Research-Stack/6-Documentation/docs/MORPHIC_DSP_RECONFIGURATION_SPEC.md

Morphic DSP Reconfiguration Specification

Date: 2026-04-26T19:52:00 Status: Concept reconfiguration complete Task: Swarm-assisted DSP concept reconfiguration via morphic scalar Lean Source: 0-Core-Formalism/lean/Semantics/Semantics/MorphicDSP.lean Swarm Script: scripts/execute_swarm_dsp_reconfiguration.py

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Overview

This document specifies the reconfiguration of the DSP (Digital Signal Processing) concept from fixed-function hardware to morphic-scalar-controlled reconfigurable processing units. The network swarm was assigned to analyze the current DSP implementation and propose a morphic-scalar-based reconfiguration.

Current DSP Concept Analysis

Existing DSP Modules

1. DSPTranslation.lean

• Purpose: DSP to neuromorphic formal bridge
• Features:
  • Q16.16 fixed-point arithmetic
  • STDP learning update
  • Geodesic cost calculation
  • Translation matrix operations
• Limitation: Fixed-function DSP operations, not reconfigurable

2. DspErasureCoding.lean

• Purpose: DSP-aware 3-stream erasure coding
• Features:
  • 3-stream redundancy scheme
  • Spectral analysis for erasure detection
  • FPGA DSP slice integration
  • Q16.16 fixed-point
• Limitation: DSP slices used as fixed multipliers, not adaptive

Current DSP Concept

Traditional DSP:

• Fixed-function hardware (multipliers, adders, MAC units)
• Predefined operation modes
• Static resource allocation
• No adaptation to signal characteristics

FPGA DSP Slices:

• 8 DSP slices on Lattice iCE40 HX8K
• Used as fixed multipliers in current implementation
• [BEAUTIFUL_PROVISIONAL - 62.5% utilization (5 slices) in optimized morphic scalar - requires synthesis verification evidence with corpus provenance]
• No runtime reconfiguration

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Proposed Morphic DSP Concept

Core Principle

DSP as Reconfigurable Processing Unit:

• DSP slices are not fixed multipliers but reconfigurable processing units
• Morphic scalar state machine controls DSP configuration
• OEPI threshold determines DSP allocation priority
• DSP modes adapt to signal characteristics via scalar collapse

Key Changes

1. Reconfigurable DSP Modes

   • multiply: Standard multiplication
   • accumulate: Accumulation for dot products
   • convolution: Convolution kernel
   • fft: FFT butterfly operations
   • filter: Digital filtering
   • adaptive: Adaptive filtering (OEPI-controlled)

2. State-to-Mode Mapping

   • Morphic scalar state determines DSP operation mode
   • 16 scalar states map to 6 DSP modes
   • Dynamic reconfiguration based on scalar collapse

3. OEPI-Based Allocation

   • Critical OEPI (≥95): All 5 DSP slices
   • Medium OEPI (70-95): 3 DSP slices
   • Low OEPI (<70): 1 DSP slice
   • Adaptive resource allocation

4. FPGA Integration

   • 5 DSP slices for morphic scalar (62.5% of 8 available)
   • Parallel OEPI calculation uses 5 DSP slices
   • Reconfigurable based on scalar state
   • Remaining 3 DSP slices for other functions

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Lean Implementation

Module: Semantics.MorphicDSP

File: 0-Core-Formalism/lean/Semantics/Semantics/MorphicDSP.lean

Key Types:

/-- DSP operation mode (reconfigurable via morphic scalar). -/
inductive DspMode where
  | multiply       -- Standard multiplication
  | accumulate     -- Accumulation for dot products
  | convolution    -- Convolution kernel
  | fft           -- FFT butterfly operations
  | filter         -- Digital filtering
  | adaptive       -- Adaptive filtering (OEPI-controlled)

/-- DSP slice configuration. -/
structure DspConfig where
  mode : DspMode
  operandA : Q16_16
  operandB : Q16_16
  accumulator : Q16_16
  oepiThreshold : Q16_16

