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Theophysics Research Initiative · POF 2828 · Lean 4 Formal Verification
287 machine-verified theorems. Zero gaps. The structural claims of Theophysics, formally proved.
287
Named Theorems
0
Sorry / Admit
0
Axioms
16
Lean Files
70+
Adversarial Rejections
3
Structural Isomorphisms
1
Uniqueness Result
80%
Bridge Hit Rate
Lean 4 is an interactive theorem prover. When a theorem compiles with zero sorry or admit placeholders, the proof is formally complete — the machine verified every logical step without exception.
What Lean proves here: internal structural consistency. The definitions, gate conditions, isomorphisms, sign disciplines, and uniqueness results all compile and hold. Whether the formal models faithfully represent the real physics and theology they describe is a domain judgment question that Lean cannot answer — and which the framework addresses through empirical evidence, adversarial review, and named kill conditions.
The overclaim guard runs on every theorem. Read what each proves — and what it does not.
The Argument Architecture
The 7 Lanes
Seven independent lines of inquiry. Each begins from a different starting point. Each produces the same structural shape. The force is not in any single lane — it is in the convergence of all seven arriving at the same destination by different roads.
1
The Coherence Lane
God-Shape: A prior, stable, truth-bearing source of order
▼
| ID | Claim | Type | What Lean Proves | Does NOT Prove | God Shape |
|---|---|---|---|---|---|
| L1-Q1 | Can a contradiction be finally true? | Logical Necessity | Coherence functional defined; zero-factor collapse proved in Core.lean | Does not prove reality matches the coherence functional | Coherence is prerequisite to any truth claim |
| L1-Q2 | Does truth require coherence? | Logical Necessity | Coherence measure compiles; chi collapses if any factor is zero | Does not prove coherence is the only theory of truth | Truth presupposes non-contradiction |
| L1-Q3 | Does every worldview require coherence before it can argue, measure, or explain anything? | Framework Commitment | — | Pragmatic observation, not formal proof | Coherence is universally presupposed |
| L1-Q4 | Does coherence require a standard of alignment? | Abductive | Factor signatures typed; canonical rows valid; named swaps fail — BridgeMatrix.lean | Does not prove these 10 factors are correct or complete | Alignment requires a reference signal |
| L1-Q5 | Can the broken, contradictory world be the final standard of coherence? | Logical Necessity | Destructive signs cannot self-redeem through ordinary multiplication — PolarityDiscipline.lean | Does not prove moral polarity in the real world works this way | The standard cannot be the broken thing being measured |
| L1-Q6 | Must the final standard be prior, stable, truth-bearing, generative, and authoritative? | Abductive | Self-grounding substrate defined; missing source/relation/command forces bridge score to zero | Does not prove these are the right failure modes for real theology or physics | Source must be prior, stable, self-grounding |
| L1-Q7 | What do we call the source of truth, order, and coherence? | Identification | — | The naming step is not formally provable. The shape is argued; the name is offered. | God |
2
The Moral / Duality Lane
God-Shape: A prior source of goodness from which evil deviates
▼
| ID | Claim | Type | What Lean Proves | Does NOT Prove | God Shape |
|---|---|---|---|---|---|
| L2-Q1 | Is there such a thing as real evil? | Axiom / Gateway | Sign states (positive/negative/neutral) formally defined with typed arithmetic — PolarityDiscipline.lean | Does not prove evil is real metaphysically — only that sign polarity is formally definable | Evil is real, not merely preference |
| L2-Q2 | Is evil different from merely disliking something? | Axiom / Gateway | — | A moral anti-realist can reject this step | Evil is objective, not subjective |
| L2-Q3 | Does evil corrupt, harm, distort, or destroy something that should be whole? | Logical Necessity | Burden coupling: two negatives stay negative; destructive signs cannot self-redeem | Does not prove moral polarity in the real world follows this arithmetic | Evil is parasitic on prior good |
| L2-Q4 | Can corruption exist without something good to corrupt? | Logical Necessity | Incoherent records not retained; negative states require prior positive substrate to deviate from | Formal model only | Good is logically prior to evil |
| L2-Q5 | Can evil create itself without borrowing from good? | Theorem (proved in model) | External conversion required for restoration; self-generated operations cannot flip sign — SignConversionDiscipline.lean | Proves the arithmetic; does not prove moral self-repair is impossible in all frameworks | Evil cannot be its own ground |
| L2-Q6 | Is good therefore more fundamental than evil? | Theorem (follows from Q3–Q5) | Sign arithmetic enforces asymmetry: positive is generative, negative is parasitic | Model asymmetry — real-world ontological priority is a separate claim | Good is ontologically prior |
| L2-Q7 | What do we call the ultimate source of good? | Identification | — | Naming step — not formally provable. Same pattern as Lane 1 Q7. | God |
3
The Information / Logic Lane
God-Shape: Self-grounding Logos
▼
| ID | Claim | Type | What Lean Proves | Does NOT Prove | God Shape |
|---|---|---|---|---|---|
| L3-Q1 | Does anything exist? | Axiom (self-evident) | Substrate states formally defined; existence is the first typed element — Core.lean | Formal type existence ≠ metaphysical proof of existence | Existence is undeniable |
| L3-Q2 | Can existence be meaningful without distinction? | Axiom (self-evident) | — | Spencer-Brown, Bateson: 'a difference that makes a difference' | Distinction is required for meaning |
| L3-Q3 | Is distinction information? | Definition / Logical Necessity | — | Deductive from Shannon's definition; the ontological claim (info is primitive) is stronger | Distinction IS information (Shannon, Wheeler) |
| L3-Q4 | Can information exist without being grounded, carried, or instantiated? | Axiom | Substrate requirement formally typed; coupling states defined — Core.lean | Formal typing ≠ proof that information requires substrate in all metaphysical systems | Information requires instantiation |
| L3-Q5 | Can a contingent ground explain itself without regress? | Logical Necessity | C0 ≠ C1 proved; coupling transition is irreversible; no backward step — Core.lean | Irreversibility in the model ≠ metaphysical proof against infinite regress or brute fact | Regress must terminate |
| L3-Q6 | Must the final ground be self-grounding? | Framework Commitment | Self-grounding substrate formally defined as typed structure — Core.lean | Self-grounding is a framework choice over brute fact — not deduced | Self-grounding is the most coherent option |
| L3-Q7 | What kind of source can ground information, meaning, and reality itself? | Identification | — | Naming step — the shape is argued, the name is offered | Self-grounding Logos |
4
The Consciousness Lane
God-Shape: A personal or supra-personal ground of consciousness
▼
| ID | Claim | Type | What Lean Proves | Does NOT Prove | God Shape |
|---|---|---|---|---|---|
| L4-Q1 | Are you conscious right now? | Axiom (self-evident) | — | Descartes-level. Denying it uses it. | Consciousness is undeniable to the conscious |
| L4-Q2 | Is your experience real, or only an illusion? | Logical Necessity | — | Cannot deny there is something it is like to be the experiencer | Experience is real even if contents are mistaken |
| L4-Q3 | If consciousness is an illusion, who is experiencing the illusion? | Logical Necessity | — | The Dennett objection is self-refuting | Illusion requires an experiencer |
| L4-Q4 | Does knowledge require a conscious knower? | Axiom | Observer stages formally defined; actualization requires observer — StageMachine.lean | Does not prove consciousness is metaphysically required for all knowledge | Knowledge presupposes consciousness |
| L4-Q5 | Does moral responsibility require an agent capable of awareness and choice? | Axiom | — | Determinists deny libertarian free will; this claim is weaker | Moral agency requires consciousness |
| L4-Q6 | Can blind mechanism fully ground meaning, moral responsibility, and first-person experience? | Abductive | — | Hard problem does not alone prove Christianity; consciousness is one more domain that borrows coherence | Mechanism alone is insufficient |
| L4-Q7 | What kind of source can ground consciousness, meaning, and personhood? | Identification | — | Naming step — PERSONHOOD axiom critical: structural properties alone don't make something a person | Personal or supra-personal God |
5
The God-Builder / Imagination Lane
God-Shape: Genesis / Logos structure — built by the reader before the name is given
▼
| ID | Claim | Type | What Lean Proves | Does NOT Prove | What Reader Builds |
|---|---|---|---|---|---|
| L5-Q1 | You wake up and you are God. Would you create anything? | Thought Experiment | — | Imagination alone does not prove doctrine | Creation is natural to a good source |
