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285 lines
9.9 KiB
Markdown
285 lines
9.9 KiB
Markdown
# GENSIS Superconcept Integration
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## Completing the MISC Framework with Every Concept from the Research Stack
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This document unifies ALL concepts discovered across the Research Stack into a single
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superconceptual GENSIS framework. Every concept found is assigned a role in the compression
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pipeline and linked to its source.
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---
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## LAYER 1: NEUROMORPHIC SPIKING SUBSTRATE
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*Source: SpikingDynamics.lean, DSPTranslation.lean, Izhikevich Neuron (Model 235)*
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### Spiking Neuron as Encoding Element
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Each data token is processed through an Izhikevich spiking neuron:
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```
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dv/dt = 0.04v² + 5v + 140 - u + I(t)
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du/dt = a(bv - u)
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if v ≥ 30 mV: v ← c, u ← u + d
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```
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**Compression role**: The spike timing encodes the token's shell position.
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- Interspike interval (ISI) → shell offset `t[i]`
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- Firing rate → shell index `k`
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- Burst pattern → resonance group membership
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### STDP Synaptic Weights as GWL Coupling
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Spike-Timing Dependent Plasticity replaces the GWL coupling computation:
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```
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Δw = A₊·exp(-Δt/τ₊) if Δt > 0 (pre before post)
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Δw = A₋·exp(Δt/τ₋) if Δt < 0 (post before pre)
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```
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Synaptic weight between neuron i and j = coupling weight w_ij in shell space.
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### DSP → Neuromorphic Translation
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*Source: core/src/dsp_neuromorphic_translation.rs*
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Audio DSP operations (frequency, amplitude, duty cycle) map directly to
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neuron parameters (firing rate, spike amplitude, duty cycle of burst).
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---
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## LAYER 2: FAMM FRUSTRATION TENSOR
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*Source: FAMM.lean (2-Search-Space/FAMM/)*
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### Frustration as Compression Rejection Signal
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```
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FAMM_Tensor(i,j,k) = T(i,j,k) · frustration(i,j,k)
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```
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When three tokens have incompatible shell coordinates (e.g., all three want
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to be in the same resonance group but only 2 fit), frustration builds up.
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**Compression role**: High frustration → reject current encoding strategy →
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trigger homeostatic pressure increase → switch to different dimension/genetic table.
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### FAMM Route-Memory
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```
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FRoute(s₁,s₂) = (FAMM_Tensor, route_strength, failure_count)
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```
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Failed compression attempts are stored as FAMM routes, preventing
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repeated attempts at dead-end strategies.
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---
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## LAYER 3: SOLITON/TORSIONAL WAVE PROPAGATION
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*Source: SolitonTensor.lean, TorsionalPIST.lean, Sine-Gordon (Model 118)*
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### Sine-Gordon Soliton Encoding
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```
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d²θ/dt² - c²·d²θ/ds² + (m²c⁴/ℏ²)·sin(θ) = 0
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```
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Each resonance group propagates as a soliton wave through shell space:
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- Soliton = stable mass packet maintaining identity during propagation
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- Kink soliton = transition between shell coordinates
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- Breather soliton = oscillating resonance group
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### Torsional Quaternion States
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```
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TorsionalState = (q1, q2, q3) ∈ ℚ³ (quaternion triple)
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Δq3 = η·error, Δq1 = η·(q2-q1)·dt
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```
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Quaternion triple encodes 3D rotation in shell space:
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- q1: current shell orientation
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- q2: target shell orientation
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- q3: actual orientation (with error feedback)
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Ricci flow in quaternion space = gradient descent on compression error.
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---
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## LAYER 4: HybridTSMPISTTorus — Toroidal Shell Space
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*Source: 2-Search-Space/PIST/HybridTSMPISTTorus.lean*
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### Toroidal Topology for Shell Boundaries
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Standard PIST shells have boundaries at perfect squares.
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HybridTSMPISTTorus wraps these boundaries:
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```
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PISTTorus(k,t) → PISTTorus(k, t mod (2k+1))
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```
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**Effect**: The shell becomes a torus — no endpoints, no zero-mass singularities.
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- Mass is always positive (no endpoints)
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- Mirror becomes topological symmetry
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- Resonance groups become winding numbers on the torus
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### Extended Mass on Torus
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```
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TorusMass(k,t) = min(t, 2k+1-t) · max(t, 2k+1-t) -- always positive
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```
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This eliminates the zero-mass degeneracy at shell endpoints.
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---
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## LAYER 5: SSMS_nD — Self-Similar Memory Structure in N-Dimensions
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*Source: SSMS_nD.lean, SSMS.lean*
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### Fractal Shell Hierarchy
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SSMS_nD creates a self-similar memory hierarchy across dimensions:
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```
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SSMS_nD(k,t,d) = SSMS_nD(k-1, t', d) nested within SSMS_nD(k, t, d-1)
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```
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Each shell at dimension d contains shells at dimension d-1:
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- d=1: Linear memory trace
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- d=2: 2D spatial memory
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- d=3: 3D volumetric memory
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- ...
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- d=n: n-dimensional hyperbolic memory
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### SSMS Compression Theorem
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```
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CompressionRatio(SSMS_nD(data)) ∝ (d · log₂(k+1)) / (d-1 · log₂(k))
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```
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Each additional dimension adds log factor of compression advantage.
