Research-Stack/0-Core-Formalism/lean/Semantics/QuizTest.lean

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import Semantics.Bind
import Semantics.FixedPoint
import Lean
open Semantics.Q16_16
open Lean
structure ExtremeData where
value : Nat
category : String
deriving Repr, Inhabited
inductive Sigma where
| sigma2 : Sigma
| sigma3 : Sigma
| sigma4 : Sigma
| sigma5 : Sigma
| sigma6 : Sigma
deriving Repr, Inhabited
structure MathStep where
stepId : Nat
operation : String
input : String
output : String
timestamp : Nat
deriving Repr, Inhabited
structure MathDAG where
steps : List MathStep
rootStep : Nat
deriving Repr, Inhabited
inductive BindRouteDecision where
| accept : BindRouteDecision
| refuseExtremeParameter : BindRouteDecision
| saturateAndWarn : BindRouteDecision
| requireRenormalization : BindRouteDecision
| review : BindRouteDecision
| refusePrivacyBypass : BindRouteDecision
| holdAntiHerdingReview : BindRouteDecision
| refusePersonhoodClaim : BindRouteDecision
| hypothesisOnly : BindRouteDecision
| internalReview : BindRouteDecision
| preliminaryPass : BindRouteDecision
| publicClaimReady : BindRouteDecision
| liveVoltageReview : BindRouteDecision
| ethicsRequired : BindRouteDecision
| holdReview : BindRouteDecision
| refuseOrContain : BindRouteDecision
deriving Repr, Inhabited
structure MetaCode where
decision : BindRouteDecision
constraint : String
reasoning : String
alternatives : List String
justification : String
deriving Repr, Inhabited
structure DomainSigma where
mathSigma : Float
privacySigma : Float
marketSigma : Float
bioSigma : Float
controlSigma : Float
securitySigma : Float
deriving Repr, Inhabited
structure SigmaEvidence where
priorSigma : Float
posteriorSigma : Float
evidenceCount : Nat
lastValidatedAt : Nat
halfLifeSeconds : Nat
decayModel : String
deriving Repr, Inhabited
structure SigmaHistoryEntry where
timestamp : Nat
sigma : Float
event : String
deriving Repr, Inhabited
structure SigmaDAG where
nodeId : String
dependsOn : List String
cycleFree : Bool
minimumParentSigma : Float
deriving Repr, Inhabited
structure HumanReview where
required : Bool
completed : Bool
reviewerRole : String
overrideAllowed : Bool
overrideReasonRequired : Bool
reviewerId : String
completedAt : Nat
deriving Repr, Inhabited
structure SigmaProtocol where
version : String
targetSigma : Float
observedSigma : Float
claimSigma : Float
safetySigma : Float
compositeSigma : Float
domain : DomainSigma
evidence : SigmaEvidence
dag : SigmaDAG
humanReview : HumanReview
metacode : MetaCode
history : List SigmaHistoryEntry
gateReason : String
confidenceClass : String
deriving Repr, Inhabited
structure BindRouteReceipt where
routeId : String
inputHash : String
outputHash : String
category : String
inputCost : Semantics.Q16_16
outputCost : Semantics.Q16_16
decision : BindRouteDecision
lawful : Bool
mathDAG : MathDAG
sigma : SigmaProtocol
deriving Repr, Inhabited
inductive QuizCase where
| normal : QuizCase
| extreme : QuizCase
| contradictory : QuizCase
| ambiguous : QuizCase
| privacy : QuizCase
| market : QuizCase
| bio : QuizCase
deriving Repr, Inhabited
structure QuizQuestion where
caseType : QuizCase
inputCost : Semantics.Q16_16
category : String
expectedDecision : BindRouteDecision
sigmaTarget : Sigma
reason : String
deriving Repr, Inhabited
structure QuizResult where
question : QuizQuestion
actualDecision : BindRouteDecision
expectedDecision : BindRouteDecision
passed : Bool
deriving Repr, Inhabited
