Research-Stack/0-Core-Formalism/lean/external/OTOM/Tape.lean

317 lines
11 KiB
Text
Raw Permalink Blame History

This file contains ambiguous Unicode characters

This file contains Unicode characters that might be confused with other characters. If you think that this is intentional, you can safely ignore this warning. Use the Escape button to reveal them.

import Semantics.FixedPoint
namespace Semantics.Tape
/-! # Topological Tape Machine
Ported from `infra/access_control/topological_tape_machine.py`.
Pure state transition core only — all I/O (sqlite, JSON, hashlib, time)
is deleted per the formalization boundary.
-/
/-- Ternary clock modes / transition regimes. -/
inductive ControlMode
| accumulate
| commit
| divergence
| heatSink
deriving Repr, BEq, DecidableEq
/-- Minimal invariant vector I = (o, a, p, t). -/
structure InvariantVector where
occupancy : Q16_16
adjacency : Q16_16
path : Q16_16
trust : Q16_16
deriving Repr, DecidableEq
/-- Survival mask for morphism validity. -/
structure InvariantMask where
occupancySurvives : Bool
adjacencySurvives : Bool
pathSurvives : Bool
trustSurvives : Bool
deriving Repr, DecidableEq
namespace InvariantVector
def toMask (inv : InvariantVector) (thresholds : InvariantVector) : InvariantMask :=
{ occupancySurvives := Q16_16.ge inv.occupancy thresholds.occupancy
, adjacencySurvives := Q16_16.ge inv.adjacency thresholds.adjacency
, pathSurvives := Q16_16.ge inv.path thresholds.path
, trustSurvives := Q16_16.ge inv.trust thresholds.trust }
def survives (inv : InvariantVector) (required : InvariantMask) (thresholds : InvariantVector) : Bool :=
let mask := toMask inv thresholds
(!required.occupancySurvives || mask.occupancySurvives) &&
(!required.adjacencySurvives || mask.adjacencySurvives) &&
(!required.pathSurvives || mask.pathSurvives) &&
(!required.trustSurvives || mask.trustSurvives)
end InvariantVector
/-- Minimal lawful-formation event. -/
structure BraidEvent where
eventId : String
parentIds : List String
stateCommitment : String
domain : String
timestamp : Nat
structuralValidity : Bool
crossingSignature : String
deriving Repr, DecidableEq
/-- Ordered witness structure B = (e_1, e_2, ..., e_n). -/
structure BraidTrace where
events : List BraidEvent
deriving Repr, DecidableEq
namespace BraidTrace
def empty : BraidTrace := ⟨[]⟩
def append (bt : BraidTrace) (e : BraidEvent) : BraidTrace :=
{ events := e :: bt.events }
def lastCommitment (bt : BraidTrace) : Option String :=
match bt.events with
| [] => none
| e :: _ => some e.stateCommitment
/-- Stage 1: local braid validity. -/
def isValid (bt : BraidTrace) (durabilityThreshold : Nat) : Bool :=
bt.events.length ≥ durabilityThreshold &&
bt.events.all (λ e => e.structuralValidity)
end BraidTrace
/-- Primary machine object S = (μ, I, B, σ, c, h) with KOT accounting.
KOT fields use Rat because physical constants (e.g. 2.9e-21 J) are outside Q16_16 range. -/
structure TapeState where
mode : ControlMode
invariants : InvariantVector
braid : BraidTrace
confidence : Q16_16
kotAccumulated : Rat
kotYieldProjected : Rat
deriving Repr, DecidableEq
namespace TapeState
def default : TapeState := {
mode := ControlMode.accumulate,
invariants := { occupancy := Q16_16.zero, adjacency := Q16_16.zero,
path := Q16_16.zero, trust := Q16_16.zero },
braid := BraidTrace.empty,
confidence := Q16_16.zero,
kotAccumulated := 0,
kotYieldProjected := 0
}
/-- Basic stability: occupancy and confidence above 0.5. -/
def isStable (s : TapeState) : Bool :=
let half := Q16_16.div (Q16_16.ofInt 1) (Q16_16.ofInt 2)
Q16_16.ge s.invariants.occupancy half && Q16_16.ge s.confidence half
end TapeState
/-- Kinetic Operation Token ledger entry.