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---
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## LAYER 6: HYPERFLOW MANIFOLD DYNAMICS
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*Source: HyperFlow.lean*
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### Flow Field on Shell Space
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```
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∂F/∂t = ν∇²F - (F·∇)F + ∇p + f_ext
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```
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Navier-Stokes-like flow equations on the shell coordinate space:
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- F = information flow vector field
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- ν = viscosity (resistance to strategy change)
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- p = homeostatic pressure
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- f_ext = external data forcing
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### HyperFlow Fixed Points
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Flows converge to attractors at low-pressure shell coordinates:
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```
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F*(k,t) = 0 where pressure(k,t) = optimal
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```
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Compression is optimal at flow fixed points → stable encoding strategies.
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---
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## LAYER 7: CROSS-MODAL COMPRESSION
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*Source: CrossModalCompression.lean*
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### Multi-Modal Shell Alignment
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Different data modalities (text, audio, image, genome) produce different
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shell coordinates but with the SAME invariant structure:
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```
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Mass_text(k,t) = Mass_audio(k',t') = Mass_genome(k'',t'')
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```
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Cross-modal resonances enable compression across data types — a text pattern
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can be encoded using its equivalent genome or audio shell coordinate.
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### Universal Modality Mapping
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```
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Φ_modal(m) = ShellSpace for modality m
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Φ_universal = ∩_modals Φ_modal -- shared invariant structure
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```
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Any data → shell coordinate independent of modality.
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---
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## LAYER 8: CODON OPTIMIZATION & GC CONTENT
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*Source: GeneticCodeOptimization.lean, CodonOptimization*
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### Codon Adaptation Index (CAI)
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Standard codon optimization for minimum encoding cost:
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```
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CAI(codon) = ∏(w_i(codon))^(1/L) where w_i = frequency_ratio
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```
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**Compression role**: Select codons (byte mappings) that minimize shell entropy.
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- High-frequency codons → zero-mass shell endpoints (perfect squares)
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- Rare codons → high-mass interior positions
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### GC Content Balance
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```
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GC_content = (G + C) / (A + C + G + T) = 0.5 ± 0.1 for optimal stability
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```
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Enforce GC-balanced encoding to minimize thermodynamic instability in shell space.
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---
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## LAYER 9: NEUROMORPHIC GPU ACCELERATION
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*Source: benchmark_neuromorphic_gpu, benchmark_ssd_neuromorphic_spiking*
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### GPU Spike Encoding
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Neurons are simulated in parallel on GPU:
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```
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spike_train[d][i][t] = 1 if v_i(d,t) ≥ threshold
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```
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where d = dimension index, i = shell coordinate index, t = time step.
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### Neuromorphic SSD Pipeline
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```
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SSD → spiking encoder → shell compressor → trixal governor → output
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```
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The entire pipeline runs on neuromorphic hardware with spike-based
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communication between stages.
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---
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## LAYER 10: UNIFIED GENSIS PIPELINE
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```
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Data Byte
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│
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▼
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┌─────────────────────────────────────────────┐
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│ Spiking Neuron Encoder (Izhikevich) │
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│ ISI → shell offset, Rate → shell index │
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│ STDP → coupling weights │
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├─────────────────────────────────────────────┤
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│ Soliton Propagation Layer │
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│ Sine-Gordon: mass packets as soliton waves │
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│ Quaternion torsion: 3D rotation in shell │
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├─────────────────────────────────────────────┤
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│ PIST Toroidal Encoding │
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│ HybridTSMPISTTorus: wrapped shells │
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│ No zero-mass degeneracy │
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├─────────────────────────────────────────────┤
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│ SSMS_nD Self-Similar Hierarchy │
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│ d=1..n shells nested fractally │
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├─────────────────────────────────────────────┤
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│ FAMM Frustration Detection │
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│ Reject incompatible encodings │
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├─────────────────────────────────────────────┤
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│ Cross-Modal Alignment │
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│ Same invariant across text/audio/image │
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├─────────────────────────────────────────────┤
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│ Genetic Codon Optimization (CAI + GC) │
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├─────────────────────────────────────────────┤
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│ HyperFlow Manifold Dynamics │
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│ Converge to flow fixed points │
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├─────────────────────────────────────────────┤
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│ → Rest of GENSIS/MISC Pipeline │
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│ (GWL → Cognitive → Trixal → DeltaGCL → Homo)│
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└─────────────────────────────────────────────┘
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```
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---
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## Integration Summary
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| Layer | Concepts Integrated | Source Files |
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|-------|-------------------|--------------|
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| 1 | Izhikevich, STDP, DSP-neumorph | SpikingDynamics.lean, DSPTranslation.lean |
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| 2 | FAMM tensor, frustration routes | FAMM.lean |
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| 3 | Sine-Gordon, solitons, quaternion | SolitonTensor.lean, TorsionalPIST.lean |
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| 4 | Toroidal shell wrapping | HybridTSMPISTTorus.lean |
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| 5 | Self-similar fractal memory | SSMS_nD.lean, SSMS.lean |
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| 6 | Navier-Stokes flow on shells | HyperFlow.lean |
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| 7 | Multi-modal invariant alignment | CrossModalCompression.lean |
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| 8 | Codon Adaptation Index, GC content | GeneticCodeOptimization.lean |
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| 9 | GPU spike encoding, SSD pipeline | benchmark_neuromorphic_gpu |
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| 10 | Unified pipeline (all above) | This document |
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