import Axiom

namespace kdvdwae2

structure CapabilityCompressionTransferObservation where
  sourceEntropyUnits : Nat
  compressedSignalUnits : Nat
  recipientNodes : Nat
  transferredSignals : Nat
  validatedRecipientUses : Nat
  sourceCostCents : Nat
  compressionCostCents : Nat
  transferCostCents : Nat
  validationCostCents : Nat
  recipientCorrectionWork : Nat
  isolatedModelCostCents : Nat
  isolatedModelValidatedUses : Nat
  routedModelCostCents : Nat
  routedModelValidatedUses : Nat


def WellFormedCapabilityCompressionTransferObservation (o : CapabilityCompressionTransferObservation) : Prop :=
  0 < o.sourceEntropyUnits ∧
    0 < o.recipientNodes ∧
    o.compressedSignalUnits ≤ o.sourceEntropyUnits ∧
    o.validatedRecipientUses ≤ o.transferredSignals ∧
    o.isolatedModelValidatedUses ≤ o.recipientNodes ∧
    o.routedModelValidatedUses ≤ o.recipientNodes


def StephLikeNetworkCapabilityCost (o : CapabilityCompressionTransferObservation) : Nat :=
  o.sourceCostCents +
    o.compressionCostCents +
    o.transferCostCents +
    o.validationCostCents


def NetworkedCompressionReachesRecipients (o : CapabilityCompressionTransferObservation) : Prop :=
  o.validatedRecipientUses * o.recipientNodes ≥
    o.isolatedModelValidatedUses * o.recipientNodes ∧
    o.validatedRecipientUses ≥ o.routedModelValidatedUses


def NetworkedCompressionHasLowerCost (o : CapabilityCompressionTransferObservation) : Prop :=
  StephLikeNetworkCapabilityCost o < o.isolatedModelCostCents ∧
    StephLikeNetworkCapabilityCost o < o.routedModelCostCents

def connected_compression_capabilityPayload :=
  "A connected human capability can add value beyond source-level reasoning when it absorbs high-entropy input, compresses it into a recipient-legible signal, selects or reaches connected recipient nodes, and produces validated recipient use. The capability therefore includes compression, translation, routing, and recipient absorption rather than summarization alone."
axiom connected_compression_capability_auth : Axiom.AuthenticatedTerm ("hitchhiker2thefuture", connected_compression_capabilityPayload, 1786205891)
def connected_compression_capability : Axiom.Statement "hitchhiker2thefuture" connected_compression_capabilityPayload 1786205891 := ⟨connected_compression_capability_auth⟩

def isolated_model_is_not_network_parity_controlPayload :=
  "An isolated model is a necessary baseline for a connected-compression experiment, but it is not an equivalent network control. It receives the source task without the recipient graph, recipient-specific context, routing path, or downstream absorption receipts. A routed model control must be evaluated separately."
axiom isolated_model_is_not_network_parity_control_auth : Axiom.AuthenticatedTerm ("hitchhiker2thefuture", isolated_model_is_not_network_parity_controlPayload, 1786205891)
def isolated_model_is_not_network_parity_control : Axiom.Statement "hitchhiker2thefuture" isolated_model_is_not_network_parity_controlPayload 1786205891 := ⟨isolated_model_is_not_network_parity_control_auth⟩

def capability_compression_transfer_protocolPayload :=
  "Evaluate a connected compression capability on redacted high-entropy source packets with a frozen recipient set. Compare a human source node, an isolated model, and a model with equivalent recipient profiles and routing. Measure source entropy, compressed signal size, transfer cost, recipient-specific translation, validated recipient uses, recipient correction work, source and model costs, and reuse. Do not count a summary as a successful transfer unless a recipient uses the signal or passes a blinded absorption test."
axiom capability_compression_transfer_protocol_auth : Axiom.AuthenticatedTerm ("hitchhiker2thefuture", capability_compression_transfer_protocolPayload, 1786205891)
def capability_compression_transfer_protocol : Axiom.Statement "hitchhiker2thefuture" capability_compression_transfer_protocolPayload 1786205891 := ⟨capability_compression_transfer_protocol_auth⟩

def networked_capability_cost_boundaryPayload :=
  "The cost of a connected compression capability is source acquisition plus compression, transfer, and validation cost. A lower cost than an isolated or routed model is admissible only when recipient usefulness and correction burden are measured on the same task suite. A smaller message is not automatically better compression, and temporal proximity is not proof of causal transfer."
axiom networked_capability_cost_boundary_auth : Axiom.AuthenticatedTerm ("hitchhiker2thefuture", networked_capability_cost_boundaryPayload, 1786205891)
def networked_capability_cost_boundary : Axiom.Statement "hitchhiker2thefuture" networked_capability_cost_boundaryPayload 1786205891 := ⟨networked_capability_cost_boundary_auth⟩

end kdvdwae2