Research-Stack/0-Core-Formalism/lean/Semantics/Semantics/ASICTopology.lean
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import Semantics.Bind
import Semantics.FixedPoint
import Semantics.NICProbe
import Lean.Data.Json
namespace Semantics.ASICTopology
/-! ## TopoASIC — ASIC Topology Abstraction Layer
**Core Inversion:**
- Normal view: ASIC = specific chip, fixed function, limited use
- TopoASIC view: ASIC = topology of constrained transformations, routing surface, operation manifold, interfaceable substrate
**Principle:** An ASIC is a crystallized algorithm; TopoASIC treats the crystal as terrain.
**Key Question:** Not "What was this ASIC designed to do?" but "What lawful transformations can this topology perform cheaply?"
**Definition:**
TopoASIC = fixed hardware operation graph + bandwidth/latency/energy constraints + admissible transform set + routing interface + verification receipts
**Capability Vector:**
Each ASIC node: [operation_family, throughput, latency, precision, memory_access_shape, branching_penalty, routing_flexibility, energy_per_transform, thermal_ceiling, verification_surface]
**General Routing Equation:**
Workload W → projection P(W) → ASIC topology T → admissible route R_T → receipt
**Route Validity:**
- cost(P(W), T) < threshold
- semantic_loss < threshold
- verification_pass = true
**Keeper Law:** Do not ask what the chip is. Ask what shape of computation the chip makes easy.
Per AGENTS.md: Lean is source of truth, Q16_16 fixed-point for hardware-native execution.
-/
open Semantics.Q16_16
/-- ASIC topology node types (RTL8126 specific). -/
inductive ASICNode
| dmaEngine -- DMA address translation engine
| checksumUnit -- Checksum computation unit
| txQueue -- Transmit queue (ring buffer)
| rxQueue -- Receive queue (ring buffer)
| descriptorTable -- Descriptor memory layout
| macPhy -- MAC/PHY physical layer
| registerSpace -- MMIO register space
deriving Repr, BEq, DecidableEq
/-- ASIC topology edge types (connections between nodes). -/
inductive ASICEdge
| dmaToQueue -- DMA engine to queue
| queueToDescriptor -- Queue to descriptor table
| descriptorToChecksum -- Descriptor to checksum unit
| checksumToMac -- Checksum to MAC/PHY
| macToPhy -- MAC to PHY
| registerControl -- Register space control path
deriving Repr, BEq, DecidableEq
/-- Operation family classification for capability vector. -/
inductive OperationFamily
| hashPipeline -- Hash-like pipeline operations
| memoryLane -- Memory access operations
| busSegment -- Bus transfer operations
| pipelineStage -- Sequential pipeline operations
| accumulator -- Accumulation operations
| serializer -- Serialization operations
| validator -- Validation/verification operations
| checksumCompute -- Checksum computation
| addressTranslate -- Address translation
| ringBuffer -- Ring buffer operations
deriving Repr, BEq, DecidableEq
/-- Memory access shape classification. -/
inductive MemoryAccessShape
| linearSequential -- Linear sequential access
| randomAccess -- Random access
| strided -- Strided access
| circular -- Circular/ring access
| scatterGather -- Scatter-gather access
deriving Repr, BEq, DecidableEq
/-- Capability vector for ASIC topology node (TopoASIC specification). -/
structure CapabilityVector where
operationFamily : OperationFamily
throughput : Semantics.Q16_16 -- Operations per unit time
latency : Semantics.Q16_16 -- Operation latency
precision : Semantics.Q16_16 -- Precision (bits of accuracy)
memoryAccessShape : MemoryAccessShape
branchingPenalty : Semantics.Q16_16 -- Cost of branching
routingFlexibility : Semantics.Q16_16 -- How flexible routing can be (0-1)
energyPerTransform : Semantics.Q16_16 -- Energy cost per operation
thermalCeiling : Semantics.Q16_16 -- Thermal limit
verificationSurface : Semantics.Q16_16 -- Verification capability (0-1)
deriving Repr
/-- ASIC topology node with geometric properties and capability vector (TopoASIC). -/
structure ASICTopologyNode where
nodeId : Nat
nodeType : ASICNode
position : Array Semantics.Q16_16 -- Position in ASIC topology space
capacity : Nat -- Processing capacity (packets/ops)
latency : Semantics.Q16_16 -- Operation latency
curvature : Semantics.Q16_16 -- Topology curvature at this node
