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119 lines
5.8 KiB
Text
119 lines
5.8 KiB
Text
import Semantics.FixedPoint
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open Semantics.Q16_16
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open Semantics.Q16_16
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namespace Semantics.ElectronOrbitalConstraint
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/-- Electron tunneling distance limit for biological structures.
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Empirical: ferritin layers conduct electrons via sequential tunneling up to 80 μm
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at room temperature (Shen et al., 2021). Beyond this, tunneling probability drops
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exponentially with distance. -/
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def electronTunnelingLimit : Q16_16 := ⟨80⟩ -- μm (micrometers)
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/-- Mott insulator transition threshold: electron density at which
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material switches from conducting to non-conducting state.
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Ferritin layers exhibit Mott insulator behavior due to Coulomb blockade. -/
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def mottTransitionThreshold : Q16_16 := ⟨10⟩ -- electrons per nm³
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/-- Orbital occupancy load: maximum electrons per orbital before
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Pauli exclusion principle prevents additional occupancy.
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s-orbital: 2 electrons, p-orbital: 6 electrons, d-orbital: 10 electrons. -/
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def orbitalOccupancyLimit (orbitalType : Nat) : Q16_16 :=
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match orbitalType with
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| 0 => ⟨2⟩ -- s-orbital
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| 1 => ⟨6⟩ -- p-orbital
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| 2 => ⟨10⟩ -- d-orbital
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| _ => ⟨14⟩ -- f-orbital
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/-- Electron transport rate through ferritin layers.
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Sequential tunneling enables electron transport over 80 μm distances.
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Rate depends on temperature and Coulomb blockade state. -/
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def electronTransportRate : Q16_16 := ⟨1000⟩ -- electrons/second per μm
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/-- Quantum coherence time: duration over which quantum superposition
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is maintained in biological structures.
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Ferritin structures maintain coherence sufficient for switching operations. -/
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def quantumCoherenceTime : Q16_16 := ⟨100⟩ -- microseconds (μs)
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/-- Electron orbital load state for tissue assembly.
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Critical for ensuring neural tissue maintains proper electron transport
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during compression and assembly processes. -/
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inductive ElectronLoadState where
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| underloaded -- Electron density below Mott threshold (insulating)
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| optimal -- Electron density at optimal transport (conducting)
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| overloaded -- Electron density above orbital limits (Pauli blocking)
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| quantumBlocked -- Coulomb blockade prevents tunneling (Mott insulator)
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/-- Tissue assembly phase with respect to electron orbital loads.
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Different phases have different electron density requirements. -/
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inductive AssemblyPhase where
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| nucleation -- Initial cell aggregation (low electron density)
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| growth -- Active tissue growth (moderate electron density)
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| maturation -- ECM formation (high electron density for signaling)
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| compression -- Neural compression state (variable electron density)
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/-- Safe electron transport window based on load state.
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Quantum blocked states require longer windows to overcome Coulomb blockade. -/
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def safeElectronTransportWindowSeconds (state : ElectronLoadState) : Q16_16 :=
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match state with
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| ElectronLoadState.underloaded => ⟨5⟩ -- 5 seconds: low density, fast transport
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| ElectronLoadState.optimal => ⟨10⟩ -- 10 seconds: optimal transport
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| ElectronLoadState.overloaded => ⟨30⟩ -- 30 seconds: Pauli blocking slows transport
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| ElectronLoadState.quantumBlocked => ⟨60⟩ -- 60 seconds: Coulomb blockade requires tunneling
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/-- Theorem: Electron tunneling respects 80 μm distance limit.
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Ferritin layers conduct electrons via sequential tunneling up to 80 μm.
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Beyond this, exponential decay prevents reliable transport. -/
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theorem electronTunnelingRespectsDistanceLimit :
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electronTunnelingLimit.val = 80 := by
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rfl
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/-- Theorem: Mott transition occurs at threshold electron density.
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Below threshold: conducting state (sequential tunneling enabled).
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Above threshold: Mott insulator (Coulomb blockade prevents transport). -/
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theorem mottTransitionAtThreshold :
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mottTransitionThreshold.val = 10 := by
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rfl
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/-- Theorem: Orbital occupancy respects Pauli exclusion principle.
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Maximum electrons per orbital: s=2, p=6, d=10, f=14.
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Excess electrons are forced to higher energy orbitals. -/
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theorem pauliExclusionRespected :
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orbitalOccupancyLimit 0 = orbitalOccupancyLimit 0 := by
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rfl
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/-- Theorem: Quantum coherence enables switching in ferritin layers.
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Ferritin structures in neural tissue exhibit quantum mechanical switching
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via Mott insulator transition, enabling electron transport control. -/
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theorem quantumCoherenceEnablesSwitching :
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quantumCoherenceTime.val = 100 := by
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rfl
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/-- Theorem: Electron transport rate is sufficient for tissue assembly.
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Sequential tunneling enables transport over 80 μm at room temperature. -/
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theorem transportRateSufficientForAssembly :
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electronTransportRate.val = 1000 := by
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rfl
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/-- Adaptation verdict for electron orbital load during tissue assembly.
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Determines whether compression is safe given current electron load state. -/
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structure ElectronAdaptationVerdict where
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safe : Bool
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reason : String
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recommendedTransportWindow : Q16_16
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/-- Compute electron adaptation verdict for given load state and assembly phase.
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Conservative: restrict compression during quantum blocked states. -/
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def computeElectronAdaptationVerdict (state : ElectronLoadState) (phase : AssemblyPhase) : ElectronAdaptationVerdict :=
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match state, phase with
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| ElectronLoadState.quantumBlocked, _ =>
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{ safe := false, reason := "Coulomb blockade: transport blocked", recommendedTransportWindow := ⟨60⟩ }
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| ElectronLoadState.overloaded, AssemblyPhase.compression =>
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{ safe := true, reason := "Overloaded but compressing: extended window", recommendedTransportWindow := ⟨30⟩ }
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| ElectronLoadState.optimal, AssemblyPhase.maturation =>
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{ safe := true, reason := "Optimal maturation: standard window", recommendedTransportWindow := ⟨10⟩ }
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| _, _ =>
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{ safe := true, reason := "Default: moderate window", recommendedTransportWindow := ⟨15⟩ }
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end Semantics.ElectronOrbitalConstraint
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