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867 lines
37 KiB
Text
867 lines
37 KiB
Text
import Semantics.Bind
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import Semantics.FixedPoint
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import Semantics.NICProbe
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import Lean.Data.Json
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namespace Semantics.ASICTopology
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/-! ## TopoASIC — ASIC Topology Abstraction Layer
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**Core Inversion:**
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- Normal view: ASIC = specific chip, fixed function, limited use
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- TopoASIC view: ASIC = topology of constrained transformations, routing surface, operation manifold, interfaceable substrate
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**Principle:** An ASIC is a crystallized algorithm; TopoASIC treats the crystal as terrain.
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**Key Question:** Not "What was this ASIC designed to do?" but "What lawful transformations can this topology perform cheaply?"
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**Definition:**
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TopoASIC = fixed hardware operation graph + bandwidth/latency/energy constraints + admissible transform set + routing interface + verification receipts
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**Capability Vector:**
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Each ASIC node: [operation_family, throughput, latency, precision, memory_access_shape, branching_penalty, routing_flexibility, energy_per_transform, thermal_ceiling, verification_surface]
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**General Routing Equation:**
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Workload W → projection P(W) → ASIC topology T → admissible route R_T → receipt
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**Route Validity:**
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- cost(P(W), T) < threshold
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- semantic_loss < threshold
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- verification_pass = true
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**Keeper Law:** Do not ask what the chip is. Ask what shape of computation the chip makes easy.
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Per AGENTS.md: Lean is source of truth, Q16_16 fixed-point for hardware-native execution.
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-/
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open Semantics.Q16_16
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/-- ASIC topology node types (RTL8126 specific). -/
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inductive ASICNode
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| dmaEngine -- DMA address translation engine
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| checksumUnit -- Checksum computation unit
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| txQueue -- Transmit queue (ring buffer)
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| rxQueue -- Receive queue (ring buffer)
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| descriptorTable -- Descriptor memory layout
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| macPhy -- MAC/PHY physical layer
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| registerSpace -- MMIO register space
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deriving Repr, BEq, DecidableEq
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/-- ASIC topology edge types (connections between nodes). -/
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inductive ASICEdge
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| dmaToQueue -- DMA engine to queue
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| queueToDescriptor -- Queue to descriptor table
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| descriptorToChecksum -- Descriptor to checksum unit
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| checksumToMac -- Checksum to MAC/PHY
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| macToPhy -- MAC to PHY
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| registerControl -- Register space control path
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deriving Repr, BEq, DecidableEq
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/-- Operation family classification for capability vector. -/
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inductive OperationFamily
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| hashPipeline -- Hash-like pipeline operations
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| memoryLane -- Memory access operations
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| busSegment -- Bus transfer operations
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| pipelineStage -- Sequential pipeline operations
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| accumulator -- Accumulation operations
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| serializer -- Serialization operations
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| validator -- Validation/verification operations
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| checksumCompute -- Checksum computation
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| addressTranslate -- Address translation
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| ringBuffer -- Ring buffer operations
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deriving Repr, BEq, DecidableEq
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/-- Memory access shape classification. -/
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inductive MemoryAccessShape
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| linearSequential -- Linear sequential access
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| randomAccess -- Random access
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| strided -- Strided access
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| circular -- Circular/ring access
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| scatterGather -- Scatter-gather access
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deriving Repr, BEq, DecidableEq
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/-- Capability vector for ASIC topology node (TopoASIC specification). -/
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structure CapabilityVector where
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operationFamily : OperationFamily
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throughput : Semantics.Q16_16 -- Operations per unit time
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latency : Semantics.Q16_16 -- Operation latency
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precision : Semantics.Q16_16 -- Precision (bits of accuracy)
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memoryAccessShape : MemoryAccessShape
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branchingPenalty : Semantics.Q16_16 -- Cost of branching
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routingFlexibility : Semantics.Q16_16 -- How flexible routing can be (0-1)
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energyPerTransform : Semantics.Q16_16 -- Energy cost per operation
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thermalCeiling : Semantics.Q16_16 -- Thermal limit
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verificationSurface : Semantics.Q16_16 -- Verification capability (0-1)
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deriving Repr
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/-- ASIC topology node with geometric properties and capability vector (TopoASIC). -/
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structure ASICTopologyNode where
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nodeId : Nat
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nodeType : ASICNode
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position : Array Semantics.Q16_16 -- Position in ASIC topology space
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capacity : Nat -- Processing capacity (packets/ops)
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latency : Semantics.Q16_16 -- Operation latency
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curvature : Semantics.Q16_16 -- Topology curvature at this node
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torsion : Semantics.Q16_16 -- Topology torsion at this node
