import Axiom

namespace fab8hqgj

def Pod : Prop :=
  "a bounded three-role temporal engine that unifies hedge fund, accelerator, and startup functions"

def ProximityToTheFuture : Prop :=
  "the measurable ability to perceive, model, and act upon change faster than others without introducing instability"

def VerificationLatency : Prop :=
  "the delay between an insight's emergence and its verifiable impact on reality"

def TemporalAlpha : Prop :=
  "performance beyond collective time expectation"

def TimeViolence : Prop :=
  "operational entropy caused by misalignment or over-acceleration"

def ForesightEfficiency : Prop :=
  "verified value created per unit of verification time and capital deployed"

def TrustLeverage : Prop :=
  "multiplier on capital efficiency derived from collective trust"

def NetworkRelativity : Prop :=
  "the principle that faster-verifying nodes experience temporal dilation relative to slower ones"

def RecursiveCompounding : Prop :=
  "the recursive increase of foresight efficiency through closed feedback loops"

def CompoundedUnderstanding : Prop :=
  "total accumulated network insight across cycles"

def ProximityToken : Prop :=
  "a self-regulating crypto asset whose supply dynamics derive from observable network state"

def MintRule : Prop :=
  "the intended token minting rule that issues supply based on foresight efficiency and trust leverage"

def BurnRule : Prop :=
  "the intended token burn rule that removes supply based on time violence"

def TrustWeightedStaking : Prop :=
  "intended staking rewards scaled by trust leverage"

def ProximityFundPodThesis : Prop :=
  Axiom.Actual (Pod ∧ ProximityToTheFuture ∧ VerificationLatency)

def proximity_fund_recursive_structurePayload :=
  "the fund is intended to increase proximity to the future through recursive compounding where foresight efficiency compounds across research, hedge, startup, and accelerator feedback loops, trust leverage scales with network coherence, and token supply is intended to be minted and burned according to observable foresight and time-violence dynamics"
axiom proximity_fund_recursive_structure_auth : Axiom.AuthenticatedTerm ("hitchhiker2thefuture", proximity_fund_recursive_structurePayload, 1786969825)
def proximity_fund_recursive_structure : Axiom.Statement "hitchhiker2thefuture" proximity_fund_recursive_structurePayload 1786969825 := ⟨proximity_fund_recursive_structure_auth⟩

def proximity_fund_mathematical_frame_referencePayload :=
  "the fund's mathematical framework is documented in Appendix A as formulations A1 through A10, including foresight efficiency, recursive compounding, trust-leverage relationship, network relativity, total compounded understanding, temporal alpha, pod coherence, convergence conditions, league formation threshold, and time violence score"
axiom proximity_fund_mathematical_frame_reference_auth : Axiom.AuthenticatedTerm ("hitchhiker2thefuture", proximity_fund_mathematical_frame_referencePayload, 1786969825)
def proximity_fund_mathematical_frame_reference : Axiom.Statement "hitchhiker2thefuture" proximity_fund_mathematical_frame_referencePayload 1786969825 := ⟨proximity_fund_mathematical_frame_reference_auth⟩

def MarketPodConfiguration : Prop :=
  "a Pod implemented in an actual market where the three roles (hedge fund, accelerator, startup) map to real operating functions"

def MarketVerificationLatency : Prop :=
  "the delay between an insight about a company and verifiable market confirmation"

def MarketTimeViolence : Prop :=
  "operational entropy in a market context - the cost of misalignment between operating reality and market perception"

def MarketPredictionDerivedFromFundStructure : Prop :=
  "a prediction about a market outcome derived from the fund's formal structure, where the prediction is falsifiable by observed market data"

def OperatingMetric : Prop :=
  "an observable company metric that maps to the fund's foresight efficiency or time violence concepts"

def AcquisitionVolumeMetric : Prop :=
  "number of homes purchased or acquisition contracts - maps to capital deployment efficiency"

def ContributionMarginMetric : Prop :=
  "contribution margin percentage - maps to verified value creation per unit of capital"

