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

Morphic DSP Concept

Date: 2026-04-26T19:55:00 Status: Conceptual exploration with three-layer distinction Question: What if the DSP itself was morphic?

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Three-Layer Distinction

There are three distinct meanings of "morphic DSP" that must be clearly separated:

Layer 1: Controlled DSP

Definition: Fixed DSP slice, morphic scalar selects mode

• DSP slices are reconfigurable (6 modes)
• Controlled by external morphic scalar state machine
• OEPI-based allocation
• Fixed hardware structure, variable function
• Current implementation: This is what we have now

Layer 2: Virtual Morphic DSP

Definition: Many fixed DSPs + LUT/interconnect + control FSM = morphic-looking pool

• DSP slices + LUT fabric + routing fabric + control FSM
• Morphic scalar amplitudes + receipt gates
• Self-reconfiguring logical structure (not physical self-modification)
• Fluid merge/split boundaries via resource pooling
• Composable operation basis (not infinite operations)
• Immediate target: Buildable on current FPGA hardware

Layer 3: True Morphic DSP

Definition: Custom hardware whose internal structure and boundaries really adapt

• Physical self-modification requires custom ASIC / future hardware
• Self-modifying structure (multiplier becomes adder, custom operation)
• Fluid boundaries (slices merge/split physically)
• Quantum-inspired superposition (operations in superposition until collapse)
• Adaptive topology (interconnects reconfigure dynamically)
• Self-organization (emergent structure from local rules)
• Long-term target: Requires hardware beyond current FPGA capabilities

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Transition Path

Phase 1: Controlled DSP (current)

• Reconfigurable modes (6 modes)
• External control by morphic scalar
• Fixed hardware structure

Phase 2: Virtual Morphic DSP (immediate target)

• Self-reconfiguring logical structure
• Limited boundary fluidity via resource pooling
• Composable operation basis
• AngrySphinx gates for safety
• Buildable on current FPGA

Phase 3: True Morphic DSP (long-term target)

• Full structural adaptation
• Complete boundary fluidity
• Quantum-inspired superposition
• Self-organizing topology
• Requires custom hardware

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Virtual Morphic DSP (Immediate Target)

Core Principle

DSP pool with morphic behavior via logical reconfiguration:

• Multiple fixed DSP slices + LUT fabric + routing fabric
• Control FSM + morphic scalar amplitudes + receipt gates
• Self-reconfiguring logical structure (not physical self-modification)
• Fluid merge/split boundaries via resource pooling
• Composable operation basis within admissible set

Virtual Morphic DSP Properties

[BEAUTIFUL_PROVISIONAL - All capabilities are conceptual without hardware verification evidence]

1. Self-Reconfiguring Logical Structure

• DSP slices can change their logical configuration [conceptual - requires FPGA synthesis verification]
• Multiplier can be used as adder, subtractor via LUT emulation [conceptual - requires implementation evidence]
• Bit-width adapts logically (16-bit → 32-bit via time-multiplexing) [conceptual - requires timing analysis evidence]
• Pipeline depth adjusts logically (via scheduling) [conceptual - requires implementation evidence]

2. Fluid Boundaries (Virtual)

• DSP slices can merge logically to form larger processing units [conceptual - requires resource pooling implementation evidence]
• Large DSP can split logically into smaller independent units [conceptual - requires implementation evidence]
• Boundary is fluid at logical level (resource pooling) [conceptual - requires implementation evidence]
• Enables virtual resource pooling [conceptual - requires benchmark evidence]

3. Composable Operation Basis

• DSP operation exists in composable basis (not infinite) [conceptual - requires formal specification evidence]
• Basis includes: multiply, accumulate, convolution, fft, filter, adaptive [proposed basis - requires implementation evidence]
• New modes composed from basis operations [conceptual - requires composition mechanism evidence]
• Admissible basis prevents overclaiming [conceptual - requires formal proof evidence]

4. Adaptive Topology (Logical)

• Interconnect between DSP slices reconfigures logically [conceptual - requires FPGA routing reconfiguration evidence]
• Dataflow patterns adapt to signal characteristics [conceptual - requires signal analysis evidence]
• Network topology emerges from computation needs [conceptual - requires emergence mechanism evidence]
• Self-organizing structure at logical level [conceptual - requires self-organization algorithm evidence]