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capability : CapabilityVector -- TopoASIC capability vector
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deriving Repr
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/-- ASIC topology edge with geometric properties. -/
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structure ASICTopologyEdge where
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sourceNodeId : Nat
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targetNodeId : Nat
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edgeType : ASICEdge
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weight : Semantics.Q16_16 -- Edge weight (cost/bandwidth)
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length : Semantics.Q16_16 -- Geodesic length
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flowCapacity : Semantics.Q16_16 -- Flow capacity
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deriving Repr
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/-- Complete ASIC topology structure. -/
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structure ASICTopology where
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nodes : Array ASICTopologyNode
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edges : Array ASICTopologyEdge
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globalCurvature : Semantics.Q16_16 -- Overall manifold curvature
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globalTorsion : Semantics.Q16_16 -- Overall manifold torsion
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dimension : Nat -- Topology dimension
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deriving Repr
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/-- Default RTL8126 ASIC topology with capability vectors (TopoASIC specification). -/
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def rtl8126Topology : ASICTopology := {
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nodes := #[ -- 7 nodes representing RTL8126 components with capability vectors
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{
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nodeId := 0,
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nodeType := ASICNode.dmaEngine,
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position := #[zero, zero, zero],
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capacity := 1000,
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latency := 0x00000020,
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curvature := zero,
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torsion := zero,
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capability := {
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operationFamily := OperationFamily.addressTranslate,
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throughput := 0x00010000, -- Q16_16: 1.0
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latency := 0x00000020,
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precision := 0x00004000, -- 64-bit precision
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memoryAccessShape := MemoryAccessShape.scatterGather,
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branchingPenalty := 0x00000500, -- Low branching penalty
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routingFlexibility := 0x00008000, -- 0.5 flexibility
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energyPerTransform := 0x00000100,
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thermalCeiling := 0x00020000,
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verificationSurface := 0x00004000 -- Low verification capability
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}
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},
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{
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nodeId := 1,
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nodeType := ASICNode.txQueue,
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position := #[0x00010000, zero, zero],
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capacity := 256,
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latency := 0x00000010,
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curvature := 0x00000500,
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torsion := zero,
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capability := {
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operationFamily := OperationFamily.ringBuffer,
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throughput := 0x00020000, -- Q16_16: 2.0
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latency := 0x00000010,
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precision := 0x00001000,
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memoryAccessShape := MemoryAccessShape.circular,
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branchingPenalty := 0x00001000,
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routingFlexibility := 0x00002000, -- Low flexibility (fixed ring)
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energyPerTransform := 0x00000050,
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thermalCeiling := 0x00010000,
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verificationSurface := 0x00001000
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}
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},
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{
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nodeId := 2,
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nodeType := ASICNode.rxQueue,
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position := #[zero, 0x00010000, zero],
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capacity := 256,
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latency := 0x00000010,
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curvature := 0x00000500,
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torsion := zero,
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capability := {
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operationFamily := OperationFamily.ringBuffer,
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throughput := 0x00020000,
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latency := 0x00000010,
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precision := 0x00001000,
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memoryAccessShape := MemoryAccessShape.circular,
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branchingPenalty := 0x00001000,
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routingFlexibility := 0x00002000,
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energyPerTransform := 0x00000050,
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thermalCeiling := 0x00010000,
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verificationSurface := 0x00001000
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}
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},
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{
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nodeId := 3,
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nodeType := ASICNode.descriptorTable,
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position := #[0x00010000, 0x00010000, zero],
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capacity := 512,
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latency := 0x00000040,
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curvature := zero,
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torsion := zero,
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capability := {
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operationFamily := OperationFamily.memoryLane,
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throughput := 0x00008000,
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latency := 0x00000040,
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precision := 0x00004000,
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memoryAccessShape := MemoryAccessShape.linearSequential,
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branchingPenalty := 0x00000800,
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routingFlexibility := 0x00004000,
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energyPerTransform := 0x00000080,
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thermalCeiling := 0x00008000,
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verificationSurface := 0x00002000
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}
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},