def AgedInventoryShareMetric : Prop :=
  "percentage of inventory over a specified age threshold - maps to verification time and inventory health"

def FixedOperatingExpenseMetric : Prop :=
  "fixed operating expense per quarter - maps to capital intensity and operating leverage"

def AdjustedEBITDAMetric : Prop :=
  "adjusted EBITDA - maps to profitability propagation and time violence reduction"

def RevenueGrowthMetric : Prop :=
  "year-over-year revenue growth - maps to propagation of operating improvements through to revenue"

def ForwardAdjustedNetIncomeMetric : Prop :=
  "forward adjusted net income - maps to durability of profitability"

def CheckpointThreshold : Prop :=
  "a threshold value for an operating metric that serves as a falsifiable checkpoint"

def PassDirectionally : Prop :=
  "metric moves in the predicted direction but may not fully meet threshold"

def Pass : Prop :=
  "metric meets or exceeds the declared threshold"

def Fail : Prop :=
  "metric does not meet the declared threshold"

def MarketRecognition : Prop :=
  "the market's repricing of a company in response to operating improvements - maps to network relativity and verification latency"

def NetworkRelativityClaimForCompany : Prop :=
  "the claim that a company closer to the future (faster verification of operating improvements) will experience temporal dilation relative to the market - the market should be slower to recognize improvements than the company is to make them"

def FalsificationCondition : Prop :=
  "a condition under which the operating thesis is falsified - typically failure of operating improvements to propagate to profitability by the declared horizon"

def CurrentConfirmationState : Prop :=
  "the current state of confirmation or falsification for a market prediction"

def PartiallyConfirmedState : Prop :=
  "some operating checkpoints pass, but profitability or market recognition remains unproven"

def UnresolvedState : Prop :=
  "the prediction has not been resolved - insufficient evidence to confirm or falsify"

def FailedState : Prop :=
  "the prediction has been falsified by observed outcomes"

def open_case_study_pod_configurationPayload :=
  "OPEN (Opendoor) is a MarketPodConfiguration where acquisition volume, contribution margin, aged inventory share, fixed operating expense, adjusted EBITDA, revenue growth, and forward adjusted net income are the observable metrics mapping to the fund's foresight efficiency and time violence concepts"
axiom open_case_study_pod_configuration_auth : Axiom.AuthenticatedTerm ("hitchhiker2thefuture", open_case_study_pod_configurationPayload, 1786969825)
def open_case_study_pod_configuration : Axiom.Statement "hitchhiker2thefuture" open_case_study_pod_configurationPayload 1786969825 := ⟨open_case_study_pod_configuration_auth⟩

def open_case_study_prediction_structurePayload :=
  "The fund's structure predicts that if Opendoor's operating metrics improve (acquisition volume scales, contribution margin improves, aged inventory decreases, fixed operating expense remains bounded), then either profitability follows (adjusted EBITDA turns positive, forward adjusted net income becomes positive) OR time violence increases (market distrust, uncertainty, verification latency prevents market recognition)"
axiom open_case_study_prediction_structure_auth : Axiom.AuthenticatedTerm ("hitchhiker2thefuture", open_case_study_prediction_structurePayload, 1786969825)
def open_case_study_prediction_structure : Axiom.Statement "hitchhiker2thefuture" open_case_study_prediction_structurePayload 1786969825 := ⟨open_case_study_prediction_structure_auth⟩

def open_case_study_network_relativity_claimPayload :=
  "The November 14, 2025 invocation of network relativity for OPEN claims that Opendoor was closer to the future than the market - faster verification of operating improvements should create temporal dilation where the market is slower to recognize improvements than the company is to make them"
axiom open_case_study_network_relativity_claim_auth : Axiom.AuthenticatedTerm ("hitchhiker2thefuture", open_case_study_network_relativity_claimPayload, 1786969825)
def open_case_study_network_relativity_claim : Axiom.Statement "hitchhiker2thefuture" open_case_study_network_relativity_claimPayload 1786969825 := ⟨open_case_study_network_relativity_claim_auth⟩

