import Axiom

namespace n3p2f8mv

structure CapabilityParityObservation where
  networkCostCents : Nat
  modelTrainingCostCents : Nat
  modelEvaluationCostCents : Nat
  networkAttemptedTasks : Nat
  networkUsefulTasks : Nat
  modelAttemptedTasks : Nat
  modelUsefulTasks : Nat
  networkCorrectionWork : Nat
  modelCorrectionWork : Nat
  networkValidationWork : Nat
  modelValidationWork : Nat


def WellFormedCapabilityParityObservation (o : CapabilityParityObservation) : Prop :=
  0 < o.networkAttemptedTasks ∧
    0 < o.modelAttemptedTasks ∧
    o.networkUsefulTasks ≤ o.networkAttemptedTasks ∧
    o.modelUsefulTasks ≤ o.modelAttemptedTasks


def NetworkReachesModelCapabilityParity (o : CapabilityParityObservation) : Prop :=
  o.networkUsefulTasks * o.modelAttemptedTasks ≥
    o.modelUsefulTasks * o.networkAttemptedTasks ∧
    o.networkCorrectionWork ≤ o.modelCorrectionWork ∧
    o.networkValidationWork ≤ o.modelValidationWork


def NetworkHasLowerAcquisitionCost (o : CapabilityParityObservation) : Prop :=
  o.networkCostCents < o.modelTrainingCostCents + o.modelEvaluationCostCents


def NetworkCostAdvantageAtParity (o : CapabilityParityObservation) : Prop :=
  WellFormedCapabilityParityObservation o ∧
    NetworkReachesModelCapabilityParity o ∧
    NetworkHasLowerAcquisitionCost o

def capability_parity_cost_modelPayload :=
  "Compare a human/AI network with a trained model only on a frozen, held-out capability suite. Record network operating and coordination cost, model training cost, model evaluation cost, useful-task completion, correction work, and validation work in the same observation. A network has a cost advantage at parity only when it reaches at least the model's useful-task rate without greater correction or validation burden and its measured network cost is lower than measured model training plus evaluation cost."
axiom capability_parity_cost_model_auth : Axiom.AuthenticatedTerm ("hitchhiker2thefuture", capability_parity_cost_modelPayload, 1786205213)
def capability_parity_cost_model : Axiom.Statement "hitchhiker2thefuture" capability_parity_cost_modelPayload 1786205213 := ⟨capability_parity_cost_model_auth⟩

def forty_two_dollar_candidate_boundaryPayload :=
  "A reported 42-dollar network cost is a candidate observation, not an established parity result. It becomes admissible only when the receipt identifies the cost window, included human and AI costs, currency and timestamp, task suite, useful-output rule, correction work, validation work, and comparison model. Missing provider USD telemetry is not zero cost, and a low operating cost is not equivalent to the cost of training a new language model."
axiom forty_two_dollar_candidate_boundary_auth : Axiom.AuthenticatedTerm ("hitchhiker2thefuture", forty_two_dollar_candidate_boundaryPayload, 1786205213)
def forty_two_dollar_candidate_boundary : Axiom.Statement "hitchhiker2thefuture" forty_two_dollar_candidate_boundaryPayload 1786205213 := ⟨forty_two_dollar_candidate_boundary_auth⟩

def capability_parity_is_not_general_intelligence_parityPayload :=
  "Capability parity is task-suite-relative. Matching a frozen set of observed network capabilities does not establish general intelligence parity, model replacement, equal robustness, equal transfer, or equal social and coordination value."
axiom capability_parity_is_not_general_intelligence_parity_auth : Axiom.AuthenticatedTerm ("hitchhiker2thefuture", capability_parity_is_not_general_intelligence_parityPayload, 1786205213)
def capability_parity_is_not_general_intelligence_parity : Axiom.Statement "hitchhiker2thefuture" capability_parity_is_not_general_intelligence_parityPayload 1786205213 := ⟨capability_parity_is_not_general_intelligence_parity_auth⟩

end n3p2f8mv