Research-Stack/6-Documentation/docs/specs/CBF_Hardware_Spec.md

Chromatic Braid Field (CBF) Hardware Specification

Version: 1.0-CBF
Status: Design phase — FPGA Warden Node rewrite
Date: 2026-04-17

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1. Overview

The Chromatic Braid Field (CBF) core unifies:

• DIAT local tuple encoding
• Corrected AMMR vector accumulation
• Bracket-based admissibility calculus
• AVMR hierarchical strand aggregation
• CMYK channel decomposition

Formal identity:

CBF = DIAT ∘ AMMR ∘ Bracket ∘ AVMR ∘ CMYK ∘ Rope/MIMO

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2. Processing Pipeline

Input bytes / local samples
    ↓
[Segmenter / Leaf Builder]
    ↓
build DIATLeaf(a, b, ab, a-b, residue, slot, parity, jitter)
    ↓
[DIAT Lift]
    ↓
Φ(DIATLeaf) → PhaseVec(x, y)
    ↓
[φ-Accumulator + Prime Counter + Void Mask LUT]
    ↓
deterministic address / resonance basis
proximity / modulation contribution
carrier-local weighting
    ↓
[AMMR Vector Accumulator]
    ↓
Σ PhaseVec over active leaves / modes / strands
    ↓
[Bracket Step]
    ↓
κ = ||z_φ||
φ = atan2(z_y, z_x)
lower / upper / gap
admissible?
    ↓
[CMYK Colorizer]
    ↓
C = coherence
M = modulation
Y = yield
K = constraint
    ↓
[Braid Cross / AVMR Merge]
    ↓
merge phaseAcc linearly
merge metadata
recompute bracket
recompute color
    ↓
[Colored Rope Binder]
    ↓
bundle all strands for this cycle
    ↓
[Carrier Encoder / MIMO Projection]
    ↓
audio projection
video projection
caption projection
timing projection
    ↓
[Processor / Channel / Detangler]
    ↓
recover strands for next cycle

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3. Core Principles

3.1 Linear Accumulation Discipline

All strand and carrier composition occurs by linear accumulation in vector space. Only after accumulation is complete does the core perform:

1. Single nonlinear projection to derive magnitude and phase
2. Bracket-shell construction
3. Chromatic channel assignment

Result: Nonlinear work moved out of the inner loop; associativity, commutativity, and parallel recombination preserved.

3.2 Q16.16 Fixed-Point Arithmetic

All arithmetic uses Q16.16 fixed-point:

• κ approximation: octagonal norm
• atan2: quadrant-aware polynomial approximation
• Zero-vector handling: ϕ = 0 when (x, y) = (0, 0)

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4. Module Specifications

4.1 DIAT Leaf Builder

Input: Raw bytes / samples
Output: DIATLeaf structure

Field	Type	Description
a	Q16.16	Primary value
b	Q16.16	Secondary value
ab	Q16.16	Product a·b
diff	Q16.16	Difference a-b
residue	Q16.16	Local residue
slot	UInt32	Timing slot
parity	Bool	Strand parity
jitterTolerance	Q16.16	Jitter bound

Lift function:

Φ(DIATLeaf) → PhaseVec:
    x = a - b
    y = ab + residue

4.2 AMMR Vector Accumulator

Input: PhaseVec contributions
Output: Accumulated PhaseVec

z_φ = Σ Φᵢ

Properties:

• Associative
• Commutative
• Parallelizable
• No nonlinear operations in-loop

4.3 Bracket Step

Input: Accumulated PhaseVec
Output: BraidBracket

κ = ||z_φ||          (octagonal approximation)
ϕ = atan2(z_y, z_x)  (safe, total function)

lower = -κ
upper = κ
gap = upper - lower
admissible = gap ≤ threshold

4.4 CMYK Colorizer

Input: BraidBracket + AVMRMeta
Output: CMYKWeights

Channel	Mapping	Semantics
C	bracket.kappa	Coherence
M	meta.totalInteraction	Modulation
Y	half if admissible else quarter	Yield
K	quarter if admissible else one	Constraint

4.5 Braid Cross / AVMR Merge

Input: Two BraidStrand objects
Output: Merged BraidStrand

Merge rules:

phaseAcc = l.phaseAcc + r.phaseAcc      (linear)
meta = metaMerge(l.meta, r.meta)         (hierarchical)
bracket = bracketStep(phaseAcc)       (recomputed)
color = colorize(bracket, meta)         (recomputed)

Crossing residual:

Rᵢⱼ = Bᵢⱼ - (Bᵢ + Bⱼ)

4.6 Colored Rope Binder

Input: Array of BraidStrand
Output: ColoredRope

Bundles all strands for the current cycle into a multiplexed rope object.

4.7 MIMO Carrier Encoder

Input: ColoredRope
Output: Carrier projections

Carrier	Projection	Channel
Audio	rope.audio()	Φ⁽ᵃ⁾
Video	rope.video()	Φ⁽ᵛ⁾
Caption	rope.caption()	Φ⁽ᶜ⁾
Timing	rope.timing()	Φ⁽ᵗ⁾

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5. Target Hardware

5.1 Primary Target: Lattice iCE40 HX8K

Resource	Required	Budget	Utilisation
LUT cells (logic)	~300	7,680	3.9%
LUTRAM (void mask)	512 bits	8KB	6.3%
Flip-flops	~150	7,680	2.0%
Block RAM	0	128KB	0%
DSP slices	0	8	0%

5.2 Performance

• Clock: 50 MHz (20ns/cycle)
• Accumulation latency: N_MODES × 1 cycle
• Final projection: 4 cycles (pipelined)
• Total per attestation: ~20 cycles = 400ns
• Throughput: 2.5M attestations/second

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6. Files

File	Role
Semantics/CBFCore.lean	Formal core (DIAT, AMMR, Bracket, AVMR, CMYK)
hardware/cbf_warden.v	Verilog: CBF Warden implementation
hardware/diat_builder.v	DIAT leaf construction
hardware/ammr_accum.v	PhaseVec accumulator
hardware/bracket_step.v	Bracket calculus unit
hardware/cmyk_colorizer.v	CMYK channel assignment
hardware/braid_cross.v	Strand merge / crossing
hardware/rope_binder.v	Colored rope assembly
hardware/mimo_encoder.v	Carrier projection
hardware/q16_norm.v	Octagonal norm approximation
hardware/q16_atan2.v	Safe atan2 implementation

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7. One-Line Summary

CBF reduces processing by moving nonlinear work out of the inner loop, preserving associativity through linear AMMR accumulation, and applying bracket calculus only after complete strand state is known.

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Attestation Hash: SHA256(CBF ∘ AMMR ∘ Bracket ∘ CMYK)
Registry Entry: pkg/cbf-hardware/v1.0
Tier: CRYSTALLINE