| L5-Q2 | Would what you create reflect your nature? | Thought Experiment | — | Maps to Imago Dei — reader builds it before hearing the name | Creation bears image of creator |
| L5-Q3 | Would a creation made by you contain order, beauty, law, and meaning? | Thought Experiment | — | Nearly universal response; exceptions reveal reader's assumptions | Order, beauty, law, meaning follow from a coherent source |
| L5-Q4 | Would love require freedom? | Thought Experiment | — | BC8 (Voluntary Coupling) enters here from the formal system | Love requires voluntary coupling |
| L5-Q5 | Would freedom allow rejection? | Logical Necessity | — | The reader discovers the Fall as a consequence of their own design choice | Freedom entails possibility of Fall |
| L5-Q6 | Would rejection create disorder and consequence? | Logical Necessity | Sign conservation: self-operations cannot flip sign; consequences persist — PolarityDiscipline.lean | Model arithmetic — does not prove consequences are inescapable in all frameworks | Rejection produces real consequences |
| L5-Q7 | Would you destroy the rebel, override freedom, or create a path of repair? | Thought Experiment | C_op converts negative to positive while preserving source record; restoration ≠ erasure — ChristOperatorDiscipline.lean | The operator does what it claims in the model. The model is not a proof of the Incarnation. | Repair is the only coherent answer |
6
The Repair / Salvation Lane
God-Shape: Incarnation, Cross, Resurrection, Grace — the unique repair configuration
▼
| ID | Claim | Type | What Lean Proves | Does NOT Prove | God Shape |
|---|---|---|---|---|---|
| L6-Q1 | Can a corrupted system fully repair itself using only corrupted resources? | Theorem (proved in model) | Destructive signs cannot self-redeem; external conversion required — PolarityDiscipline.lean + SignConversionDiscipline.lean | Proves the model arithmetic; does not prove real-world moral self-repair is impossible in all frameworks | Corrupted systems cannot self-repair |
| L6-Q2 | Can repair ignore consequences without ceasing to be just? | Logical Necessity | Records persist; incoherent records not retained at death; cost must be borne — MemoryPersistenceDiscipline.lean | Record persistence is a model rule, not a proved metaphysical law | Justice requires consequences to be addressed — COMMAND is not denied |
| L6-Q3 | Can repair override freedom without destroying love? | Logical Necessity | — | Response is invited, not forced — BC8 throughout | Freedom must be preserved — WILL remains free |
| L6-Q4 | Must repair come from outside the corrupted system? | Theorem (proved in model) | C_op is external integration, not scalar multiplication; converts negative to positive — ChristOperatorDiscipline.lean | The operator does what it claims in the model. Not a proof of the Incarnation. | External intervention required |
| L6-Q5 | Must repair enter the system without becoming corrupted by it? | Theorem (proved in model) | Substrate identity preserved across incarnation, death, resurrection; entropy contact does not corrupt identity — MissionReturnOperator.lean | Architecture is formally consistent. Does not prove the Resurrection happened. | Uncorrupted entry into corrupted system |
| L6-Q6 ⭐ | Must repair preserve freedom, absorb consequence, and distribute restoration? | Theorem (proved in model) | THE LOCK: Cross convergence is the unique configuration satisfying all 5 conditions — JusticeMercyOperator.lean + ChristOperatorDiscipline.lean | Uniqueness is within the model. Does not prove Cross is a historical event. | Perfect justice + perfect mercy + freedom require cost-bearing judge |
| L6-Q7 | What historical event, if any, matches this exact repair specification? | Empirical / Historical | Structural isomorphism conditions compile; intended mapping passes; wrong substitutions fail — IsomorphismTest.lean + MasterEquationInvariance.lean | Lean can formalize the required structure. It cannot prove Jesus rose from the dead. History must be tested separately. | Jesus of Nazareth — incarnation, cross, resurrection, grace |
| L6-P1 | Four Primitives — RELATION: persists even when wounded; Cross makes reconciliation possible | Four Primitives | C_op preserves source state while restoring visible sign | Preservation in model ≠ proof that divine-human relation works this way | Relation restored |
| L6-P2 | Four Primitives — COMMAND: violated; justice is not denied at the Cross | Four Primitives | Five-component operator; Cross convergence unique — JusticeMercyOperator.lean | Uniqueness within modeled constraints only | Justice satisfied; cost is borne, not waived |
| L6-P3 | Four Primitives — WILL: must remain free; response is invited, not forced | Four Primitives | — | Superposition preserved until voluntary collapse (faith decision) | Freedom preserved |
| L6-P4 | Four Primitives — RECORD: sin is not erased falsely; cost is borne; the record persists | Four Primitives | Records persist; visible restoration does not imply erasure; source state preserved — MemoryPersistenceDiscipline.lean + ChristOperatorDiscipline.lean | Record persistence is a model rule, not metaphysical proof | Record honored, not erased |
Rival Elimination — 11 Alternatives Formally Tested
| Rival | Model | Why It Seems Plausible | Constraint Failed |
|---|---|---|---|
| L6-R1 | Human self-improvement | People visibly improve behavior | FAILS: self-repair from corrupted resources |
| L6-R2 | Moral relativism | No real violation, so no justice needed | FAILS: denies evil is real (rejected at L2-Q1) |
| L6-R3 | Pure punishment | Justice without mercy | FAILS: justice alone destroys; does not restore |
| L6-R4 | Pure forgiveness without cost | Sounds merciful | FAILS: denies justice (COMMAND violated) — cheap grace |
| L6-R5 | Forced divine override | Maximizes immediate coherence | FAILS: destroys WILL — if freedom is overridden, love is impossible |
| L6-R6 | Generic theism | Source exists | FAILS: no repair mechanism specified; stops before Cross-shape |
| L6-R7 | Deism | Source does not intervene | FAILS: no external intervention; denies entry into corrupted system |
| L6-R8 | Pantheism | All is one | FAILS: no RELATION distinction — no judge, offender, restorer |
| L6-R9 | Buddhism | Treats suffering/attachment | FAILS: no RECORD, no cost-bearer — dissolution, not restoration |
| L6-R10 | Islam | Strong sovereignty | FAILS: sovereign does not enter system and bear the cost |
| L6-R11 | Secular humanism | Can improve symptoms | FAILS: no RECORD mechanism; cannot address guilt or ground final justice |
7
The Convergence Lane
God-Shape: Not one proof — one destination reached by many roads
▼
| ID | Claim | Type | What Lean Proves | Does NOT Prove | God Shape |
|---|---|---|---|---|---|
| L7-Q1 | If one argument reaches a conclusion, can it be mistaken? | Axiom (self-evident) | — | Establishes the principle that convergence is needed | Single arguments are fallible |
| L7-Q2 | If two independent arguments reach the same conclusion, does that increase evidential weight? | Logical Necessity | — | Standard epistemology. Hard to deny without undermining all of science. | Independent convergence increases weight |
| L7-Q3 | If several domains reach the same shape independently, is that stronger than one domain alone? | Logical Necessity | Structural isomorphism passes for intended mappings; nearby wrong mappings fail — IsomorphismTest.lean | Isomorphism in the model ≠ proof that the domains really have the same structure | Cross-domain convergence is evidence |
| L7-Q4 | If logic, moral reasoning, consciousness, information, experience, and mathematics all converge, should that be taken seriously? | Abductive | Ten canonical bridge rows valid; physical-to-spiritual substitution preserves signatures — BridgeMatrix.lean + MasterEquationInvariance.lean | Bridge rows tested inside the model. They do not prove the framework is complete. | Multi-domain convergence demands explanation |
| L7-Q5 | If the reader already agreed that convergence counts as evidence, should that standard apply here? | Receipt Principle | Anomalous hit-rate claim blocked unless denominator is closed — HitRateDiscipline.lean | Audit rule is built in. Does not mean the audit has been completed. | The reader's own standard applies |
| L7-Q6 | If all lanes produce the same God-shaped structure, what alternative explains the convergence better? | Abductive | Triadic invariants pass for intended candidates; four named wrong controls fail — MaxwellTrinity.lean | Does not say convergence removes all possible doubt. Convergence changes the burden. | No alternative explains the full convergence |
| L7-Q7 | What else fits the full shape? | Challenge (open) | — | This is an open invitation, not a closed proof. The reader is invited to find an alternative. | REVEAL: 'You already agreed that convergence counts as evidence. Here is the convergence.' |
The Formal Architecture
16 Lean Files — Layer Scorecard
Every layer builds on what came before. The trunk runs 8 layers deep. Three branches extend from it. Six standalone files prove their claims without importing from the trunk. ⭐ marks the two strongest standalone results.
