leech-density-guidance-reduction

name	leech-density-guidance-reduction
description	Apply Leech lattice density guidance to hybrid M24/M12 K22 reductions with Golay-derived norm-4 vectors, Agda-extracted verification guards, and SRAC-safe tie-breaking. Use when the user mentions Leech density, kissing number 196560, Construction A, Golay code, hybrid reduction, reduce_k22_hybrid_m24_m12, verify_leech_guidance, leech_density_score, apply_leech_density_guidance, Phase 2 Task 2.2, or runs /leech-density-guidance-reduction. Triggers for notebook evcxr cells, triweavon-cudarc wiring, and Agda preservation proofs.
version	1.0.0

Leech Density Guidance Reduction

One-click workflow for Leech-density-aware hybrid M24/M12 K22 reduction. Grounds executable reduction in the formal invariant: Leech lattice Λ₂₄ kissing number = 196,560 (optimal, unique up to isometry), constructed via binary Golay code and Construction A.

Hard Invariants (never override alone)

Invariant	Value	Role
Kissing number	196,560	Geometric anchor for density prior
α + ω	15	Conservation law
tomczak_lift	preserved	Structural foldability
Betti proxy delta	≤ 0.05	Mirrored verification tolerance
WAVE	≥ 0.85 (target 1.0)	Coherence gate

Treat kissing number as one hard invariant among several — not the sole selector. This preserves topological bendability for lower-dimensional projections.

When to Invoke

• Wiring leech.rs / golay.rs into triweavon-cudarc
• Running diagnostic_tick_with_leech_verifier after sm_100 roundtrip
• Filling Agda holes in TriWeavon.K22.LeechDensityGuidance
• Phase 2 Task 2.1 + 2.2 (hybrid reduction + Leech layer)
• A/B testing use_golay_vectors vs toy norm-4 table

Execution Workflow

1. Configure Leech prior

let leech_cfg = LeechDensityConfig::default().with_weight(0.35);
// weight 0.0–1.0; norm_threshold 4.0 for minimal vectors

2. Run hybrid reduction

let guided = reduce_k22_hybrid_m24_m12(&fragment, level)?;

Three-tier tie-breaker (documented in m24.rs):

1. Primary: higher leech_density_score
2. Secondary: lower betti_proxy on density tie
3. Tertiary: deterministic average

3. Verify with Agda-extracted guard

let verified = verify_leech_guidance(&leech_cfg, &baseline, &guided)?;

Guard checks:

• rigid_lift_check() (tomczak preserved)
• betti_proxy_delta ≤ 0.05
• burst reduction ≥ weight * 0.4
• density improvement per leech-density-reduces-burst-rate postulate

4. Log telemetry + coherence-mcp

wire_leech_telemetry(witness, Some(density), Some(weight));

Emit to coherence-mcp: wave_coherence_check, trigger_correction_burst if guard fails.

5. Formal cross-check

Agda module: TriWeavon.K22.LeechDensityGuidance (v0.4.1+)

• leech-guidance-preserves-tomczak-lift
• leech-guidance-bounded-betti-delta
• leech-density-reduces-burst-rate

Filled proof variant uses pathToEquiv + ua transport (see LeechDensityGuidance (1).agda).

Artifact Paths

File	Location
leech.rs	Downloads/ → triweavon-cudarc/src/leech.rs
golay.rs	Downloads/ → triweavon-cudarc/src/golay.rs
m24.rs	hybrid + mirrored verification
LeechGuidanceExtracted.rs	Agda → Rust guard prototype
diagnostic_tick_with_leech_verifier.rs	CutileHarness integration
LeechDensityGuidance.agda	formal preservation theorems

Success Criteria

• tomczak_preserved = true after guidance
• Betti divergence < 3% on hybrid path
• verify_leech_guidance returns Ok(true) on representative fragments
• coherence-mcp invoke invariant_check passes

Skill Chain

leech-density-guidance-reduction
  → crystalline-tessellation-projection (lower-D slice viz)
  → srac-lattice-restoration-visual (surge → restored density)

Read references/invariant-manifest.json for full kissing + Ricci + Golay linkage.