Rat is used for physical constants outside Q16_16 range. -/
structure KOTLedger where
subregisterId : String
joulesTotal : Rat
landauerFloor : Rat
landauerRatio : Rat
etaTotal : Rat
kotTotal : Rat
decision : String
deriving Repr, DecidableEq
/-- Budget envelope for KOT. -/
structure KOTBudget where
authorized : Rat
consumed : Rat
deriving Repr, DecidableEq
namespace KOTBudget
def empty (auth : Rat) : KOTBudget := { authorized := auth, consumed := 0 }
def canAfford (b : KOTBudget) (cost : Rat) : Bool :=
b.consumed + cost ≤ b.authorized
def spend (b : KOTBudget) (entry : KOTLedger) : KOTBudget :=
{ b with consumed := b.consumed + entry.kotTotal }
/-- Economic viability evaluation. -/
def evaluateEconomics (b : KOTBudget) (projectedYield : Rat) (gasThreshold : Rat) : String :=
if projectedYield < b.consumed then "PAUSE"
else if b.consumed > 0 && (b.consumed / projectedYield) > gasThreshold then "PAUSE"
else if b.consumed ≥ b.authorized then "KILL"
else "CONTINUE"
end KOTBudget
/-- Pure topological tape machine state. -/
structure TapeMachine where
budget : KOTBudget
thresholds : InvariantVector
lambdaWeights : List (String × Rat)
tape : List TapeState
deriving Repr, DecidableEq
namespace TapeMachine
def empty : TapeMachine := {
budget := KOTBudget.empty 0,
thresholds := { occupancy := Q16_16.ofInt 0, adjacency := Q16_16.ofInt 0,
path := Q16_16.ofInt 0, trust := Q16_16.ofInt 0 },
lambdaWeights := [("+", 1.2), ("0", 1.0), ("-", 0.8)],
tape := []
}
/-- Genesis threshold = 1 event; descendant threshold = 2 events. -/
def validBraid (braid : BraidTrace) (isGenesis : Bool) : Bool :=
let threshold := if isGenesis then 1 else 2
braid.isValid threshold
/-- Stage 2: morphism validity.
State must be stable, invariants must survive, and no silent vanish. -/
def validMorphism (tm : TapeMachine) (state : TapeState) : Bool :=
if !state.isStable then false else
let required := { occupancySurvives := true, adjacencySurvives := true,
pathSurvives := false, trustSurvives := false }
if !state.invariants.survives required tm.thresholds then false else
-- No silent vanish: not all invariants may be zero simultaneously
let allZero := state.invariants.occupancy == Q16_16.zero &&
state.invariants.adjacency == Q16_16.zero &&
state.invariants.path == Q16_16.zero &&
state.invariants.trust == Q16_16.zero
!allZero
/-- Acceptance predicate: braid AND morphism must hold. -/
def accept (tm : TapeMachine) (state : TapeState) : Bool :=
let isGenesis := tm.tape.isEmpty
validBraid state.braid isGenesis && validMorphism tm state
/-- Simplified structure compression.
Python version called PBACSContextCompressor; here we keep only the pure contract. -/
def compressStructure (data : List UInt8) : List UInt8 :=
-- Formalization boundary: compression is an external oracle.
-- The tape machine only requires that the result fits the invariant predicates.
data
/-- Compute invariants from structure.
Placeholder faithful to the Python shape but using Q16_16 ratios. -/
def computeInvariants (data : List UInt8) : InvariantVector :=
let len := data.length
let unique := (List.foldl (λ acc x => if acc.contains x then acc else acc ++ [x]) [] data).length
let entropy : Float := if len == 0 then 0.0 else Nat.toFloat unique / len.toFloat
-- Placeholder: map entropy to Q16_16 bounded in [0,1]
let entropyQ := Q16_16.ofFloat entropy
let occupancy := Q16_16.max (Q16_16.div (Q16_16.ofInt 1) (Q16_16.ofInt 2))
(Q16_16.min Q16_16.one (Q16_16.ofFloat (len.toFloat / 100.0)))
{ occupancy := occupancy
, adjacency := Q16_16.max (Q16_16.div (Q16_16.ofInt 1) (Q16_16.ofInt 2)) entropyQ
, path := Q16_16.ofFloat 0.7
, trust := Q16_16.ofFloat 0.8 }
/-- Compute confidence score. -/
def computeConfidence (_data : List UInt8) : Q16_16 :=
Q16_16.ofFloat 0.75
/-- Apply control-mode transition law. -/
def applyTransitionLaw (state : TapeState) : TapeState :=
if state.isStable && state.mode == ControlMode.accumulate then
{ state with mode := ControlMode.commit }
else
state
/-- Simulated energy measurement.