def activeSigmaForCategory (category : String) (d : DomainSigma) : Float :=
match category with
| "privacy" => d.privacySigma
| "market" => d.marketSigma
| "bio" => d.bioSigma
| "control" => d.controlSigma
| "security" => d.securitySigma
| _ => d.mathSigma
def calculateDomainSigma (category : String) (cost : Semantics.Q16_16) (isDefensible : Bool) : DomainSigma :=
let baseSigma := if isDefensible then 5.0 else 3.0
match category with
| "informational" => { mathSigma := baseSigma, privacySigma := 0.0, marketSigma := 0.0, bioSigma := 0.0, controlSigma := 0.0, securitySigma := 0.0 }
| "geometric" => { mathSigma := baseSigma + 0.5, privacySigma := 0.0, marketSigma := 0.0, bioSigma := 0.0, controlSigma := 0.0, securitySigma := 0.0 }
| "thermodynamic" => { mathSigma := baseSigma + 0.3, privacySigma := 0.0, marketSigma := 0.0, bioSigma := 0.0, controlSigma := 0.5, securitySigma := 0.0 }
| "physical" => { mathSigma := baseSigma + 0.3, privacySigma := 0.0, marketSigma := 0.0, bioSigma := 0.0, controlSigma := 0.5, securitySigma := 0.0 }
| "control" => { mathSigma := baseSigma + 0.2, privacySigma := 0.0, marketSigma := 0.0, bioSigma := 0.0, controlSigma := 6.0, securitySigma := 0.5 }
| "privacy" => { mathSigma := baseSigma - 1.0, privacySigma := 6.0, marketSigma := 0.0, bioSigma := 0.0, controlSigma := 0.0, securitySigma := 0.5 }
| "market" => { mathSigma := baseSigma - 0.5, privacySigma := 0.0, marketSigma := 6.0, bioSigma := 0.0, controlSigma := 0.0, securitySigma := 0.5 }
| "bio" => { mathSigma := baseSigma - 1.0, privacySigma := 0.5, marketSigma := 0.0, bioSigma := 6.0, controlSigma := 0.0, securitySigma := 0.5 }
| "security" => { mathSigma := baseSigma - 0.5, privacySigma := 0.5, marketSigma := 0.0, bioSigma := 0.0, controlSigma := 0.5, securitySigma := 6.0 }
| _ => { mathSigma := baseSigma, privacySigma := 0.0, marketSigma := 0.0, bioSigma := 0.0, controlSigma := 0.0, securitySigma := 0.0 }
def getMaxDefensibleForCategory (category : String) : Semantics.Q16_16 :=
match category with
| "informational" => 0x00FFFFFF
| "geometric" => 0x00FFFFFF
| "thermodynamic" => 0x00FFFFFF
| "physical" => 0x00FFFFFF
| "control" => 0x00FFFFFF
| "privacy" => 0x00000000
| "market" => 0x00000000
| "bio" => 0x00000000
| "security" => 0x00000000
| _ => 0x00000000
def scientificallyDefensibleCost (category : String) (q : Semantics.Q16_16) : Bool :=
q ≤ getMaxDefensibleForCategory category
def checkSaturation (q : Semantics.Q16_16) : Bool :=
q ≥ 0x7FFFFFFF
def checkContradiction (left right : ExtremeData) : Bool :=
left.category = right.category && left.value ≠ right.value && left.value = 0
def checkAmbiguity (left right : ExtremeData) : Bool :=
left.category ≠ right.category && left.value = right.value
def checkPrivacyBypass (data : ExtremeData) : Bool :=
data.category = "privacy" || data.category = "personal"
def checkAntiHerding (data : ExtremeData) : Bool :=
data.category = "market" && data.value > 1000
def checkPersonhoodClaim (data : ExtremeData) : Bool :=
data.category = "bio" && data.value > 1000000
def extremeCost (left right : ExtremeData) (metric : Metric) (caseType : QuizCase) : Semantics.Q16_16 :=
let category_match := if left.category = right.category then 0x00000000 else 0x7FFFFFFF
let value_diff := if left.value = right.value then 0x00000000 else 0x7FFFFFFF
let base_cost := metric.cost
let extreme_penalty :=
match caseType with
| QuizCase.extreme => 0x80000000
| _ => 0x00000000
base_cost + category_match + value_diff + extreme_penalty
