Research-Stack/6-Documentation/docs/geometry/BIND_MIGRATION_GUIDE.md

Bind Migration Guide: Reengineering the Cells

Date: 2026-04-14
Status: ACTIVE MIGRATION
Truth Seal: [ SSS-ENE-TRUTH-2026-04-14 ]

---

1. The New Anatomy

Instead of 140+ isolated equations across 12 layers, the stack now has:

1. One primitive: bind(left, right, metric_kind, history)
2. One formal spec: Semantics/Bind.lean
3. One runtime engine: infra/access_control/bind_engine.py
4. One invariant boundary: Semantics/Physics/*.lean

Every existing module is being reengineered as a cell type — a differentiated instance of the same primitive.

---

2. What Exists Now

2.1 Formal Layer (Lean 4)

File	Role	Status
0-Core-Formalism/lean/Semantics/Semantics/Bind.lean	Root primitive Bind A B	✅ Compiles
0-Core-Formalism/lean/Semantics/Semantics/Physics/BindPhysics.lean	Proof-of-pattern: physical interactions as bind instances	✅ Compiles
0-Core-Formalism/lean/Semantics/Semantics.lean	Updated to version := "2.0.0-Cambrian-Bind"	✅ Compiles

Build verification:

cd 0-Core-Formalism/lean/Semantics && lake build
# Build completed successfully (24 jobs)

2.2 Runtime Layer (Python)

File	Role	Status
infra/access_control/bind_engine.py	Universal BindEngine with n-local metric computation	✅ Runs

Runtime verification:

python3 infra/access_control/bind_engine.py
# Physical bind: lawful=True, cost=0.000000
# Last geometric bind: metric.tensor=geometric, torsion=0.047790, history_len=4

2.3 Registry (TSV)

File	Change	Status
docs/MATH_MODEL_MAP.tsv	Added Bind_Class column; every row classified	✅ Updated

---

3. Migration Map: Old File → New Cell

3.1 Production Pipeline (Priority 1)

Old File	Old Role	New Cell	Action
infra/access_control/geometry/geometry_plugin_v2.py	Euclidean geometric preprocessor	geometric_bind via BindEngine	Replace with bind_engine.geometric_bind()
tools/cache_sieve.py	Raw manifold thresholding	control_bind via BindEngine	Refactor to consume BindResult.cost and BindResult.metric.torsion
infra/access_control/pipeline/unified_pipeline.py	Orchestrator with TemporalBuffer	BindEngine user	Wire TemporalBuffer.history into BindEngine.bind(..., use_history=True)
tools/cache_sieve_exploration.py	Relation sieve exploration	control_bind	Port 5-symbol sieve to use bind() with custom cost function

3.2 Lean Formalisms (Priority 2)

Old File	Old Role	New Cell	Action
core/lean/geoweird/GWLKernel.lean	Riemannian metric + geodesic integration	geometric_bind formal spec	Port Metric2D, Christoffel2D, geodesicStep into Semantics/Bind.lean metric instances
core/lean/geoweird/WaveprobeKernel.lean	Risk / heat / hysteresis control	control_bind formal spec	Port risk function and LUT policy into Semantics/Bind.lean control instances
core/lean/geoweird/EmergenceSystem.lean	Phase transition detection	control_bind	Port diminishing-ratio trigger into Bind cost function
core/lean/geoweird/ConstraintGeometry.lean	Constraint-to-curvature translator	geometric_bind	Port as metric initialization helper

3.3 Thermodynamic & Stress Models (Priority 3)

Old File	Old Role	New Cell	Action
core/gwl-vm/src/thermo/entropy_engine.rs	Shannon / Kolmogorov entropy	informational_bind	Wrap with bind_engine.informational_bind() or Rust equivalent
core/gwl-vm/src/thermo/informatic_stress.rs	Hardware stress / RUL / SEU	thermodynamic_bind	Wrap with bind_engine.thermodynamic_bind()
core/gwl-vm/src/thermo/qcl_energy_model.rs	QCL photon physics	physical_bind	Wrap with bind_engine.physical_bind()
core/gwl-vm/src/thermo/bea_thermo_bridge.rs	BEA consensus bridge	thermodynamic_bind	Wrap