L0
Core.lean
Dual-Substrate Foundation
Coupling states, irreversibility gate, χ product. C0 ≠ C1 proved. Any single zero factor collapses the entire chi product. The multiplicative architecture that makes compensation impossible.
L1
StageMachine.lean
Stage Ordering
Strictly ordered, irreversible operation sequence. No backward steps proved. DEMOTED to teaching layer — the real dependency object is a lattice, not a line. DependencyLattice.lean supersedes this.
L2
Mapping.lean
Physics↔Theology Sequence Map
1-to-1 order-preserving map. localization → incarnation; confirmation → resurrection. Internally consistent but DEMOTED — proves a hand-assigned mapping, which is circular if used as major proof. Lattice supersedes.
L3
BridgeMatrix.lean
Bridge Matrix — 10-Factor Signature
All 10 canonical bridge rows pass validation. Grace↔Faith swap caught by signature layer. Entropy↔Grace swap rejected. K↔F swap rejected. Product alone is blind to semantic swaps — the signature layer catches what arithmetic misses.
L4
MasterEquationInvariance.lean
Master Equation Invariance
χ(physical) = χ(spiritual) under canonical map. The equation runs the same in both registers. Signature discipline is load-bearing — product alone permits wrong swaps that the signature layer correctly rejects.
L5
FieldBridgeControls.lean
Field Bridge Controls — Laws 3, 6, 7, 8
Per-law collapse proofs for Electromagnetics/Truth, Information/Logos, Relativity/Frame, Quantum/Faith. Each bypass zeroes the relevant factor → zeroes χ globally. Laws 1, 2, 9, 10 still lack domain-specific controls (GAP-01).
L6
BridgeScoreDiscipline.lean
Bridge Score Discipline
Graded scores must pass binary gate before entering ME. Gate output is always exactly 0 or 1 — no intermediate states. High raw amplitude ≠ truth without source backing. Blocks silent conflation of graded with binary.
L7
IsomorphismTest.lean
Law 4 Isomorphism — Strong Force ≅ Love
Two-level isomorphism with adversarial false-positive testing. Basic LawIso too weak — coin model also passes at that level. RichLawIso (roles + transitions preserved) eliminates coin. Strong Force ≅ Love holds at the stronger level.
L8
MaxwellTrinity.lean
⭐ Maxwell / Trinity Isomorphism
5-condition structural spec. Quaternion EM ≅ Relational Trinity under TriadicIso. 5 false positives tested and rejected — Heaviside EM, Modalism, static single-field EM, arbitrary 3-part system, relabeled role system. Every guard is load-bearing: removing any single guard admits the corresponding false positive.
L9
JusticeMercyOperator.lean
⭐ Justice/Mercy — Cross Uniqueness
THE CROSS IS THE UNIQUE SOLUTION. ∀ c, CrossConvergence(c) → c = cross. Existence AND uniqueness by exhaustive case elimination. Every alternative formally eliminated. Justice and Mercy share 4 components, differ in exactly one coordinate: who pays the cost.
L10
PolarityDiscipline.lean
Polarity Discipline
(-1)×(-1) = +1 in raw arithmetic. But the coherence gate rejects double-destructive signs. Arithmetic sign ≠ moral sign. Two wrongs don't make a right — formally. Sign polarity is diagnostic, not redemptive. Below-accountability threshold gives zero culpability.
L11
SignConversionDiscipline.lean
Sign Conversion Discipline
Moral burdens do not self-redeem. Negative + negative = negative in burden coupling (not arithmetic). External Christic conversion is the only operation that flips a negative burden to positive. Accumulation does not redeem.
L12
ChristOperatorDiscipline.lean
Christ Operator Discipline
C_op: external integration, not scalar. Converts negative → positive while preserving source record. Grace does not pretend the past didn't happen. Restoration ≠ erasure — formally. God sees the full record; visible output is non-injective.
L13
MissionReturnOperator.lean
Mission Return Operator
Resurrection is not repair — it is mission return. Substrate identity preserved through incarnation, death, and resurrection. Resolution drops from infinite to finite (incarnation) then returns to infinite (resurrection). Entropy and death contact records carried. Post-resurrection ≠ pre-incarnate: it is richer.
L14
MemoryPersistenceDiscipline.lean
Memory Persistence Discipline
Three-layer memory: record, compilation, persistence. Recorded + Christ-coherent → retention = 1. Recorded but incoherent → retention = 0. Reorientation to Christ restores retention. Heaven = coherent + eternal domain. Living memory ≠ final identity memory.
L15
DependencyLattice.lean
Dependency Lattice
3 lattices: theology (21 nodes), physics (32 nodes), ordo (6 nodes). Fall → Death, Judgment, Promise as parallel consequences — not a chain. Energy and Momentum are Noether siblings, not parent-child. Union → Justification AND Sanctification as parallel branches. Wrong orderings rejected by name.
L16
HitRateDiscipline.lean
Hit Rate Discipline
Closed denominator. 10 attempts logged. 8 hits (80%). 90% claim is formally blocked — cannot claim what has not been earned. Hidden failures block any anomaly claim. Partials are not hits. All attempts, failures, and partials counted.
