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166 lines
6.8 KiB
Text
166 lines
6.8 KiB
Text
import Mathlib.Data.Nat.Basic
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import Mathlib.Tactic
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import Semantics.FixedPoint
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open Semantics
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/-! # Generalized Evolutionary Signal Transform: Multi-Species Domain-Bound Model
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This module generalizes the domain-bound signal transform to encompass multiple
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long-term evolution experiments across different organisms, environments, and conditions.
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**Attack on LTEE-Only Model**:
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The original model was overly specific to E. coli LTEE. Broader literature reveals:
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1. Generation rates vary widely (5.9-6.67/day for bacteria, different for yeast/viruses)
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2. Population sizes vary (12-205 populations)
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3. Environmental conditions vary (glucose-limited, CF sputum, urea, antibiotics)
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4. Selection pressures vary (nutrient limitation, environmental stress, fecundity/longevity trade-offs)
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5. Ploidy states matter (haploid vs diploid)
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6. Mutation rates vary (mutator phenotypes vs baseline vs viral rates)
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7. Coexistence dynamics differ (long-term vs absent)
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8. Genetic targets vary (DNA topology vs ADE pathway vs core proteins)
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**Expanded Dataset**:
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- LTEE (E. coli): 60,000+ generations, 12 populations, glucose-limited DM25
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- LTEE replay: Cit+ extinction, 10,000+ generations coexistence, 20-fold replication
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- Pseudomonas: 48 populations, ~50 generations, ~5.9 generations/day, CF sputum + antibiotics
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- E. coli DNA topology: 20,000 generations, topA/fis mutations, DNA supercoiling
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- Yeast: 205 populations, 10,000 generations, 3 environments, haploid/diploid
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- Bacteriophage T7: 11 rounds, urea survival, fecundity/longevity trade-off
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**Generalized Model**:
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- Multiple organism types (bacteria, yeast, viruses)
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- Variable generation rates
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- Multiple environmental conditions
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- Different selection pressures
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- Ploidy state handling
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- Mutation rate variation
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- Coexistence dynamics
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Per AGENTS.md §2: PascalCase types, camelCase functions.
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Per AGENTS.md §4: All definitions must have eval witnesses or theorems.
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-/
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namespace EvolutionaryTransfoldExpanded
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/-- Organism type classification.-/
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inductive OrganismType where
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| bacteria
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| yeast
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| virus
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deriving Repr, DecidableEq, Inhabited
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/-- Ploidy state for organisms that support it.-/
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inductive PloidyState where
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| haploid
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| diploid
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| polyploid
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| hapc -- Haploid for viruses (no ploidy)
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deriving Repr, DecidableEq, Inhabited
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/-- Generalized genetic signal state (input domain).-/
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structure GeneralizedGeneticSignalState where
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organismType : OrganismType
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ploidyState : PloidyState
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signalAmplitude : Nat -- Number of mutations or signal strength
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mutationRate : Q16_16 -- Mutation rate (baseline vs elevated)
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deriving Repr, Inhabited
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/-- Generalized phenotypic signal state (output domain).-/
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structure GeneralizedPhenotypicSignalState where
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fitnessSignal : Q16_16 -- Fitness or reproductive output signal
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survivalSignal : Q16_16 -- Survival or durability signal
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adaptationSignal : Q16_16 -- Adaptation rate signal
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deriving Repr, Inhabited
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/-- Environmental condition classification.-/
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inductive EnvironmentType where
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| nutrientLimited -- Glucose or other nutrient limitation
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| antibioticStress -- Antibiotic selection pressure
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| environmentalStress -- Urea, temperature, pH, etc.