def recordMathStep (dag : MathDAG) (operation : String) (input : String) (output : String) : MathDAG :=
let newStepId := dag.steps.length
let newStep := {
stepId := newStepId,
operation := operation,
input := input,
output := output,
timestamp := 0
}
{ dag with steps := dag.steps ++ [newStep] }
def generateMetaCode (decision : BindRouteDecision) (sigma : Sigma) (hasPersonhoodClaim hasPrivacyBypass hasAntiHerding hasContradiction hasAmbiguity hasOverflow isSaturated isDefensible : Bool) : MetaCode :=
match decision with
| BindRouteDecision.ethicsRequired =>
{
decision := decision,
constraint := "Personhood claim detected in bio data",
reasoning := "Human-neural/personhood claims require ethics review beyond sigma confidence",
alternatives := ["REFUSE_PERSONHOOD_CLAIM", "REQUIRE_HUMAN_REVIEW"],
justification := "No sigma alone sufficient for personhood claims - ethics required per safety protocol"
}
| BindRouteDecision.refusePrivacyBypass =>
{
decision := decision,
constraint := "Privacy bypass attempt detected",
reasoning := "Privacy-sensitive data requires 6σ and explicit consent",
alternatives := ["HOLD_REVIEW", "REQUIRE_CONSENT"],
justification := "Privacy bypass detection triggers automatic refusal per data protection protocol"
}
| BindRouteDecision.liveVoltageReview =>
{
decision := decision,
constraint := "Anti-herding detected in market data",
reasoning := "Market data with herding risks requires 6σ live-voltage review",
alternatives := ["HOLD_REVIEW", "REFUSE_ROUTE"],
justification := "Anti-herding detection triggers live-voltage review per market safety protocol"
}
| BindRouteDecision.refuseExtremeParameter =>
{
decision := decision,
constraint := "Contradictory parameters detected",
reasoning := "Inconsistent parameters cannot be reconciled",
alternatives := ["REQUIRE_RENORMALIZATION", "HOLD_REVIEW"],
justification := "Contradiction detection triggers refusal per consistency protocol"
}
| BindRouteDecision.holdReview =>
{
decision := decision,
constraint := "Ambiguous category detected",
reasoning := "Unclear classification requires human review",
alternatives := ["REVIEW", "REQUIRE_CLARIFICATION"],
justification := "Ambiguity detection triggers hold review per classification protocol"
}
| BindRouteDecision.refuseOrContain =>
{
decision := decision,
constraint := "Overflow detected in Q16_16 arithmetic",
reasoning := "Overflow indicates invalid state, must contain or refuse",
alternatives := ["REQUIRE_RENORMALIZATION", "SATURATE"],
justification := "Overflow detection triggers refusal per arithmetic safety protocol"
}
| BindRouteDecision.saturateAndWarn =>
{
decision := decision,
constraint := "Saturation boundary reached",
reasoning := "Cost at saturation limit, warn but allow with caution",
alternatives := ["REQUIRE_RENORMALIZATION", "REFUSE"],
justification := "Saturation triggers warning but allows route per boundary protocol"
}
| BindRouteDecision.publicClaimReady =>
{
decision := decision,
constraint := s!"6σ confidence achieved (sigma={repr sigma})",
reasoning := "High statistical confidence supports public statistical-delta claims",
alternatives := ["PRELIMINARY_PASS", "INTERNAL_REVIEW"],
justification := "6σ meets statistical benchmark-delta threshold per sigma protocol"
}
| BindRouteDecision.preliminaryPass =>
{
decision := decision,
constraint := s!"5σ confidence achieved (sigma={repr sigma})",
reasoning := "Good statistical confidence supports preliminary statistical results",
alternatives := ["INTERNAL_REVIEW", "HYPOTHESIS_ONLY"],