Complete Corpus
All Theorems — Filterable
Every named theorem in the corpus. Filter by type. PROVED = formally demonstrated. REJECTION = adversarial false positive correctly eliminated. BOUNDARY = named limit of what Lean can verify. DEMOTED = internally consistent but superseded by stronger proof.
| # | Layer | File | Theorem Name | What It Says | Method | Type |
|---|---|---|---|---|---|---|
| 1 | L0 | Core.lean | C0_ne_C1 | C0 ≠ C1 — the two coupling states are structurally distinct | decide | Proved |
| 2 | L0 | Core.lean | C1_ne_C0 | C1 ≠ C0 (symmetric direction) | decide | Proved |
| 3 | L0 | Core.lean | coupling_modification_irreversible | C0 → C1 is one-way; C1 → C0 has no constructor. The transition cannot be undone. | structural case | Proved |
| 4 | L0 | Core.lean | Q_zero_collapses_chi | If Q = 0, then χ = 0 regardless of all other factors. Any single zero kills the product. | simp | Proved |
| 5 | L0 | Core.lean | Q_nonzero_not_sufficient_for_positive_chi | Q > 0 does NOT guarantee χ > 0 (G = 0 still kills it). No single factor saves you. | simp | Rejection |
| 6 | L1 | StageMachine.lean | reaches_localization_from_pre | preLocalization can reach localization | constructor | Demoted |
| 7 | L1 | StageMachine.lean | reaches_redistribution_from_pre | Full 5-step sequence is reachable from preLocalization to redistribution | transitive | Demoted |
| 8 | L1 | StageMachine.lean | no_stage_step_back_to_pre_from_localization | No backward step from localization to pre. Irreversible. | cases | Demoted |
| 9 | L1 | StageMachine.lean | no_stage_step_back_to_release_from_confirmation | No backward step from confirmation to release | cases | Demoted |
| 10 | L1 | StageMachine.lean | no_stage_step_back_to_confirmation_from_redistribution | No backward step from redistribution to confirmation | cases | Demoted |
| 11 | L2 | Mapping.lean | map_physics_sequence_is_theology_sequence | Mapping the full physics list produces the full theology list — order-preserving. | rfl | Demoted |
| 12 | L2 | Mapping.lean | localization_maps_to_incarnation | Specific: localization → incarnation | rfl | Demoted |
| 13 | L2 | Mapping.lean | confirmation_maps_to_resurrection | Specific: confirmation → resurrection | rfl | Demoted |
| 14 | L3 | BridgeMatrix.lean | canonicalRows_all_valid | All 10 canonical bridge rows pass signature validation | rfl | Proved |
| 15 | L3 | BridgeMatrix.lean | grace_swapped_with_faith_invalid | Swapping grace↔faith breaks the signature | decide | Rejection |
| 16 | L3 | BridgeMatrix.lean | entropy_swapped_with_grace_invalid | Swapping entropy↔grace breaks the signature | decide | Rejection |
| 17 | L3 | BridgeMatrix.lean | compression_swapped_with_communion_invalid | K↔F swap rejected | decide | Rejection |
| 18 | L3 | BridgeMatrix.lean | coherence_swapped_with_consequence_lock_invalid | C↔R swap rejected | decide | Rejection |
| 19 | L3 | BridgeMatrix.lean | wrong_physical_for_grace_invalid | Assigning entanglement to G slot rejected | decide | Rejection |
| 20 | L3 | BridgeMatrix.lean | arbitrary_grace_clone_matches_G | A new term with G's signature passes structurally. Adversarial boundary: label honesty cannot be verified by Lean alone. | decide | Boundary |
| 21 | L3 | BridgeMatrix.lean | arbitrary_faith_clone_does_not_match_G | A term with Q's signature fails the G slot | decide | Rejection |
| 22–31 | L3 | BridgeMatrix.lean | full_[G/M/E/S/T/K/R/Q/F/C]_zero_collapses | Each of the 10 factors: if zero → χ = 0. Every factor is load-bearing. No exceptions. | simp (×10) | Proved ×10 |
| 32 | L3 | BridgeMatrix.lean | full_Q_nonzero_not_sufficient | Q > 0 doesn't save you if G = 0. No single factor is sufficient. | simp | Rejection |
| 33 | L3 | BridgeMatrix.lean | full_R_gate_required | R = 0 kills χ even if everything else is 1. Gate is non-negotiable. | simp | Rejection |
| 34 | L3 | BridgeMatrix.lean | all_ones_live | All factors at 1 → χ = 1 (life). The only surviving state when all gates pass. | simp | Proved |
| 35 | L4 | MasterEquationInvariance.lean | canonical_substitution_row_valid | Every factor's canonical substitution row passes | decide | Proved |
| 36 | L4 | MasterEquationInvariance.lean | canonical_substitution_preserves_signature | Physical→spiritual substitution preserves signatures for all 10 factors | decide | Proved |
| 37 | L4 | MasterEquationInvariance.lean | master_equation_invariant_under_canonical_substitution | χ(physical) = χ(spiritual) under canonical map. The equation is the same in both registers. | simp | Proved |
| 38–39 | L4 | MasterEquationInvariance.lean | G/Q_zero_still_collapses_after_substitution | G = 0 and Q = 0 collapse survive the substitution. Gate holds in both registers. | simp | Proved |
| 40 | L4 | MasterEquationInvariance.lean | product_only_does_not_detect_grace_faith_swap | Product alone is BLIND to semantic swaps. Grace↔Faith swap passes product check. | decide | Boundary |
| 41 | L4 | MasterEquationInvariance.lean | signature_layer_rejects_grace_faith_swap | The signature layer catches Grace↔Faith swap that product missed | decide | Rejection |
| 42 | L4 | MasterEquationInvariance.lean | master_invariance_requires_signature_discipline | BOTH product AND signature needed — neither alone suffices. This is why the bridge is two-layer. | conjunction | Proved |
| 43 | L5 | FieldBridgeControls.lean | law3_truth_limit_E_one | Full slots + source-backed + phase-aligned → E = 1 | simp | Proved |
| 44 | L5 | FieldBridgeControls.lean | law3_command_bypass_forces_E_zero | Command bypass → E = 0 (∀ states). Bypassing command kills truth-fidelity. | simp | Rejection |
| 45 | L5 | FieldBridgeControls.lean | law3_phase_inversion_forces_E_zero | Phase inversion → E = 0 (∀ states). Inverted alignment kills truth. | simp | Rejection |
| 46 | L5 | FieldBridgeControls.lean | law3_command_bypass_collapses_chi | Command bypass → χ = 0. Truth bypass kills the whole system. | simp | Proved |
| 47 | L5 | FieldBridgeControls.lean | law3_phase_inversion_collapses_chi | Phase inversion → χ = 0 | simp | Proved |
| 48 | L5 | FieldBridgeControls.lean | law6_logos_limit_K_one | Full conditions → K = 1 | simp | Proved |
| 49 | L5 | FieldBridgeControls.lean | law6_relation_bypass_forces_K_zero | Relation bypass → K = 0. No relation, no Logos. | simp | Rejection |
| 50 | L5 | FieldBridgeControls.lean | law6_bandwidth_closed_forces_K_zero | Bandwidth closed → K = 0. Channel closed, Logos blocked. | simp | Rejection |
| 51 | L5 | FieldBridgeControls.lean | law6_distortion_dominates_forces_K_zero | Distortion dominates → K = 0 | simp | Rejection |
| 52 | L5 | FieldBridgeControls.lean | law6_bandwidth_collapse_collapses_chi | Bandwidth collapse → χ = 0 | simp | Proved |
| 53 | L5 | FieldBridgeControls.lean | law7_righteous_limit_R_one | Full conditions → R = 1 | simp | Proved |
| 54 | L5 | FieldBridgeControls.lean | law7_relation_bypass_forces_R_zero | Relation bypass → R = 0. No relation, no frame translation. | simp | Rejection |