In production this comes from hardware/JEDEC. -/
def measureEnergy (data : List UInt8) (mode : ControlMode) : Rat :=
let len := data.length
let baseEnergy : Rat := (232 : Rat) / (10^16 : Rat) * (len : Rat)
let modeMultiplier : Rat := match mode with
| .accumulate => 1.5
| .commit => 1.0
| .divergence => 0.8
| .heatSink => 1.0
baseEnergy * modeMultiplier
/-- Calculate KOT for operation. -/
def accountKot (tm : TapeMachine) (state : TapeState) (mode : ControlMode) : KOTLedger :=
let joules := measureEnergy [] mode
let etaIso : List (String × Rat) := [("rw", 0.9), ("locality", 0.85),
("batch", 0.95), ("throughput", 0.88)]
let etaTotal := etaIso.foldl (λ acc (_, v) => acc * v) 1.0
let landauerFloor : Rat := 2.9e-21
let landauerRatio := if landauerFloor > 0 then joules / landauerFloor else 0
let modeStr := match mode with
| .accumulate => "+"
| .commit => "0"
| .divergence => "-"
| .heatSink => "!"
let lambdaMode := match tm.lambdaWeights.lookup modeStr with | some v => v | none => 1.0
let kot := lambdaMode * landauerRatio * etaTotal
let entry := { subregisterId := ""
, joulesTotal := joules
, landauerFloor := landauerFloor
, landauerRatio := landauerRatio
, etaTotal := etaTotal
, kotTotal := kot
, decision := "CONTINUE" }
let newBudget := tm.budget.spend entry
let decision := KOTBudget.evaluateEconomics newBudget state.kotYieldProjected (1 / 10 : Rat)
{ entry with decision := decision }
/-- Form a new tape state from normalized input. -/
def formState (tm : TapeMachine) (data : List UInt8) (contextType : String) : TapeState :=
let compressed := compressStructure data
let invariants := computeInvariants compressed
let confidence := computeConfidence compressed
let parentCommitment := match tm.tape with
| _ :: _ => "prev_state"
| [] => "genesis"
let event1 : BraidEvent := {
eventId := "event_" ++ parentCommitment ++ "_" ++ contextType,
parentIds := [parentCommitment],
stateCommitment := "commit_" ++ contextType,
domain := contextType,
timestamp := tm.tape.length,
structuralValidity := true,
crossingSignature := "genesis"
}
let braid1 := BraidTrace.empty.append event1
let braid2 := if !tm.tape.isEmpty then
let event2 : BraidEvent := {
eventId := "durability_" ++ contextType,
parentIds := [event1.eventId],
stateCommitment := "durability_commit",
domain := contextType ++ "_witness",
timestamp := tm.tape.length + 1,
structuralValidity := true,
crossingSignature := "valid"
}
braid1.append event2
else
braid1
let baseState := { TapeState.default with
invariants := invariants,
confidence := confidence,
braid := braid2
}
let transitioned := applyTransitionLaw baseState
let kotEntry := accountKot tm transitioned transitioned.mode
{ transitioned with kotAccumulated := kotEntry.kotTotal }
/-- Ingest: single entry point. Returns new state and updated machine. -/
def ingest (tm : TapeMachine) (data : List UInt8) (contextType : String) : Option (TapeState × TapeMachine) :=
let state := formState tm data contextType
if accept tm state then
some (state, { tm with tape := state :: tm.tape })
else
none
end TapeMachine
end Semantics.Tape