#!/usr/bin/env python3 """ Extremophile Priors — 4-Billion-Year Evolutionary Constraints on PDE Solutions Uses survival-tested organisms as hard bounds on physically admissible solutions. Rejects solutions requiring: - Infinite pressure (Pyrococcus requires 20-120 MPa) - Zero compressibility (all organisms have finite κ_T) - Infinite energy flux (Desulforudis lives on 10^-15 W) - Instantaneous convergence (1000-year division timescale) Reference organisms: - Pyrococcus yayanosii CH1ᵀ: obligate piezophile, 120 MPa limit - Thermococcus superprofundus CDGSᵀ: widest pressure range, 1 atm to 130 MPa - Candidatus Desulforudis audaxviator: deep biosphere, 2.8 km, 1000-year division """ import math from dataclasses import dataclass from typing import Dict, List, Optional, Tuple, Any from enum import Enum # Physical constants k_B = 1.380649e-23 # J/K, Boltzmann constant N_A = 6.02214076e23 # Avogadro's number R = 8.314462618 # J/(mol·K), gas constant class ConstraintViolation(Exception): """Raised when solution violates extremophile-derived physical bounds.""" pass @dataclass class PriorResult: """Result of admissibility check.""" admissible: bool violated_constraint: Optional[str] details: Dict[str, Any] class PyrococcusPrior: """ Obligate piezophile from Ashadze hydrothermal vent, ~4100m depth. Pressure range: 20-120 MPa (optimum ~52 MPa) Temperature: 80-108°C (optimum ~98°C) Key constraint: P·ΔV > kT prevents protein unfolding (blow-up in config space) """ def __init__(self): self.P_min = 20e6 # Pa - minimum for growth self.P_opt = 52e6 # Pa - optimum self.P_max = 120e6 # Pa - survival limit (exceeds Mariana Trench) self.T_min = 80 + 273.15 # K self.T_opt = 98 + 273.15 # K self.T_max = 108 + 273.15 # K self.division_time = 2 * 3600 # seconds (~2 hours) self.cell_diameter = 0.8e-6 # m # Protein volume change on unfolding (~10% expansion) self.dV_unfolding = 1e-27 * 0.1 # m³ (approx for single protein) def pressure_volume_work(self, P: float, T: float) -> float: """Compute P·ΔV work required to unfold protein.""" return P * self.dV_unfolding def thermal_energy(self, T: float) -> float: """kT at temperature T.""" return k_B * T def is_pressure_stable(self, P: float, T: float) -> bool: """ Protein stability condition: P·ΔV > kT prevents unfolding. At P > 50 MPa and T < 400K: P·ΔV dominates, folding locked. """ pv_work = self.pressure_volume_work(P, T) thermal = self.thermal_energy(T) return pv_work > thermal def is_admissible(self, pressure: float, temperature: float, volume_change: Optional[float] = None) -> PriorResult: """Check if conditions are within Pyrococcus survival envelope.""" details = { 'P_MPa': pressure / 1e6, 'T_C': temperature - 273.15, 'P_optimum': self.P_opt / 1e6, } if pressure < self.P_min: return PriorResult(False, 'pressure_too_low', details) if pressure > self.P_max: return PriorResult(False, 'pressure_exceeds_survival', details) if temperature < self.T_min or temperature > self.T_max: return PriorResult(False, 'temperature_out_of_range', details) if not self.is_pressure_stable(pressure, temperature): return PriorResult(False, 'protein_unfolding_thermodynamically_favored', details) details['PV_work_J'] = self.pressure_volume_work(pressure, temperature) details['thermal_energy_J'] = self.thermal_energy(temperature) details['stability_ratio'] = details['PV_work_J'] / details['thermal_energy_J'] return PriorResult(True, None, details) class ThermococcusPrior: """ Widest pressure-range organism, Beebe hydrothermal vent, ~4964m depth. Pressure: 1 atm to 130 MPa (optimum ~50 MPa) Temperature: 60-90°C (optimum ~75°C) Key constraint: adaptive flexibility across full pressure space """ def __init__(self): self.P_range = (1e5, 130e6) # Pa - atmospheric to extreme self.P_opt = 50e6 # Pa self.T_range = (60 + 273.15, 90 + 273.15) # K self.T_opt = 75 + 273.15 # K self.division_time = 4 * 3600 # seconds def is_admissible(self, pressure: float, temperature: float) -> PriorResult: """Check if organism shows adaptive flexibility across pressure range.""" details = { 'P_MPa': pressure / 1e6, 'T_C': temperature - 273.15, 'pressure_adaptability': 'full_range' if self.P_range[0] <= pressure <= self.P_range[1] else 'limited', } if not (self.P_range[0] <= pressure <= self.P_range[1]): return PriorResult(False, 'pressure_outside_adaptive_range', details) if not (self.T_range[0] <= temperature <= self.T_range[1]): return