/-- DSP slice state (controlled by morphic scalar). -/
structure DspSlice where
  sliceId : Nat
  config : DspConfig
  active : Bool
  morphicState : Morphic.ScalarState

/-- DSP slice bank (5 slices for morphic scalar FPGA). -/
structure DspBank where
  slices : Array DspSlice
  totalSlices : Nat
  activeSlices : Nat

Key Functions:

/-- Map morphic scalar state to DSP mode. -/
def stateToDspMode (state : Morphic.ScalarState) : DspMode

/-- Configure DSP slice based on morphic scalar state and OEPI. -/
def configureDspSlice (slice : DspSlice) (oepi : Q16_16) : DspSlice

/-- Execute reconfigurable DSP operation based on mode. -/
def executeDspOp (config : DspConfig) : Q16_16

/-- Initialize DSP bank with 5 slices. -/
def initDspBank : DspBank

/-- Allocate DSP slices based on OEPI threshold. -/
def allocateDspSlices (bank : DspBank) (oepi : Q16_16) : DspBank

Theorems:

/-- Theorem: Superposed state maps to adaptive DSP mode. -/
theorem superposedMapsToAdaptive :
  stateToDspMode Morphic.ScalarState.superposed = DspMode.adaptive

/-- Theorem: Critical OEPI allocates all 5 DSP slices. -/
theorem criticalOepiAllocatesAll (bank : DspBank) (oepi : Q16_16) :
  let critical := Q16_16.ofInt 95
  oepi >= critical → (allocateDspSlices bank oepi).activeSlices = 5

/-- Theorem: DSP bank has exactly 5 slices. -/
theorem dspBankHasFiveSlices (bank : DspBank) :
  bank.totalSlices = 5

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State-to-Mode Mapping

Morphic Scalar State	DSP Mode	Rationale
SUPERPOSED	adaptive	Superposition requires adaptive processing
SCOUTING	filter	Scouting filters signal characteristics
MEASURE_LOCAL_NEED	convolution	Measurement requires convolution analysis
COLLAPSED_PROFILE	multiply	Collapsed profile uses standard multiplication
EXECUTE	accumulate	Execution accumulates results
RECEIPT	filter	Receipt generation filters outputs
AMPLITUDE_UPDATE	accumulate	Amplitude updates accumulate changes
QUERY_COLLECTIVE	fft	Collective queries use FFT for frequency analysis
COLLECTIVE_RESPONSE	adaptive	Collective response requires adaptive processing
QUERY_LLM	convolution	LLM queries use convolution for embedding
DIRECTED	multiply	Directed operations use multiplication
HOLD	multiply	Hold state maintains multiplication
OPERATOR_ALERT	adaptive	Operator alert triggers adaptive processing
LOW_POWER_PASSIVE_MODE	filter	Low power mode uses filtering
QUARANTINE	multiply	Quarantine uses simple multiplication
MIGRATE	fft	Migration uses FFT for transformation

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OEPI-Based Resource Allocation

Allocation Rules

Critical OEPI (≥95):

• Allocation: 5 DSP slices (100% of morphic scalar bank)
• Rationale: Maximum processing power for critical situations
• Use Case: Operator alert, emergency response, safety-critical operations

Medium OEPI (70-95):

• Allocation: 3 DSP slices (60% of morphic scalar bank)
• Rationale: Balanced processing for moderate priority
• Use Case: Normal operation, query processing, collective response

Low OEPI (<70):

• Allocation: 1 DSP slice (20% of morphic scalar bank)
• Rationale: Minimal processing for low-priority tasks
• Use Case: Idle state, low power mode, background processing

Dynamic Reconfiguration

DSP slices are dynamically reconfigured based on:

1. Morphic scalar state transitions
2. OEPI threshold changes
3. Signal characteristics (via scalar collapse)
4. Operator availability (affects OEPI)

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FPGA Integration

Target Hardware: Lattice iCE40 HX8K

DSP Slice Budget:

• Total DSP slices: 8
• Morphic scalar allocation: 5 (62.5%)
• Remaining for other functions: 3 (37.5%)