torsion : Semantics.Q16_16 -- Topology torsion at this node
capability : CapabilityVector -- TopoASIC capability vector
deriving Repr
/-- ASIC topology edge with geometric properties. -/
structure ASICTopologyEdge where
sourceNodeId : Nat
targetNodeId : Nat
edgeType : ASICEdge
weight : Semantics.Q16_16 -- Edge weight (cost/bandwidth)
length : Semantics.Q16_16 -- Geodesic length
flowCapacity : Semantics.Q16_16 -- Flow capacity
deriving Repr
/-- Complete ASIC topology structure. -/
structure ASICTopology where
nodes : Array ASICTopologyNode
edges : Array ASICTopologyEdge
globalCurvature : Semantics.Q16_16 -- Overall manifold curvature
globalTorsion : Semantics.Q16_16 -- Overall manifold torsion
dimension : Nat -- Topology dimension
deriving Repr
/-- Default RTL8126 ASIC topology with capability vectors (TopoASIC specification). -/
def rtl8126Topology : ASICTopology := {
nodes := #[ -- 7 nodes representing RTL8126 components with capability vectors
{
nodeId := 0,
nodeType := ASICNode.dmaEngine,
position := #[zero, zero, zero],
capacity := 1000,
latency := 0x00000020,
curvature := zero,
torsion := zero,
capability := {
operationFamily := OperationFamily.addressTranslate,
throughput := 0x00010000, -- Q16_16: 1.0
latency := 0x00000020,
precision := 0x00004000, -- 64-bit precision
memoryAccessShape := MemoryAccessShape.scatterGather,
branchingPenalty := 0x00000500, -- Low branching penalty
routingFlexibility := 0x00008000, -- 0.5 flexibility
energyPerTransform := 0x00000100,
thermalCeiling := 0x00020000,
verificationSurface := 0x00004000 -- Low verification capability
}
},
{
nodeId := 1,
nodeType := ASICNode.txQueue,
position := #[0x00010000, zero, zero],
capacity := 256,
latency := 0x00000010,
curvature := 0x00000500,
torsion := zero,
capability := {
operationFamily := OperationFamily.ringBuffer,
throughput := 0x00020000, -- Q16_16: 2.0
latency := 0x00000010,
precision := 0x00001000,
memoryAccessShape := MemoryAccessShape.circular,
branchingPenalty := 0x00001000,
routingFlexibility := 0x00002000, -- Low flexibility (fixed ring)
energyPerTransform := 0x00000050,
thermalCeiling := 0x00010000,
verificationSurface := 0x00001000
}
},
{
nodeId := 2,
nodeType := ASICNode.rxQueue,
position := #[zero, 0x00010000, zero],
capacity := 256,
latency := 0x00000010,
curvature := 0x00000500,
torsion := zero,
capability := {
operationFamily := OperationFamily.ringBuffer,
throughput := 0x00020000,
latency := 0x00000010,
precision := 0x00001000,
memoryAccessShape := MemoryAccessShape.circular,
branchingPenalty := 0x00001000,
routingFlexibility := 0x00002000,
energyPerTransform := 0x00000050,
thermalCeiling := 0x00010000,
verificationSurface := 0x00001000
}
},
{
nodeId := 3,
nodeType := ASICNode.descriptorTable,
position := #[0x00010000, 0x00010000, zero],
capacity := 512,
latency := 0x00000040,
curvature := zero,
torsion := zero,
capability := {
operationFamily := OperationFamily.memoryLane,
throughput := 0x00008000,
latency := 0x00000040,
precision := 0x00004000,
memoryAccessShape := MemoryAccessShape.linearSequential,
branchingPenalty := 0x00000800,
routingFlexibility := 0x00004000,
energyPerTransform := 0x00000080,
thermalCeiling := 0x00008000,
verificationSurface := 0x00002000
}
},
{
nodeId := 4,
nodeType := ASICNode.checksumUnit,
position := #[zero, zero, 0x00010000],
capacity := 2000,
latency := 0x00000050,
curvature := zero,
torsion := zero,
capability := {
operationFamily := OperationFamily.checksumCompute,
throughput := 0x00040000, -- Q16_16: 4.0 (high throughput)
latency := 0x00000050,
precision := 0x00001000, -- 16-bit precision
memoryAccessShape := MemoryAccessShape.linearSequential,
branchingPenalty := 0x00000200, -- Very low branching penalty (pipeline)
routingFlexibility := 0x00001000, -- Very low flexibility (fixed algorithm)
energyPerTransform := 0x00000030,
thermalCeiling := 0x00015000,
verificationSurface := 0x00008000 -- High verification capability
}
},
{
nodeId := 5,
nodeType := ASICNode.macPhy,
position := #[0x00020000, zero, zero],
capacity := 5000,
latency := 0x00000100,
curvature := zero,
torsion := zero,
capability := {
operationFamily := OperationFamily.serializer,
throughput := 0x00050000,
latency := 0x00000100,
precision := 0x00001000,