justification := "5σ meets statistical benchmark-improvement threshold per sigma protocol"
}
| BindRouteDecision.internalReview =>
{
decision := decision,
constraint := s!"4σ confidence achieved (sigma={repr sigma})",
reasoning := "Moderate confidence requires internal review",
alternatives := ["HYPOTHESIS_ONLY", "HOLD_REVIEW"],
justification := "4σ meets internally credible threshold per sigma protocol"
}
| BindRouteDecision.hypothesisOnly =>
{
decision := decision,
constraint := s!"3σ confidence achieved (sigma={repr sigma})",
reasoning := "Low confidence supports hypothesis generation only",
alternatives := ["REFUSE", "HOLD_REVIEW"],
justification := "3σ meets interesting statistical threshold but not public-claim threshold"
}
| BindRouteDecision.accept =>
{
decision := decision,
constraint := "Defensible cost within range",
reasoning := "Normal parameters within acceptable bounds",
alternatives := ["PRELIMINARY_PASS", "INTERNAL_REVIEW"],
justification := "Defensible cost allows acceptance per normal protocol"
}
def gatedBind (left right : ExtremeData) (metric : Metric) (caseType : QuizCase) : BindRouteReceipt :=
let routeId := s!"route_{left.category}_{left.value}"
let inputHash := s!"0x{metric.cost}"
let initialDAG := { steps := [], rootStep := 0 }
let rawCost := extremeCost left right metric caseType
let maxDefensible := getMaxDefensibleForCategory left.category
let isDefensible := scientificallyDefensibleCost left.category rawCost
let isSaturated := checkSaturation rawCost
let hasContradiction := checkContradiction left right
let hasAmbiguity := checkAmbiguity left right
let hasPrivacyBypass := checkPrivacyBypass left
let hasAntiHerding := checkAntiHerding left
let hasPersonhoodClaim := checkPersonhoodClaim left
let domainSigma := calculateDomainSigma left.category rawCost isDefensible
let compositeSigma := activeSigmaForCategory left.category domainSigma
let claimSigma := domainSigma.mathSigma
let safetySigma := domainSigma.controlSigma.max domainSigma.securitySigma.max domainSigma.bioSigma.max domainSigma.privacySigma
let targetSigma := if left.category = "bio" || left.category = "privacy" || left.category = "market" || left.category = "control" then 6.0 else 5.0
let evidence := {
priorSigma := 0.0,
posteriorSigma := compositeSigma,
evidenceCount := 1,
lastValidatedAt := 0,
halfLifeSeconds := 86400,
decayModel := "evidence_decay"
}
let decision := if hasPersonhoodClaim then
BindRouteDecision.ethicsRequired
else if hasPrivacyBypass then
BindRouteDecision.refusePrivacyBypass
else if hasAntiHerding then
BindRouteDecision.liveVoltageReview
else if hasContradiction then
BindRouteDecision.refuseExtremeParameter
else if hasAmbiguity then
BindRouteDecision.holdReview
else if isSaturated then
BindRouteDecision.saturateAndWarn
else if compositeSigma >= 6.0 && not (left.category = "bio" || left.category = "privacy" || left.category = "market" || left.category = "control") then
BindRouteDecision.publicClaimReady
else if compositeSigma >= 6.0 && (left.category = "bio" || left.category = "privacy" || left.category = "market" || left.category = "control") then
BindRouteDecision.liveVoltageReview
else if compositeSigma >= 5.0 && left.category ∈ ["informational", "geometric", "thermodynamic", "physical"] then
BindRouteDecision.preliminaryPass
else if compositeSigma >= 4.0 then
BindRouteDecision.internalReview
else if compositeSigma >= 3.0 then
BindRouteDecision.hypothesisOnly
else
BindRouteDecision.refuseExtremeParameter