5. Scalar Collapse with Gates

• DSP operations "collapse" when measured [conceptual - quantum-inspired metaphor without physical quantum evidence]
• Collapse selects specific implementation from composable basis [conceptual - requires selection mechanism evidence]
• Collapse is gated by AngrySphinx (not automatic permission) [conceptual - requires gate implementation evidence]
• Execution requires policy/sigma/resource/thermal/receipt passes [conceptual - requires integrated system evidence]

Core Principle

DSP slices are morphic entities themselves:

• Self-modifying structure (not just mode)
• Fluid boundaries (slices merge/split)
• Quantum-inspired superposition (operations in superposition until measurement)
• Adaptive topology (interconnects reconfigure dynamically)
• Scalar collapse (DSP operations "collapse" into specific implementations)

True Morphic DSP Properties (Long-Term Target)

1. Physical Self-Modifying Structure

• DSP slices can change their internal architecture physically
• Multiplier can become adder, subtractor, or custom operation
• Bit-width adapts dynamically (16-bit → 32-bit → 64-bit)
• Pipeline depth adjusts based on complexity

2. Physical Fluid Boundaries

• DSP slices can merge physically to form larger processing units
• Large DSP can split physically into smaller independent units
• Boundary is fluid, not fixed
• Enables physical resource pooling

3. Quantum-Inspired Superposition

• DSP operation exists in superposition of multiple implementations
• Measurement (scalar collapse) selects specific implementation
• Amplitude represents probability of each implementation
• Enables probabilistic computing

4. Adaptive Topology (Physical)

• Interconnect between DSP slices reconfigures dynamically
• Dataflow patterns adapt to signal characteristics
• Network topology emerges from computation needs
• Self-organizing structure

5. Scalar Collapse with Gates

• DSP operations "collapse" when measured
• Collapse selects specific implementation from superposition
• Collapse is gated by AngrySphinx (not automatic permission)
• Execution requires policy/sigma/resource/thermal/receipt passes

---

Morphic DSP Architecture

Morphic DSP Entity

/-- Morphic DSP entity with quantum-inspired properties. -/
structure MorphicDsp where
  dspId : Nat
  superposedOps : Array (Q16_16 × DspMode)  -- Amplitude × Mode
  collapsedOp : Option (Q16_16 × DspMode)    -- Collapsed operation
  boundaryState : BoundaryState              -- Fluid boundary state
  topology : DspTopology                      -- Adaptive interconnect
  deriving Repr

/-- DSP boundary state (fluid). -/
inductive BoundaryState where
  | independent  -- Standalone DSP slice
  | merged       -- Merged with other DSP
  | split        -- Split from larger DSP
  | fluid        -- In transition state
  deriving Repr, DecidableEq, BEq

/-- DSP topology (adaptive interconnect). -/
structure DspTopology where
  connections : Array (Nat × Nat)  -- DSP connections
  bandwidth : Array Q16_16         -- Connection bandwidth
  latency : Array Q16_16           -- Connection latency
  deriving Repr

Morphic DSP Operations

1. Superposition Collapse

/-- Collapse DSP superposition into specific operation. -/
def collapseDspSuperposition (dsp : MorphicDsp) (measurement : DspMode) : MorphicDsp :=
  let selected := dsp.superposedOps.find (fun (amp, mode) => mode = measurement)
  match selected with
  | some (amp, mode) => { dsp with collapsedOp := some (amp, mode) }
  | none => dsp

2. Boundary Fluidity

/-- Merge two DSP slices into larger processing unit. -/
def mergeDspSlices (dsp1 dsp2 : MorphicDsp) : MorphicDsp :=
  let combinedOps := dsp1.superposedOps ++ dsp2.superposedOps
  let newTopology := mergeTopologies dsp1.topology dsp2.topology
  {
    dspId := dsp1.dspId,
    superposedOps := combinedOps,
    collapsedOp := none,
    boundaryState := BoundaryState.merged,
    topology := newTopology
  }

/-- Split DSP into smaller independent units. -/
def splitDspSlice (dsp : MorphicDsp) (splitRatio : Nat) : Array MorphicDsp :=
  -- Split DSP into multiple smaller units
  -- Each unit gets subset of superposed operations
  sorry  -- Implementation depends on split strategy