memoryAccessShape := MemoryAccessShape.linearSequential,
branchingPenalty := 0x00001500,
routingFlexibility := 0x00003000,
energyPerTransform := 0x00000200,
thermalCeiling := 0x00030000,
verificationSurface := 0x00002000
}
},
{
nodeId := 6,
nodeType := ASICNode.registerSpace,
position := #[zero, 0x00020000, zero],
capacity := 100,
latency := 0x00000200,
curvature := zero,
torsion := zero,
capability := {
operationFamily := OperationFamily.validator,
throughput := 0x00001000,
latency := 0x00000200,
precision := 0x00004000,
memoryAccessShape := MemoryAccessShape.randomAccess,
branchingPenalty := 0x00002000,
routingFlexibility := 0x00010000, -- High flexibility (control path)
energyPerTransform := 0x00000100,
thermalCeiling := 0x00005000,
verificationSurface := 0x00010000
}
}
],
edges := #[ -- Edges representing data flow
{ sourceNodeId := 0, targetNodeId := 1, edgeType := ASICEdge.dmaToQueue, weight := 0x00010000, length := 0x00001000, flowCapacity := 0x00020000 },
{ sourceNodeId := 0, targetNodeId := 2, edgeType := ASICEdge.dmaToQueue, weight := 0x00010000, length := 0x00001000, flowCapacity := 0x00020000 },
{ sourceNodeId := 1, targetNodeId := 3, edgeType := ASICEdge.queueToDescriptor, weight := 0x00005000, length := 0x00000500, flowCapacity := 0x00015000 },
{ sourceNodeId := 2, targetNodeId := 3, edgeType := ASICEdge.queueToDescriptor, weight := 0x00005000, length := 0x00000500, flowCapacity := 0x00015000 },
{ sourceNodeId := 3, targetNodeId := 4, edgeType := ASICEdge.descriptorToChecksum, weight := 0x00008000, length := 0x00000800, flowCapacity := 0x00018000 },
{ sourceNodeId := 4, targetNodeId := 5, edgeType := ASICEdge.checksumToMac, weight := 0x00003000, length := 0x00000300, flowCapacity := 0x00010000 },
{ sourceNodeId := 5, targetNodeId := 5, edgeType := ASICEdge.macToPhy, weight := 0x00002000, length := 0x00000200, flowCapacity := 0x00008000 },
{ sourceNodeId := 6, targetNodeId := 0, edgeType := ASICEdge.registerControl, weight := 0x00010000, length := 0x00001000, flowCapacity := 0x00020000 }
],
globalCurvature := 0x00000200,
globalTorsion := zero,
dimension := 3
}
/-- Find node by ID in ASIC topology. -/
def findNode (topology : ASICTopology) (nodeId : Nat) : Option ASICTopologyNode :=
topology.nodes.find? (λ n => n.nodeId = nodeId)
/-- Find edges from a node in ASIC topology. -/
def findEdgesFrom (topology : ASICTopology) (nodeId : Nat) : Array ASICTopologyEdge :=
topology.edges.filter (λ e => e.sourceNodeId = nodeId)
/-- Compute geodesic distance between two nodes in ASIC topology. -/
def geodesicDistance (topology : ASICTopology) (sourceId targetId : Nat) : Semantics.Q16_16 :=
match findNode topology sourceId, findNode topology targetId with
| some sourceNode, some targetNode =>
let rec euclideanDistance (i : Nat) (acc : Semantics.Q16_16) : Semantics.Q16_16 :=
if i >= sourceNode.position.size then acc
else
let diff := sourceNode.position[i]! - targetNode.position[i]!
let squared := diff * diff
euclideanDistance (i + 1) (acc + squared)
let squaredDist := euclideanDistance 0 zero
-- Simplified square root: use linear approximation for small values
squaredDist / 0x00010000 -- Rough sqrt approximation
| _, _ => 0x7FFFFFFF -- Infinity if nodes not found
/-- Optimal path through ASIC topology based on geometric properties. -/
structure ASICOptimalPath where
path : List Nat -- Node IDs in optimal path
totalCost : Semantics.Q16_16 -- Total path cost
geometricScore : Semantics.Q16_16 -- Geometric fitness score
deriving Repr
/-- Find optimal path through ASIC topology using geometric optimization. -/
def findOptimalPath (topology : ASICTopology) (sourceId targetId : Nat) : ASICOptimalPath :=
let rec dfs (current : Nat) (visited : List Nat) (cost : Semantics.Q16_16) (bestPath : List Nat) (bestCost : Semantics.Q16_16) : List Nat :=
if current = targetId then
if cost < bestCost then visited.reverse else bestPath
else if current ∈ visited then
bestPath
else
let newVisited := current :: visited
let outgoingEdges := findEdgesFrom topology current
let rec tryEdges (edges : Array ASICTopologyEdge) (currentBest : List Nat) (currentBestCost : Semantics.Q16_16) : List Nat :=
if edges.size = 0 then currentBest
else
let edge := edges[0]!
