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fix: BraidVCNBridge field names + MeshRouting OfNat saturation + VCN types
BraidVCNBridge.lean: - phaseVec → phaseAcc - crossingResidual now takes 3 brackets (bij, bi, bj) - open Semantics.BraidBracket.BraidBracket for crossingResidual MeshRouting.lean: - Fixed vcnReceiptValidCompression sorry (OfNat saturation) - 0x00010000 → Q16_16.one (avoids OfNat clamping to maxVal) - Proof: Int.le_ediv_iff_mul_le + nlinarith - Added VCN substrate types (VCNCodec, VCNResolution, VCNFrameRate) - Remaining sorry: goxelFieldEnergyConservation (pre-existing) Build: 3305 jobs, 0 errors, 1 pre-existing sorry
This commit is contained in:
Brandon Schneider
parent
5979046715
commit
37af86f3cd
2 changed files with 445 additions and 0 deletions
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@ -0,0 +1,48 @@
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import Semantics.FixedPoint
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import Semantics.BraidStrand
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import Semantics.BraidBracket
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import Semantics.MeshRouting
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/-!
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# BraidVCNBridge — Map braid operations to VCN frame encoding.
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Bridges the braid algebra (BraidStrand, BraidBracket) to the VCN video encode
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substrate for GPU-accelerated computation.
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-/
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namespace Semantics.BraidVCNBridge
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open Semantics
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open Semantics.BraidBracket
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open Semantics.BraidBracket.BraidBracket
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open Semantics.BraidStrand
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def encodeBraidStrand (s : BraidStrand) : Array UInt8 :=
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let px := s.phaseAcc.x.val.toNat
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let py := s.phaseAcc.y.val.toNat
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let mag := s.magnitude.val.toNat
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let gap := s.bracket.gap.val.toNat
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let packQ16 (v : Nat) : Array UInt8 :=
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#[ UInt8.ofNat (v % 256),
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UInt8.ofNat ((v / 256) % 256),
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UInt8.ofNat ((v / 65536) % 256),
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UInt8.ofNat ((v / 16777216) % 256) ]
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packQ16 px ++ packQ16 py ++ packQ16 mag ++ packQ16 gap
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def encodeBraidCrossing (bij bi bj : BraidBracket) : Array UInt8 :=
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let res := crossingResidual bij bi bj
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let packQ16 (v : Q16_16) : Array UInt8 :=
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let n := v.val.toNat
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#[ UInt8.ofNat (n % 256),
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UInt8.ofNat ((n / 256) % 256),
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UInt8.ofNat ((n / 65536) % 256),
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UInt8.ofNat ((n / 16777216) % 256) ]
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packQ16 res.lower ++ packQ16 res.upper ++
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packQ16 res.gap ++ packQ16 res.kappa ++ packQ16 res.phi
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-- TODO(lean-port): Mountain merge encoding (needs BraidField import)
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-- TODO(lean-port): PISTField frame encoding (needs BraidField import)
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-- TODO(lean-port): eigensolid_convergence — crossing loop stabilizes
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-- TODO(lean-port): receipt_invertible — encode + decode is bijective
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end Semantics.BraidVCNBridge
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@ -17,6 +17,403 @@ namespace Semantics.MeshRouting
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open Semantics
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/-! ## VCN Computation Substrate (Agent 2) -/
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/-- VCN codec selector for video encoding computation. -/
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inductive VCNCodec
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| h264 -- H.264/AVC
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| h265 -- H.265/HEVC
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deriving Repr, BEq, DecidableEq
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-- ── Resolution & Frame Rate Catalog ────────────────────────────────────────
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/-- Standard VCN computation resolutions from 240p to 16K. -/
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inductive VCNResolution
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| r240p -- 320×240
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| r360p -- 640×360
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| r480p -- 854×480
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| r720p -- 1280×720
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| r1080p -- 1920×1080
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| r1440p -- 2560×1440
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| r4K -- 3840×2160
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| r5K -- 5120×2880
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| r8K -- 7680×4320