Morphic Scalar DSP Usage:

• OEPI calculation: 5 parallel multipliers (5 DSP slices)
• State-dependent reconfiguration: Dynamic mode switching
• Adaptive processing: OEPI-controlled operation selection

Performance Impact:

• Without reconfiguration: Fixed 5 DSP slices for multiplication only
• With reconfiguration: 5 DSP slices for 6 different modes
• Flexibility gain: 6x operational flexibility
• Resource efficiency: Same hardware, more capabilities

Integration with Optimized FPGA

The morphic DSP concept integrates with the optimized FPGA implementation:

1. Parallel OEPI Calculation

   • Uses 5 DSP slices for parallel multiplication
   • Tree-structured addition for minimal latency
   • Reconfigurable based on scalar state

2. State Machine Control

   • Scalar state machine controls DSP mode selection
   • Auto-transition to low power mode affects DSP allocation
   • Operator unavailable triggers adaptive DSP mode

3. Adaptive Processing

   • OEPI threshold determines DSP slice allocation
   • Signal characteristics (via scalar collapse) affect DSP mode
   • Dynamic reconfiguration without hardware changes

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Swarm Task Execution

Task: execute_swarm_dsp_reconfiguration.py

Purpose: Assign network swarm to reconfigure DSP concept

Steps:

1. Analyze current DSP concept in Lean codebase
2. Propose morphic-scalar-based DSP concept
3. Generate Lean code for MorphicDSP module
4. Integrate with FPGA DSP slice utilization
5. Save results to data/swarm_dsp_reconfiguration_result.json

Output:

• Current DSP analysis
• Morphic DSP proposal
• Lean code for MorphicDSP module
• FPGA integration details
• State-to-mode mapping
• OEPI allocation rules

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Benefits of Morphic DSP Reconfiguration

1. Flexibility

• Before: Fixed DSP operations
• After: 6 reconfigurable modes
• Gain: 6x operational flexibility

2. Adaptivity

• Before: Static resource allocation
• After: OEPI-based dynamic allocation
• Gain: Adaptive resource usage based on priority

3. Integration

• Before: Separate DSP and scalar systems
• After: Unified morphic-scalar-controlled DSP
• Gain: Tighter integration, better coordination

4. Efficiency

• Before: 5 DSP slices for multiplication only
• After: 5 DSP slices for 6 different operations
• Gain: Same hardware, more capabilities

5. Safety

• Before: Fixed processing regardless of situation
• After: Adaptive processing based on OEPI and operator availability
• Gain: Safety-critical situations get maximum resources

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Next Steps

1. Lean Verification: Complete Lean theorem proofs in MorphicDSP.lean
2. Verilog Integration: Add morphic DSP reconfiguration to optimized FPGA
3. Simulation: Test DSP reconfiguration with Verilog testbench
4. Synthesis: Verify DSP slice utilization with Yosys
5. Performance Testing: Measure performance gains from reconfiguration
6. Documentation: Update FPGA Warden Node spec with morphic DSP

Files

File	Role
0-Core-Formalism/lean/Semantics/Semantics/MorphicDSP.lean	Lean morphic DSP implementation
scripts/execute_swarm_dsp_reconfiguration.py	Swarm task script
docs/MORPHIC_DSP_RECONFIGURATION_SPEC.md	This document
0-Core-Formalism/lean/Semantics/Semantics/DSPTranslation.lean	Original DSP module
0-Core-Formalism/lean/Semantics/Semantics/DspErasureCoding.lean	Original DSP erasure coding
hardware/morphic_scalar_fpga_optimized.v	Optimized FPGA with DSP slices

References

• AGENTS.md - Lean extraction rules
• 0-Core-Formalism/lean/Semantics/MorphicScalar.lean - Morphic scalar implementation
• 0-Core-Formalism/lean/Semantics/OEPI.lean - OEPI calculation
• docs/FPGA_MORPHIC_SCALAR_OPTIMIZED_SPEC.md - Optimized FPGA specification