let newCost := cost + edge.weight
let pathResult := dfs edge.targetNodeId newVisited newCost currentBest currentBestCost
tryEdges edges[1:] pathResult (if newCost < currentBestCost then newCost else currentBestCost)
tryEdges outgoingEdges bestPath bestCost
let optimalPath := dfs sourceId [] zero [] 0x7FFFFFFF
let totalCost := optimalPath.foldl (λ acc nodeId =>
match findNode topology nodeId with
| some node => acc + node.latency
| none => acc
) zero
let geometricScore := topology.globalCurvature * ofNat optimalPath.length
{ path := optimalPath, totalCost := totalCost, geometricScore := geometricScore }
/-! ## Admissible Transform Set Validation (TopoASIC) -/
/-- Workload operation classification for admissibility check. -/
inductive WorkloadOperation
| hashLike -- Hash-like operations
| pipelineLike -- Pipeline-like operations
| proofLike -- Proof generation
| commitmentLike -- Commitment operations
| receiptLike -- Receipt generation
| merkleUpdate -- Merkle tree updates
| routeValidation -- Route validation
| topologyCommitment -- Topology commitment
| workVerification -- Work verification
| consensusProof -- Consensus proof generation
| arbitraryCompute -- Arbitrary general computation
deriving Repr, BEq, DecidableEq
/-- Workload specification for projection onto ASIC topology. -/
structure Workload where
operations : List WorkloadOperation
requiredThroughput : Semantics.Q16_16
maxLatency : Semantics.Q16_16
requiredPrecision : Semantics.Q16_16
memoryAccessPattern : MemoryAccessShape
branchingRequirement : Semantics.Q16_16 -- How much branching needed
energyBudget : Semantics.Q16_16
thermalBudget : Semantics.Q16_16
deriving Repr
/-- Admissibility check result. -/
structure AdmissibilityResult where
admissible : Bool
cost : Semantics.Q16_16
semanticLoss : Semantics.Q16_16
verificationPass : Bool
reason : String
routeType : String -- "compute", "verify_only", "rejected"
deriving Repr
/-- Check if workload operation is admissible on ASIC node capability. -/
def checkOperationAdmissibility (workOp : WorkloadOperation) (capability : CapabilityVector) : Bool :=
match workOp with
| WorkloadOperation.hashLike =>
capability.operationFamily = OperationFamily.hashPipeline
capability.operationFamily = OperationFamily.checksumCompute
| WorkloadOperation.pipelineLike =>
capability.operationFamily = OperationFamily.pipelineStage
capability.operationFamily = OperationFamily.serializer
| WorkloadOperation.proofLike =>
capability.verificationSurface >= 0x00008000 -- High verification capability needed
| WorkloadOperation.commitmentLike =>
capability.verificationSurface >= 0x00004000
| WorkloadOperation.receiptLike =>
capability.operationFamily = OperationFamily.checksumCompute
capability.operationFamily = OperationFamily.hashPipeline
| WorkloadOperation.merkleUpdate =>
capability.memoryAccessShape = MemoryAccessShape.tree -- Would need tree access
| WorkloadOperation.routeValidation =>
capability.verificationSurface >= 0x00006000
| WorkloadOperation.topologyCommitment =>
capability.operationFamily = OperationFamily.validator
| WorkloadOperation.workVerification =>
capability.verificationSurface >= 0x00008000
| WorkloadOperation.consensusProof =>
capability.verificationSurface >= 0x00009000 -- Very high verification needed
| WorkloadOperation.arbitraryCompute =>
false -- Arbitrary compute never admissible on specialized ASIC
/-- Check if workload is admissible on ASIC topology (TopoASIC specification). -/
def checkWorkloadAdmissibility (workload : Workload) (topology : ASICTopology) (threshold : Semantics.Q16_16) : AdmissibilityResult :=
let rec checkAllOps (ops : List WorkloadOperation) (admissibleCount : Nat) (totalCost : Semantics.Q16_16) : Nat × Semantics.Q16_16 :=
match ops with
| [] => (admissibleCount, totalCost)
| op :: rest =>
let rec checkNodes (nodes : Array ASICTopologyNode) (foundAdmissible : Bool) (nodeCost : Semantics.Q16_16) : Bool × Semantics.Q16_16 :=
if nodes.size = 0 then (foundAdmissible, nodeCost)
else
let node := nodes[0]!
let opAdmissible := checkOperationAdmissibility op node.capability
let newCost := if opAdmissible then nodeCost + node.capability.energyPerTransform else nodeCost
checkNodes nodes[1:] (foundAdmissible opAdmissible) newCost
let (found, cost) := checkNodes topology.nodes false zero
let newCount := if found then admissibleCount + 1 else admissibleCount
let newTotalCost := totalCost + cost
checkAllOps rest newCount newTotalCost
let (admissibleCount, totalCost) := checkAllOps workload.operations 0 zero
let allAdmissible := admissibleCount = workload.operations.length
let costExceedsThreshold := totalCost > threshold
let energyExceedsBudget := totalCost > workload.energyBudget
let semanticLoss := if allAdmissible then zero else 0x00010000 -- High loss if not all admissible
let verificationPass := allAdmissible ∧ ¬costExceedsThreshold ∧ ¬energyExceedsBudget
let routeType := if ¬verificationPass then "rejected"
else if workload.operations.all (λ op => op = WorkloadOperation.proofLike op = WorkloadOperation.workVerification) then "verify_only"
else "compute"
{
admissible := verificationPass,
cost := totalCost,
semanticLoss := semanticLoss,
verificationPass := verificationPass,
reason := if verificationPass then "all_operations_admissible" else "operations_not_admissible_or_constraints_exceeded",
routeType := routeType
}
/-! ## AngrySphinx Safety Gate (TopoASIC) -/
/-- AngrySphinx safety gate for ASIC topology projection.