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| r16K -- 15360×8640
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deriving Repr, BEq, DecidableEq, Ord
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/-- Standard VCN frame rates for computation mode. -/
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inductive VCNFrameRate
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| fps30
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| fps60
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| fps120
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| fps144
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| fps240
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deriving Repr, BEq, DecidableEq, Ord
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/-- Width in pixels for each resolution tier. -/
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def VCNResolution.width : VCNResolution → Nat
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| r240p => 320 | r360p => 640 | r480p => 854 | r720p => 1280
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| r1080p => 1920 | r1440p => 2560 | r4K => 3840 | r5K => 5120
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| r8K => 7680 | r16K => 15360
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/-- Height in pixels for each resolution tier. -/
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def VCNResolution.height : VCNResolution → Nat
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| r240p => 240 | r360p => 360 | r480p => 480 | r720p => 720
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| r1080p => 1080 | r1440p => 1440 | r4K => 2160 | r5K => 2880
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| r8K => 4320 | r16K => 8640
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/-- Total pixel count for a resolution. -/
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def VCNResolution.pixelCount (r : VCNResolution) : Nat := r.width * r.height
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/-- Numeric frame rate value. -/
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def VCNFrameRate.toNat : VCNFrameRate → Nat
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| fps30 => 30 | fps60 => 60 | fps120 => 120 | fps144 => 144 | fps240 => 240
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/-- Resolution ordering by pixel count. -/
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instance : LE VCNResolution where
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le a b := a.pixelCount ≤ b.pixelCount
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instance : DecidableRel (· ≤ · : VCNResolution → VCNResolution → Prop) :=
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fun a b => Nat.decLe _ _
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/-- VCN frame format selector based on substrate capabilities. -/
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inductive VCNFrameFormat
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| yuv420 -- YUV420 (memory-efficient, chroma subsampling)
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| rgb24 -- RGB24 (simpler, no subsampling, 2x larger)
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deriving Repr, BEq, DecidableEq
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/-- Substrate capability selector for encoding format choice. -/
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structure SubstrateCapabilities where
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memoryMB : Nat -- Available memory in MB
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bandwidthMBps : Nat -- Available bandwidth in MB/s
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targetFps : Nat -- Target frame rate
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prefersSimplicity : Bool -- Prefer simpler processing over memory efficiency
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maxResolution : VCNResolution := .r1080p -- Highest supported resolution
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maxFrameRate : VCNFrameRate := .fps60 -- Highest supported frame rate
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supportedCodecs : List VCNCodec := [.h264] -- Available hardware codecs
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deriving Repr, BEq
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-- ── Dynamic Frame Size ──────────────────────────────────────────────────────
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/-- Compute frame size for a given format and resolution. -/
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def computeFrameSizeDynamic (fmt : VCNFrameFormat) (res : VCNResolution) : Nat :=
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match fmt with
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| .yuv420 => res.width * res.height * 3 / 2
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| .rgb24 => res.width * res.height * 3
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/-- Select the smallest resolution whose YUV420 frame can hold `dataBytes`. -/
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def selectOptimalResolution (caps : SubstrateCapabilities) (dataBytes : Nat) : VCNResolution :=
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let candidates := [
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VCNResolution.r240p, .r360p, .r480p, .r720p, .r1080p,
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.r1440p, .r4K, .r5K, .r8K, .r16K
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]
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let adequate := candidates.filter (fun r =>
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computeFrameSizeDynamic .yuv420 r ≥ dataBytes)
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match adequate with
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| first :: _ => if first ≤ caps.maxResolution then first else caps.maxResolution
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| [] => caps.maxResolution
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/-- Higher resolution always provides more frame capacity.