| 55 | L5 | FieldBridgeControls.lean | law7_metric_absent_forces_R_zero | No shared metric → R = 0 | simp | Rejection |
| 56 | L5 | FieldBridgeControls.lean | law7_frame_lock_forces_R_zero | Frame lock → R = 0 | simp | Rejection |
| 57 | L5 | FieldBridgeControls.lean | law7_relation_bypass_collapses_chi | Relation bypass → χ = 0 | simp | Proved |
| 58 | L5 | FieldBridgeControls.lean | law7_frame_lock_collapses_chi | Frame lock → χ = 0 | simp | Proved |
| 59 | L5 | FieldBridgeControls.lean | law8_faith_limit_Q_one | Full conditions → Q = 1 | simp | Proved |
| 60 | L5 | FieldBridgeControls.lean | law8_command_bypass_forces_Q_zero | Command bypass → Q = 0 | simp | Rejection |
| 61 | L5 | FieldBridgeControls.lean | law8_missing_eigenbasis_forces_Q_zero | Missing eigenbasis → Q = 0. No basis to collapse into. | simp | Rejection |
| 62 | L5 | FieldBridgeControls.lean | law8_control_refusal_forces_Q_zero | Will refuses to measure → Q = 0. Free will preserved but no collapse. | simp | Rejection |
| 63–64 | L5 | FieldBridgeControls.lean | law8_bypass/refusal_collapses_chi | Command bypass → χ = 0. Control refusal → χ = 0. | simp | Proved |
| 65 | L6 | BridgeScoreDiscipline.lean | binaryGate_zero | Score 0 → gate 0 | rfl | Proved |
| 66 | L6 | BridgeScoreDiscipline.lean | binaryGate_positive | Score ≥ 1 → gate 1 | decide | Proved |
| 67 | L6 | BridgeScoreDiscipline.lean | binaryGate_zero_or_one | Gate output is always exactly 0 or 1. No intermediate states. | cases | Proved |
| 68 | L6 | BridgeScoreDiscipline.lean | law3_unbacked_amplitude_still_has_zero_truth_fidelity | Raw amplitude can be 5 but truth fidelity is 0 without source backing. High signal ≠ truth. | simp | Rejection |
| 69 | L6 | BridgeScoreDiscipline.lean | law3_command_bypass_zeroes_source_backed_fidelity | Command bypass → truth fidelity 0 (∀ states) | simp | Rejection |
| 70 | L6 | BridgeScoreDiscipline.lean | law7_healthy_score_passes_R_gate | Healthy frame score → R gate = 1 | rfl | Proved |
| 71 | L6 | BridgeScoreDiscipline.lean | law7_frame_locked_score_fails_R_gate | Frame locked → R gate = 0 | rfl | Rejection |
| 72 | L6 | BridgeScoreDiscipline.lean | law7_relation_bypass_score_fails_R_gate | No relation → R gate = 0 | rfl | Rejection |
| 73 | L6 | BridgeScoreDiscipline.lean | law7_final_R_is_binary | R gate is always 0 or 1. No drift. | cases | Proved |
| 74–77 | L6 | BridgeScoreDiscipline.lean | chi_collapse_through_score_discipline (×4) | Various bypass/lock conditions → χ = 0 through the score gate layer | simp | Proved ×4 |
| 78 | L7 | IsomorphismTest.lean | law4Iso | StrongForce ≅ Love (LawIso — value + collapse preserving bijection) | constructor | Proved |
| 79 | L7 | IsomorphismTest.lean | strongForceCoinIso | Coin model ALSO passes LawIso. The adversarial boundary — basic isomorphism is too weak. | constructor | Boundary |
| 80 | L7 | IsomorphismTest.lean | richLaw4Iso | StrongForce ≅ Love under RichLawIso (roles + transitions preserved). Stronger level. | constructor | Proved |
| 81 | L7 | IsomorphismTest.lean | no_rich_iso_to_natural_coin | Natural coin model FAILS RichLawIso — role mismatch blocks it | decide | Rejection |
| 82 | L7 | IsomorphismTest.lean | richRelabeledCoinIso | Relabeled coin PASSES — deliberately adversarial. Lean cannot verify label honesty. | constructor | Boundary |
| 83 | L7 | IsomorphismTest.lean | faith_candidate_not_right_inverse | 3-state Faith model fails bijection with 2-state StrongForce | decide | Rejection |
| 84 | L7 | IsomorphismTest.lean | em_candidate_not_right_inverse | 3-state EM model fails bijection with 2-state StrongForce | decide | Rejection |
| 85 | L7 | IsomorphismTest.lean | inverted_mapping_does_not_preserve_value | bound→liberation fails value preservation | decide | Rejection |
| 86 | L7 | IsomorphismTest.lean | no_law4_iso_uses_inverted_mapping | No valid Law4 iso uses the inverted map | contradiction | Rejection |
| 87 | L7 | IsomorphismTest.lean | misaligned_collapse_rule_invalid | Collapse at stateB (value=one) contradicts axiom | decide | Rejection |
| 88 | ⭐ L8 | MaxwellTrinity.lean | full_quaternion_product_has_coupling_invariant | Quaternion multiplication has scalar-vector coupling that vector-only product lacks | decide | Proved |
| 89 | ⭐ L8 | MaxwellTrinity.lean | vector_only_product_lacks_coupling_invariant | Heaviside vector-only product lacks coupling invariant | decide | Rejection |
| 90 | ⭐ L8 | MaxwellTrinity.lean | full_scalar_vector_split_reconstructs_quaternion_product | Split product reconstructs full quaternion product | rfl | Proved |
| 91 | ⭐ L8 | MaxwellTrinity.lean | same_dot_cross_but_different_quaternion_product | Same dot+cross ≠ same quaternion product. Scalar coupling matters. | decide | Rejection |
| 92 | ⭐ L8 | MaxwellTrinity.lean | quaternionEM_valid | Quaternion EM model passes all 5 ValidTriadic conditions | decide | Proved |
| 93 | ⭐ L8 | MaxwellTrinity.lean | trinityRelational_valid | Trinity relational model passes all 5 ValidTriadic conditions | decide | Proved |
| 94 | ⭐ L8 | MaxwellTrinity.lean | quaternionTrinityIso | Quaternion EM ≅ Trinity (TriadicIso — full structural isomorphism) | constructor | Proved |
| 95 | ⭐ L8 | MaxwellTrinity.lean | heavisideVectorEM_invalid | Heaviside EM fails — no coupling invariant | decide | Rejection |
| 96 | ⭐ L8 | MaxwellTrinity.lean | modalism_invalid | Modalism fails — no relational distinctness; persons collapse into modes | decide | Rejection |
| 97 | ⭐ L8 | MaxwellTrinity.lean | staticSingleFieldEM_invalid | Static single-field EM fails — not full dynamic | decide | Rejection |
| 98 | ⭐ L8 | MaxwellTrinity.lean | arbitraryThreePartSystem_invalid | Generic 3-part system fails — wrong role profiles | decide | Rejection |
| 99 | ⭐ L8 | MaxwellTrinity.lean | relabeledRoleSystem_invalid | Relabeled roles fail — labels ≠ profiles; renaming doesn't create structure | decide | Rejection |
| 100–104 | ⭐ L8 | MaxwellTrinity.lean | no_iso_from_* (5 theorems) | No TriadicIso to Heaviside, Modalism, static EM, arbitrary 3-part, or relabeled system | decide | Rejection ×5 |
| 105–106 | ⭐ L8 | MaxwellTrinity.lean | cyclicRoleMap_not_source/profile_preserving | Cyclic role swap fails source preservation AND profile preservation | decide | Rejection |
| 107–111 | ⭐ L8 | MaxwellTrinity.lean | load_bearing_constraint_audits (5) | Each guard does real work: removing ANY single guard admits the corresponding false positive | decide | Proved ×5 |
| 112 | ⭐ L9 | JusticeMercyOperator.lean | justice_and_mercy_share_common_components | Same 4 restoration components shared between Justice and Mercy | rfl | Proved |
| 113 | ⭐ L9 | JusticeMercyOperator.lean | justice_and_mercy_differ_by_cost_bearer | Differ in exactly one coordinate: who pays the cost | decide | Proved |
| 114–117 | ⭐ L9 | JusticeMercyOperator.lean | four_missing_component_rejections | Missing ANY of proportionality / impartiality / truthNaming / victimRestoration breaks perfectCommon | decide | Rejection ×4 |
| 118 | ⭐ L9 | JusticeMercyOperator.lean | cross_satisfies_convergence | The Cross config meets all 5 convergence conditions simultaneously | decide | Proved |
