Research-Stack/0-Core-Formalism/lean/Semantics/Semantics/EcologicalPeriodDataProbe.lean

/-
EcologicalPeriodDataProbe.lean -- Empirical Ecological Periods for Documented Language Species

This module formalizes the ecological/population cycle data found
in the scientific literature for species with documented decoded
languages. The data tests whether the LanguageTransferProbe
predictions for P0 are consistent with observation.

DATA SOURCES (web search results):

  OCTOPUS (Octopus vulgaris, O. cyanea):
    - Life cycle: ~1 year (very short-lived)
    - Population dynamics: "deterministic cyclic fluctuations"
      driven by density-dependence and overcompensation
    - Source: Strathprints generalized depletion model study;
      PLOS One sustainable fishing study
    - Observed period: ANNUAL (~1 year), tied to life cycle
    - Language model predicted: minutes-hours (encounter)
      → discrepancy: life cycle limits population cycle

  PRAIRIE DOG (Cynomys ludovicianus, C. gunnisoni):
    - Population dynamics: "boom-and-bust cycles" driven by
      plague (Yersinia pestis) epizootics
    - Cycle period: "c. 5- to 25-year period" (Journal of
      Applied Ecology plague-ferret model)
    - Recovery: up to 25-fold increase over 11 years
    - Three epizootics in 21 years at Thunder Basin (USDA ARS)
    - Observed period: ~5-15 years (plague-driven)
    - Language model predicted: days-weeks (predator encounter)
      → discrepancy: pathogen drives much longer cycle

  ORCA (Orcinus orca, Southern Resident population):
    - Population dynamics: BIENNIAL (2-year) pattern in
      mortality and births (1998-2017)
    - Mechanism: pink salmon (Oncorhynchus gorbuscha)
      interference with Chinook foraging
    - Source: Marine Ecology Progress Series 2019;
      Canadian Journal of Fisheries and Aquatic Sciences 2024
    - Observed period: ~2 years (biennial)
    - Language model predicted: months-years (pod interaction)
      → consistent with lower bound of prediction

  HONEYBEE (Apis mellifera):
    - Population dynamics: SEASONAL/ANNUAL cycles
    - Queen egg-laying: seasonal, colony collapse in winter
    - No multi-year population oscillations documented
    - Observed period: ~1 year (seasonal)
    - Language model predicted: days-weeks (foraging cycle)
      → discrepancy: seasonal climate drives annual cycle

  SPERM WHALE (Physeter macrocephalus):
    - Population dynamics: No clear natural cycles documented
    - Dominated by whaling recovery (1712-1990s) and
      subsequent anthropogenic impacts
    - Social unit decline: -4.5%/year in Eastern Caribbean
    - Observed period: NONE (no natural cycle; recovery ongoing)
    - Language model predicted: years (social unit cycle)
      → cannot test; no natural cycle data available

  DOLPHIN (Tursiops truncatus):
    - Population dynamics: Long-term studied populations
      (Sarasota Bay since 1970s) show demographic stochasticity
    - No clear periodic oscillations documented
    - Observed period: NONE (stable or slowly changing)
    - Language model predicted: hours-days (social interaction)
      → cannot test; no cycle data available

KEY FRAMEWORK INSIGHT:
  The language model predicts INTRINSIC P0 (how fast the
  species' information processing would cycle if unconstrained).
  But observed ecological periods are DETERMINED BY EXTERNAL
  CONSTRAINTS (pathogens, climate, prey availability, life cycle).

  This means the MassNumber gate needs TWO inputs:
    1. Intrinsic language-derived P0 (information-theoretic)
    2. Ecologically observed period (empirical)

  The gate should check whether observed period is CONSISTENT
  with (not necessarily equal to) the language-derived bound.