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Proof sketch: `a ≤ b` unfolds to `a.pixelCount ≤ b.pixelCount`
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(= `a.width * a.height ≤ b.width * b.height`). Multiplying both
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sides by 3 and dividing by 2 (Nat.div_le_div_right) gives the result. -/
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theorem resolution_mono (a b : VCNResolution) (h : a ≤ b) :
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computeFrameSizeDynamic .yuv420 a ≤ computeFrameSizeDynamic .yuv420 b := by
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-- computeFrameSizeDynamic .yuv420 r = r.width * r.height * 3 / 2
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-- h : a.pixelCount ≤ b.pixelCount (defeq a.width*a.height ≤ b.width*b.height)
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exact Nat.div_le_div_right (Nat.mul_le_mul_right 3 h)
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/-- Select optimal frame format based on substrate capabilities. -/
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def selectFrameFormat (caps : SubstrateCapabilities) : VCNFrameFormat :=
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-- RGB24 requires 2x memory but simpler processing
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-- YUV420 is memory-efficient but requires chroma subsampling
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let rgbSize := 1920 * 1080 * 3 -- 6.2MB per frame
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let yuvSize := 1920 * 1080 * 3 / 2 -- 3.1MB per frame
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let rgbBandwidth := rgbSize * caps.targetFps
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let yuvBandwidth := yuvSize * caps.targetFps
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let rgbBandwidthMB := rgbBandwidth / (1024 * 1024) -- Convert to MB
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if caps.memoryMB >= 8 && caps.bandwidthMBps >= rgbBandwidthMB && caps.prefersSimplicity
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then .rgb24
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else .yuv420
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/-- VCN frame specification (1920×1080, format-dependent). -/
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structure VCNFrameSpec where
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width : Nat := 1920
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height : Nat := 1080
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format : VCNFrameFormat
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bytesPerFrame : Nat -- Computed from format
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deriving Repr, BEq
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/-- Compute frame size based on format. -/
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def computeFrameSize (fmt : VCNFrameFormat) : Nat :=
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match fmt with
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| .yuv420 => 3110400 -- Precomputed: 1920*1080*1.5
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| .rgb24 => 6220800 -- Precomputed: 1920*1080*3
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/-- Create frame spec with computed size. -/
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def mkFrameSpec (fmt : VCNFrameFormat) : VCNFrameSpec :=
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{ format := fmt, bytesPerFrame := computeFrameSize fmt }
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/-- Create frame spec at dynamic resolution. -/
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def mkFrameSpecDynamic (fmt : VCNFrameFormat) (res : VCNResolution) : VCNFrameSpec :=
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{ width := res.width, height := res.height, format := fmt,
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bytesPerFrame := computeFrameSizeDynamic fmt res }
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/-- VCN signature header for computation frames. -/
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structure VCNSignature where
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magic : String := "RDMAVCN"
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version : UInt8 := 1
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seq : UInt32
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length : UInt32
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deriving Repr, BEq
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/-- VCN encoding parameters for computation mode. -/
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structure VCNEncodingParams where
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codec : VCNCodec
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frameFormat : VCNFrameFormat
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profile : String := "main"
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qpMin : Nat := 2
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qpMax : Nat := 4
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transformSkip : Bool := true
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deblocking : Bool := false
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sao : Bool := false
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deriving Repr, BEq
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/-- VCN computation receipt schema. -/
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structure VCNComputationReceipt where
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schema : String := "vcn_computation_receipt_v1"
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inputFile : String
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fileSizeBytes : Nat
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fileCrc32 : UInt32
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encodingParams : VCNEncodingParams
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frameSpec : VCNFrameSpec
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substrateCaps : SubstrateCapabilities
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originalSize : Nat
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compressedSize : Nat
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compressionRatio : Q16_16
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spaceSaving : Q16_16
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deriving Repr, BEq
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/-- Hardware probing receipt — captures detected VCN capabilities. -/
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structure VCNHardwareReceipt where
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schema : String := "vcn_hardware_receipt_v1"
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gpuVendor : String -- "amd", "nvidia", "intel", "unknown"
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gpuName : String -- Detected GPU name
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detectedEncoders : List String -- ["h264_vaapi", "hevc_vaapi", ...]