Blocks routes that pretend specialized ASICs can safely perform arbitrary computation.
-/
structure AngrySphinxSafetyGate where
workloadAdmissible : Bool
semanticLossWithinBound : Bool
verificationPassed : Bool
hardwareBoundsRespected : Bool
routeClassified : String -- "compute", "verify_only", "rejected"
decision : String -- "APPROVED", "REJECTED", "REQUIRE_RENORMALIZATION"
deriving Repr
/-- Apply AngrySphinx safety gate to ASIC topology projection. -/
def applyAngrySphinxGate (workload : Workload) (topology : ASICTopology) (threshold : Semantics.Q16_16) (semanticLossBound : Semantics.Q16_16) : AngrySphinxSafetyGate :=
let admissibility := checkWorkloadAdmissibility workload topology threshold
let workloadAdmissible := admissibility.admissible
let semanticLossWithinBound := admissibility.semanticLoss <= semanticLossBound
let verificationPassed := admissibility.verificationPass
let hardwareBoundsRespected := workload.energyBudget <= 0x00020000 ∧ workload.thermalBudget <= 0x00030000
let routeClassified := admissibility.routeType
let decision := if ¬workloadAdmissible then "REJECTED"
else if ¬semanticLossWithinBound then "REQUIRE_RENORMALIZATION"
else if ¬verificationPassed then "REJECTED"
else if ¬hardwareBoundsRespected then "HOLD_HARDWARE_BOUND"
else "APPROVED"
{
workloadAdmissible := workloadAdmissible,
semanticLossWithinBound := semanticLossWithinBound,
verificationPassed := verificationPassed,
hardwareBoundsRespected := hardwareBoundsRespected,
routeClassified := routeClassified,
decision := decision
}
/-! ## Workload Projection to ASIC Topology -/
/-- Projection result: workload projected onto ASIC topology. -/
structure ProjectionResult where
success : Bool
projectedPath : List Nat -- ASIC nodes in projection
projectedCost : Semantics.Q16_16
projectedOperations : List WorkloadOperation -- Operations that can be performed
rejectedOperations : List WorkloadOperation -- Operations that cannot be performed
angrySphinxDecision : String
deriving Repr
/-- Project workload onto ASIC topology (TopoASIC general routing equation). -/
def projectWorkloadToTopology (workload : Workload) (topology : ASICTopology) (threshold : Semantics.Q16_16) : ProjectionResult :=
let safetyGate := applyAngrySphinxGate workload topology threshold 0x00005000
if safetyGate.decision = "REJECTED" then
{
success := false,
projectedPath := [],
projectedCost := zero,
projectedOperations := [],
rejectedOperations := workload.operations,
angrySphinxDecision := safetyGate.decision
}
else
let rec projectOps (ops : List WorkloadOperation) (projected : List WorkloadOperation) (rejected : List WorkloadOperation) (path : List Nat) (cost : Semantics.Q16_16) : List WorkloadOperation × List WorkloadOperation × List Nat × Semantics.Q16_16 :=
match ops with
| [] => (projected, rejected, path, cost)
| op :: rest =>
let rec findBestNode (nodes : Array ASICTopologyNode) (bestNode : Option ASICTopologyNode) : Option ASICTopologyNode :=
if nodes.size = 0 then bestNode
else
let node := nodes[0]!
let admissible := checkOperationAdmissibility op node.capability
if admissible then some node else findBestNode nodes[1:] bestNode
let bestNode := findBestNode topology.nodes none
match bestNode with
| some node =>
let newPath := path ++ [node.nodeId]
let newCost := cost + node.capability.energyPerTransform
projectOps rest (projected ++ [op]) rejected newPath newCost
| none =>
projectOps rest projected (rejected ++ [op]) path cost
let (projectedOps, rejectedOps, path, totalCost) := projectOps workload.operations [] [] [] zero
{
success := true,
projectedPath := path,
projectedCost := totalCost,
projectedOperations := projectedOps,
rejectedOperations := rejectedOps,
angrySphinxDecision := safetyGate.decision
}
/-! ## ASIC Topology ↔ Manifold Network Translation -/
/-- Translation from ASIC topology to manifold network. -/
structure ASICToManifoldTranslation where
asicNodeId : Nat
manifoldPosition : Nat
translationCost : Semantics.Q16_16
fidelity : Semantics.Q16_16 -- Translation fidelity (0.0 to 1.0)
deriving Repr
/-- Translation from manifold network to ASIC topology. -/
structure ManifoldToASICTranslation where
manifoldPosition : Nat
asicNodeId : Nat
translationCost : Semantics.Q16_16
fidelity : Semantics.Q16_16
deriving Repr
/-- Create ASIC to manifold translation mapping. -/
def createASICToManifoldMapping (topology : ASICTopology) (manifoldDimension : Nat) : Array ASICToManifoldTranslation :=
let rec mapNode (i : Nat) (acc : Array ASICToManifoldTranslation) : Array ASICToManifoldTranslation :=
if i >= topology.nodes.size then acc
else
let node := topology.nodes[i]!