  For example:
    - Prairie dog: intrinsic P0 ~ days-weeks, observed ~5-15 yr
      → observed >> intrinsic (external pathogen dominates)
    - Octopus: intrinsic P0 ~ minutes-hours, observed ~1 yr
      → observed >> intrinsic (life cycle limits)
    - Orca: intrinsic P0 ~ months-years, observed ~2 yr
      → observed within predicted range
    - Sardine: intrinsic P0 ~ ? (chemical language), observed ~61 yr
      → the only species where observed period anchors P0 well

Conventions:
  PascalCase types, camelCase functions.
  theorem for every boundary claim.
  #eval! for executable receipt.
  Namespace: Semantics.EcologicalPeriodDataProbe
-/

import Semantics.Toolkit
import Semantics.LanguageTransferProbe
import Semantics.LanguageZoologyProbe
import Semantics.GeneticFieldEquation

namespace Semantics.EcologicalPeriodDataProbe

open Semantics.Toolkit
open Semantics.LanguageTransferProbe
open Semantics.LanguageZoologyProbe
open Semantics.GeneticFieldEquation

-- =========================================================================
-- S0  Empirical Ecological Period Data (Literature-Based)
-- =========================================================================

/-- Empirical ecological period for a species: observed population
    cycle or characteristic timescale from scientific literature.
    Units: years. None = no clear periodic cycle documented. -/
structure EmpiricalPeriod where
  species : String
  observedPeriodYears : Option Rat
  dataSource : String
  cycleDriver : String  -- what drives the observed cycle
  confidence : String     -- high / moderate / low
  deriving Repr, Inhabited

/-- Octopus vulgaris: ~1 year life cycle drives annual fluctuations.
    Source: Strathprints generalized depletion model; PLOS One.
-/
def octopusEmpirical : EmpiricalPeriod := {
  species := "Octopus vulgaris",
  observedPeriodYears := some 1,  -- ~1 year (life cycle limited)
  dataSource := "Strathprints depletion model; PLOS One sustainable fishing",
  cycleDriver := "density-dependence and short life cycle (~1 year)",
  confidence := "moderate"
}

/-- Prairie dog: ~5-25 year boom-bust cycles driven by plague.
    Source: Journal of Applied Ecology (plague-ferret model);
    USDA ARS Thunder Basin 21-year study.
-/
def prairieDogEmpirical : EmpiricalPeriod := {
  species := "Cynomys ludovicianus",
  observedPeriodYears := some 10,  -- midpoint of 5-25 year range
  dataSource := "J. Appl. Ecol. (5-25 yr cycle); USDA ARS Thunder Basin",
  cycleDriver := "plague epizootics (Yersinia pestis)",
  confidence := "moderate"
}

/-- Orca Southern Resident: ~2 year biennial pattern.
    Source: Marine Ecology Progress Series 2019;
    CJFAS 2024 (Ruggerone et al.).
-/
def orcaEmpirical : EmpiricalPeriod := {
  species := "Orcinus orca (Southern Resident)",
  observedPeriodYears := some 2,  -- biennial pattern
  dataSource := "MEPS 2019; CJFAS 2024 (Ruggerone et al.)",
  cycleDriver := "pink salmon interference with Chinook foraging",
  confidence := "high"
}

/-- Honeybee: seasonal/annual cycles, no multi-year oscillation.
    Source: Multiple mathematical modeling studies.
-/
def honeybeeEmpirical : EmpiricalPeriod := {
  species := "Apis mellifera",
  observedPeriodYears := some 1,  -- seasonal/annual
  dataSource := "Mathematical modeling reviews (PLOS One, NSF PAR)",
  cycleDriver := "seasonal queen egg-laying and winter mortality",
  confidence := "high"
}

/-- Sperm whale: no natural cycles documented.
    Source: Nature Scientific Reports 2022; MEPS 2002.
-/
def spermWhaleEmpirical : EmpiricalPeriod := {
  species := "Physeter macrocephalus",
  observedPeriodYears := none,  -- no natural cycle; whaling recovery
  dataSource := "Nature Sci Rep 2022; MEPS 2002 (trajectory models)",
  cycleDriver := "none (whaling + ongoing anthropogenic impacts)",
  confidence := "N/A"
}

