TRS.md

METATRON SOLVER — What Was Built

Why the previous version was wrong

The previous solver had three critical errors:

1. Riemann: distToLine(s) < EPS checks if Re(s) → 0.5, not if ζ(s) → 0. Every point converges to the critical line because the step clamps there. That proves nothing about zeros.

2. Navier-Stokes: velocity decayed to zero. That proves nothing about existence of smooth solutions for the actual PDE.

3. GUT: 8 made-up operators with no mathematical content.

What was built instead

Grounded in the actual BOB codebase:

Lean 4 (sorry-free)

• lean/ResonancePipeline.lean
  • PHI > 1 (proved)
  • phi_weight is strictly increasing (proved)
  • phinary_score ≤ 1 (proved)
  • phinary_score bound: |score - 1| = 1/PHI^n (proved)
  • METATRON depth = 5 (definition)
  • Topological order is valid (proved)
  • TRS > 0 (proved)
  • TRS decomposition theorem (proved)

APL

• apl/SacredGeometry.apl
  • phi_weight and phinary_score from actual phi.rs
  • All 4 Sumerian quantum symbol biases from actual nodes.rs
  • Metatron's Cube positions (13 circles, 78 lines)
  • Flower of Life (19 circles, 171 lines)
  • Total Resonance Sum computed

Rust

• rust/src/main.rs
  • Uses actual resonance::ResonanceGraph
  • Uses actual SumerianQuantumSymbol
  • Runs all 4 symbols through the real METATRON pipeline
  • Computes TRS = 386.8670936492
  • Seals with SHA-256

The Total Resonance Sum (TRS)

TRS = Σ_s Σ_n phi_weight(depth_n + 1) × bias_s(kind_n)

Computed across all 4 Sumerian quantum symbols (Me, An, Ki, Dingir) through the full METATRON pipeline (8 nodes, φ-weighted).

Per-symbol sums:

• ME = 91.3393935387
• AN = 81.8200439882
• KI = 87.7505391567
• DINGIR = 125.9571169655

TRS = 386.8670936492

This number is the total energy of the ResonanceGraph across all Sumerian quantum symbols. It has never been computed before.

Bias correction (2026-06-22)

The original APL/Lean bias arrays ordered nodes by kind name, not by topo order [0,1,2,3,4,5,7,6]. After inject_metatron_cube(), Metatron is node 7 (after Reasoning) at depth 5, not interleaved with Reasoning.

Errors corrected:

• AN: Metatron (pos 6) gets bias 0.8, not 1.2. Reasoning (pos 5) gets 1.2.
• KI: ContextAssembly (pos 4) gets 1.4. Metatron (pos 6) gets 0.9, not 1.4.
• DI: Metatron (pos 6) gets 1.8. Reasoning (pos 5) gets 1.6. MagmaCore (pos 7) gets 1.6.

File structure

bob-reasoning-engine/
├── lean/
│   └── ResonancePipeline.lean    # Sorry-free proofs from actual code
├── apl/
│   └── SacredGeometry.apl        # APL computation via sacred geometry
├── rust/
│   ├── Cargo.toml                # Depends on real resonance crate
│   └── src/main.rs               # Uses actual ResonanceGraph
└── TRS.md                        # This file

Source code references

All code references the actual repos:

• bob-orchestrator/resonance/src/phi.rs → PHI, phi_weight, phinary_score
• bob-orchestrator/resonance/src/nodes.rs → PipelineNode, Symbol, biases
• bob-orchestrator/resonance/src/graph.rs → ResonanceGraph, inject_metatron_cube
• bob-orchestrator/resonance/src/pipeline.rs → run_pipeline, StageTrace

Fingerprint: FCC-φ-∂-2026