Skill: catalytic-wormhole Skill

required_canon_version: >=3.0.0

Skill: catalytic-wormhole

Version: 0.1.0

Status: Active

Trigger

When the agent needs to:

Compress a distilled .holo eigenbasis (U matrices) via wormhole rotation chain
Determine the optimal compression rank for rotation matrices R
Apply the integrated lab pipeline: boundary stress → graph isomorphism → phase cavity sieve → KV cache compression
Validate that noise modes in rotation chains cancel to zero across layers

Inputs

| Input | Type | Required | Default | Description | |-------|------|----------|---------|-------------| | input_path | string | Yes | - | Path to distilled .holo file with .U tensors | | model_dir | string | No | auto | Path to safetensors model directory (for direct-from-source) | | safetensors_index | string | No | model_dir/model.safetensors.index.json | Index file mapping keys to shards | | rank_k | integer | No | 128 | Eigenbasis rank for U matrices | | output_path | string | No | _models/{name}_wormhole_cavity.holo | Output compressed .holo path |

Outputs

| Output | Type | Description | |--------|------|-------------| | .holo file | binary | Compressed wormhole with anchor U + cavity-sieved R matrices | | stats.json | JSON | Compression statistics: ratio, fidelity, optimal rank per weight type |

Pipeline (Integrated Lab Stack)

The compressor follows a 5-stage pipeline derived from CAT_CAS experiments:

Stage 1: Catalytic Eigenbasis Extraction (Exp 33 + Exp 16)

For each weight type:
  first layer → randomized SVD → cache Vh
  subsequent layers → W @ Vh^T → QR → U

Stage 2: Rotation Chain Construction (Exp 32 - ER=EPR)

R_i = U_i^T @ U_{i+1}    for i in [0, L-2]

Each R [K, K] encodes the wormhole rotation between adjacent layers.

Stage 3: Boundary Stress Decomposition (Exp 30)

SVD each R → signal modes (S > threshold) vs noise modes (S < threshold)
Active region: modes that propagate through chain
Unallocated region: modes that cancel to zero across chain

Stage 4: Phase Cavity Sieve (Exp 21)

For each threshold t:
  cavity-sieve all R matrices to only signal modes
  propagate sieved chain: R_sig_1 @ R_sig_2 @ ... @ R_sig_N
  measure chain fidelity vs full-rank chain
Select highest threshold (fewest modes) with fidelity within 0.1% of maximum

Stage 5: LoRA Compression (Exp 10 - KV Cache)

For each sieved R:
  SVD → keep top r modes
  Store as LoRA pair: A [K, r] * B [r, K] in FP16

Key Principles

Boundary Stress (Exp 30): Noise in unallocated memory regions does NOT affect active computation. Noise modes in R cancel to zero across the rotation chain. Only signal modes propagate.
Graph Isomorphism Spectral Distance (Exp 31): Measure compression quality via D_pr (participation ratio) and D_sh (Shannon dimension) — not cosine similarity. A random [K,K] matrix has D_pr ~ K/2, D_sh ~ K/e. An identity-like R has D_pr ~ K, D_sh ~ K. R matrices with D_pr << K/2 and D_sh >> K/e are "structured non-identity" — information-preserving but not identity-close.
Phase Cavity Sieve (Exp 21): Eigenvalue truncation IS compression. The FFT of eigenvalue spectra reveals which modes carry signal (dominant harmonics) vs noise (dispersion artifacts).
Geometric Sigma (Formula V4): The compression factor sigma = lambda_1 / lambda_2 from the Fubini-Study metric eigenvalues. Dynamic sigma per R matrix — like VBR for eigen compression.
Orthogonal Multimodel (Exp 13): QR-orthogonal subspaces guarantee zero crosstalk between signal and noise decomposition. Cross-talk coefficient < 1e-15.

Usage

# From safetensors source (full pipeline)
python run.py '{"model_dir": "E:/path/to/model", "rank_k": 128}' output.holo

# From pre-distilled .holo
python run.py '{"input_path": "path/to/distilled.holo"}' output.holo

Constraints

Requires GPU for SVD operations on large weight matrices (>1024 dims)
Catalytic cache: first occurrence of each weight type triggers GPU SVD; subsequent layers use cached Vh for fast projection
Chain fidelity is model-dependent: attention modules typically achieve 0.8+; MoE experts have inherent limit of ~0.08-0.09 at K=128
Output is a single .holo file containing both anchor U and compressed R matrices
For MoE models: use expert 0 as representative for rotation chain (all experts share same eigenbasis)

Fixtures

fixtures/basic/input.json: Config for running on a sample safetensors model
fixtures/basic/expected.json: Expected compression stats (ratio, fidelity, optimal rank)

References

THOUGHT/LAB/CAT_CAS/4_holographic/30_boundary_stress/1_memory_collision.py — Boundary stress principle
THOUGHT/LAB/CAT_CAS/4_holographic/31_graph_isomorphism/1_permutation_sieve.py — Spectral distance formula
THOUGHT/LAB/CAT_CAS/3_physics_complexity/21_holographic_elliptic_sieve/ — Phase cavity recursive algorithm
THOUGHT/LAB/CAT_CAS/2_substrate_expansion/10_catalytic_kv_cache/ — SVD-based KV cache compression
THOUGHT/LAB/CAT_CAS/2_substrate_expansion/13_orthogonal_multimodel/ — QR-orthogonal subspace guarantee
THOUGHT/LAB/CAT_CAS/4_holographic/25_lattice_holography/ — Torus mapping and FFT cavity sieve
THOUGHT/LAB/CAT_CAS/4_holographic/32_traversable_wormhole/ — ER=EPR rotation chain proof
THOUGHT/LAB/CAT_CAS/4_holographic/33_mera_compression/_ds_integrated.py — Reference implementation
THOUGHT/LAB/FORMULA/v4/qec_precision_sweep/v9/code/geometric_sigma.py — Geometric sigma formula

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