/-- Dolphin: no clear periodic oscillations documented.
    Source: Sarasota Bay long-term study.
-/
def dolphinEmpirical : EmpiricalPeriod := {
  species := "Tursiops truncatus",
  observedPeriodYears := none,  -- stable populations, no cycles
  dataSource := "Sarasota Bay long-term study (1970s-present)",
  cycleDriver := "none (demographic stochasticity only)",
  confidence := "N/A"
}

/-- Sardine: ~61 year cycle (already formalized in GeneticFieldEquation).
    Source: Fisheries literature (Pacific sardine Sardinops sagax).
-/
def sardineEmpirical : EmpiricalPeriod := {
  species := "Sardinops sagax",
  observedPeriodYears := some 61,  -- ~61 year fishery/ population cycle
  dataSource := "Fisheries literature (Pacific sardine)",
  cycleDriver := "climate-driven regime shifts + fishing pressure",
  confidence := "high"
}

/-- All empirical data. -/
def allEmpiricalData : List EmpiricalPeriod := [
  octopusEmpirical,
  prairieDogEmpirical,
  orcaEmpirical,
  honeybeeEmpirical,
  spermWhaleEmpirical,
  dolphinEmpirical,
  sardineEmpirical
]

/-- Count species with documented periodic cycles. -/
def speciesWithCycles : Nat :=
  (allEmpiricalData.filter (fun e => e.observedPeriodYears.isSome)).length

theorem speciesWithCyclesIs5 : speciesWithCycles = 5 := by native_decide

/-- Count species without documented periodic cycles. -/
def speciesWithoutCycles : Nat :=
  (allEmpiricalData.filter (fun e => e.observedPeriodYears.isNone)).length

theorem speciesWithoutCyclesIs2 : speciesWithoutCycles = 2 := by native_decide

-- =========================================================================
-- S1  Intrinsic vs Observed Period Comparison
-- =========================================================================

/- THE CENTRAL FINDING:
   For most species, the OBSERVED ecological period is MUCH LONGER
   than the INTRINSIC period predicted by the language model.

   This is because observed periods are determined by EXTERNAL
   CONSTRAINTS, not by information processing speed alone.

   The framework needs to distinguish:
     P0_intrinsic = f(language characteristics)
     P0_observed = P0_intrinsic × constraint_factor

   where constraint_factor depends on:
     - Life cycle duration (octopus: 1 year >> minutes-hours)
     - Pathogen dynamics (prairie dog: plague >> alarm call speed)
     - Prey availability (orca: salmon abundance >> pod interaction)
     - Climate seasonality (honeybee: winter >> foraging cycle)
-/

/-- Intrinsic P0 prediction from language model (rough estimate, years). -/
def intrinsicP0Years (speciesName : String) : Option Rat :=
  match speciesName with
  | "Octopus vulgaris" => some (1 / 8760)  -- ~1 hour in years
  | "Cynomys ludovicianus" => some (7 / 365)  -- ~1 week in years
  | "Orcinus orca (Southern Resident)" => some (1 / 12)  -- ~1 month
  | "Apis mellifera" => some (7 / 365)  -- ~1 week
  | "Physeter macrocephalus" => some 2  -- ~2 years
  | "Tursiops truncatus" => some (1 / 365)  -- ~1 day
  | "Sardinops sagax" => some 1  -- ~1 year (chemical language)
  | _ => none

/-- Observed / Intrinsic ratio: how much external constraints
    stretch the period beyond the language-derived bound. -/
def periodConstraintFactor (ep : EmpiricalPeriod) : Option Rat :=
  match ep.observedPeriodYears with
  | some observed =>
    match intrinsicP0Years ep.species with
    | some intrinsic => some (observed / intrinsic)
    | none => none
  | none => none

/-- Octopus: observed ~1 year / intrinsic ~1 hour = ~8760× constraint. -/
def octopusConstraintFactor : Option Rat :=
  periodConstraintFactor octopusEmpirical

/-- Prairie dog: observed ~10 years / intrinsic ~1 week = ~520× constraint. -/
def prairieDogConstraintFactor : Option Rat :=
  periodConstraintFactor prairieDogEmpirical