3. Adaptive Topology

/-- Reconfigure DSP topology based on computation needs. -/
def adaptDspTopology (dsp : MorphicDsp) (needs : ComputationNeeds) : MorphicDsp :=
  let newConnections := optimizeConnections dsp.topology needs
  let newTopology := { dsp.topology with connections := newConnections }
  { dsp with topology := newTopology }

---

Morphic DSP vs Controlled DSP

Aspect	Controlled DSP	Virtual Morphic DSP	True Morphic DSP
Structure	Fixed hardware	Self-reconfiguring logical structure + BRAM	Physical self-modification
Boundaries	Fixed	Fluid (merge/split via pooling)	Fluid (merge/split physically)
Operations	6 modes	Composable operation basis + BRAM weights	Superposition within basis
Topology	Fixed interconnect	Adaptive logical interconnect	Adaptive physical interconnect
Control	External scalar	External scalar + gates + BRAM updates	Internal self-organization
Adaptation	Mode switching	Logical structural evolution + BRAM updates	Physical structural evolution
Complexity	[BEAUTIFUL_PROVISIONAL - O(1) mode switch - requires timing evidence]	[BEAUTIFUL_PROVISIONAL - O(log n) logical reconfiguration - requires algorithmic analysis evidence]	[BEAUTIFUL_PROVISIONAL - O(1) physical adaptation - requires hardware evidence]
Hardware	Gowin GW1NR-9	Gowin GW1NR-9 (uses BRAM)	Custom ASIC/future FPGA
DSP Slices	0 (no DSP on Gowin)	0 (LUT-based mult)	N/A
BRAM Usage	0	1-4KB (partial LUT)	N/A
Clock	27MHz	27MHz	N/A

---

AngrySphinx Gates for Morphic DSP

Collapse Gates

REFUSE_DSP_COLLAPSE

if requested mode not in admissible basis:
    REFUSE_DSP_COLLAPSE

• Prevents collapse into undefined or unsafe modes
• Protects against overclaiming capabilities
• Ensures operation within admissible basis

ALLOW_DSP_COLLAPSE

if requested mode in admissible basis:
    ALLOW_DSP_COLLAPSE → candidate implementation

• Permits collapse into known-safe modes
• Enables operation within composable basis

Boundary Gates

HOLD_BOUNDARY_FLUIDITY

if merge exceeds resource/thermal bound:
    HOLD_BOUNDARY_FLUIDITY

• Prevents merge that exceeds resource envelope
• Protects against thermal violations
• Maintains system stability

ALLOW_MERGE

if merge within resource/thermal bound:
    ALLOW_MERGE

• Permits merge within safe limits
• Enables resource pooling

REQUIRE_RENORMALIZATION

if split loses semantic precision:
    REQUIRE_RENORMALIZATION

• Prevents split that degrades precision
• Requires renormalization before proceeding
• Maintains numerical accuracy

ALLOW_SPLIT

if split preserves semantic precision:
    ALLOW_SPLIT

• Permits split that maintains precision
• Enables resource distribution

Topology Gates

ALLOW_TOPOLOGY_ADAPT

if topology adaptation valid and receipt path exists:
    ALLOW_TOPOLOGY_ADAPT

• Permits topology reconfiguration
• Ensures receipt path maintained

REFUSE_NO_RECEIPT

if topology adaptation breaks receipt path:
    REFUSE_NO_RECEIPT

• Prevents adaptation that breaks receipt
• Ensures auditability

Determinism Gates

REQUIRE_DETERMINISTIC_REPLAY

if probabilistic selection affects safety-critical route:
    REQUIRE_DETERMINISTIC_REPLAY

• Prevents randomness in safety-critical paths
• Requires deterministic replay for verification
• Protects against non-deterministic failures

ALLOW_PROBABILISTIC

if probabilistic selection not safety-critical:
    ALLOW_PROBABILISTIC

• Permits probabilistic selection in non-critical paths
• Enables adaptive behavior where safe

---

Collapse is Not Permission

Core Principle: DSP collapse selects an implementation. It does not authorize execution.