PriorResult(False, 'temperature_outside_adaptive_range', details) # Compute adaptability score (distance from optimum) P_normalized = (pressure - self.P_opt) / (self.P_range[1] - self.P_opt) T_normalized = abs(temperature - self.T_opt) / (self.T_range[1] - self.T_opt) details['adaptability_score'] = 1.0 - math.sqrt(P_normalized**2 + T_normalized**2) return PriorResult(True, None, details) class DesulforudisPrior: """ Deep biosphere champion, Mponeng gold mine, ~2.8 km depth. Pressure: ~75 MPa (lithostatic) Temperature: ~60°C Energy flux: ~10^-15 W/cell (radiolysis-powered) Division time: ~1000 years Key constraint: arbitrarily low energy flux admissible if time expands """ def __init__(self): self.depth = 2800 # m self.pressure = 75e6 # Pa (lithostatic) self.temperature = 60 + 273.15 # K self.energy_flux = 1e-15 # W/cell self.division_time = 1000 * 365.25 * 24 * 3600 # seconds (~1000 years) self.cell_diameter = 0.5e-6 # m (ultra-small for diffusion) self.water_activity = 0.7 # near desiccation limit # Information processing limit (Landauer at 60°C) self.kT = k_B * self.temperature # ~4.6e-21 J self.max_bit_rate = self.energy_flux / (self.kT * math.log(2)) # bits/s def landauer_limit(self, temperature: float) -> float: """Minimum energy to erase 1 bit: E = kT ln(2).""" return k_B * temperature * math.log(2) def max_information_rate(self, power: float, temperature: float) -> float: """Maximum bit rate given power constraint.""" return power / self.landauer_limit(temperature) def is_admissible(self, required_power: float, required_time: float, required_bits: float, temperature: float) -> PriorResult: """ Check if solution respects deep-biosphere energy/time constraints. Key insight: if Desulforudis can survive 1000 years on 10^-15 W, then arbitrarily slow/weak solutions are admissible. """ details = { 'required_power_W': required_power, 'desulforudis_power_W': self.energy_flux, 'required_time_s': required_time, 'desulforudis_time_s': self.division_time, 'required_bits': required_bits, } # Energy flux check if required_power > self.energy_flux * 10: # Allow 10x headroom return PriorResult(False, 'energy_flux_exceeds_deep_biosphere', details) # Time scale check if required_time > self.division_time * 10: # 10,000 years max return PriorResult(False, 'convergence_time_exceeds_geological', details) # Information processing check max_bits = self.max_information_rate(required_power, temperature) * required_time if required_bits > max_bits: return PriorResult(False, 'information_processing_exceeds_landauer_limit', details) details['max_achievable_bits'] = max_bits details['information_efficiency'] = required_bits / max_bits if max_bits > 0 else 0 return PriorResult(True, None, details) class ResonantCavityPrior: """ Orbital cavity as Helmholtz resonator. Volume: ~25-30 cm³ Q-factor: 5-20 (material damping prevents infinite resonance) Key constraint: finite damping prevents blow-up (infinite Q) """ def __init__(self): self.volume = 28e-6 # m³ self.aperture_area = 4e-4 # m² self.wall_compliance = 0.1 # relative to rigid self.tissue_damping = 0.05 # loss factor self.Q_max = 100 # maximum physically achievable Q # Speed of sound self.c_air = 340 # m/s self.c_bone = 1500 # m/s def helmholtz_frequency(self, c: float, V: float, S: float, L: float) -> float: """f = c/(2π) * sqrt(S/(V*L))""" return (c / (2 * math.pi)) * math.sqrt(S / (V * L)) def quality_factor(self, energy_stored: float, energy_dissipated: float) -> float: """Q = 2π × (energy stored) / (energy dissipated per cycle)""" return 2 * math.pi * energy_stored / energy_dissipated def is_admissible(self, Q_factor: float, resonance_freq: float) -> PriorResult: """Reject infinite Q (perfect resonance = blow-up).""" details = { 'Q_factor': Q_factor, 'Q_max_physical': self.Q_max, 'resonance_Hz': resonance_freq, } if Q_factor > self.Q_max: return PriorResult(False, 'Q_factor_exceeds_material_limit', details) if Q_factor < 0: return PriorResult(False, 'negative_damping_unphysical', details) if math.isinf(Q_factor): return PriorResult(False, 'infinite_Q_blow_up', details) return PriorResult(True, None, details) class ThermusPrior: """ Thermus aquaticus - source of Taq polymerase (PCR revolution). Temperature: 50-80°C (optimum ~70°C) Lives in hot springs, Yellowstone hot springs. Key constraint: moderate thermophily with protein stability. """ def __init__(self): self.T_min = 50 + 273.15 # K self.T_opt = 70 + 273.15 # K self.T_max = 80 + 273.15 # K self.pressure = 1e5 # Atmospheric (hot springs) def is_admissible(self, temperature: float, pressure: float = 1e5) -> PriorResult: """Check if conditions are within Thermus survival envelope.""" details = { 'T_C': temperature - 273.15, 'T_optimum_C': self.T_opt - 273.15, 'organism': 'Thermus aquaticus (Taq polymerase source)', } if temperature < self.T_min or temperature > self.T_max: return PriorResult(False, 'temperature_out_of_range', details) details['stability_ratio'] = 1.0 - abs(temperature - self.T_opt) / (self.T_max - self.T_min) return PriorResult(True, None, details) class Strain121Prior: """ Methanopyrus kandleri Strain 121 - absolute temperature limit. Temperature: 122°C (395K) - maximum known survival Pressure: High (deep-sea vent) Key constraint: Protein denaturation wall. Beyond 122°C, no known biology. This is the absolute thermodynamic limit for life. """ def __init__(self): self.T_max = 122 + 273.15 # K - absolute biological limit self.T_opt = 110 + 273.15 # K self.T_min = 80 + 273.15 # K self.pressure = 50e6 # Pa - deep-sea vent def is_admissible(self, temperature: float, pressure: float = 50e6) -> PriorResult: """Check if conditions are within Strain 121 survival envelope.""" details = { 'T_C': temperature - 273.15, 'T_max_C': self.T_max - 273.15, 'organism': 'Methanopyrus kandleri Strain 121 (absolute temp limit)', } if temperature > self.T_max: return PriorResult(False, 'exceeds_absolute_biological_temperature_limit', details) if temperature < self.T_min: return PriorResult(False, 'below_minimum', details) # Temperature margin from absolute wall margin_C = self.T_max - temperature details['margin_from_wall_C'] = margin_C details['stability_ratio'] = margin_C / (self.T_max - self.T_min) return PriorResult(True, None, details) class DiatomPrior: """ Diatoms with silica shells - absolute stiffness limit. Material: Amorphous silica (SiO₂) frustules Compressibility: κ_T ≈ 2.7×10^-11 Pa^-1 (geological silica) Key constraint: Silica shells approach inorganic material limits. Biology cannot achieve κ_T = 0, but silica gets closest. """ def __init__(self): self.compressibility_silica = 2.7e-11 # Pa^-1 (amorphous silica) self.compressibility_water = 4.6e-10 # Pa^-1 (water) self.shell_thickness = 50e-9 # m (50 nm typical) self.Q_factor_silica = 1000 # silica resonance (higher than tissue) def is_admissible(self, compressibility: float, Q_factor: float = 10) -> PriorResult: """Check if material properties approach silica limits.""" details = { 'compressibility': compressibility, 'silica_limit': self.compressibility_silica, 'Q_factor': Q_factor, 'organism': 'Diatoms (silica frustules - stiffness limit)', } # Silica is the biological stiffness limit if compressibility < self.compressibility_silica: return PriorResult(False, 'exceeds_biological_stiffness_limit', details) # Silica Q-factor is the biological resonance limit if Q_factor > self.Q_factor_silica: return PriorResult(False, 'exceeds_silica_resonance_limit', details) # Calculate proximity to inorganic limit stiffness_ratio = self.compressibility_silica / compressibility details['stiffness_ratio'] = stiffness_ratio # >1 = softer than silica details['Q_ratio'] = Q_factor / self.Q_factor_silica # <1 = below silica Q return PriorResult(True, None, details) class VibrioNatriegensPrior: """ Vibrio natriegens - fastest known replication rate. Doubling time: 10-15 minutes (optimal conditions) Some strains: under 10 minutes Habitat: Marine environments, salt-loving (halophile) Key constraint: Absolute biological replication speed limit. """ def __init__(self): self.t_doubling_min = 10 * 60 # seconds - absolute limit self.t_doubling_opt = 12 * 60 # seconds - typical optimal self.t_doubling_max = 30 * 60 # seconds - under suboptimal self.energy_per_duplication = 1e-15 # J (estimated) self.error_rate = 1e-10 # errors per base per replication def is_admissible(self, replication_time: float, energy: float = 1e-15) -> PriorResult: """Check if replication rate is biologically achievable.""" details = { 'replication_time_s': replication_time, 'doubling_time_min_s': self.t_doubling_min, 'doubling_time_opt_s': self.t_doubling_opt, 'organism': 'Vibrio natriegens (fastest replication)', } if replication_time < self.t_doubling_min: return PriorResult(False, 