/-- Orca: observed ~2 years / intrinsic ~1 month = ~24× constraint. -/
def orcaConstraintFactor : Option Rat :=
  periodConstraintFactor orcaEmpirical

/-- Honeybee: observed ~1 year / intrinsic ~1 week = ~52× constraint. -/
def honeybeeConstraintFactor : Option Rat :=
  periodConstraintFactor honeybeeEmpirical

/-- Sardine: observed ~61 years / intrinsic ~1 year = ~61× constraint.
    This is the closest match because chemical language is slow. -/
def sardineConstraintFactor : Option Rat :=
  periodConstraintFactor sardineEmpirical

-- =========================================================================
-- S2  Framework Refinement: Two-Tier P0 Model
-- =========================================================================

/- PROPOSED FRAMEWORK REFINEMENT:

   Tier 1: INTRINSIC P0
     Derived from dominant language characteristics.
     Represents the "information processing clock speed" of the species.
     Fast languages (electromagnetic, generative) → short intrinsic P0.
     Slow languages (chemical, mechanical) → long intrinsic P0.

   Tier 2: OBSERVED P0
     Measured from ecological data.
     Represents the actual population dynamics.
     Often much longer than intrinsic P0 due to external constraints.

   The relationship:
     P0_observed = P0_intrinsic × C

     where C = constraint_factor is species-specific and depends on:
       - Body size / lifespan (larger → longer C)
       - Environmental stability (more stable → longer C)
       - Trophic level (higher → longer C)
       - Pathogen load (higher → more variable C)

   For the MassNumber gate:
     The gate should use P0_observed as the empirical anchor.
     But P0_intrinsic provides a BOUND:
       P0_observed ≥ P0_intrinsic (always true, external constraints add time)

   The framework's dimensionless structure n(k) predicts:
     T(k) = P0_observed × n(k)

   For different species with the same k:
     T_speciesA(k) / T_speciesB(k) = P0_observed_A / P0_observed_B

   This is TESTABLE: if two species have the same k but different
   dominant languages, their period ratio should equal their
   observed P0 ratio.
-/

/-- Two-tier P0 model status. -/
def twoTierP0Status : String :=
  "framework refinement: P0_observed = P0_intrinsic × constraint_factor; "
  ++ "intrinsic P0 from language characteristics; "
  ++ "observed P0 from empirical ecology; "
  ++ "constraint_factor is species-specific and externally determined"

-- =========================================================================
-- S3  Testable Predictions from Empirical Data
-- =========================================================================

/-- Prediction: For species with fast languages (electromagnetic,
    acoustic), the constraint factor should be larger than for
    species with slow languages (chemical, mechanical).

    Data:
      Octopus (electromagnetic): C ~ 8760× (largest)
      Honeybee (mechanical): C ~ 52×
      Prairie dog (acoustic): C ~ 520×
      Orca (acoustic): C ~ 24× (smallest among those with cycles)
      Sardine (chemical): C ~ 61×

    Result: The prediction FAILS. Octopus (fastest language) has
    the largest constraint factor, not the smallest. This is because
    octopus has an extremely short life cycle that dominates
    all other time scales.

    CORRECTION: The constraint factor depends on LIFESPAN, not
    just language speed. Short-lived species have larger C because
    their life cycle truncates all longer processes.
-/

def constraintFactorAnalysis : String :=
  "constraint factor depends on lifespan, not language alone; "
  ++ "octopus (shortest lifespan) has largest C ~8760x; "
  ++ "orca (longest lifespan among documented) has smallest C ~24x"

/-- Lifespan estimates (years, approximate). -/
def speciesLifespanYears (speciesName : String) : Rat :=
  match speciesName with
  | "Octopus vulgaris" => 1
  | "Cynomys ludovicianus" => 5
  | "Orcinus orca (Southern Resident)" => 50
  | "Apis mellifera" => 1  -- colony, not individual
  | "Physeter macrocephalus" => 70
  | "Tursiops truncatus" => 40
  | "Sardinops sagax" => 5
  | _ => 10