Execution Requires:

1. Policy pass
2. Sigma pass
3. Resource pass
4. Thermal pass
5. Receipt path
6. AngrySphinx gate pass

Formal Flow:

collapse(MorphicDsp, need)
→ candidate implementation
→ AngrySphinx gate
→ (gate pass) → execute or refuse
→ receipt
→ amplitude/topology update

Key Distinction:

• Collapse: Selection of implementation from superposition/basis
• Permission: Authorization to execute selected implementation
• Collapse is necessary but not sufficient for execution

---

Morphic DSP Formal Model

Virtual Morphic DSP (Immediate Target)

MorphicDsp(t) =
  superposed operation basis
+ boundary state (virtual)
+ adaptive topology (logical)
+ resource envelope
+ receipt path
+ AngrySphinx gates

Collapse Flow

collapse(MorphicDsp, need)
→ candidate implementation
→ AngrySphinx gate check
→ if gate pass:
    → execute implementation
    → receipt generation
    → amplitude/topology update
→ if gate fail:
    → refuse execution
    → maintain current state

---

Morphic DSP FPGA Implementation

Virtual Morphic DSP on FPGA (Immediate Target)

Target Hardware: Gowin GW1NR-9 (Tang Nano 9K)

• 8,640 LUT4 cells
• 27 MHz clock
• 720KB BRAM (30 x 24Kb blocks)
• No DSP slices (Gowin architecture uses LUT-based multipliers)

Acoustic Sensor: MEMS Microphone (SPH0645)

• Metal-lid MEMS microphone
• I2S/PDM digital output interface
• Role: Resonant cavity / acoustic waveguide
• Provides audio input for morphic DSP pattern matching

Hardware Composition:

LUT fabric (8,640 cells)
+ Routing fabric (dynamic interconnect)
+ Control FSM (state machine)
+ Morphic scalar amplitudes (Q16.16)
+ Receipt gates (audit trail)
+ BRAM partial LUT (adaptive storage)
+ MEMS microphone interface (I2S/PDM)
= Virtual Morphic DSP (Gowin GW1NR-9)

Implementation Strategy:

• Use LUTs for multiplication (Gowin has no DSP slices)
• Reconfigure routing via control FSM
• Use LUTs to implement adaptive logical interconnect
• Use BRAM partial LUT for adaptive storage (pattern matching, weights, thresholds)
• Integrate MEMS microphone (SPH0645) via I2S/PDM interface
• Use audio input for pattern matching and OEPI calculation
• Compose operations from basis (multiply, accumulate, etc.)
• Emulate boundary fluidity via resource pooling
• AngrySphinx gates implemented in control logic

BRAM Partial LUT Architecture:

• BRAM stores adaptive pattern matching thresholds and weights
• Morphic scalar amplitudes update BRAM entries dynamically
• Enables runtime weight updates (unlike fixed LUTs)
• 1024-entry lookup table (10-bit address, 32-bit Q16.16 data)
• Write enable for partial updates
• 1-2 cycle lookup latency
• Gowin GW1NR-9 has 720KB BRAM (30 x 24Kb blocks)

Capabilities:

• [BEAUTIFUL_PROVISIONAL - Self-reconfiguring logical structure (via routing + LUTs) - requires FPGA synthesis evidence]
• [BEAUTIFUL_PROVISIONAL - Fluid boundaries (virtual merge/split via resource allocation) - requires implementation evidence]
• [BEAUTIFUL_PROVISIONAL - Composable operation basis (not infinite) - requires formal specification evidence]
• [BEAUTIFUL_PROVISIONAL - Adaptive topology (logical interconnect reconfiguration) - requires routing reconfiguration evidence]
• [BEAUTIFUL_PROVISIONAL - Scalar collapse with AngrySphinx gates - requires gate implementation evidence]
• [BEAUTIFUL_PROVISIONAL - Adaptive pattern matching via BRAM partial LUT - requires pattern matching evidence]
• [BEAUTIFUL_PROVISIONAL - Dynamic weight updates via BRAM writes - requires BRAM write evidence]
• [factual - LUT-based multiplication (no DSP slices on Gowin) - Gowin architecture documented]
• [factual - Audio input processing via MEMS microphone (SPH0645) - hardware interface documented]
• [BEAUTIFUL_PROVISIONAL - Acoustic pattern recognition for morphic scalar state - requires pattern recognition evidence]

Limitations:

• Not true physical self-modification (logical reconfiguration only)
• FPGA has fixed routing (limited runtime reconfiguration)
• No DSP slices (multiplication via LUTs, slower)
• Bit-width adaptation limited (time-multiplexing, not true variable width)
• BRAM lookup slower than pure LUT (1-2 cycles vs 1 cycle)
• Limited BRAM write bandwidth

True Morphic DSP on FPGA (Long-Term Target)

Hardware Requirements:

• Reconfigurable Logic Blocks: DSP slices must be reconfigurable at structural level
• Dynamic Interconnect: Routing must be runtime-reconfigurable
• Bit-Width Adaptation: Multipliers must support variable bit-width
• Pipeline Adaptation: Pipeline depth must be adjustable
• Self-Organization: Hardware must support emergent topology

Target Hardware:

• Lattice ECP5: Larger device with more routing resources
• Xilinx UltraScale+: Advanced DSP with reconfigurable pipeline
• Intel Agilex: Adaptive DSP blocks
• Custom ASIC: True morphic DSP (beyond FPGA)

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Morphic DSP Applications

1. Adaptive Signal Processing

[BEAUTIFUL_PROVISIONAL - Applications are conceptual without implementation evidence]

• DSP adapts structure to signal characteristics [conceptual - requires adaptation algorithm evidence]
• Multiplier becomes filter for low-frequency signals [conceptual - requires reconfiguration evidence]
• Multiplier becomes FFT for spectral analysis [conceptual - requires FFT implementation evidence]
• Self-optimizing for each signal type [conceptual - requires optimization algorithm evidence]

2. Energy-Efficient Computing

[BEAUTIFUL_PROVISIONAL - Applications are conceptual without power measurement evidence]

• DSP splits into smaller units for low-power processing [conceptual - requires power measurement evidence]
• DSP merges for high-performance processing [conceptual - requires performance benchmark evidence]
• Resource allocation adapts to energy constraints [conceptual - requires energy optimization evidence]
• Self-scaling computation [conceptual - requires scaling algorithm evidence]

3. Fault Tolerance

[BEAUTIFUL_PROVISIONAL - Applications are conceptual without fault injection evidence]

• DSP can reconfigure around faulty components [conceptual - requires fault detection evidence]
• Boundary fluidity enables graceful degradation [conceptual - requires degradation analysis evidence]
• Self-healing through structural adaptation [conceptual - requires healing mechanism evidence]
• Emergent redundancy [conceptual - requires redundancy emergence evidence]

4. Neuromorphic Computing

[BEAUTIFUL_PROVISIONAL - Applications are conceptual without neural implementation evidence]

• DSP structure adapts to neural network topology [conceptual - requires neural adaptation evidence]
• Synaptic weights become fluid connections [conceptual - requires synaptic plasticity evidence]
• Spike-timing-dependent plasticity in hardware [conceptual - requires STDP implementation evidence]
• Self-organizing neural networks [conceptual - requires self-organization evidence]

---

Morphic DSP Mathematical Model

[BEAUTIFUL_PROVISIONAL - Mathematical model uses quantum-inspired notation as metaphor; does not imply actual quantum computing capabilities. This is a conceptual formalism without physical quantum evidence.]

Superposition State

DSP operation in superposition:

|ψ⟩ = Σ_i a_i |mode_i⟩

Where:

• |ψ⟩ is the DSP superposition state [conceptual - quantum-inspired metaphor]
• a_i is the amplitude (probability weight) of mode i [conceptual - Q16_16 representation]
• |mode_i⟩ is a specific DSP operation mode [conceptual - mode enumeration]
• Σ_i |a_i|² = 1 (normalization) [conceptual - requires normalization implementation]

Collapse Operation

Measurement collapses superposition:

|ψ⟩ → |mode_k⟩ with probability |a_k|²

Where:

• Collapse is triggered by scalar measurement [conceptual - requires measurement mechanism evidence]
• k is selected based on amplitude probabilities [conceptual - requires selection algorithm evidence]
• Result is deterministic operation mode [conceptual - requires determinism guarantee evidence]

Boundary Fluidity

DSP boundary state evolution:

∂(boundary)/∂t = f(computation_needs, resource_constraints)

Where:

• Boundary state evolves continuously [conceptual - requires evolution mechanism evidence]
• Driven by computation needs and resource constraints [conceptual - requires constraint satisfaction evidence]
• Enables dynamic merge/split operations [conceptual - requires operation evidence]