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{
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nodeId := 4,
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nodeType := ASICNode.checksumUnit,
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position := #[zero, zero, 0x00010000],
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capacity := 2000,
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latency := 0x00000050,
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curvature := zero,
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torsion := zero,
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capability := {
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operationFamily := OperationFamily.checksumCompute,
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throughput := 0x00040000, -- Q16_16: 4.0 (high throughput)
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latency := 0x00000050,
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precision := 0x00001000, -- 16-bit precision
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memoryAccessShape := MemoryAccessShape.linearSequential,
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branchingPenalty := 0x00000200, -- Very low branching penalty (pipeline)
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routingFlexibility := 0x00001000, -- Very low flexibility (fixed algorithm)
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energyPerTransform := 0x00000030,
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thermalCeiling := 0x00015000,
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verificationSurface := 0x00008000 -- High verification capability
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}
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},
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{
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nodeId := 5,
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nodeType := ASICNode.macPhy,
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position := #[0x00020000, zero, zero],
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capacity := 5000,
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latency := 0x00000100,
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curvature := zero,
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torsion := zero,
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capability := {
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operationFamily := OperationFamily.serializer,
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throughput := 0x00050000,
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latency := 0x00000100,
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precision := 0x00001000,
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memoryAccessShape := MemoryAccessShape.linearSequential,
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branchingPenalty := 0x00001500,
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routingFlexibility := 0x00003000,
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energyPerTransform := 0x00000200,
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thermalCeiling := 0x00030000,
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verificationSurface := 0x00002000
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}
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},
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{
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nodeId := 6,
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nodeType := ASICNode.registerSpace,
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position := #[zero, 0x00020000, zero],
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capacity := 100,
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latency := 0x00000200,
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curvature := zero,
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torsion := zero,
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capability := {
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operationFamily := OperationFamily.validator,
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throughput := 0x00001000,
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latency := 0x00000200,
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precision := 0x00004000,
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memoryAccessShape := MemoryAccessShape.randomAccess,
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branchingPenalty := 0x00002000,
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routingFlexibility := 0x00010000, -- High flexibility (control path)
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energyPerTransform := 0x00000100,
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thermalCeiling := 0x00005000,
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verificationSurface := 0x00010000
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}
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}
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],
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edges := #[ -- Edges representing data flow
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{ sourceNodeId := 0, targetNodeId := 1, edgeType := ASICEdge.dmaToQueue, weight := 0x00010000, length := 0x00001000, flowCapacity := 0x00020000 },
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{ sourceNodeId := 0, targetNodeId := 2, edgeType := ASICEdge.dmaToQueue, weight := 0x00010000, length := 0x00001000, flowCapacity := 0x00020000 },
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{ sourceNodeId := 1, targetNodeId := 3, edgeType := ASICEdge.queueToDescriptor, weight := 0x00005000, length := 0x00000500, flowCapacity := 0x00015000 },
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{ sourceNodeId := 2, targetNodeId := 3, edgeType := ASICEdge.queueToDescriptor, weight := 0x00005000, length := 0x00000500, flowCapacity := 0x00015000 },
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{ sourceNodeId := 3, targetNodeId := 4, edgeType := ASICEdge.descriptorToChecksum, weight := 0x00008000, length := 0x00000800, flowCapacity := 0x00018000 },
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{ sourceNodeId := 4, targetNodeId := 5, edgeType := ASICEdge.checksumToMac, weight := 0x00003000, length := 0x00000300, flowCapacity := 0x00010000 },
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{ sourceNodeId := 5, targetNodeId := 5, edgeType := ASICEdge.macToPhy, weight := 0x00002000, length := 0x00000200, flowCapacity := 0x00008000 },
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{ sourceNodeId := 6, targetNodeId := 0, edgeType := ASICEdge.registerControl, weight := 0x00010000, length := 0x00001000, flowCapacity := 0x00020000 }
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],
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globalCurvature := 0x00000200,
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globalTorsion := zero,
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dimension := 3
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}
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/-- Find node by ID in ASIC topology. -/
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def findNode (topology : ASICTopology) (nodeId : Nat) : Option ASICTopologyNode :=
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topology.nodes.find? (λ n => n.nodeId = nodeId)
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/-- Find edges from a node in ASIC topology. -/
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def findEdgesFrom (topology : ASICTopology) (nodeId : Nat) : Array ASICTopologyEdge :=
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topology.edges.filter (λ e => e.sourceNodeId = nodeId)
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/-- Compute geodesic distance between two nodes in ASIC topology. -/
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def geodesicDistance (topology : ASICTopology) (sourceId targetId : Nat) : Semantics.Q16_16 :=
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match findNode topology sourceId, findNode topology targetId with
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| some sourceNode, some targetNode =>
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let rec euclideanDistance (i : Nat) (acc : Semantics.Q16_16) : Semantics.Q16_16 :=
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if i >= sourceNode.position.size then acc
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else
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let diff := sourceNode.position[i]! - targetNode.position[i]!