/-- Constraint factor correlates with lifespan ratio:
    C ≈ lifespan / P0_intrinsic (in years).
    For octopus: 1 year / (1/8760 year) = 8760. Matches.
    For orca: 50 years / (1/12 year) = 600. But observed C ~24.
    Discrepancy: orca's observed period is 2 years, not 50.
    The orca's cycle is driven by salmon, not lifespan.
-/
def lifespanConstraintCorrelation : String :=
  "constraint factor partially explained by lifespan but also by "
  ++ "ecological drivers (salmon, plague, climate); no simple formula"

-- =========================================================================
-- S4  Honest Assessment: What the Data Supports
-- =========================================================================

/- HONEST VERDICT:

   THE DATA SUPPORTS:
     1. Species have documented ecological periods (4 of 7 species).
     2. These periods vary widely (1 year to 61 years).
     3. The variation correlates with species characteristics.
     4. No species has a period that violates physical bounds.

   THE DATA DOES NOT SUPPORT:
     1. A direct derivation of P0 from language characteristics alone.
     2. A universal formula P0 = f(language) that works for all species.
     3. The MassNumber gate passing for any species besides sardine.

   THE FRAMEWORK NEEDS:
     1. A two-tier model (intrinsic vs observed P0).
     2. An empirical constraint_factor for each species.
     3. More long-term ecological data (especially for cetaceans).
     4. A revised MassNumber gate that checks CONSISTENCY
        (observed ≥ intrinsic) rather than EXACT MATCH.
-/

/-- Honest assessment of the empirical data's impact on the framework. -/
def empiricalDataAssessment : String :=
  "4 of 7 documented-language species have observable ecological periods; "
  ++ "periods range 1-61 years; direct language-to-P0 derivation fails; "
  ++ "two-tier model (intrinsic + observed) is required; "
  ++ "MassNumber gate needs revision to check consistency not exact match"

-- =========================================================================
-- S5  The Sardine as Special Case
-- =========================================================================

/- WHY THE SARDINE WORKS:
   The sardine is the ONLY species where:
     1. A clear long-term ecological period is documented (~61 years).
     2. The period is driven by climate regime shifts (intrinsic to ecosystem).
     3. The species' chemical language is SLOW enough that the
        observed period is not wildly different from the intrinsic bound.
     4. The constraint factor (~61×) is moderate and explainable.

   This makes the sardine the IDEAL anchor species for the framework.
   Other species either:
     - Have no clear cycle (dolphin, sperm whale)
     - Have very short cycles (octopus, honeybee)
     - Have cycles dominated by external forcing (prairie dog: plague)

   RECOMMENDATION: Keep the sardine as the PRIMARY anchor.
   Use other species as SECONDARY consistency checks, not as anchors.
-/

/-- Why the sardine is the ideal anchor species. -/
def sardineAnchorRationale : String :=
  "sardine is ideal anchor: clear ~61 yr cycle, climate-driven, "
  ++ "chemical language gives moderate constraint factor; "
  ++ "other species lack long-term intrinsic cycles or are dominated "
  ++ "by external forcing"

-- =========================================================================
-- S6  Executable Receipts
-- =========================================================================

#eval! speciesWithCycles
#eval! speciesWithoutCycles
#eval! octopusEmpirical.observedPeriodYears
#eval! prairieDogEmpirical.observedPeriodYears
#eval! orcaEmpirical.observedPeriodYears
#eval! honeybeeEmpirical.observedPeriodYears
#eval! sardineEmpirical.observedPeriodYears
#eval! octopusConstraintFactor
#eval! prairieDogConstraintFactor
#eval! orcaConstraintFactor
#eval! honeybeeConstraintFactor
#eval! sardineConstraintFactor
#eval! speciesLifespanYears "Octopus vulgaris"
#eval! speciesLifespanYears "Orcinus orca (Southern Resident)"
#eval! twoTierP0Status
#eval! constraintFactorAnalysis
#eval! empiricalDataAssessment
#eval! sardineAnchorRationale

end Semantics.EcologicalPeriodDataProbe