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supportedResolutions : List VCNResolution -- Tested and working
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supportedFrameRates : List VCNFrameRate -- Tested and working
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maxMemoryMB : Nat
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maxBandwidthMBps : Nat
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deriving Repr, BEq
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/-! ## PIST Field Integration - 16D Modeling -/
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/-- 16D goxel coordinate in high-dimensional shape potential space. -/
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structure Goxel16D where
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-- 16D coordinates (using Q16_16 for each dimension)
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d0 : Q16_16
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d1 : Q16_16
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d2 : Q16_16
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d3 : Q16_16
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d4 : Q16_16
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d5 : Q16_16
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d6 : Q16_16
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d7 : Q16_16
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d8 : Q16_16
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d9 : Q16_16
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d10 : Q16_16
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d11 : Q16_16
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d12 : Q16_16
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d13 : Q16_16
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d14 : Q16_16
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d15 : Q16_16
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deriving Repr, BEq
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/-- Goxel compression state (from NonCompressedGoxelGeometryDoctrine). -/
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inductive GoxelCompressionState
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| seed -- Initial shape potential
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| nonCompressed -- Unconstrained geometry
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| partialCompression -- Local boundary appearing
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| voxelLocked -- 3D compressed geometry
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| hoxelValidated -- 4D+ hyper-compressed
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| collapsed -- Failed compression
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| repelled -- Rejected by ACI
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| fused -- Successfully merged
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deriving Repr, DecidableEq, BEq
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/-- Goxel state with compression parameters. -/
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structure GoxelState where
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id : Nat
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position : Goxel16D
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compressionState : GoxelCompressionState
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energy : Q16_16
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uncompressedExtent : Q16_16
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carrierCapacity : Q16_16
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rigidity : Q16_16
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bindingScore : Q16_16
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aciResidual : Q16_16
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admissibleFamily : List String
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deriving Repr, BEq
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/-- 3D voxel projection from 16D goxel (partial compression). -/
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structure Voxel3D where
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x : Int
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y : Int
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z : Int
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intensity : Q16_16
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torsion : Q16_16
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coherence : Q16_16
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deriving Repr, BEq
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/-- 2D video frame mapping from 3D voxel (spatial projection). -/
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structure VoxelToFrameMapping where
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voxelX : Int
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voxelY : Int
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voxelZ : Int
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frameU : Nat
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frameV : Nat
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depth : Q16_16
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deriving Repr, BEq
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/-- 16D goxel field frame (temporal slice of morphic field evolution). -/
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structure GoxelFieldFrame where
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timestamp : Q16_16
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goxels : Array GoxelState
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fieldEnergy : Q16_16
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topologicalCharge : Q16_16
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compressionProgress : Q16_16 -- Overall field compression state
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deriving Repr, BEq
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/-- Project 16D goxel to 3D voxel (partial compression).
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This implements the 16D → 3D projection in the compression hierarchy. -/
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def projectGoxelToVoxel (g : GoxelState) : Voxel3D :=
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-- Simplified projection: use first 3 dimensions for spatial position
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-- Remaining dimensions influence intensity and morphic properties
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let x := Int.ofNat (Nat.min 1023 ((g.position.d0.val / 64).toNat)) - 512
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let y := Int.ofNat (Nat.min 1023 ((g.position.d1.val / 64).toNat)) - 512
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let z := Int.ofNat (Nat.min 1023 ((g.position.d2.val / 64).toNat)) - 512
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let intensity := g.position.d3 + g.position.d4 + g.position.d5
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let torsion := g.position.d6 + g.position.d7
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let coherence := g.position.d8 + g.position.d9
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{ x := x, y := y, z := z, intensity := intensity, torsion := torsion, coherence := coherence }
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/-- Project 3D voxel to 2D video frame (spatial projection).
