/- Holy Diver / ENE Reality-Contract Mass-Number Forest A Lean 4 core-only module encoding the ontology-derived ruleset: - every domain is a reality-local field; - candidates are reduced only through certified domain-local reductions; - residuals are preserved, not erased; - mass numbers are admissible reduction divided by residual risk; - phi is normalized reducibility; - autodoc pressure decides whether the forest writes/updates documentation; - every candidate receives one finite decision. This file intentionally avoids Mathlib so it can be dropped into a plain Lean 4 project. The analytic/logarithmic phi-distance from the prose model is represented here by a rational cost surrogate: distanceCost = residual / (admissible + 1) which preserves the intended order: more admissible reduction lowers distance; more residual risk raises distance. -/ namespace HolyDiver namespace ENE /-! ## Core enumerations -/ inductive DomainKind where | mathematics | physics | biology | computation | cognition | language | social | cryptography | engineering | unknown deriving Repr, DecidableEq inductive ComparisonLevel where | substrate | operator | transition | observable | contract | truth deriving Repr, DecidableEq inductive MassKind where | anchor | transport | symmetry | topology | dimension | cognitiveLoad | phaseCoherence | proteinTemplate | categoryErrorCorrection | criticalLineAnchor | rationalPointRank | arithmeticAnalyticBridge | radiantTransportMomentum | eigenmodeTransport | physicsNumerologyRisk | other deriving Repr, DecidableEq inductive ResidualKind where | unresolved | contradiction | missingVariable | frameMismatch | observableGap | implementationGap | categoryError | highCognitiveLoad | shoreMirage | domainDrift | oracleBoundary deriving Repr, DecidableEq inductive Decision where | promote | edgeSurvivor | quarantine | banReduce deriving Repr, DecidableEq inductive DocAction where | createNew | updateExisting | edgeSurvivorNote | ignore deriving Repr, DecidableEq /-! ## Reality contracts -/ /-- A domain is not merely a topic. It is a reality-local field with its own contract for what counts as a state, operation, observation, invariant, failure, boundary, and handoff target. -/ structure RealityContract where domain : DomainKind substrate : String validStates : List String validOperators : List String observables : List String invariants : List String failureModes : List String boundaries : List String handoffTargets : List DomainKind deriving Repr /-- A candidate being evaluated by the forest. -/ structure Candidate where name : String claim : String domains : List DomainKind massKinds : List MassKind truthStatus : String deriving Repr /-- A reference frame names the local context in which reductions are evaluated. -/ structure ReferenceFrame where name : String description : String deriving Repr /-! ## Certified reductions -/ /-- A raw domain-local reduction contribution. All quantities are natural-number weights. This keeps the core executable without importing rationals/reals. Think of each value as a nonnegative score from a calibrated registry. -/ structure DomainReduction where fieldName : String weight : Nat reductionStrength : Nat contractCompatibility : Nat activation : Nat deriving Repr /-- The contribution of a reduction to admissible mass. -/ def DomainReduction.term (r : DomainReduction) : Nat := r.weight * r.reductionStrength * r.contractCompatibility * r.activation /-- Certified reductions are proof-carrying: they cannot enter mass-number scoring unless compatibility and activation are strictly positive. -/ structure CertifiedReduction where raw : DomainReduction compat_ok : raw.contractCompatibility > 0 active_ok : raw.activation > 0 deriving Repr /-- The certified contribution to admissible mass. -/ def CertifiedReduction.term (r : CertifiedReduction) : Nat := r.raw.term /-! ## Residual risk -/ /-- Residual risk is the denominator pressure: near-miss tension, shore mirage, load, violation, oracle boundary, and domain drift. -/ structure ResidualRisk where tension : Nat shoreMirage : Nat load : Nat violation : Nat oracle : Nat drift : Nat deriving Repr /-- Denominator contribution: always at least 1. -/ def ResidualRisk.denominator (r : ResidualRisk) : Nat := 1 + r.tension + r.shoreMirage + r.load + r.violation + r.oracle + r.drift /-- Residual amount excluding the stabilizing `1`. -/ def ResidualRisk.amount (r : ResidualRisk) : Nat := r.tension + r.shoreMirage + r.load + r.violation + r.oracle + r.drift /-! ## Rational-like nonnegative scores -/ /-- A nonnegative rational-like score `num / den` with proof that the denominator is nonzero. This avoids importing rational numbers while preserving the structure of the equations. -/ structure Score where num : Nat den : Nat den_ne : den ≠ 0 deriving Repr /-- A safe constructor for scores with denominator `n + 1`. -/ def Score.ofNatOverSucc (num denMinusOne : Nat) : Score := { num := num, den := denMinusOne + 1, den_ne := by simp } /-- Natural-number cross-multiplication comparison. -/ def Score.ge (a b : Score) : Prop := a.num * b.den ≥ b.num * a.den /-- Natural-number cross-multiplication strict comparison. -/ def Score.gt (a b : Score) : Prop := a.num * b.den > b.num * a.den /-! ## Mass number, phi, distance, and autodoc equations -/ /-- Sum a list of natural numbers. -/ def sumNat (xs : List Nat) : Nat := xs.foldl (fun acc x => acc + x) 0 /-- Total admissible reduction from certified reductions. -/ def admissibleReduction (rs : List CertifiedReduction) : Nat := sumNat (rs.map CertifiedReduction.term) /-- Master mass-number equation, executable core form: M_D,R(x) = admissible / (1 + residual risk) -/ def massNumber (rs : List CertifiedReduction) (risk : ResidualRisk) : Score := { num := admissibleReduction rs, den := risk.denominator, den_ne := by unfold ResidualRisk.denominator simp } /-- Mass-number phi: normalized reducibility. phi = admissible / (admissible + residual) When both admissible and residual are zero, the denominator is stabilized to 1. -/ def massPhi (rs : List CertifiedReduction) (risk : ResidualRisk) : Score := let a := admissibleReduction rs let u := risk.amount if h : a + u = 0 then { num := 0, den := 1, den_ne := by simp } else { num := a, den := a + u, den_ne := h } /-- A Lean-core surrogate for phi distance. The prose equation used `-log(phi + epsilon)`. Here we encode the same order as an admissibility cost: d_phi_cost = residual / (admissible + 1) -/ def phiDistanceCost (rs : List CertifiedReduction) (risk : ResidualRisk) : Score := { num := risk.amount, den := admissibleReduction rs + 1, den_ne := by simp } /-- Additional factors controlling documentation pressure. -/ structure AutodocFactors where novelty : Nat compression : Nat handoffValue : Nat unresolved : Nat deriving Repr /-- Autodoc pressure: A_doc = M * novelty * compression * handoff / (1 + unresolved + drift + load + violation) Because `M` is itself a score, we multiply its numerator and extend its denominator. -/ def autodocPressure (rs : List CertifiedReduction) (risk : ResidualRisk) (f : AutodocFactors) : Score := let m := massNumber rs risk { num := m.num * f.novelty * f.compression * f.handoffValue, den := m.den * (1 + f.unresolved + risk.drift + risk.load + risk.violation), den_ne := by apply Nat.mul_ne_zero · exact m.den_ne · simp } /-! ## Candidate records and forest nodes -/ structure TypedResidual where kind : ResidualKind description : String handoffTo : List DomainKind deriving Repr structure NativeReductionRecord where domain : DomainKind reduction : CertifiedReduction note : String deriving Repr /-- A full candidate record: this is the object the forest can score, route, document, promote, quarantine, or preserve as an edge survivor. -/ structure CandidateRecord where candidate : Candidate frame : ReferenceFrame comparisonLevel : ComparisonLevel contracts : List RealityContract nativeReductions : List NativeReductionRecord residuals : List TypedResidual risk : ResidualRisk observableProjection : String formalProjection : String failureModes : List String deriving Repr /-- Pull certified reductions out of a full record. -/ def CandidateRecord.reductions (r : CandidateRecord) : List CertifiedReduction := r.nativeReductions.map (fun nr => nr.reduction) /-- Mass number of a full record. -/ def CandidateRecord.mass (r : CandidateRecord) : Score := massNumber r.reductions r.risk /-- Phi of a full record. -/ def CandidateRecord.phi (r : CandidateRecord) : Score := massPhi r.reductions r.risk /-- Distance-cost of a full record. -/ def CandidateRecord.distance (r : CandidateRecord) : Score := phiDistanceCost r.reductions r.risk /-- Autodoc pressure of a full record. -/ def CandidateRecord.autodoc (r : CandidateRecord) (f : AutodocFactors) : Score := autodocPressure r.reductions r.risk f /-! ## Decisions -/ /-- Threshold bundle for promotion and documentation. -/ structure Thresholds where promoteMass : Score edgeMass : Score maxRiskForPromote : Nat docNew : Score docUpdate : Score nearestMerge : Score deriving Repr /-- High residual means preserve as edge survivor unless promotion is justified. -/ def highResidual (r : CandidateRecord) : Prop := r.risk.amount > 0 ∧ r.residuals ≠ [] /-- A lightweight executable risk gate. -/ def riskLowEnough (r : CandidateRecord) (θ : Thresholds) : Prop := r.risk.amount ≤ θ.maxRiskForPromote /-- Prop-level promotion eligibility. -/ def canPromote (r : CandidateRecord) (θ : Thresholds) : Prop := Score.ge r.mass θ.promoteMass ∧ riskLowEnough r θ ∧ r.observableProjection ≠ "" /-- Prop-level edge-survivor eligibility. -/ def shouldBeEdgeSurvivor (r : CandidateRecord) (θ : Thresholds) : Prop := Score.ge r.mass θ.edgeMass ∧ highResidual r /-- Decidable implementation of the finite decision corridor. This takes Boolean gates as parameters so the caller can plug in proof-producing or runtime-produced tests. The ontology requires one of four outcomes only. -/ def decideCandidate (promoteGate edgeGate quarantineGate : Bool) : Decision := if promoteGate then Decision.promote else if edgeGate then Decision.edgeSurvivor else if quarantineGate then Decision.quarantine else Decision.banReduce /-- The decision corridor is finite by construction. -/ theorem decision_is_finite (p e q : Bool) : decideCandidate p e q = Decision.promote ∨ decideCandidate p e q = Decision.edgeSurvivor ∨ decideCandidate p e q = Decision.quarantine ∨ decideCandidate p e q = Decision.banReduce := by unfold decideCandidate by_cases hp : p <;> simp [hp] by_cases he : e <;> simp [he] by_cases hq : q <;> simp [hq] /-- Autodoc action. `nearest` is the nearest-page overlap score. The comparison gates are deliberately passed as Booleans to let a runtime or proof layer decide thresholds. -/ def decideDocAction (newGate updateGate nearestMergeGate massNonzero residualHigh : Bool) : DocAction := if newGate && not nearestMergeGate then DocAction.createNew else if updateGate && nearestMergeGate then DocAction.updateExisting else if massNonzero && residualHigh then DocAction.edgeSurvivorNote else DocAction.ignore /-! ## Ontology rules as checkable predicates -/ /-- Rule: analogy never promotes alone. A promoted cross-domain candidate needs at least one projection. -/ def hasProjection (r : CandidateRecord) : Prop := r.observableProjection ≠ "" ∨ r.formalProjection ≠ "" /-- Rule: residuals must remain typed. In this encoding, any residual object is typed by construction. -/ theorem residuals_typed_by_construction (r : CandidateRecord) : ∀ res ∈ r.residuals, ∃ k : ResidualKind, res.kind = k := by intro res h exact ⟨res.kind, rfl⟩ /-- Rule: every native reduction is certified by construction. -/ theorem native_reductions_certified (r : CandidateRecord) : ∀ nr ∈ r.nativeReductions, nr.reduction.raw.contractCompatibility > 0 ∧ nr.reduction.raw.activation > 0 := by intro nr h exact ⟨nr.reduction.compat_ok, nr.reduction.active_ok⟩ /-- Rule: mass denominator is always nonzero. -/ theorem mass_denominator_nonzero (r : CandidateRecord) : r.mass.den ≠ 0 := by exact r.mass.den_ne /-- Rule: distance denominator is always nonzero. -/ theorem distance_denominator_nonzero (r : CandidateRecord) : r.distance.den ≠ 0 := by exact r.distance.den_ne /-! ## Example canonical records -/ /-- A tiny helper reduction with compatibility and activation both equal to 1. -/ def certifiedUnitReduction (name : String) (w strength : Nat) : CertifiedReduction := { raw := { fieldName := name, weight := w, reductionStrength := strength, contractCompatibility := 1, activation := 1 }, compat_ok := by simp, active_ok := by simp } /-- Mathematics contract used for examples. -/ def mathContract : RealityContract := { domain := DomainKind.mathematics, substrate := "formal objects, axioms, proofs, models", validStates := ["definition", "theorem", "construction", "counterexample"], validOperators := ["proof", "equivalence", "model construction", "refutation"], observables := ["formal derivation", "checked proof", "countermodel"], invariants := ["logical consistency relative to axioms"], failureModes := ["analogy mistaken for theorem"], boundaries := ["unproved conjecture", "axiom dependence"], handoffTargets := [DomainKind.computation, DomainKind.physics] } /-- Biology contract used for examples. -/ def biologyContract : RealityContract := { domain := DomainKind.biology, substrate := "living systems, cells, enzymes, evolution, biochemical mechanisms", validStates := ["molecule", "pathway", "phenotype", "assay state"], validOperators := ["mechanistic assay", "structural determination", "fitness test"], observables := ["phenotype", "structure", "activity", "growth effect"], invariants := ["biochemical compatibility", "evolutionary viability"], failureModes := ["molecular possibility mistaken for engineering control"], boundaries := ["unknown generalizability", "unmeasured toxicity"], handoffTargets := [DomainKind.computation, DomainKind.engineering] } /-- Example: imaginary numbers as a promoted category-error rescue object. -/ def imaginaryNumbersRecord : CandidateRecord := { candidate := { name := "Imaginary numbers", claim := "Real-line impossibility becomes stable phase rotation in the complex plane.", domains := [DomainKind.mathematics, DomainKind.cognition], massKinds := [MassKind.dimension, MassKind.categoryErrorCorrection], truthStatus := "established mathematics" }, frame := { name := "complex-plane frame", description := "state-space expansion from line to plane" }, comparisonLevel := ComparisonLevel.contract, contracts := [mathContract], nativeReductions := [ { domain := DomainKind.mathematics, reduction := certifiedUnitReduction "algebraic closure / phase rotation" 5 5, note := "sqrt(-1) fails on the real line but stabilizes in the complex plane." } ], residuals := [], risk := { tension := 0, shoreMirage := 0, load := 1, violation := 0, oracle := 0, drift := 0 }, observableProjection := "rotations, magnitudes, phase, signal and quantum projections", formalProjection := "complex number construction", failureModes := ["treating imaginary component as directly physical without projection"] } /-- Example: DRT3 as protein-template category breaker. -/ def drt3Record : CandidateRecord := { candidate := { name := "DRT3 defense system", claim := "Protein active-site geometry can enforce sequence-specific DNA synthesis.", domains := [DomainKind.biology, DomainKind.computation], massKinds := [MassKind.proteinTemplate, MassKind.categoryErrorCorrection], truthStatus := "reported experimental biochemistry" }, frame := { name := "bacterial anti-phage defense", description := "sequence specificity through constraint geometry" }, comparisonLevel := ComparisonLevel.operator, contracts := [biologyContract], nativeReductions := [ { domain := DomainKind.biology, reduction := certifiedUnitReduction "protein-template sequence constraint" 5 4, note := "The active site acts as a structural template rather than a nucleic-acid template." } ], residuals := [ { kind := ResidualKind.observableGap, description := "Engineering generality, error rate, substrate range, and toxicity remain unresolved.", handoffTo := [DomainKind.engineering, DomainKind.computation] } ], risk := { tension := 1, shoreMirage := 0, load := 2, violation := 0, oracle := 0, drift := 1 }, observableProjection := "alternating DNA product and anti-phage phenotype", formalProjection := "protein-template mass record", failureModes := ["assuming arbitrary programmable DNA writing from one mechanism"] } /-! ## Forest registry -/ /-- The first seed forest. -/ def seedForest : List CandidateRecord := [imaginaryNumbersRecord, drt3Record] /-- A compact export row for external tools. -/ structure ForestRow where name : String massNum : Nat massDen : Nat phiNum : Nat phiDen : Nat distNum : Nat distDen : Nat deriving Repr /-- Convert a candidate record into a numeric export row. -/ def CandidateRecord.toRow (r : CandidateRecord) : ForestRow := { name := r.candidate.name, massNum := r.mass.num, massDen := r.mass.den, phiNum := r.phi.num, phiDen := r.phi.den, distNum := r.distance.num, distDen := r.distance.den } /-- Export the seed forest as rows. -/ def seedForestRows : List ForestRow := seedForest.map CandidateRecord.toRow end ENE end HolyDiver