# 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`

---

## 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

---

## 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

---

## Lean Implementation

### Module: Semantics.MorphicDSP

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

**Key Types:**

```lean
/-- 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:**

```lean
/-- 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:**

```lean
/-- 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
```

---

## 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 |

---

## 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)

---

## 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

---

## 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

---

## 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

---

## 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