_provenance_derived` flipped under Jon's D-A ruling: its provenance conjunct holds at MODEL strength under the named adoptions (never derived), on top of the four recovery strengths at theorem strength (`classical_recovery_strengths_hold`). Pillar 2 closed the same day (flag 9, at derived action shape plus MODEL super-critical strength). Pillar 3 stays open: both flag-11 conjuncts are `false`, with residual E_lat and the sky. Nothing was un-proved to produce either closure, and no Boolean was flipped down. Renamed from `pillar1_and_pillar3_open_pillar2_closed` the day Pillar 1 closed. -/ theorem pillar1_and_pillar2_closed_pillar3_open : Pillar1Closed fullTheoryBenchmarks ∧ Pillar2Closed fullTheoryBenchmarks ∧ ¬ Pillar3Closed fullTheoryBenchmarks := full_theory_open_pillar3_alone.2pillars one and two are closed under the repaired criterion, pillar three remains open pillar1_and_pillar2_closed_pillar3_open · IndisputableMonolith/Gravity/SevenGaps/FullTheoryLedger.lean