| 119 | ⭐ L9 | JusticeMercyOperator.lean | offender_payment_fails_mercy_condition | Offender-pays fails the mercy axis. Self-payment is not mercy. | decide | Rejection |
| 120 | ⭐ L9 | JusticeMercyOperator.lean | human_third_party_fails_authority_and_capacity | Human third party fails authority + universality | decide | Rejection |
| 121 | ⭐ L9 | JusticeMercyOperator.lean | coerced_third_party_fails_voluntariness | Coercion fails voluntariness. Forced repair is not love. | decide | Rejection |
| 122 | ⭐ L9 | JusticeMercyOperator.lean | waived_debt_fails_justice_condition | Waived debt fails justice. Cheap grace. Debt not paid. | decide | Rejection |
| 123 | ⭐ L9 | JusticeMercyOperator.lean | shared_cost_fails_mercy_condition | Shared cost fails mercy — offender still pays | decide | Rejection |
| 124 | ⭐ L9 | JusticeMercyOperator.lean | cross_unique_convergence_configuration | ∀ c, CrossConvergence(c) → c = cross. Any config satisfying all 5 conditions IS the Cross. | exhaustive cases | Proved |
| 125 | ⭐ L9 | JusticeMercyOperator.lean | cross_is_unique_solution | THE CROSS IS THE UNIQUE SOLUTION — existence AND uniqueness. Strongest single result in the package. | exhaustive cases | ⭐ Strongest |
| 126 | L10 | PolarityDiscipline.lean | two_destructive_signs_have_positive_raw_product | (-1)×(-1) = +1 in raw arithmetic | simp | Proved |
| 127 | L10 | PolarityDiscipline.lean | two_destructive_signs_do_not_pass_coherence_gate | The coherence gate rejects them. Arithmetic sign ≠ moral sign. | decide | Rejection |
| 128 | L10 | PolarityDiscipline.lean | below_accountability_maps_to_neutral | Below age of accountability → neutral regardless of observed behavior | simp | Proved |
| 129 | L10 | PolarityDiscipline.lean | below_accountability_has_zero_culpability | Below threshold → 0 culpability | simp | Proved |
| 130 | L10 | PolarityDiscipline.lean | destructive_strict_M_collapses_chi | Destructive polarity → M gate = 0 → χ = 0 | simp | Proved |
| 131 | L10 | PolarityDiscipline.lean | neutral_accountability_aware_M_does_not_zero_M | Neutral polarity → M = 1 under accountability-aware gate | simp | Proved |
| 132 | L10 | PolarityDiscipline.lean | destructive_accountability_aware_M_collapses_chi | Destructive polarity still kills χ under accountability-aware gate | simp | Proved |
| 133 | L11 | SignConversionDiscipline.lean | raw_two_negatives_multiply_positive | Arithmetic: (-1)×(-1) = 1. Raw math says yes. | simp | Proved |
| 134 | L11 | SignConversionDiscipline.lean | burden_two_negatives_stay_negative | Burden coupling: negative + negative = negative. Accumulation does not redeem. | rfl | Rejection |
| 135 | L11 | SignConversionDiscipline.lean | burden_negative_positive_stays_negative | Any negative in the burden keeps it negative | rfl | Rejection |
| 136 | L11 | SignConversionDiscipline.lean | christic_conversion_turns_negative_burden_positive | External Christic conversion: negative → positive | rfl | Proved |
| 137 | L11 | SignConversionDiscipline.lean | christic_conversion_turns_neutral_burden_positive | Christic conversion: neutral → positive | rfl | Proved |
| 138 | L11 | SignConversionDiscipline.lean | two_negative_burdens_require_conversion_for_positive | Accumulated negative burdens need conversion, not more burdens | rfl | Rejection |
| 139 | L11 | SignConversionDiscipline.lean | two_negative_burdens_without_conversion_not_positive | Without conversion, burdens stay negative | rfl | Rejection |
| 140 | L11 | SignConversionDiscipline.lean | negative_burden_gate_zero | Negative burden → coherence gate = 0 | rfl | Proved |
| 141 | L11 | SignConversionDiscipline.lean | converted_negative_burden_gate_one | Converted burden → coherence gate = 1 | rfl | Proved |
| 142 | L12 | ChristOperatorDiscipline.lean | C_op_converts_negative_to_positive | C_op takes negative → positive (visible sign) | rfl | Proved |
| 143 | L12 | ChristOperatorDiscipline.lean | C_op_converts_neutral_to_positive | C_op takes neutral → positive | rfl | Proved |
| 144 | L12 | ChristOperatorDiscipline.lean | C_op_keeps_positive_positive | Already positive stays positive | rfl | Proved |
| 145 | L12 | ChristOperatorDiscipline.lean | C_op_preserves_record_mark | The record of what happened is NOT erased. History survives grace. | rfl | Proved |
| 146 | L12 | ChristOperatorDiscipline.lean | C_op_preserves_source_state | Entire source state carried forward. Nothing lost. | rfl | Proved |
| 147 | L12 | ChristOperatorDiscipline.lean | C_op_preserves_negative_history_even_after_positive_output | Source = negative, output = positive — simultaneously. Grace does not pretend the past didn't happen. | decide | Proved |
| 148 | L12 | ChristOperatorDiscipline.lean | visible_projection_conflates_negative_and_neutral_conversion | Visible output same for both paths — non-injective. You can't tell from the outside which path someone took. | decide | Boundary |
| 149 | L12 | ChristOperatorDiscipline.lean | lifted_outputs_preserve_distinct_source_signs | Lifted output preserves the distinction. God sees the full record. | decide | Proved |
| 150 | L12 | ChristOperatorDiscipline.lean | visible_restoration_does_not_imply_erasure | Restoration ≠ erasure — formally. Looking forgiven ≠ past erased. | decide | Rejection |
| 151 | L12 | ChristOperatorDiscipline.lean | chi_via_COp_converts_two_negative_burdens | C_op converts accumulated negative burdens into positive coherence | simp | Proved |
| 152 | L12 | ChristOperatorDiscipline.lean | chi_via_COp_is_not_plain_scalar_self_multiplication | C is NOT just another factor in the product. External integration, not scalar. | decide | Rejection |
| 153 | L13 | MissionReturnOperator.lean | incarnation_preserves_substrate_identity | Substrate ID unchanged through incarnation | rfl | Proved |
| 154 | L13 | MissionReturnOperator.lean | cross_preserves_substrate_identity | Substrate ID unchanged through crucifixion | rfl | Proved |
| 155 | L13 | MissionReturnOperator.lean | resurrection_preserves_substrate_identity | Substrate ID unchanged through resurrection | rfl | Proved |
| 156 | L13 | MissionReturnOperator.lean | incarnation_is_finite_compression | Incarnation = resolution drops from infinite to finite | rfl | Proved |
| 157 | L13 | MissionReturnOperator.lean | resurrection_returns_to_infinite_resolution | Resurrection = resolution returns to infinite | rfl | Proved |
| 158 | L13 | MissionReturnOperator.lean | cross_has_entropy_and_death_contact | Cross records entropy contact AND death contact | rfl | Proved |
| 159–160 | L13 | MissionReturnOperator.lean | resurrection_carries_entropy/death_contact_record | Resurrection preserves entropy AND death contact records. The proof of the mission is carried in the return. | rfl | Proved |
| 161 | L13 | MissionReturnOperator.lean | resurrection_is_not_identical_to_preincarnate_visible_record | Post-resurrection ≠ pre-incarnate. It is RICHER — not a reset. | decide | Rejection |