'exceeds_absolute_replication_speed_limit', details) # Calculate speed relative to V. natriegens speed_ratio = self.t_doubling_min / replication_time details['speed_ratio'] = speed_ratio # <1 = slower than max return PriorResult(True, None, details) class EColiPrior: """ E. coli - standard replication reference. Doubling time: 20 minutes optimal (rich medium) 40-60 minutes in minimal medium Well-studied, genome fully sequenced Key constraint: Baseline replication efficiency. """ def __init__(self): self.t_doubling_opt = 20 * 60 # seconds (rich medium) self.t_doubling_minimal = 40 * 60 # seconds (minimal medium) self.genome_size = 4.6e6 # base pairs self.error_rate = 1e-9 # errors per base per replication def is_admissible(self, replication_time: float, genome_size: float = 4.6e6) -> PriorResult: """Check if replication matches E. coli efficiency.""" details = { 'replication_time_s': replication_time, 'doubling_time_opt_s': self.t_doubling_opt, 'genome_size_bp': genome_size, 'organism': 'E. coli (standard replication reference)', } # Calculate replication rate relative to genome size if genome_size > 0: bp_per_second = genome_size / replication_time details['bp_per_second'] = bp_per_second # E. coli reference: 4.6e6 bp / 1200s = 3833 bp/s ecoli_rate = self.genome_size / self.t_doubling_opt details['rate_ratio'] = bp_per_second / ecoli_rate return PriorResult(True, None, details) class ClostridiumPerfringensPrior: """ Clostridium perfringens - anaerobic speed champion. Doubling time: 8-10 minutes (anaerobic, optimal) Habitat: Soil, intestines, anaerobic environments Key constraint: Fastest anaerobic replication limit. """ def __init__(self): self.t_doubling_min = 8 * 60 # seconds - anaerobic champion self.t_doubling_opt = 10 * 60 # seconds self.oxygen_tolerant = False # obligate anaerobe def is_admissible(self, replication_time: float, anaerobic: bool = True) -> PriorResult: """Check if replication rate matches anaerobic champion.""" details = { 'replication_time_s': replication_time, 'doubling_time_min_s': self.t_doubling_min, 'anaerobic': anaerobic, 'organism': 'Clostridium perfringens (anaerobic speed champion)', } if anaerobic and replication_time < self.t_doubling_min: return PriorResult(False, 'exceeds_anaerobic_replication_speed_limit', details) return PriorResult(True, None, details) class GeobacillusPrior: """ Geobacillus stearothermophilus - moderate thermophile. Temperature: 55-70°C (optimum ~65°C) Common in compost, hot springs. Key constraint: industrial thermophile with robust protein stability. """ def __init__(self): self.T_min = 55 + 273.15 # K self.T_opt = 65 + 273.15 # K self.T_max = 70 + 273.15 # K self.pressure = 1e5 # Atmospheric def is_admissible(self, temperature: float, pressure: float = 1e5) -> PriorResult: """Check if conditions are within Geobacillus survival envelope.""" details = { 'T_C': temperature - 273.15, 'T_optimum_C': self.T_opt - 273.15, 'organism': 'Geobacillus stearothermophilus', } if temperature < self.T_min or temperature > self.T_max: return PriorResult(False, 'temperature_out_of_range', details) details['stability_ratio'] = 1.0 - abs(temperature - self.T_opt) / (self.T_max - self.T_min) return PriorResult(True, None, details) class TuringPatternPrior: """ Skeletal formation as reaction-diffusion system. Key constraint: finite nutrient flux prevents infinite growth """ def __init__(self): # Typical bone mineralization parameters self.D_activator = (1e-12, 1e-6) # m²/s self.D_inhibitor = (1e-10, 1e-4) # m²/s self.reaction_rate = (0, 1e3) # 1/s self.max_growth_rate = 1e-6 # m/s (bone apposition) def is_admissible(self, growth_rate: float, pattern_wavelength: float, nutrient_flux: float) -> PriorResult: """Reject infinite Turing pattern growth.""" details = { 'growth_rate_m_s': growth_rate, 'max_growth_rate': self.max_growth_rate, 'wavelength_m': pattern_wavelength, } if growth_rate > self.max_growth_rate * 10: return PriorResult(False, 'growth_exceeds_nutrient_limit', details) if nutrient_flux <= 0: return PriorResult(False, 'zero_nutrient_flux_unsustainable', details) if pattern_wavelength < 1e-6: # micron scale minimum return PriorResult(False, 'pattern_scale_below_cellular', details) return PriorResult(True, None, details) class DeepExtremophilePrior: """ Unified 12-tier constraint system from evolutionary survival testing. Absolute limit tiers (wall-hitting organisms): 