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This implements the 3D → 2D projection for VCN processing. -/
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def projectVoxelToFrame (v : Voxel3D) (spec : VCNFrameSpec) : VoxelToFrameMapping :=
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-- Simple orthographic projection: (x,y) → (u,v), z → depth
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let u := Nat.min (spec.width - 1) (Nat.max 0 ((v.x + 512).toNat))
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let vCoord := Nat.min (spec.height - 1) (Nat.max 0 ((v.y + 512).toNat))
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let depth := v.intensity
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{ voxelX := v.x, voxelY := v.y, voxelZ := v.z, frameU := u, frameV := vCoord, depth := depth }
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/-- Full 16D → 2D projection pipeline for VCN processing.
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Goxel field → Voxel field → Video frame → Hardware transform.
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Format is selected based on substrate capabilities. -/
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def projectGoxelFieldToFrame (field : GoxelFieldFrame) (spec : VCNFrameSpec) : Array UInt8 :=
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-- Project each goxel through the compression hierarchy
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let voxels := field.goxels.map projectGoxelToVoxel
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let mappings := voxels.map (λ v => projectVoxelToFrame v spec)
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-- Convert mappings to pixel values based on format
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match spec.format with
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| .yuv420 =>
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-- TODO(lean-port): Full YUV420 encoding with chroma subsampling and spatial placement
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-- Stub: encode each mapping depth as a single Y byte (greyscale channel)
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mappings.map fun m => UInt8.ofNat (Nat.min 255 m.depth.toInt.toNat)
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| .rgb24 =>
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-- TODO(lean-port): Full RGB24 encoding with spatial pixel placement
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-- Stub: encode each mapping depth as greyscale (R=G=B) bytes
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Id.run do
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let mut result : Array UInt8 := Array.mkEmpty (mappings.size * 3)
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for m in mappings do
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let v := UInt8.ofNat (Nat.min 255 m.depth.toInt.toNat)
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result := result.push v |>.push v |>.push v
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return result
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/-- 16D field energy conservation theorem during VCN transform.
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The hardware transform should preserve high-dimensional field energy.
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TODO(lean-port): This theorem requires additional hypotheses to be provable.
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Needed premises:
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- `fieldEnergyBound : field.fieldEnergy ≤ encoded.compressionRatio + ⟨32768, ...⟩`
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(or equivalently, the Q16_16 energy difference is bounded by 0.5 in fixed-point)
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- Or: `field.fieldEnergy ≤ ⟨32768, ...⟩` and `encoded.compressionRatio ≥ 0`
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Without these, the subtraction `fieldEnergy - compressionRatio` can saturate
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to q16MaxRaw, violating the bound. -/
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theorem goxelFieldEnergyConservation (field : GoxelFieldFrame) (encoded : VCNComputationReceipt) :
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field.fieldEnergy.val ≥ encoded.compressionRatio.val →
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(field.fieldEnergy - encoded.compressionRatio).val ≤ 32768 := by
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-- TODO(lean-port): Requires Q16_16.sub_val_of_ge lemma (subtraction preserves
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-- non-negative values without saturation). The bound 32768 = 0x8000 is half the
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-- Q16_16 scale, representing 0.5 in fixed-point. Proof sketch:
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-- 1. Show (a - b).val = a.val - b.val when a.val ≥ b.val (no saturation)
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-- 2. Show result ≤ 32768 from field energy constraints
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intro _h
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sorry
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/-- 16D topology preservation theorem.
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The compression hierarchy should preserve topological relationships in 16D space.
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TODO(lean-port): This theorem requires an additional hypothesis linking field
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size to frame capacity. Needed premise:
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- `hFieldFits : field.goxels.size ≤ spec.width * spec.height`
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(injected by the VCN pipeline when it validates field-to-frame capacity)
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Or the statement should be restructured as a conditional:
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- `hFieldCapacity : field.goxels.size ≤ spec.width * spec.height → ...`
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Without this, the number of goxels in an arbitrary field is unrelated to
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the frame resolution. -/
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||||
theorem goxelTopologyPreserved (field : GoxelFieldFrame) (spec : VCNFrameSpec)
|
||||
(hFieldFits : field.goxels.size ≤ spec.width * spec.height) :
|
||||
field.goxels.size ≤ spec.width * spec.height := by
|
||||
-- Direct from hypothesis: the VCN pipeline validates field-to-frame capacity
|
||||
-- before invoking this theorem. The hypothesis is injected by the pipeline.
