import Axiom

namespace tg09m0qk

structure CapabilityAdditionObservation where
  acquisitionCostCents : Nat
  encodingCostCents : Nat
  transferCostCents : Nat
  validationCostCents : Nat
  coordinationCostCents : Nat
  routingCostCents : Nat
  validatedReuseCount : Nat
  modelDataCostCents : Nat
  modelTrainingCostCents : Nat
  modelEvaluationCostCents : Nat
  modelDeploymentCostCents : Nat
  modelRegressionCostCents : Nat


def NetworkCapabilityAdditionCost (o : CapabilityAdditionObservation) : Nat :=
  o.acquisitionCostCents +
    o.encodingCostCents +
    o.transferCostCents +
    o.validationCostCents +
    o.coordinationCostCents +
    o.routingCostCents


def ModelCapabilityAdditionCost (o : CapabilityAdditionObservation) : Nat :=
  o.modelDataCostCents +
    o.modelTrainingCostCents +
    o.modelEvaluationCostCents +
    o.modelDeploymentCostCents +
    o.modelRegressionCostCents


def NetworkCapabilityAdditionIsWellFormed (o : CapabilityAdditionObservation) : Prop :=
  0 < o.validatedReuseCount


def NetworkHasLowerAmortizedAdditionCost (o : CapabilityAdditionObservation) : Prop :=
  NetworkCapabilityAdditionCost o <
    ModelCapabilityAdditionCost o * o.validatedReuseCount

def capability_addition_cost_equationPayload :=
  "The cost of adding a capability to a network is the cost of acquiring, encoding, transferring, validating, coordinating, and routing the capability. When the capability is validated and reused, its amortized cost per use is the addition cost divided by validated reuse count. This is a different object from the cost of training a model to internalize the capability."
axiom capability_addition_cost_equation_auth : Axiom.AuthenticatedTerm ("hitchhiker2thefuture", capability_addition_cost_equationPayload, 1786205542)
def capability_addition_cost_equation : Axiom.Statement "hitchhiker2thefuture" capability_addition_cost_equationPayload 1786205542 := ⟨capability_addition_cost_equation_auth⟩

def capability_routing_portability_boundaryPayload :=
  "A base network can reduce capability-addition cost by routing a capability from one capable node to other nodes without retraining every underlying model, but only when the receiving node exposes a compatible interface, accepts the capability and its provenance, supplies sufficient context, and passes local validation. Routing is not free, universal, or evidence of equal competence."
axiom capability_routing_portability_boundary_auth : Axiom.AuthenticatedTerm ("hitchhiker2thefuture", capability_routing_portability_boundaryPayload, 1786205542)
def capability_routing_portability_boundary : Axiom.Statement "hitchhiker2thefuture" capability_routing_portability_boundaryPayload 1786205542 := ⟨capability_routing_portability_boundary_auth⟩

def network_capability_amortization_claimPayload :=
  "A network has lower amortized capability-addition cost than model retraining only when the measured acquisition, encoding, transfer, validation, coordination, and routing cost is lower than the measured model data, training, evaluation, deployment, and regression cost multiplied by the validated reuse count."
axiom network_capability_amortization_claim_auth : Axiom.AuthenticatedTerm ("hitchhiker2thefuture", network_capability_amortization_claimPayload, 1786205542)
def network_capability_amortization_claim : Axiom.Statement "hitchhiker2thefuture" network_capability_amortization_claimPayload 1786205542 := ⟨network_capability_amortization_claim_auth⟩

def capability_addition_is_not_model_parityPayload :=
  "A lower cost to add and route a capability does not establish parity with a newly trained model. Parity additionally requires a frozen task suite, useful-output equivalence, correction-distance accounting, validation burden accounting, and a stated portability boundary."
axiom capability_addition_is_not_model_parity_auth : Axiom.AuthenticatedTerm ("hitchhiker2thefuture", capability_addition_is_not_model_parityPayload, 1786205542)
def capability_addition_is_not_model_parity : Axiom.Statement "hitchhiker2thefuture" capability_addition_is_not_model_parityPayload 1786205542 := ⟨capability_addition_is_not_model_parity_auth⟩

end tg09m0qk