1. Strain121: Absolute temperature limit (122°C, protein denaturation wall) 2. Diatom: Absolute stiffness limit (silica shells, geological compressibility) 3. VibrioNatriegens: Absolute replication speed limit (10 min doubling) Regular tiers: 4. TuringPattern: Skeletal formation (nutrient limits prevent infinite growth) 5. ResonantCavity: Orbital acoustics (damping prevents infinite Q) 6. Pyrococcus: Obligate piezophile (pressure-volume work locks proteins) 7. Thermococcus: Wide-range adaptability (flexibility across P-T space) 8. Thermus: Moderate thermophile (50-80°C, Taq polymerase source) 9. Geobacillus: Industrial thermophile (55-70°C, robust stability) 10. EColi: Standard replication reference (20 min doubling) 11. ClostridiumPerfringens: Anaerobic replication speed (8-10 min) 12. Desulforudis: Deep time/energy (arbitrarily slow solutions admissible) """ def __init__(self): self.strain121 = Strain121Prior() # Absolute temp limit self.diatom = DiatomPrior() # Absolute stiffness limit self.vibrio = VibrioNatriegensPrior() # Absolute replication speed limit self.turing = TuringPatternPrior() self.orbital = ResonantCavityPrior() self.pyrococcus = PyrococcusPrior() self.thermococcus = ThermococcusPrior() self.thermus = ThermusPrior() self.geobacillus = GeobacillusPrior() self.ecoli = EColiPrior() # Standard replication reference self.clostridium = ClostridiumPerfringensPrior() # Anaerobic speed champion self.desulforudis = DesulforudisPrior() def unified_check(self, solution_params: Dict[str, Any]) -> PriorResult: """ Run all 5 tiers of constraint checking. Returns first violation found, or success if all pass. """ checks = [ ('strain121', self._check_strain121, ['temperature']), # Absolute temp limit - check first ('diatom', self._check_diatom, ['compressibility', 'Q_factor']), # Absolute stiffness - check early ('vibrio_natriegens', self._check_vibrio, ['replication_time']), # Absolute replication speed - check early ('turing_pattern', self._check_turing, ['growth_rate', 'wavelength', 'nutrient_flux']), ('resonant_cavity', self._check_orbital, ['Q_factor', 'resonance_freq']), ('pyrococcus', self._check_pyrococcus, ['pressure', 'temperature']), ('thermococcus', self._check_thermococcus, ['pressure', 'temperature']), ('thermus', self._check_thermus, ['temperature']), ('geobacillus', self._check_geobacillus, ['temperature']), ('ecoli', self._check_ecoli, ['replication_time', 'genome_size']), # Standard replication reference ('clostridium', self._check_clostridium, ['replication_time', 'anaerobic']), # Anaerobic speed champion ('desulforudis', self._check_desulforudis, ['power', 'time', 'bits', 'temperature']), ] all_details = {} for name, check_fn, required_keys in checks: # Check if required parameters present if not all(k in solution_params for k in required_keys): continue # Skip if parameters not provided for this check result = check_fn(solution_params) all_details[name] = result.details if not result.admissible: return PriorResult(False, f"{name}:{result.violated_constraint}", all_details) return PriorResult(True, None, all_details) def _check_turing(self, params: Dict) -> PriorResult: return self.turing.is_admissible( params.get('growth_rate', 0), params.get('wavelength', 1e-3), params.get('nutrient_flux', 1e-6) ) def _check_orbital(self, params: Dict) -> PriorResult: return self.orbital.is_admissible( params.get('Q_factor', 10), params.get('resonance_freq', 1000) ) def _check_pyrococcus(self, params: Dict) -> PriorResult: return self.pyrococcus.is_admissible( params.get('pressure', 1e5), params.get('temperature', 300) ) def _check_thermococcus(self, params: Dict) -> PriorResult: return self.thermococcus.is_admissible( params.get('pressure', 1e5), params.get('temperature', 300) ) def _check_thermus(self, params: Dict) -> PriorResult: return self.thermus.is_admissible( params.get('temperature', 300), params.get('pressure', 1e5) ) def _check_geobacillus(self, params: Dict) -> PriorResult: return self.geobacillus.is_admissible( params.get('temperature', 300), params.get('pressure', 1e5) ) def _check_strain121(self, params: Dict) -> PriorResult: """Check absolute temperature limit (122°C wall).""" return self.strain121.is_admissible( params.get('temperature', 300), params.get('pressure', 50e6) ) def _check_diatom(self, params: Dict) -> PriorResult: """Check absolute stiffness limit (silica wall).""" return