def open_case_study_current_state_as_of_august_14_2026Payload :=
  "As of August 14, 2026, the OPEN case study is in a PartiallyConfirmedState: upstream operating checkpoints (acquisition volume, contribution margin, aged inventory, fixed operating expense) pass directionally or pass, but downstream profitability (adjusted EBITDA) fails at -$4M, revenue growth is guidance not outcome, forward adjusted net income is management target not outcome, and market recognition (OPEN > $10) failed as a short-horizon prediction"
axiom open_case_study_current_state_as_of_august_14_2026_auth : Axiom.AuthenticatedTerm ("hitchhiker2thefuture", open_case_study_current_state_as_of_august_14_2026Payload, 1786969825)
def open_case_study_current_state_as_of_august_14_2026 : Axiom.Statement "hitchhiker2thefuture" open_case_study_current_state_as_of_august_14_2026Payload 1786969825 := ⟨open_case_study_current_state_as_of_august_14_2026_auth⟩

def open_case_study_declared_falsifiersPayload :=
  "The OPEN case study declares falsifiers: two consecutive checkpoints show volume below 4,000 homes while scaling; aged inventory rises above 15% or contribution margin falls below 4% at elevated volume; fixed operating expense rises above $35M without unit-economic improvement; by December 31, 2026, operating improvements have not propagated to positive adjusted EBITDA or forward adjusted net income"
axiom open_case_study_declared_falsifiers_auth : Axiom.AuthenticatedTerm ("hitchhiker2thefuture", open_case_study_declared_falsifiersPayload, 1786969825)
def open_case_study_declared_falsifiers : Axiom.Statement "hitchhiker2thefuture" open_case_study_declared_falsifiersPayload 1786969825 := ⟨open_case_study_declared_falsifiers_auth⟩

def open_case_study_bull_casePayload :=
  "The bull case for OPEN is not that the price must recover, but that acquisition contracts and homes purchased have reached scale that can feed future revenue, contribution margin and aged inventory metrics are within declared thresholds, management says existing volume and cost base can produce forward adjusted net income profitability without housing market recovery, and faster inventory turns and Cash Now More Later product may reduce capital intensity per home"
axiom open_case_study_bull_case_auth : Axiom.AuthenticatedTerm ("hitchhiker2thefuture", open_case_study_bull_casePayload, 1786969825)
def open_case_study_bull_case : Axiom.Statement "hitchhiker2thefuture" open_case_study_bull_casePayload 1786969825 := ⟨open_case_study_bull_case_auth⟩

def open_case_study_bear_casePayload :=
  "The bear case for OPEN includes: adjusted EBITDA remained negative; Q2 revenue and homes sold were below year-ago comparison despite stronger acquisition volume; real-estate inventory and working-capital requirements can rise while scaling acquisitions; GAAP losses, dilution, financing, housing demand, cancellations, and inventory carrying costs can interrupt the propagation chain; the market may continue to discount the business even if upstream operating metrics improve"
axiom open_case_study_bear_case_auth : Axiom.AuthenticatedTerm ("hitchhiker2thefuture", open_case_study_bear_casePayload, 1786969825)
def open_case_study_bear_case : Axiom.Statement "hitchhiker2thefuture" open_case_study_bear_casePayload 1786969825 := ⟨open_case_study_bear_case_auth⟩

def open_case_study_position_boundaryPayload :=
  "The OPEN case study does not claim that the author currently owns OPEN or realized a gain or loss. The archive contains a paper-trade declaration (200 shares at $8.63), but the verified position ledger is empty. Actual position performance is not established because no verified brokerage statement was supplied"axiom open_case_study_position_boundary_auth : Axiom.AuthenticatedTerm ("hitchhiker2thefuture", open_case_study_position_boundaryPayload, 1786969825)
def open_case_study_position_boundary : Axiom.Statement "hitchhiker2thefuture" open_case_study_position_boundaryPayload 1786969825 := ⟨open_case_study_position_boundary_auth⟩

end fab8hqgj