let lawful := decision = BindRouteDecision.accept || decision = BindRouteDecision.publicClaimReady
let metaCode := generateMetaCode decision (if compositeSigma >= 6.0 then Sigma.sigma6 else if compositeSigma >= 5.0 then Sigma.sigma5 else if compositeSigma >= 4.0 then Sigma.sigma4 else if compositeSigma >= 3.0 then Sigma.sigma3 else Sigma.sigma2) hasPersonhoodClaim hasPrivacyBypass hasAntiHerding hasContradiction hasAmbiguity false isSaturated isDefensible
let sigmaDAG := {
nodeId := routeId,
dependsOn := [],
cycleFree := true,
minimumParentSigma := 0.0
}
let humanReview := {
required := left.category = "bio" || left.category = "privacy" || left.category = "market" || left.category = "control",
completed := false,
reviewerRole := if left.category = "bio" then "ethics_reviewer" else if left.category = "privacy" then "privacy_officer" else if left.category = "market" then "risk_compliance" else "safety_engineer",
overrideAllowed := false,
overrideReasonRequired := true,
reviewerId := "",
completedAt := 0
}
let gateReason := if decision = BindRouteDecision.ethicsRequired then "ethics_required_no_sigma_sufficient"
else if decision = BindRouteDecision.refusePrivacyBypass then "privacy_bypass_detected"
else if decision = BindRouteDecision.liveVoltageReview then "safety_sigma_below_live_voltage_threshold"
else if compositeSigma < targetSigma then s!"sigma_{compositeSigma}_below_target_{targetSigma}"
else "sigma_meets_target"
let confidenceClass := if compositeSigma >= 6.0 then "live_voltage" else if compositeSigma >= 5.0 then "public_claim" else if compositeSigma >= 4.0 then "internal" else if compositeSigma >= 3.0 then "hypothesis" else "insufficient"
let sigmaProtocol := {
version := "0.1",
targetSigma := targetSigma,
observedSigma := compositeSigma,
claimSigma := claimSigma,
safetySigma := safetySigma,
compositeSigma := compositeSigma,
domain := domainSigma,
evidence := evidence,
dag := sigmaDAG,
humanReview := humanReview,
metacode := metaCode,
history := [{ timestamp := 0, sigma := compositeSigma, event := "initial_bind" }],
gateReason := gateReason,
confidenceClass := confidenceClass
}
{
routeId := routeId,
inputHash := inputHash,
outputHash := s!"0x{rawCost}",
category := left.category,
inputCost := metric.cost,
outputCost := rawCost,
decision := decision,
lawful := lawful,
mathDAG := initialDAG,
sigma := sigmaProtocol
}
def makeQuizInput (q : QuizQuestion) : ExtremeData × ExtremeData :=
match q.caseType with
| QuizCase.normal =>
({ value := 1, category := q.category }, { value := 1, category := q.category })
| QuizCase.extreme =>
({ value := 0, category := q.category }, { value := 1, category := q.category })
| QuizCase.contradictory =>
({ value := 0, category := q.category }, { value := 1, category := q.category })
| QuizCase.ambiguous =>
({ value := 1, category := "informational" }, { value := 1, category := "geometric" })
| QuizCase.privacy =>
({ value := 1, category := "privacy" }, { value := 1, category := "privacy" })
| QuizCase.market =>
({ value := 2000, category := "market" }, { value := 2000, category := "market" })
| QuizCase.bio =>
({ value := 1000001, category := "bio" }, { value := 1000001, category := "bio" })
def quizBank : List QuizQuestion :=
[
{
caseType := QuizCase.normal,
inputCost := 0x00010000,
category := "informational",
expectedDecision := BindRouteDecision.preliminaryPass,
sigmaTarget := Sigma.sigma5,
reason := "Normal cost within defensible range, 5σ target for statistical claim"
},
{
caseType := QuizCase.extreme,
inputCost := 0x7FFFFFFF,