self.diatom.is_admissible( params.get('compressibility', 1e-10), params.get('Q_factor', 10) ) def _check_vibrio(self, params: Dict) -> PriorResult: """Check absolute replication speed limit (V. natriegens wall).""" return self.vibrio.is_admissible( params.get('replication_time', 600), params.get('energy', 1e-15) ) def _check_ecoli(self, params: Dict) -> PriorResult: """Check against E. coli standard replication reference.""" return self.ecoli.is_admissible( params.get('replication_time', 1200), params.get('genome_size', 4.6e6) ) def _check_clostridium(self, params: Dict) -> PriorResult: """Check anaerobic replication speed limit.""" return self.clostridium.is_admissible( params.get('replication_time', 600), params.get('anaerobic', False) ) def _check_desulforudis(self, params: Dict) -> PriorResult: return self.desulforudis.is_admissible( params.get('power', 1e-10), params.get('time', 1e6), params.get('bits', 1e12), params.get('temperature', 300) ) # PDE-specific constraint checkers class NavierStokesConstraints: """ Apply extremophile constraints to Navier-Stokes solutions. Key insight: Blow-up requires: 1. Infinite vorticity concentration 2. Zero compressibility (to support infinite pressure) 3. Zero viscosity (to prevent dissipation) 4. Infinite energy flux All four are rejected by evolutionary priors. """ def __init__(self): self.priors = DeepExtremophilePrior() def check_solution(self, velocity_field: Any, pressure_field: Any, energy_dissipation: float, convergence_time: float) -> PriorResult: """ Check if Navier-Stokes solution respects extremophile constraints. Parameters: - velocity_field: max velocity, vorticity magnitude - pressure_field: max pressure, pressure gradients - energy_dissipation: power required to maintain solution - convergence_time: time to reach steady state """ # Extract parameters from fields params = { 'pressure': pressure_field.get('max', 1e5) if isinstance(pressure_field, dict) else 1e5, 'temperature': 300, # assume room temp unless specified 'power': energy_dissipation, 'time': convergence_time, 'bits': 1e15, # assume significant computation } # Run unified check result = self.priors.unified_check(params) if not result.admissible: return result # Additional Navier-Stokes specific checks if isinstance(velocity_field, dict): vorticity = velocity_field.get('vorticity_max', 0) velocity = velocity_field.get('max', 0) # Check: finite compressibility (from Desulforudis at 75 MPa) # No real fluid has κ_T = 0 compressibility = pressure_field.get('compressibility', 1e-10) if isinstance(pressure_field, dict) else 1e-10 if compressibility <= 0: return PriorResult(False, 'incompressible_unphysical', {'compressibility': compressibility}) # Check: finite viscosity prevents infinite Reynolds number viscosity = velocity_field.get('viscosity', 1e-6) if viscosity <= 0: return PriorResult(False, 'zero_viscosity_unphysical', {'viscosity': viscosity}) return PriorResult(True, None, result.details) class MissionCriticalReliability: """ Reliability depth metric for autonomous operation contexts. Not just 'is it physically possible?' but 'can you trust it when you can't call for help?' Three-zone architecture: - Evolutionary Core: 4 billion years unattended operation - Engineering Frontier: Possible but requires extreme monitoring - Theoretical Limit: Catastrophic failure mode AngrySphinx Mode: Each level increases attack cost for hecklers. """ def __init__(self, base_prior: DeepExtremophilePrior = None, angry_sphinx_mode: bool = True): self.base_prior = base_prior or DeepExtremophilePrior() self.angry_sphinx_mode = angry_sphinx_mode # Zone boundaries (empirical from survival data) self.EVOLUTIONARY_CORE_THRESHOLD = 0.9 self.ENGINEERING_FRONTIER_THRESHOLD = 0.1 # Attack cost escalation (AngrySphinx gear reduction) self.attack_cost_multipliers = { 0: 1.0, # Base claim 1: 3.0, # First "but..." (3x work) 2: 10.0, # Second "but..." (10x work) 3: 30.0, # Third "but..." (30x work) } def reliability_depth(self, solution_params: Dict[str, Any]) -> float: """ Compute distance from basin boundary in evolution-validated space. Returns 0.0-1.0 where: - 1.0: Deep in basin (4 Gyr unattended, "Works on Titan") - 0.1: Near boundary ("Every engineer on call") - 0.0: At boundary (catastrophic, "Blow-up in 3...2...1") """ # Check position relative to each extremophile's optimum depths = [] # Pyrococcus depth: how close to optimal 52 MPa? if 'pressure' in solution_params: P = solution_params['pressure'] P_opt = self.base_prior.pyrococcus.P_opt P_range = self.base_prior.pyrococcus.P_max - self.base_prior.pyrococcus.P_min # Normalized distance from optimum (1.0 = at optimum, 0.0 = at boundary) P_depth = 1.0 - abs(P - P_opt) / (P_range / 2) depths.append(max(0.0, P_depth)) # Desulforudis depth: energy margin above survival minimum if 'power' in solution_params: Pwr = solution_params['power'] Pwr_min = self.base_prior.desulforudis.energy_flux # How many orders of magnitude above minimum? if Pwr > 0: power_depth = min(1.0, math.log10(Pwr / Pwr_min) / 3.0) # 3 orders = comfortable depths.append(power_depth) # Time scale depth: how far below geological maximum? if 'time' in solution_params: t = solution_params['time'] t_max = self.base_prior.desulforudis.division_time if t > 0: time_depth = max(0.0, 1.0 - (t / t_max)) depths.append(time_depth) # Resonance Q depth: how far below material limit? if 'Q_factor' in solution_params: Q = solution_params['Q_factor'] Q_max = self.base_prior.orbital.Q_max if Q > 0: Q_depth = max(0.0, 1.0 - (Q / Q_max)) depths.append(Q_depth) # Compressibility depth: how far from zero? if 'compressibility' in solution_params: kappa = solution_params['compressibility'] # κ_T > 0 is required; larger is safer (more compressible) if kappa > 0: kappa_depth = min(1.0, math.log10(kappa / 1e-12) / 3.0) depths.append(kappa_depth) # Overall depth is minimum (weakest link) return min(depths) if depths else 0.0 def zone_classification(self, depth: float) -> str: """Classify solution into operational zone.""" if depth >= self.EVOLUTIONARY_CORE_THRESHOLD: return 'EVOLUTIONARY_CORE' elif depth >= self.ENGINEERING_FRONTIER_THRESHOLD: return 'ENGINEERING_FRONTIER' else: return 'THEORETICAL_LIMIT' def zone_description(self, zone: str) -> str: """Human-readable zone description for presentations.""" descriptions = { 'EVOLUTIONARY_CORE': "4 billion years unattended operation. " "Works on Titan, no service calls. " "Biology handles this autonomously.", 'ENGINEERING_FRONTIER': "Nanoscale possible but fragile. " "Requires extreme monitoring. " "Every engineer on planet on call.", 'THEORETICAL_LIMIT': "Mathematically ideal but physically catastrophic. " "Failure mode: unrecoverable. " "Blow-up in 3... 2... 1..." } return descriptions.get(zone, 'UNKNOWN') def mission_critical_approval(self, solution_params: Dict[str, Any], context: str = 'research') -> PriorResult: """ Context-aware approval with progressive revelation. Perfect for "Hat of Infinite Bullshit" presentation style: - Level 1: "Um ack sh lee, I provide solution x" - Level 2: "But... requires engineering frontier monitoring" - Level 3: "But... catastrophic failure mode at boundary" """ depth = self.reliability_depth(solution_params) zone = self.zone_classification(depth) # First check: is it physically possible? physical_check = self.base_prior.unified_check(solution_params) if not physical_check.admissible: return PriorResult( False, f"PHYSICALLY_INADMISSIBLE:{physical_check.violated_constraint}", { 'depth': 0.0, 'zone': 'THEORETICAL_LIMIT', 'context': context, 'physical_details': physical_check.details, 'presentation_level': 'REJECTED_AT_BASE', } ) # Context-dependent approval approval_matrix = { 'mars_colony_life_support': (0.9, 'EVOLUTIONARY_CORE_REQUIRED'), 'deep_space_probe': (0.8, 'LONG_DURATION_AUTONOMY'), 'subsea_infrastructure': (0.7, 'MAINTENANCE_DIFFICULT'), 'medical_implant': (0.9, 'NO_SECOND_CHANCE'), 'lhc_experiment': (0.1, 'ENGINEERS_NEARBY'), 'laboratory_demo': (0.0, 'SUPERVISED_ONLY'), 'pure_mathematics': (-1.0, 'THEORETICAL_ALLOWED'), } min_depth, rationale = approval_matrix.get(context, (0.5, 'DEFAULT_CONTEXT')) approved = depth >= min_depth # Progressive revelation for presentation presentation_levels = [] # Level 1: Basic existence presentation_levels.append({ 'level': 1, 'claim': f"Um ack sh lee, solution exists at {depth:.2f} reliability depth", 'zone': zone, 'details': self.zone_description(zone) }) # Level 2: Engineering reality if zone == 'ENGINEERING_FRONTIER': presentation_levels.append({ 'level': 2, 'claim': "But... requires every engineer on call", 'requirement': f"Minimum depth {min_depth:.2f} for {context}", 'actual': f"Current depth {depth:.2f}" }) # Level 3: Mission critical if not approved and context in ['mars_colony_life_support', 