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let squared := diff * diff
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euclideanDistance (i + 1) (acc + squared)
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let squaredDist := euclideanDistance 0 zero
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-- Simplified square root: use linear approximation for small values
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squaredDist / 0x00010000 -- Rough sqrt approximation
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| _, _ => 0x7FFFFFFF -- Infinity if nodes not found
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/-- Optimal path through ASIC topology based on geometric properties. -/
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structure ASICOptimalPath where
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path : List Nat -- Node IDs in optimal path
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totalCost : Semantics.Q16_16 -- Total path cost
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geometricScore : Semantics.Q16_16 -- Geometric fitness score
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deriving Repr
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/-- Find optimal path through ASIC topology using geometric optimization. -/
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def findOptimalPath (topology : ASICTopology) (sourceId targetId : Nat) : ASICOptimalPath :=
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let rec dfs (current : Nat) (visited : List Nat) (cost : Semantics.Q16_16) (bestPath : List Nat) (bestCost : Semantics.Q16_16) : List Nat :=
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if current = targetId then
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if cost < bestCost then visited.reverse else bestPath
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else if current ∈ visited then
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bestPath
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else
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let newVisited := current :: visited
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let outgoingEdges := findEdgesFrom topology current
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let rec tryEdges (edges : Array ASICTopologyEdge) (currentBest : List Nat) (currentBestCost : Semantics.Q16_16) : List Nat :=
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if edges.size = 0 then currentBest
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else
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let edge := edges[0]!
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let newCost := cost + edge.weight
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let pathResult := dfs edge.targetNodeId newVisited newCost currentBest currentBestCost
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tryEdges edges[1:] pathResult (if newCost < currentBestCost then newCost else currentBestCost)
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tryEdges outgoingEdges bestPath bestCost
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let optimalPath := dfs sourceId [] zero [] 0x7FFFFFFF
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let totalCost := optimalPath.foldl (λ acc nodeId =>
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match findNode topology nodeId with
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| some node => acc + node.latency
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| none => acc
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) zero
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let geometricScore := topology.globalCurvature * ofNat optimalPath.length
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{ path := optimalPath, totalCost := totalCost, geometricScore := geometricScore }
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/-! ## Admissible Transform Set Validation (TopoASIC) -/
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/-- Workload operation classification for admissibility check. -/
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inductive WorkloadOperation
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| hashLike -- Hash-like operations
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| pipelineLike -- Pipeline-like operations
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| proofLike -- Proof generation
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| commitmentLike -- Commitment operations
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| receiptLike -- Receipt generation
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| merkleUpdate -- Merkle tree updates
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| routeValidation -- Route validation
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| topologyCommitment -- Topology commitment
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| workVerification -- Work verification
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| consensusProof -- Consensus proof generation
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| arbitraryCompute -- Arbitrary general computation
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deriving Repr, BEq, DecidableEq
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/-- Workload specification for projection onto ASIC topology. -/
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structure Workload where
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operations : List WorkloadOperation
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requiredThroughput : Semantics.Q16_16
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maxLatency : Semantics.Q16_16
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requiredPrecision : Semantics.Q16_16
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memoryAccessPattern : MemoryAccessShape
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branchingRequirement : Semantics.Q16_16 -- How much branching needed
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energyBudget : Semantics.Q16_16
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thermalBudget : Semantics.Q16_16
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deriving Repr
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/-- Admissibility check result. -/
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structure AdmissibilityResult where
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admissible : Bool
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cost : Semantics.Q16_16
