import Axiom

namespace e072b9vn

structure CapabilityCompressionV3Observation where
  replicationPacketCount : Nat
  heldOutPacketCount : Nat
  repetitionCount : Nat
  validCellCount : Nat
  invalidCellCount : Nat
  isolatedReplicationCoverageMilli : Nat
  routedReplicationCoverageMilli : Nat
  isolatedHeldOutCoverageMilli : Nat
  routedHeldOutCoverageMilli : Nat
  isolatedReplicationActionMilli : Nat
  routedReplicationActionMilli : Nat
  isolatedHeldOutActionMilli : Nat
  routedHeldOutActionMilli : Nat
  isolatedReplicationCostMicros : Nat
  routedReplicationCostMicros : Nat
  isolatedHeldOutCostMicros : Nat
  routedHeldOutCostMicros : Nat


def WellFormedCapabilityCompressionV3Observation
    (o : CapabilityCompressionV3Observation) : Prop :=
  0 < o.replicationPacketCount ∧
    0 < o.heldOutPacketCount ∧
    0 < o.repetitionCount ∧
    0 < o.validCellCount ∧
    o.invalidCellCount = 0 ∧
    o.isolatedReplicationCoverageMilli ≤ 1000 ∧
    o.routedReplicationCoverageMilli ≤ 1000 ∧
    o.isolatedHeldOutCoverageMilli ≤ 1000 ∧
    o.routedHeldOutCoverageMilli ≤ 1000 ∧
    o.isolatedReplicationActionMilli ≤ 1000 ∧
    o.routedReplicationActionMilli ≤ 1000 ∧
    o.isolatedHeldOutActionMilli ≤ 1000 ∧
    o.routedHeldOutActionMilli ≤ 1000


def ReplicationCoverageProxyImproves
    (o : CapabilityCompressionV3Observation) : Prop :=
  o.routedReplicationCoverageMilli > o.isolatedReplicationCoverageMilli


def HeldOutCoverageProxyDoesNotReplicate
    (o : CapabilityCompressionV3Observation) : Prop :=
  o.routedHeldOutCoverageMilli < o.isolatedHeldOutCoverageMilli


def MachineOnlyV3Observation
    (o : CapabilityCompressionV3Observation) : Prop :=
  o.invalidCellCount = 0


def capability_compression_v3_machine_observationPayload :=
  "In a five-repetition OpenRouter machine-only control using deepseek/deepseek-v4-flash, recipient-routed prompts produced higher mean deterministic required-term coverage than isolated prompts on the three-packet replication subset: 0.422 versus 0.266. On the frozen four-packet held-out subset, routed required-term coverage was lower: 0.250 versus 0.584. Bounded-action proxy coverage was 0.200 versus 0.100 in replication and tied at 0.375 versus 0.375 held out. These are lexical and rubric proxies, not comprehension or capability transfer."
axiom capability_compression_v3_machine_observation_auth : Axiom.AuthenticatedTerm ("hitchhiker2thefuture", capability_compression_v3_machine_observationPayload, 1786294729)
def capability_compression_v3_machine_observation : Axiom.Statement "hitchhiker2thefuture" capability_compression_v3_machine_observationPayload 1786294729 := ⟨capability_compression_v3_machine_observation_auth⟩

def capability_compression_v3_harness_receiptPayload :=
  "The v3 control used five randomized repetitions, a frozen held-out suite, a warm-up request, a 1,024-token output cap, minimal reasoning with reasoning content excluded, and same-condition retries for invalid cells. All 38 recorded cells finished with stop, produced non-placeholder extracted answers, and passed the validity gate. This is a producer-integrity receipt, not evidence of human recipient use."
axiom capability_compression_v3_harness_receipt_auth : Axiom.AuthenticatedTerm ("hitchhiker2thefuture", capability_compression_v3_harness_receiptPayload, 1786294729)
def capability_compression_v3_harness_receipt : Axiom.Statement "hitchhiker2thefuture" capability_compression_v3_harness_receiptPayload 1786294729 := ⟨capability_compression_v3_harness_receipt_auth⟩

def capability_compression_v3_cost_boundaryPayload :=
  "The v3 provider receipts recorded replication costs of $0.00159054 isolated and $0.00147167 routed, and held-out costs of $0.00051296 isolated and $0.00018868 routed. These are request-level OpenRouter receipts only. They do not price human attention, correction work, validation work, recipient absorption, or matched useful output, and therefore do not establish an economic advantage."
axiom capability_compression_v3_cost_boundary_auth : Axiom.AuthenticatedTerm ("hitchhiker2thefuture", capability_compression_v3_cost_boundaryPayload, 1786294729)
def capability_compression_v3_cost_boundary : Axiom.Statement "hitchhiker2thefuture" capability_compression_v3_cost_boundaryPayload 1786294729 := ⟨capability_compression_v3_cost_boundary_auth⟩

def capability_compression_v3_claim_boundaryPayload :=
  "The v3 observation establishes only a mixed machine-side proxy result on small synthetic packets. It does not establish human capability transfer, Steph replication, recipient comprehension, validated reuse, parity, superiority, causal artifact change, model replacement, or lower total network cost."
axiom capability_compression_v3_claim_boundary_auth : Axiom.AuthenticatedTerm ("hitchhiker2thefuture", capability_compression_v3_claim_boundaryPayload, 1786294729)
def capability_compression_v3_claim_boundary : Axiom.Statement "hitchhiker2thefuture" capability_compression_v3_claim_boundaryPayload 1786294729 := ⟨capability_compression_v3_claim_boundary_auth⟩

end e072b9vn