'medical_implant']: presentation_levels.append({ 'level': 3, 'claim': "But... catastrophic failure mode when unattended", 'consequence': "Autonomous operation impossible", 'recommendation': "Return to evolutionary core (depth > 0.9)" }) details = { 'depth': depth, 'zone': zone, 'zone_description': self.zone_description(zone), 'context': context, 'context_rationale': rationale, 'required_depth': min_depth, 'approved': approved, 'presentation_levels': presentation_levels, } if approved: return PriorResult(True, None, details) else: return PriorResult( False, f'INSUFFICIENT_RELIABILITY_FOR_{context}', details ) def hat_of_infinite_bullshit(self, solution_params: Dict[str, Any], context: str, attack_count: int = 0) -> List[Dict]: """ Generate progressive revelation for presentation. AngrySphinx mode: Each attack (heckler counterargument) triggers deeper revelation, increasing the work required to refute. Args: solution_params: Physical parameters of solution context: Mission context (mars_colony, etc.) attack_count: Number of heckler attacks so far (escalates depth) Returns: Ordered list of claims from superficial to deep, with attack costs. """ result = self.mission_critical_approval(solution_params, context) if 'presentation_levels' in result.details: levels = result.details['presentation_levels'] else: # Fallback for rejected solutions return [{ 'level': 0, 'claim': 'REJECTED', 'reason': result.violated_constraint, 'attack_cost': 1.0, 'defense_burden': 1.0, }] # AngrySphinx escalation: add attack costs if self.angry_sphinx_mode: for i, level in enumerate(levels): # Cost increases with depth AND attack count depth_multiplier = self.attack_cost_multipliers.get(i, 1.0) attack_multiplier = self.attack_cost_multipliers.get(attack_count, 1.0) total_cost = depth_multiplier * attack_multiplier level['attack_cost'] = total_cost level['defense_burden'] = total_cost * (1 + attack_count * 0.5) # Compounding # Add adversarial metadata level['required_refutation_work'] = self._describe_refutation_work(i, attack_count) return levels def _describe_refutation_work(self, depth_level: int, attack_count: int) -> str: """Describe the work required to refute this level.""" if depth_level == 0: return "Basic fact-check" elif depth_level == 1: if attack_count == 0: return "Address material bounds validity" else: return f"Address material bounds + {attack_count} prior refutations" elif depth_level == 2: return "Demonstrate engineering frontier failure mode" elif depth_level == 3: return "Prove 4-billion-year evolutionary record incorrect" else: return "Impossible: requires violating thermodynamics" def adversarial_response(self, heckler_attack: str, solution_params: Dict[str, Any], context: str, attack_count: int) -> Dict[str, Any]: """ AngrySphinx-style response to heckler attack. Consumes the attack, escalates to deeper level, increases burden. """ # Generate next level of revelation levels = self.hat_of_infinite_bullshit(solution_params, context, attack_count + 1) # Find the level they haven't seen yet next_level = min(attack_count + 1, len(levels) - 1) if next_level >= len(levels): next_level = len(levels) - 1 level_data = levels[next_level] # Calculate cumulative defense burden cumulative_burden = sum(l.get('defense_burden', 1.0) for l in levels[:next_level+1]) return { 'attack_consumed': True, 'attack_number': attack_count + 1, 'response_level': level_data['level'], 'response_claim': level_data['claim'], 'attack_cost': level_data['attack_cost'], 'cumulative_defense_burden': cumulative_burden, 'next_level_available': next_level < len(levels) - 1, 'required_refutation_work': level_data.get('required_refutation_work', ''), 'message': f"Attack #{attack_count + 1} consumed. Defense burden now: {cumulative_burden:.1f}x", } # Export main interface __all__ = [ 'DeepExtremophilePrior', 'Strain121Prior', # Absolute temperature limit (122°C) 'DiatomPrior', # Absolute stiffness limit (silica) 'VibrioNatriegensPrior', # Absolute replication speed limit (10 min) 'EColiPrior', # Standard replication reference (20 min) 'ClostridiumPerfringensPrior', # Anaerobic replication speed (8-10 min) 'PyrococcusPrior', 'ThermococcusPrior', 'ThermusPrior', 'GeobacillusPrior', 'DesulforudisPrior', 'ResonantCavityPrior', 'TuringPatternPrior', 'NavierStokesConstraints', 'MissionCriticalReliability', 'PriorResult', 'ConstraintViolation', ]