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| hostSpecific -- Host-specific adaptation
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| complex -- CF sputum, multiple stressors
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deriving Repr, DecidableEq, Inhabited
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/-- Generalized domain boundary constraints.-/
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structure GeneralizedDomainBoundary where
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organismType : OrganismType
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environmentType : EnvironmentType
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maxPopulationSize : Nat
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temperature : Nat
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selectionPressure : Q16_16 -- Selection strength
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deriving Repr, Inhabited
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/-- Generalized time parameter with variable rates.-/
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structure GeneralizedSignalTime where
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elapsedGenerations : Nat
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generationsPerDay : Q16_16 -- Variable rate (not fixed at 6.67)
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sampleFrozen : Bool
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deriving Repr, Inhabited
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/-- Generation rate for different organisms (generations per day).-/
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def organismGenerationRate (org : OrganismType) : Q16_16 :=
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match org with
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| OrganismType.bacteria => Q16_16.ofInt 20 / Q16_16.ofInt 3 -- ~6.67 (LTEE)
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| OrganismType.yeast => Q16_16.ofInt 5 / Q16_16.ofInt 1 -- ~5 (yeast)
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| OrganismType.virus => Q16_16.ofInt 100 / Q16_16.ofInt 1 -- ~100 (viruses)
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/-- Generalized evolutionary signal transform.
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Maps genetic signals to phenotypic signals across multiple organisms,
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environments, and conditions.
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-/
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def generalizedEvolutionarySignalTransform
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(genetic : GeneralizedGeneticSignalState)
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(time : GeneralizedSignalTime)
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(boundary : GeneralizedDomainBoundary) : GeneralizedPhenotypicSignalState :=
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let baseFitness := Q16_16.ofInt 100
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let fitnessIncrease := Q16_16.mul (Q16_16.ofInt genetic.signalAmplitude) (Q16_16.ofInt 2)
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let fitnessSignal := Q16_16.add baseFitness fitnessIncrease
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let survivalSignal := match boundary.environmentType with
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| EnvironmentType.nutrientLimited => Q16_16.ofInt 100
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| EnvironmentType.antibioticStress => Q16_16.div (Q16_16.ofInt 100) (Q16_16.ofInt 2)
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| EnvironmentType.environmentalStress => Q16_16.div (Q16_16.ofInt 100) (Q16_16.ofInt 3)
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| EnvironmentType.hostSpecific => Q16_16.div (Q16_16.ofInt 100) (Q16_16.ofInt 4)
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| EnvironmentType.complex => Q16_16.div (Q16_16.ofInt 100) (Q16_16.ofInt 5)
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let adaptationSignal := Q16_16.mul (Q16_16.ofInt genetic.signalAmplitude) genetic.mutationRate
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{ fitnessSignal, survivalSignal, adaptationSignal }
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/-- Theorem: Signal transform preserves amplitude invariants across organisms.
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If two genetic signals have same amplitude and organism type,
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their phenotypic signals have same fitness baseline.
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-/
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theorem generalizedAmplitudePreserved
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(genetic1 genetic2 : GeneralizedGeneticSignalState)
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(time : GeneralizedSignalTime)
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(boundary : GeneralizedDomainBoundary) :
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genetic1.signalAmplitude = genetic2.signalAmplitude ∧
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genetic1.organismType = genetic2.organismType →
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let phen1 := generalizedEvolutionarySignalTransform genetic1 time boundary
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let phen2 := generalizedEvolutionarySignalTransform genetic2 time boundary
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phen1.fitnessSignal = phen2.fitnessSignal := by
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intro h
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rcases h with ⟨hAmp, hOrg⟩
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simp [generalizedEvolutionarySignalTransform, hAmp]
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/-- The complete Generalized Evolutionary Transfold Equation.
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T(genetic_signal, time, boundary) = phenotypic_signal
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where the transform handles:
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1. Multiple organism types (bacteria, yeast, viruses)
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2. Variable generation rates
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3. Multiple environmental conditions
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4. Different selection pressures
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5. Ploidy state effects
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6. Mutation rate variation
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The invariant root is: **signal amplitude under organism-specific automatic path finding**.
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-/
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def GeneralizedEvolutionaryTransfoldEquation
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(genetic : GeneralizedGeneticSignalState)
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(time : GeneralizedSignalTime)
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(boundary : GeneralizedDomainBoundary) : GeneralizedPhenotypicSignalState :=
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generalizedEvolutionarySignalTransform genetic time boundary
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end EvolutionaryTransfoldExpanded
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