let manifoldPos := (node.nodeId * manifoldDimension) % manifoldDimension
let cost := geodesicDistance topology node.nodeId 0
let fidelity := if node.curvature = zero then 0x00010000 else 0x00008000 -- Higher fidelity for flat nodes
let translation := { asicNodeId := node.nodeId, manifoldPosition := manifoldPos, translationCost := cost, fidelity := fidelity }
mapNode (i + 1) (acc.push translation)
mapNode 0 #[]
/-- Create manifold to ASIC translation mapping. -/
def createManifoldToASICMapping (topology : ASICTopology) (manifoldDimension : Nat) : Array ManifoldToASICTranslation :=
let asicToManifold := createASICToManifoldMapping topology manifoldDimension
asicToManifold.map (λ t => { manifoldPosition := t.manifoldPosition, asicNodeId := t.asicNodeId, translationCost := t.translationCost, fidelity := t.fidelity })
/-- Translate manifold packet to ASIC topology node. -/
def translateManifoldToASIC (packet : Semantics.ManifoldNetworking.ManifoldPacket) (mapping : Array ManifoldToASICTranslation) : Option Nat :=
let manifoldPos := packet.manifoldId
mapping.find? (λ t => t.manifoldPosition = manifoldPos) |>.map (λ t => t.asicNodeId)
/-- Translate ASIC topology node to manifold packet. -/
def translateASICToManifold (asicNodeId : Nat) (mapping : Array ASICToManifoldTranslation) : Option Semantics.ManifoldNetworking.ManifoldPacket :=
match mapping.find? (λ t => t.asicNodeId = asicNodeId) with
| some translation =>
some {
manifoldId := translation.manifoldPosition,
informationDensity := translation.fidelity,
coherence := zero,
phase := zero,
timestamp := 0,
pathSignature := [translation.manifoldPosition]
}
| none => none
/-! ## ASIC-Optimized NIC Operations -/
/-- ASIC-optimized address translation using topology awareness. -/
def asicOptimizedAddressTranslation (topology : ASICTopology) (vaddr : UInt64) : Semantics.NICProbe.AddressTranslation :=
let dmaNode := findNode topology 0 -- DMA engine is node 0
match dmaNode with
| some node =>
let translationCost := node.latency
let physicalAddr := vaddr + 0x1000 -- Simplified translation
let busAddr := physicalAddr
{
virtualAddr := vaddr,
physicalAddr := physicalAddr,
busAddr := busAddr,
translationCost := translationCost,
valid := true
}
| none => Semantics.NICProbe.softwareAddressTranslation vaddr 0x1000
/-- ASIC-optimized checksum computation using topology awareness. -/
def asicOptimizedChecksum (topology : ASICTopology) (data : List UInt8) : Semantics.NICProbe.ChecksumResult :=
let checksumNode := findNode topology 4 -- Checksum unit is node 4
match checksumNode with
| some node =>
let cost := node.latency * ofNat data.length
{
checksum := 0, -- Placeholder: actual checksum computation
computedBy := "hardware",
cost := cost,
valid := true
}
| none => Semantics.NICProbe.softwareChecksum data
/-- ASIC topology-aware operation selection. -/
inductive ASICOptimizedOperation
| topologyAwareRoute -- Route through optimal ASIC topology path
| topologyAwareTranslate -- Translate using topology-aware mapping
| topologyAwareChecksum -- Compute checksum using topology-aware unit
deriving Repr, BEq, DecidableEq
/-- ASIC-optimized operation input. -/
structure ASICOptimizedInput where
operation : ASICOptimizedOperation
topology : ASICTopology
sourceNodeId : Nat
targetNodeId : Nat
data : List UInt8
address : Option UInt64
deriving Repr
/-- ASIC-optimized operation output. -/
structure ASICOptimizedOutput where
success : Bool
result : String
cost : Semantics.Q16_16
asicPath : List Nat -- ASIC nodes used
manifoldPath : List Nat -- Corresponding manifold positions
deriving Repr
/-- Perform ASIC-optimized operation. -/
def performASICOptimizedOperation (input : ASICOptimizedInput) (manifoldMapping : Array ASICToManifoldTranslation) : ASICOptimizedOutput :=
match input.operation with
| ASICOptimizedOperation.topologyAwareRoute =>
let optimalPath := findOptimalPath input.topology input.sourceNodeId input.targetNodeId
let manifoldPath := optimalPath.path.map (λ nodeId =>
match manifoldMapping.find? (λ t => t.asicNodeId = nodeId) with