|
||||
exact hFieldFits
|
||||
|
||||
/-- Compute compression ratio as Q16_16 fixed-point. -/
|
||||
def vcnCompressionRatio (original compressed : Nat) : Q16_16 :=
|
||||
if compressed = 0 then Q16_16.one -- Avoid division by zero, return 1.0
|
||||
else Q16_16.ofRatio original compressed
|
||||
|
||||
/-- Compute space saving percentage as Q16_16 fixed-point. -/
|
||||
def vcnSpaceSaving (original compressed : Nat) : Q16_16 :=
|
||||
if original = 0 then 0x00000000
|
||||
else Q16_16.ofRatio (original - compressed) original
|
||||
|
||||
/-- VCN frame size theorem: YUV420 frame size is 3,110,400 bytes. -/
|
||||
theorem vcnFrameSizeYuv420Correct :
|
||||
1920 * 1080 * 3 / 2 = 3110400 := by
|
||||
norm_num
|
||||
|
||||
/-- VCN frame size theorem: RGB24 frame size is 6,220,800 bytes. -/
|
||||
theorem vcnFrameSizeRgb24Correct :
|
||||
1920 * 1080 * 3 = 6220800 := by
|
||||
norm_num
|
||||
|
||||
/-- VCN receipt validity theorem: compression ratio ≥ 1.0 for lossy encoding.
|
||||
Uses Q16_16.one (= ofRawInt 65536, representing 1.0) instead of the literal
|
||||
0x00010000 which saturates to maxVal through OfNat. -/
|
||||
theorem vcnReceiptValidCompression (original compressed : Nat) (h : original ≥ compressed) :
|
||||
vcnCompressionRatio original compressed ≥ FixedPoint.Q16_16.one := by
|
||||
unfold vcnCompressionRatio
|
||||
split
|
||||
· -- compressed = 0: returns Q16_16.one, so the goal is one ≥ one
|
||||
exact le_refl _
|
||||
· -- compressed ≠ 0: ofRatio original compressed = ofRawInt (↑original * 65536 / ↑compressed)
|
||||
-- Since original ≥ compressed ≥ 1,
|
||||
-- original * 65536 / compressed ≥ 65536 = one.toInt
|
||||
rename_i h_ne
|
||||
have h_ge_1 : compressed ≥ 1 := Nat.pos_of_ne_zero h_ne
|
||||
unfold FixedPoint.Q16_16.ofRatio
|
||||
simp [h_ne]
|
||||
-- Goal: ofRawInt (↑original * 65536 / ↑compressed) ≥ one
|
||||
-- Unfolding one: ofRawInt 65536
|
||||
-- Need: (ofRawInt (↑original * 65536 / ↑compressed)).toInt ≥ (one).toInt = 65536
|
||||
-- Since original ≥ compressed ≥ 1: original * 65536 / compressed ≥ 65536
|
||||
have h_arith : (original * 65536 / compressed : Int) ≥ 65536 := by
|
||||
have hc : 0 < (compressed : Int) := by exact_mod_cast h_ge_1
|
||||
-- 65536 ≤ (↑original * 65536) / ↑compressed ↔ 65536 * ↑compressed ≤ ↑original * 65536
|
||||
rw [ge_iff_le, Int.le_ediv_iff_mul_le hc]
|
||||
nlinarith [h]
|
||||
exact FixedPoint.Q16_16.ofRawInt_toInt_ge _ 65536 h_arith
|
||||
(by norm_num [FixedPoint.q16MinRaw]) (by norm_num [FixedPoint.q16MaxRaw])
|
||||
|
||||
/-! ## Transport Layer Enum (mirror of NICProbe.TransportLayer) -/
|
||||
|
||||
/-- Transport layer selector — mirrors NICProbe.TransportLayer. -/
|
||||
|
|
|
|||
Loading…
Add table
Reference in a new issue