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semanticLoss : Semantics.Q16_16
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verificationPass : Bool
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reason : String
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routeType : String -- "compute", "verify_only", "rejected"
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deriving Repr
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/-- Check if workload operation is admissible on ASIC node capability. -/
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def checkOperationAdmissibility (workOp : WorkloadOperation) (capability : CapabilityVector) : Bool :=
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match workOp with
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| WorkloadOperation.hashLike =>
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capability.operationFamily = OperationFamily.hashPipeline ∨
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capability.operationFamily = OperationFamily.checksumCompute
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| WorkloadOperation.pipelineLike =>
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capability.operationFamily = OperationFamily.pipelineStage ∨
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capability.operationFamily = OperationFamily.serializer
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| WorkloadOperation.proofLike =>
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capability.verificationSurface >= 0x00008000 -- High verification capability needed
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| WorkloadOperation.commitmentLike =>
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capability.verificationSurface >= 0x00004000
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| WorkloadOperation.receiptLike =>
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capability.operationFamily = OperationFamily.checksumCompute ∨
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capability.operationFamily = OperationFamily.hashPipeline
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| WorkloadOperation.merkleUpdate =>
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capability.memoryAccessShape = MemoryAccessShape.tree -- Would need tree access
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| WorkloadOperation.routeValidation =>
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capability.verificationSurface >= 0x00006000
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| WorkloadOperation.topologyCommitment =>
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capability.operationFamily = OperationFamily.validator
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| WorkloadOperation.workVerification =>
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capability.verificationSurface >= 0x00008000
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| WorkloadOperation.consensusProof =>
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capability.verificationSurface >= 0x00009000 -- Very high verification needed
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| WorkloadOperation.arbitraryCompute =>
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false -- Arbitrary compute never admissible on specialized ASIC
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/-- Check if workload is admissible on ASIC topology (TopoASIC specification). -/
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def checkWorkloadAdmissibility (workload : Workload) (topology : ASICTopology) (threshold : Semantics.Q16_16) : AdmissibilityResult :=
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let rec checkAllOps (ops : List WorkloadOperation) (admissibleCount : Nat) (totalCost : Semantics.Q16_16) : Nat × Semantics.Q16_16 :=
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match ops with
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| [] => (admissibleCount, totalCost)
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| op :: rest =>
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let rec checkNodes (nodes : Array ASICTopologyNode) (foundAdmissible : Bool) (nodeCost : Semantics.Q16_16) : Bool × Semantics.Q16_16 :=
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if nodes.size = 0 then (foundAdmissible, nodeCost)
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else
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let node := nodes[0]!
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let opAdmissible := checkOperationAdmissibility op node.capability
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let newCost := if opAdmissible then nodeCost + node.capability.energyPerTransform else nodeCost
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checkNodes nodes[1:] (foundAdmissible ∨ opAdmissible) newCost
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let (found, cost) := checkNodes topology.nodes false zero
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let newCount := if found then admissibleCount + 1 else admissibleCount
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let newTotalCost := totalCost + cost
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checkAllOps rest newCount newTotalCost
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let (admissibleCount, totalCost) := checkAllOps workload.operations 0 zero
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let allAdmissible := admissibleCount = workload.operations.length
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let costExceedsThreshold := totalCost > threshold
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let energyExceedsBudget := totalCost > workload.energyBudget
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let semanticLoss := if allAdmissible then zero else 0x00010000 -- High loss if not all admissible
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let verificationPass := allAdmissible ∧ ¬costExceedsThreshold ∧ ¬energyExceedsBudget
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let routeType := if ¬verificationPass then "rejected"
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else if workload.operations.all (λ op => op = WorkloadOperation.proofLike ∨ op = WorkloadOperation.workVerification) then "verify_only"
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else "compute"
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{
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admissible := verificationPass,
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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
|