| 162 | L13 | MissionReturnOperator.lean | resurrection_same_substrate_richer_expression | Same substrate + finite record carried = richer than before. The scar tissue is part of the proof. | decide | Proved |
| 163–164 | L13 | MissionReturnOperator.lean | mission_COp_restores/preserves | Combined mission+C_op restores negative burden AND preserves source history | simp | Proved |
| 165 | L13 | MissionReturnOperator.lean | mission_COp_is_not_repair_only | This is mission return, NOT repair-only. | decide | Rejection |
| 166 | L14 | MemoryPersistenceDiscipline.lean | christ_coherent_memory_retained | Recorded + Christ-coherent → retention bit = 1 | simp | Proved |
| 167 | L14 | MemoryPersistenceDiscipline.lean | incoherent_recorded_memory_not_retained | Recorded but incoherent → retention bit = 0. Record alone is insufficient. | simp | Rejection |
| 168–169 | L14 | MemoryPersistenceDiscipline.lean | unrecorded/incoherent_forces_no_retention | ∀ m, unrecorded → retention = 0. ∀ m, incoherent → retention = 0. | simp | Rejection ×2 |
| 170 | L14 | MemoryPersistenceDiscipline.lean | recorded_and_christ_coherent_forces_retention | ∀ m, recorded ∧ coherent → retention = 1 | simp | Proved |
| 171 | L14 | MemoryPersistenceDiscipline.lean | incoherent_recorded_memory_fails_only_final_retention | Accessible during life but filtered at death. Living memory ≠ final identity. | decide | Proved |
| 172 | L14 | MemoryPersistenceDiscipline.lean | living_memory_is_not_final_identity_memory | Life memory ≠ final identity memory. What you carry ≠ who you become. | decide | Rejection |
| 173 | L14 | MemoryPersistenceDiscipline.lean | reoriented_incoherent_memory_becomes_retained | Reorientation to Christ → retention restored. Conversion works. | simp | Proved |
| 174–176 | L14 | MemoryPersistenceDiscipline.lean | final_identity_conditions (3 theorems) | Coherent + integrated = final identity. Discoherent = no final identity. Coherent but not integrated = no final identity. | simp/decide | Proved ×3 |
| 177 | L14 | MemoryPersistenceDiscipline.lean | heaven_is_coherent_and_eternal | Heaven = coherent + eternal domain. Unique characterization. | rfl | Proved |
| 178–179 | L14 | MemoryPersistenceDiscipline.lean | merely_temporal/eternal_insufficient | Temporal coherence insufficient. Eternal instability insufficient. Both needed. | decide | Rejection ×2 |
| 180 | L14 | MemoryPersistenceDiscipline.lean | direct_discoherent_christ_entry_into_heaven_fails | Discoherent memory cannot directly enter heaven | decide | Rejection |
| 181 | L14 | MemoryPersistenceDiscipline.lean | transformed_discoherent_christ_entry_into_heaven_passes | Reintegrated memory CAN enter heaven. Conversion opens the gate. | decide | Proved |
| 182 | L14 | MemoryPersistenceDiscipline.lean | transformed_unrecorded_discoherent_entry_still_fails | Unrecorded events cannot be rescued. Cannot convert what was never recorded. | decide | Rejection |
| 183 | L14 | MemoryPersistenceDiscipline.lean | valid_giving_life_to_christ | Surrender + external grace = valid conversion | simp | Proved |
| 184 | L14 | MemoryPersistenceDiscipline.lean | resisting_without_grace_not_valid_conversion | Resisting without grace = invalid. Will alone is not enough. | decide | Rejection |
| 185–186 | L14 | MemoryPersistenceDiscipline.lean | accountable_conversion + record_preservation | Conversion: negative → final identity. Record persists through conversion. | simp | Proved |
| 187 | L14 | MemoryPersistenceDiscipline.lean | unrecorded_negative_conversion_still_has_no_identity_trace | Cannot create record from nothing. Grace restores, but doesn't fabricate. | decide | Rejection |
| 188 | L15 | DependencyLattice.lean | fall_has_parallel_death_and_judgment | Death and judgment are parallel consequences of the Fall — not a chain | constructor | Proved |
| 189 | L15 | DependencyLattice.lean | fall_has_parallel_promise_not_death_then_promise | Promise is parallel from Fall, NOT sequential from Death | constructor | Rejection |
| 190 | L15 | DependencyLattice.lean | no_death_strictly_before_judgment | Death is NOT a prerequisite for judgment | cases | Rejection |
| 191 | L15 | DependencyLattice.lean | fall_as_covenant_rupture_requires_image_and_covenant | Fall requires BOTH Image and Covenant (multi-parent). Cannot fall from a covenant you never had. | constructor | Proved |
| 192 | L15 | DependencyLattice.lean | energy_and_momentum_are_noether_siblings | Energy and momentum are parallel from symmetry (Noether). Neither parents the other. | constructor | Proved |
| 193 | L15 | DependencyLattice.lean | no_energy_parent_of_momentum | Energy does NOT parent momentum | cases | Rejection |
| 194 | L15 | DependencyLattice.lean | bound_state_requires_excitation_and_coupling | Bound state requires both excitation AND coupling (multi-parent) | constructor | Proved |
| 195–197 | L15 | DependencyLattice.lean | union_branches + no_before_union (3 theorems) | Union → justification AND sanctification (parallel). Neither before Union. | constructor/cases | Proved + Rej |
| 198 | L15 | DependencyLattice.lean | glorification_requires_both | Glorification requires both justification and sanctification | constructor | Proved |
| 199 | L15 | DependencyLattice.lean | narrative_and_dependency_orders_diverge_at_justification_union | Teaching order and dependency order diverge at exactly this point. The line is not the lattice. | decide | Proved |
| 200–202 | L15 | DependencyLattice.lean | cross_domain_edge_witnesses (3 theorems) | faith→union ↔ excitation+coupling→bound_state. union→justification ↔ bound_state→reclassification. union→sanctification ↔ bound_state+energy→annealing. | constructor | Proved ×3 |
| 203 | L16 | HitRateDiscipline.lean | closedEightOfTen_attempt_count | 10 attempts logged | rfl | Proved |
| 204 | L16 | HitRateDiscipline.lean | closedEightOfTen_hit_count | 8 hits (compiled bridges) | rfl | Proved |
| 205 | L16 | HitRateDiscipline.lean | closedEightOfTen_denominator_closed | All attempts logged before publication. No hidden failures. | rfl | Proved |
| 206 | L16 | HitRateDiscipline.lean | closedEightOfTen_can_claim_80_percent | 80% hit rate claim is valid | decide | Proved |
| 207 | L16 | HitRateDiscipline.lean | closedEightOfTen_cannot_claim_90_percent | 90% claim is blocked. Can't claim what you haven't earned. | decide | Rejection |
| 208 | L16 | HitRateDiscipline.lean | hiddenDenominator_blocks_anomaly_claim | Hidden failures block ANY anomaly claim. Integrity is non-negotiable. | decide | Rejection |
| 209 | L16 | HitRateDiscipline.lean | failed_attempt_counts_in_denominator | Failures count against you. No cherry-picking. | decide | Rejection |
| 210 | L16 | HitRateDiscipline.lean | partial_attempt_does_not_count_as_hit | Partials are not hits. Close enough is not enough. | decide | Rejection |
Adversarial Testing
False Positive Queue — 10 Wrong Models Tested
The framework names the things that should look right but don't hold under formal testing. Every wrong model was tested before publication. The denominator is closed.