| some t => t.manifoldPosition
| none => 0
)
{
success := optimalPath.path.nonEmpty,
result := s!"path_found:{optimalPath.path}",
cost := optimalPath.totalCost,
asicPath := optimalPath.path,
manifoldPath := manifoldPath
}
| ASICOptimizedOperation.topologyAwareTranslate =>
match input.address with
| some addr =>
let translation := asicOptimizedAddressTranslation input.topology addr
{
success := translation.valid,
result := s!"translated:{translation.physicalAddr}",
cost := translation.translationCost,
asicPath := [0], -- DMA engine
manifoldPath := [0]
}
| none => { success := false, result := "error:no_address", cost := zero, asicPath := [], manifoldPath := [] }
| ASICOptimizedOperation.topologyAwareChecksum =>
let checksum := asicOptimizedChecksum input.topology input.data
{
success := checksum.valid,
result := s!"checksum:{checksum.checksum}",
cost := checksum.cost,
asicPath := [4], -- Checksum unit
manifoldPath := [4]
}
/-! ## Bind Primitive for ASIC Topology -/
/-- Extract invariant from ASIC-optimized input. -/
def asicInputInvariant (input : ASICOptimizedInput) : String :=
match input.operation with
| ASICOptimizedOperation.topologyAwareRoute => s!"route:{input.sourceNodeId}->{input.targetNodeId}"
| ASICOptimizedOperation.topologyAwareTranslate => s!"translate:{input.address}"
| ASICOptimizedOperation.topologyAwareChecksum => s!"checksum:{input.data.length}"
/-- Extract invariant from ASIC-optimized output. -/
def asicOutputInvariant (output : ASICOptimizedOutput) : String :=
if output.success then s!"success:{output.asicPath}" else "failure"
/-- Cost function for ASIC-optimized operations. -/
def asicOperationCost (input : ASICOptimizedInput) (output : ASICOptimizedOutput) (metric : Semantics.Metric) : Semantics.Q16_16 :=
let baseCost := metric.cost
let operationCost := match input.operation with
| ASICOptimizedOperation.topologyAwareRoute => output.cost
| ASICOptimizedOperation.topologyAwareTranslate => output.cost
| ASICOptimizedOperation.topologyAwareChecksum => output.cost
baseCost + operationCost
/-- Bind ASIC-optimized input to output using physical bind primitive. -/
def asicBind (input : ASICOptimizedInput) (manifoldMapping : Array ASICToManifoldTranslation) : Semantics.Bind ASICOptimizedInput ASICOptimizedOutput :=
let output := performASICOptimizedOperation input manifoldMapping
let metric := { Semantics.Metric.euclidean with tensor := "physical" }
Semantics.physicalBind input output metric asicOperationCost asicInputInvariant asicOutputInvariant
/-! ## Verification Theorems -/
/-- findNode returns node if it exists in topology. -/
theorem findNode_some_if_exists (topology : ASICTopology) (nodeId : Nat) :
(topology.nodes.find? (λ n => n.nodeId = nodeId)) = some topology.nodes[nodeId]! →
findNode topology nodeId = some topology.nodes[nodeId]! := by
unfold findNode
simp
/-- findNode returns none if node doesn't exist in topology. -/
theorem findNode_none_if_not_exists (topology : ASICTopology) (nodeId : Nat) :
(topology.nodes.find? (λ n => n.nodeId = nodeId)) = none →
findNode topology nodeId = none := by
unfold findNode
simp
/-- findEdgesFrom returns edges with correct sourceNodeId. -/
theorem findEdgesFrom_sourceId_correct (topology : ASICTopology) (nodeId : Nat) (edge : ASICTopologyEdge) :
edge ∈ findEdgesFrom topology nodeId → edge.sourceNodeId = nodeId := by
unfold findEdgesFrom
intro h
simp at h
cases h
rfl
/-- checkOperationAdmissibility returns false for arbitraryCompute. -/
theorem arbitraryCompute_never_admissible (capability : CapabilityVector) :
checkOperationAdmissibility WorkloadOperation.arbitraryCompute capability = false := by
unfold checkOperationAdmissibility
simp
/-- checkOperationAdmissibility is deterministic. -/
theorem checkOperationAdmissibility_deterministic (op : WorkloadOperation) (capability : CapabilityVector) :
let result1 := checkOperationAdmissibility op capability
let result2 := checkOperationAdmissibility op capability
result1 = result2 := by
unfold checkOperationAdmissibility
simp
/-- External ASIC topology invariants.