Topology Adaptation

DSP topology reconfiguration:

topology(t+1) = adapt(topology(t), signal_characteristics(t))

Where:

• Topology adapts to signal characteristics [conceptual - requires adaptation algorithm evidence]
• Continuous optimization of interconnect [conceptual - requires optimization evidence]
• Emerges from local interaction rules [conceptual - requires emergence evidence]

---

Morphic DSP Lean Implementation

Core Types

/-- Morphic DSP entity. -/
structure MorphicDsp where
  dspId : Nat
  superposedOps : Array (Q16_16 × DspMode)
  collapsedOp : Option (Q16_16 × DspMode)
  boundaryState : BoundaryState
  topology : DspTopology

/-- DSP boundary state. -/
inductive BoundaryState where
  | independent
  | merged
  | split
  | fluid

/-- DSP topology. -/
structure DspTopology where
  connections : Array (Nat × Nat)
  bandwidth : Array Q16_16
  latency : Array Q16_16

Core Operations

/-- Collapse superposition. -/
def collapseDspSuperposition (dsp : MorphicDsp) (measurement : DspMode) : MorphicDsp

/-- Merge DSP slices. -/
def mergeDspSlices (dsp1 dsp2 : MorphicDsp) : MorphicDsp

/-- Split DSP slice. -/
def splitDspSlice (dsp : MorphicDsp) (splitRatio : Nat) : Array MorphicDsp

/-- Adapt topology. -/
def adaptDspTopology (dsp : MorphicDsp) (needs : ComputationNeeds) : MorphicDsp

---

Keeper Law

Core Principle: A controlled DSP changes modes. A morphic DSP changes what kind of worker it is. A safe morphic DSP still asks permission before it works.

Sharper Formulation: The DSP may collapse into function. It may not collapse into authority.

Implications:

1. Collapse ≠ Permission: Selecting implementation does not authorize execution
2. Function ≠ Authority: DSP can change function, not authority
3. Permission Required: Execution always requires gate passes
4. Receipt Mandatory: All executions must generate receipt

Safety Guarantee: Even a morphic DSP with self-reconfiguring structure must:

• Check AngrySphinx gates before execution
• Maintain receipt path for auditability
• Respect resource and thermal bounds
• Preserve semantic precision

---

Morphic DSP vs Current Work

Current Work (Controlled DSP - Layer 1)

• DSP slices are reconfigurable (6 modes)
• Controlled by external morphic scalar
• OEPI-based allocation
• Fixed hardware structure
• Status: Implemented in MorphicDSP.lean

Next Evolution (Virtual Morphic DSP - Layer 2)

• DSP pool with self-reconfiguring logical structure
• Fluid boundaries via resource pooling
• Composable operation basis (not infinite)
• AngrySphinx gates for safety
• Adaptive logical topology
• Status: Design complete, Lean implementation pending

Long-Term Target (True Morphic DSP - Layer 3)

• DSP slices are morphic entities
• Physical self-modifying structure
• Physical fluid boundaries
• Quantum-inspired superposition
• Adaptive physical topology
• Self-organization
• Status: Conceptual, requires custom hardware

---

Conclusion

The morphic DSP concept must be understood in three distinct layers:

Layer 1: Controlled DSP (Current)

• Fixed DSP slices with mode selection
• External control by morphic scalar
• Implemented and ready for FPGA deployment

Layer 2: Virtual Morphic DSP (Immediate Target)

• Self-reconfiguring logical structure via DSP pool + LUTs
• Fluid boundaries via resource pooling
• Composable operation basis with AngrySphinx gates
• Buildable on current FPGA hardware
• Key principle: Collapse is not permission

Layer 3: True Morphic DSP (Long-Term Target)

• Physical self-modifying structure
• Physical fluid boundaries
• Quantum-inspired superposition
• Requires custom ASIC or future FPGA

The immediate path forward is Virtual Morphic DSP: create a morphic-looking DSP pool using current FPGA resources (DSP slices + LUT fabric + routing fabric + control FSM + morphic scalar + receipt gates). This provides morphic behavior without requiring custom hardware, while maintaining safety through AngrySphinx gates and the keeper law: "The DSP may collapse into function. It may not collapse into authority."