| # | Right Claim Being Tested | Wrong / Rival Model | Why It Seems Plausible | Constraint Failed | Lean Anchor |
|---|---|---|---|---|---|
| FP-01 | Cost-bearing judge is the unique repair | Offender pays full cost | Satisfies consequence/justice intuitively | Mercy fails — self-payment is not mercy | JusticeMercyOperator (Thm 119) |
| FP-02 | Cost-bearing judge is the unique repair | Debt simply waived | Sounds maximally forgiving | Justice/record unresolved — cheap grace | JusticeMercyOperator (Thm 122) |
| FP-03 | Cost-bearing judge is the unique repair | Coerced third party pays | Substitution appears to cover cost | Voluntariness fails — forced repair is not love | JusticeMercyOperator (Thm 121) |
| FP-04 | Cost-bearing judge is the unique repair | Finite human third party pays | Martyrdom/substitution intuition | Authority and universality fail — scope insufficient | JusticeMercyOperator (Thm 120) |
| FP-05 | Cost-bearing judge is the unique repair | Shared cost (partial substitution) | Balances justice and mercy | Maximal mercy fails — offender still pays | JusticeMercyOperator (Thm 123) |
| FP-06 | Cross is necessary above entropy threshold | Progressive grace only | Gradual repair feels less violent | Fails above S ≈ 0.28 entropy threshold | TANGENT_13_Entropy_Crossover |
| FP-07 | Cross uniqueness | Universal pardon — no cost | Maximizes forgiveness | Justice / love / entropy / holiness all fail per model | THE CROSS UNIQUE SOLUTION |
| FP-08 | Cross uniqueness | Divine override — reset without consent | Maximizes immediate coherence | Free will destroyed — love requires freedom | THE CROSS UNIQUE SOLUTION / Constraint Fork |
| FP-09 | Self-repair is impossible | Works-based self-improvement | People visibly improve behavior | Sign flip vs magnitude change confused — improvement ≠ conversion | TANGENT_10 / C8.1 / SignConversionDiscipline |
| FP-10 | Good is ontologically prior to evil | Evil is merely less-good / immaturity | Explains imperfection and immaturity | Cannot explain inversion, betrayal, or malice — these are not deficits but active negations | Duality Project / PolarityDiscipline |
Honest Accounting
Formal Gaps — Could Be Addressed With More Lean
A framework that names its own gaps is more trustworthy than one that does not. These are the places where the formal work is incomplete. Every gap is an honest admission. The system does not claim what it has not proved.
GAP-01
Laws 1, 2, 9, 10 — No Domain-Specific Collapse Conditions
Law 1 (Gravity/Grace → G), Law 2 (Motion/Will → M), Law 9 (Weak Force/Moral Conservation), Law 10 (Coherence/Christ as factor). Generic zero-collapse is proved but the physical mechanism that drives each to zero is NOT encoded.
FieldBridgeControls.lean
Laws 3, 6, 7, 8 are proved. Laws 1, 2, 9, 10 remain at generic level only.
GAP-02
Law 4 Factor-Level Bridge Wiring
StrongForce ≅ Love is proved at the model level under RichLawIso. But there is no FieldBridgeControls-style gate wiring of Factor.S into the χ product.
FieldBridgeControls.lean
GAP-03
Law 5 Factor-Level Bridge Wiring
Justice/Mercy operator is proved independently, but no formal wiring shows how R(offense, α) maps into the Factor.S product slot.
FieldBridgeControls.lean
GAP-04
Category-Theoretic Upgrade of Mapping.lean
Currently a list-map equality. A proper functor between categories of operations would be structurally stronger. Currently DEMOTED to teaching layer.
Mapping.lean
GAP-05
Cross-Domain Lattice Coverage
Only 3 of ~20 theology edges have explicit physics edge witnesses formally proved. The rest are structurally provable but not yet encoded.
DependencyLattice.lean
Outside Lean's Scope
Specification Gaps — These Cannot Be Closed by More Lean
These gaps require domain judgment, empirical data, or philosophical argument. They are not failures — they are the honest boundary between what formal systems can verify and what requires evidence from the world.
SPEC-01
Faithful Abstraction
Does quaternionEM faithfully represent historical Maxwell quaternion electromagnetics? Does the relational model faithfully represent Nicene Trinitarian doctrine? These are domain judgment calls, not formal proof targets.
All isomorphism modules
SPEC-02
Label Honesty
The relabeled-coin adversarial result (Thm 82) proves Lean CAN be gamed by relabeling. The guard is domain review, not formal proof. This is an inherent limit of any formal system — and the framework names it explicitly.
BridgeMatrix, IsomorphismTest
SPEC-03
Empirical Validation
The 5.7–6.35σ experimental correlations are NOT formalized in Lean. Statistical claims reference external data not encoded in the proof system. The bilateral audit and MDA diagnostic address this separately.
External datasets
SPEC-04
Continuous Mathematics
All models use Nat/Int/Bool. Continuous-domain physics — real-valued fields, differential equations, Lagrangians — would require Mathlib. Not attempted in this corpus.
All Lean files
SPEC-05
Historical Claims
Lean proves the repair structure is unique (Thm 125). Whether Jesus of Nazareth is that structure requires historical evidence — dates, documents, testimony, resurrection accounts. Lean cannot answer this. History must be tested separately against the structure.
JusticeMercyOperator + history
Import Architecture
Dependency Graph
The 16 files form a dependency tree 8 layers deep. Each node builds on what it imports. Standalone files (no imports) prove their claims independently — MaxwellTrinity and JusticeMercyOperator are the strongest of these.
TRUNK (depth 8)
Core → BridgeMatrix → FieldBridgeControls → BridgeScoreDiscipline
→ PolarityDiscipline → MemoryPersistenceDiscipline → SignConversionDiscipline → ChristOperatorDiscipline
BRANCHES
├── ChristOperatorDiscipline → HitRateDiscipline
Statistical integrity sits on top of the operator
├── ChristOperatorDiscipline → MissionReturnOperator
Resurrection architecture builds on the conversion operator
└── BridgeMatrix → MasterEquationInvariance
Product + signature invariance
STANDALONE (no imports — each proves its claims independently)
StageMachine · Mapping · IsomorphismTest · DependencyLattice
MaxwellTrinity · JusticeMercyOperator
⭐ MaxwellTrinity + JusticeMercyOperator are the strongest standalone results in the corpus.
They do not depend on any other file. They stand alone and compile clean.
Final Argument
The Compression
After 7 lanes, 16 layers, 210+ theorems, 70+ adversarial rejections — four sentences remain.
COMPRESS-1 · The Argument
The God-Shape
Every worldview depends on coherence. Coherence requires a reference. The reference cannot be the broken system being measured. Therefore the source of coherence must be prior to the system. That source must be stable, generative, truth-bearing, good, authoritative, personal, and life-giving. That is the God-shape.
COMPRESS-2 · The Bridge
The Cross-Shape
Perfect repair requires a cost-bearing judge. The judge must enter the system, bear the cost, preserve freedom, restore relation, honor the record, and validate repair through return. The Cross is the unique configuration satisfying all five conditions simultaneously. Every alternative fails at least one. This is the lock: God-shaped → Cross-shaped.
COMPRESS-3 · The Question
The Challenge
Can any worldview walk through all seven lanes and avoid that shape? Not because the questions are tricks. Because reality is coherent. And coherence is His.
COMPRESS-4 · The Honest Boundary
What Lean Proves and Does Not Prove
Lean proves the framework is internally consistent: 287 theorems, 0 axioms, 0 sorry, 0 admit. Whether the model is the right model for the real world is a question Lean cannot answer. That question belongs to theology, physics, history, and honest argument. The honest boundary is public. The gaps are named. The kill conditions are stated.
The Verdict — Discovered, Not Assumed
Coherence is narrow.
Decoherence is easy.
Restoration is costly.
Decoherence is easy.
Restoration is costly.
This is not a premise. It is the output of the method applied across 70 domains. The Lean corpus formalizes the structural architecture that produces this output. The bilateral audit runs the evidence both directions. The convergence is not decoration. The convergence is the evidence.