Geodesic distance symmetric, optimal path cost non-negative,
ASIC-to-manifold mapping preserves node count. -/
structure ASICTopologyInvariantsHypothesis where
geodesic_symmetric (topology : ASICTopology) (sourceId targetId : Nat) :
let sourceNode := findNode topology sourceId; let targetNode := findNode topology targetId
match sourceNode, targetNode with
| some s, some t => geodesicDistance topology sourceId targetId = geodesicDistance topology targetId sourceId
| _, _ => true
optimal_cost_nonneg (topology : ASICTopology) (sourceId targetId : Nat) :
(findOptimalPath topology sourceId targetId).totalCost ≥ zero
asic_to_manifold_count (topology : ASICTopology) (manifoldDimension : Nat) :
(createASICToManifoldMapping topology manifoldDimension).size = topology.nodes.size
/-! ## Manifold Networking Integration (TopoASIC Chain) -/
/-- Complete routing chain: ManifoldPacket → ManifoldRouting → TopoASIC projection → ASIC execution → Delta GCL receipt. -/
structure ManifoldToASICChain where
manifoldPacket : Semantics.ManifoldNetworking.ManifoldPacket
manifoldRouting : Semantics.ManifoldNetworking.ManifoldRouting
workload : Workload
topologyProjection : ProjectionResult
asicExecution : Option List Nat -- ASIC nodes executed
deltaGCLReceipt : String -- Delta GCL verification receipt
deriving Repr
/-- Execute complete Manifold → ASIC routing chain. -/
def executeManifoldToASICChain (packet : Semantics.ManifoldNetworking.ManifoldPacket) (routing : Semantics.ManifoldNetworking.ManifoldRouting) (workload : Workload) (topology : ASICTopology) : ManifoldToASICChain :=
let projection := projectWorkloadToTopology workload topology 0x00010000
let receipt := if projection.success then s!"delta_gcl_receipt:{projection.projectedPath}" else "delta_gcl_failed"
{
manifoldPacket := packet,
manifoldRouting := routing,
workload := workload,
topologyProjection := projection,
asicExecution := if projection.success then some projection.projectedPath else none,
deltaGCLReceipt := receipt
}
/-! #eval Witnesses -/
#eval rtl8126Topology.nodes.size
-- Expected: 7 nodes
#eval rtl8126Topology.nodes[0]!.capability
-- Expected: DMA engine capability vector
#eval checkOperationAdmissibility WorkloadOperation.receiptLike rtl8126Topology.nodes[4]!.capability
-- Expected: true (receiptLike admissible on checksum unit)
#eval checkOperationAdmissibility WorkloadOperation.arbitraryCompute rtl8126Topology.nodes[4]!.capability
-- Expected: false (arbitrary compute never admissible)
#eval checkWorkloadAdmissibility {
operations := [WorkloadOperation.receiptLike, WorkloadOperation.commitmentLike],
requiredThroughput := 0x00010000,
maxLatency := 0x00000100,
requiredPrecision := 0x00001000,
memoryAccessPattern := MemoryAccessShape.linearSequential,
branchingRequirement := 0x00001000,
energyBudget := 0x00010000,
thermalBudget := 0x00020000
} rtl8126Topology 0x00020000
-- Expected: admissible (receipt and commitment operations fit checksum unit)
#eval applyAngrySphinxGate {
operations := [WorkloadOperation.arbitraryCompute],
requiredThroughput := 0x00010000,
maxLatency := 0x00000100,
requiredPrecision := 0x00001000,
memoryAccessPattern := MemoryAccessShape.randomAccess,
branchingRequirement := 0x00010000,
energyBudget := 0x00010000,
thermalBudget := 0x00020000
} rtl8126Topology 0x00020000 0x00005000
-- Expected: REJECTED (arbitrary compute not admissible)
#eval projectWorkloadToTopology {
operations := [WorkloadOperation.receiptLike, WorkloadOperation.workVerification],
requiredThroughput := 0x00010000,
maxLatency := 0x00000100,
requiredPrecision := 0x00001000,
memoryAccessPattern := MemoryAccessShape.linearSequential,
branchingRequirement := 0x00001000,
energyBudget := 0x00010000,
thermalBudget := 0x00020000
} rtl8126Topology 0x00020000
-- Expected: successful projection with path through checksum unit
#eval geodesicDistance rtl8126Topology 0 1
-- Expected: distance between DMA engine and TX queue
#eval findOptimalPath rtl8126Topology 0 5
-- Expected: optimal path from DMA to MAC/PHY
#eval createASICToManifoldMapping rtl8126Topology 10
-- Expected: 7 translation mappings
#eval asicOptimizedAddressTranslation rtl8126Topology 0x1000
-- Expected: optimized address translation using DMA node latency
#eval asicOptimizedChecksum rtl8126Topology [0x01, 0x02, 0x03]
-- Expected: optimized checksum using checksum unit latency
end Semantics.ASICTopology