Trace Reciprocity Graph Flow

Public status boundary. This route is a network-class trace surrogate for review. It does not assert accepted physics or proof status.

Model Purpose

The Trace Reciprocity Graph Flow simulation is a Network-Class computational model designed to stress-test the structural recoverability of a global system's trace from its distributed components. It evaluates the admissibility of network partitions and the invariance of trace identity across disjoint boundaries.

Simulation Class: Network Model
Status: S1 Prototype
Formalization Target: Lean 4 (Fabrica.TraceReciprocity · thm_trace_involution, thm_trace_dual_symmetry, thm_trace_dual_reflexive)

Spine Position

This model is rooted in the Trace Reciprocity Principle and the Science of Fabric Reality, evaluating how trace identity persists under topological partition.

Observables & Metrics

• Global Trace: The trace computed from the global operator network matrix.
• Local Trace Sum: The scalar sum of traces computed across all decomposed disjoint domains.
• Reconstruction Error: The absolute differential between the Global Trace and the Local Trace Sum ($|\text{GlobalTrace}-\sum _i{\text{LocalTrace}}_i|$).
• Proposed Reciprocity Residual (${\epsilon }_{\text{rec}}$): Evaluates whether source-target state exchanges satisfy adjoint/pairing reciprocity:$${\epsilon }_{\text{rec}}=\frac{|\mathcal{B}(Tx,y)-\mathcal{B}(x,T^{\ast }y)|}{\parallel Tx\parallel \parallel y\parallel +\parallel x\parallel \parallel T^{\ast }y\parallel +{\epsilon }_{\text{tol}}}$$

Fixture Classification: This numerical surrogate is classified as TRACE_PARTITION_ADDITIVITY_FIXTURE. It evaluates trace additivity under network partitioning; it does not constitute empirical evidence of categorical or adjoint reciprocity unless source-target exchanges are directly evaluated.

Invariants

• TR1_Trace_Preservation: The reconstruction error must remain infinitesimal (computationally bounded to ~0), indicating perfect recoverability.

Failure Conditions

• decomposition_failure: The reconstruction error exceeds computational tolerance due to non-admissible network decomposition.
• trace_divergence: The structural divergence becomes macroscopically large (error > 0.5), breaking the partition additivity requirement.

Output Schema

Outputs strictly adhere to the SimulationOutput ontology.

Reproducibility

• default: Configured with an admissible, disjoint, boundary-matched decomposition, simulating stable TR1 trace preservation.
• stress: Configured with an overlapping or incomplete matrix decomposition, designed to artificially breach reciprocity and track invariant failure points.

Simulation Logs