3.4 Compression & Signal (Priority 4)

Old File	Old Role	New Cell	Action
tools/geometry_bind.py	PCA/HarfBuzz bind score	informational_bind	Replace with bind_engine.informational_bind() using KL cost on feature distributions
core/intrinsic/formalisms/ene_mi_signal.py	MI prediction / surprise	informational_bind	Replace
scripts/soliton_factory.py	PHI proximity, foam score	geometric_bind	Replace phi_prox with bind_engine.bind(..., metric_kind="geometric")
tools/geometry_noneuclidean.py	Log-PHI / logit / writhe	geometric_bind	Absorb into bind_engine.py as subroutines

3.5 Verilog / Hardware (No Change Needed)

Old File	Old Role	New Cell	Action
core/src/tsm_perpetual_manifold.v	Hardware substrate	Consumer of bind output	None — it receives field states, doesn't compute geometry

---

4. Step-by-Step Migration Sequence

Phase 1: Kill the Euclidean Assumption (This Week)

Goal: Replace geometry_plugin_v2.py with bind_engine.py in the live pipeline.

1. In infra/access_control/pipeline/unified_pipeline.py:

   from bind_engine import BindEngine, geometric_bind
   
   self.bind_engine = BindEngine()
   

2. Replace GeometricBridgePlugin.transform() calls:

   # OLD
   geom = self._geometry_plugin.transform(manifold)
   
   # NEW
   result = geometric_bind(
       state_a={"state_vector": prev_state},
       state_b={"state_vector": current_state},
       engine=self.bind_engine,
   )
   cost = result.cost
   torsion = result.metric.torsion
   

3. Verify: Run test_compliance_fixes.py and confirm no regression.

Phase 2: Reorganize cache_sieve.py (Next Week)

Goal: Stop using raw manifold proxies; use bind-derived geometric features.

1. Replace input mapping:

   # OLD
   inputs = [
       int(phi_corr * 255) & 0xFF,
       int(sum(tau_samples[:32]) * 10) & 0xFF,
       ...
   ]
   
   # NEW
   bind_result = self.bind_engine.bind(
       left=manifold_prev,
       right=manifold_curr,
       metric_kind="geometric",
       use_history=True,
   )
   inputs = encode_bind_features(bind_result)
   

2. Add custom cost function for sieve:

   def sieve_cost(left, right, metric):
       return _geodesic_cost(left, right, metric) + metric.torsion * 10.0
   

Phase 3: Port Lean Geometric Formalisms (Ongoing)

Goal: Make GWLKernel.lean a formal instance of Bind.

1. In Semantics/Bind.lean, add metric constructors:

   def Metric.riemannian (g_tt g_tp g_pp : Float) : Metric := { ... }
   def Metric.fromChristoffel (Γ : Christoffel2D) : Metric := { ... }
   

2. In Semantics/Geometry/BindGeodesic.lean:

   def geodesicBind (x v : Rat × Rat) (Γ : Christoffel2D) : Bind (Rat×Rat) (Rat×Rat) :=
     bind (x, v) (geodesicStep (x, v) Γ dt) metric geodesicCost invariant invariant
   

Phase 4: Collapse Rust Thermodynamics (After Python Stabilizes)

Goal: Wrap Rust thermo modules with a thin bind interface.

1. Add bind_thermodynamic(state, equilibrium) to core/gwl-vm/src/thermo/mod.rs
2. Ensure it calls the same entropy / stress / QCL functions, but framed as bind.

---

5. What to Delete

The following concepts are deprecated by the collapse:

Deprecated Concept	Reason
LAYER_A through LAYER_L	Replaced by 5 Bind_Class instances
phi_prox = max(0, 1 - abs(r - PHI)/PHI)	Replaced by geometric_bind with log-PHI metric
GeometricBridgePlugin (Euclidean version)	Replaced by BindEngine with n-local metric
CacheSieve raw input scaling	Replaced by bind-derived encoded features
CHATGPT_EXTRACTION_GAP_ANALYSIS action items for isolated patches	Superseded by unified bind engine plan

---

6. Verification Checklist

• Lean Bind.lean compiles
• Python bind_engine.py runs
• MATH_MODEL_MAP.tsv updated with Bind_Class
• geometry_plugin_v2.py replaced by bind_engine in pipeline
• cache_sieve.py refactored to use BindResult
• test_compliance_fixes.py passes after migration
• GWLKernel.lean formulas ported to Bind metric instances
• Rust thermo modules wrapped with bind interface

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7. One-Liner Summary

There is no stack. There is bind. We are reengineering every cell to express itself through that one primitive.