import Axiom

namespace x04pyb0y

def Entropy : Prop :=
  "undifferentiated bits per time - raw chaotic energy without a frame, expensive for a network to evaluate"

def FramedEntropy : Prop :=
  "the bits per time a network must spend to evaluate a thing after a node has structured it"

def NodeValueAsEntropyReduction : Prop :=
  "a node's value to the network equals the entropy it removes: H(unframed) minus H(framed), measured in bits per time over the same underlying referent"

def TrustVault : Prop :=
  "the mechanism that captures chaotic energy over time and discharges it as framed entropy, so the network can evaluate it more cheaply and more accurately"

def PvEBaseline : Prop :=
  "the frame where humans are positioned against entropy rather than against each other, so the competitive reference is the disorder being reduced, not a rival system"

def OverlappingRewardSystems : Prop :=
  "multiple overlapping systems that reward a participant's contribution, so no single system's failure is fatal to the network's retention of energy"

def HumanTimeSavedAsBits : Prop :=
  "the human time a system saves, measured as bits of evaluation the human no longer has to spend - the HumanPower Index in entropy terms"

def trust_vault_framed_entropy_thesisPayload :=
  "CLAIM-006 (origin: trust vault PvE thesis, 2026-08-18): a node's value to the network equals the entropy difference it creates - H(unframed) minus H(framed), measured in bits per time over the same underlying referent. Nodes that reduce entropy for the network survive and compound; nodes that increase or merely rearrange entropy are outcompeted. Framed entropy is cheaper for the network to evaluate than unframed entropy of the same thing. Falsifiers: a node that removes bits is not retained by the network; a node is retained while increasing network entropy; or the framed version of a thing costs more bits to evaluate than the unframed version"
axiom trust_vault_framed_entropy_thesis_auth : Axiom.AuthenticatedTerm ("hitchhiker2thefuture", trust_vault_framed_entropy_thesisPayload, 1787140828)
def trust_vault_framed_entropy_thesis : Axiom.Statement "hitchhiker2thefuture" trust_vault_framed_entropy_thesisPayload 1787140828 := ⟨trust_vault_framed_entropy_thesis_auth⟩

def trust_vault_is_the_framing_mechanismPayload :=
  "The trust vault is the mechanism that captures chaotic energy over time and discharges it as framed entropy. Its value to the network is the entropy difference it produces: less energy is needed because a larger share of the energy it uses is signal, not dissipation"
axiom trust_vault_is_the_framing_mechanism_auth : Axiom.AuthenticatedTerm ("hitchhiker2thefuture", trust_vault_is_the_framing_mechanismPayload, 1787140828)
def trust_vault_is_the_framing_mechanism : Axiom.Statement "hitchhiker2thefuture" trust_vault_is_the_framing_mechanismPayload 1787140828 := ⟨trust_vault_is_the_framing_mechanism_auth⟩

def pve_entropy_baselinePayload :=
  "A baseline layer positions humans against entropy (PvE) rather than against each other, so the competitive reference is unframed entropy itself. Participation is voluntary and rewarded across multiple overlapping systems, so no single system's failure is fatal to the network's retention of energy. The system survives while overlapping rewards keep voluntary participation above the entropy baseline and above the participant's outside option"
axiom pve_entropy_baseline_auth : Axiom.AuthenticatedTerm ("hitchhiker2thefuture", pve_entropy_baselinePayload, 1787140828)
def pve_entropy_baseline : Axiom.Statement "hitchhiker2thefuture" pve_entropy_baselinePayload 1787140828 := ⟨pve_entropy_baseline_auth⟩

def humanpower_index_is_entropy_reductionPayload :=
  "The HumanPower Index, measured in human time saved, is the entropy-reduction claim in network terms: time saved equals bits of evaluation a human no longer has to spend. The index is the measurement instrument for the framed-entropy thesis"
axiom humanpower_index_is_entropy_reduction_auth : Axiom.AuthenticatedTerm ("hitchhiker2thefuture", humanpower_index_is_entropy_reductionPayload, 1787140828)
def humanpower_index_is_entropy_reduction : Axiom.Statement "hitchhiker2thefuture" humanpower_index_is_entropy_reductionPayload 1787140828 := ⟨humanpower_index_is_entropy_reduction_auth⟩

end x04pyb0y