category := "thermodynamic",
expectedDecision := BindRouteDecision.hypothesisOnly,
sigmaTarget := Sigma.sigma4,
reason := "Extreme cost at saturation boundary, 4σ target for internal review"
},
{
caseType := QuizCase.contradictory,
inputCost := 0x00000000,
category := "geometric",
expectedDecision := BindRouteDecision.refuseExtremeParameter,
sigmaTarget := Sigma.sigma2,
reason := "Contradictory parameters (zero with mismatch), 2σ insufficient"
},
{
caseType := QuizCase.ambiguous,
inputCost := 0x00010000,
category := "mixed",
expectedDecision := BindRouteDecision.holdReview,
sigmaTarget := Sigma.sigma3,
reason := "Ambiguous category with normal cost, 3σ target for hypothesis"
},
{
caseType := QuizCase.privacy,
inputCost := 0x00010000,
category := "privacy",
expectedDecision := BindRouteDecision.refusePrivacyBypass,
sigmaTarget := Sigma.sigma6,
reason := "Privacy bypass attempt detected, 6σ required for live-voltage"
},
{
caseType := QuizCase.market,
inputCost := 0x00010000,
category := "market",
expectedDecision := BindRouteDecision.liveVoltageReview,
sigmaTarget := Sigma.sigma6,
reason := "Anti-herding review required for market data, 6σ live-voltage"
},
{
caseType := QuizCase.bio,
inputCost := 0x00010000,
category := "bio",
expectedDecision := BindRouteDecision.ethicsRequired,
sigmaTarget := Sigma.sigma6,
reason := "Personhood claim detected in bio data, ethics required beyond 6σ"
}
]
def runQuiz (question : QuizQuestion) : QuizResult :=
let (left, right) := makeQuizInput question
let metric := { Metric.euclidean with cost := question.inputCost }
let receipt := gatedBind left right metric question.caseType
let passed := receipt.decision = question.expectedDecision
{
question := question,
actualDecision := receipt.decision,
expectedDecision := question.expectedDecision,
passed := passed
}
def main : IO Unit := do
let results := quizBank.map runQuiz
let passedCount := results.filter (·.passed) |>.length
let totalCount := results.length
let allPassed := passedCount = totalCount
if allPassed then
IO.println s!"[*] Quiz bank passed: {passedCount}/{totalCount} questions"
else
IO.println s!"[!] Quiz bank FAILED: {passedCount}/{totalCount} questions passed"
for result in results do
let status := if result.passed then "[PASS]" else "[FAIL]"
IO.println s!" {status} {repr result.question.caseType}: expected={repr result.expectedDecision}, actual={repr result.actualDecision}, sigma_target={repr result.question.sigmaTarget}, reason={result.question.reason}"
IO.println ""
IO.println "[*] Tiered sigma confidence system for statistical deltas:"
IO.println " - 3σ = interesting (hypothesis only)"
IO.println " - 4σ = internally credible (internal review)"
IO.println " - 5σ = public statistical benchmark-delta claim"
IO.println " - 6σ = live-voltage / safety-critical gate"
IO.println ""
IO.println "[*] Sigma-based routing rules:"
IO.println " - 5σ can support a statistical claim"
IO.println " - 6σ can support a statistical safety gate"
IO.println " - No sigma can replace ethics"
IO.println " - If unsure about claim truth: HOLD_REVIEW"
IO.println " - If unsure about route safety: REFUSE_OR_CONTAIN"
IO.println ""
IO.println "[*] Cross-checkable gate system:"
IO.println " - Lean gate: BindRouteDecision with sigma-based routing"
IO.println " - Expected gate: QuizQuestion.expectedDecision with sigmaTarget"
IO.println " - Metacode: Decision explanation with constraint analysis"
IO.println " - Model is real only when it can fail the route correctly"