silva_mesh_inference Reproduction Dossier

typed center-free linear-Gaussian relaxation. This dossier connects the source mechanism to its SILVA implementation, compact evidence, replaceable components, and source-scale route. Existing tests and notebooks remain the executable authority.

Evidence boundary

The mechanism is compact-verified in the package suite. The final source-scale stage remains planned until the cited data, complete optimization budget, checkpoints, and evaluation protocol have actually run.

Identity and Sources

Field	Value
Domain	graphs and distributed systems
Task contract	private anchors, typed observations, admission weights, and emission carriers -> joint answer
Source relation	paper-adaptation
References	[63]
Repositories	https://github.com/sym-bot/mesh-memory-protocol
Editable scale plan	experiments/reproduction/configs/silva_mesh_inference.json

Governing Equation

The domain-level state contract is

\[ Z^\star=T_\theta(Z^\star;X,A,E,b),\qquad \widehat Y=Q_\psi(Z^\star). \]

The implementation registry specializes it operationally as

z_i_star=(b_i+sum_j w_ij z_j_star)/(lambda_i+tau_i+sum_j w_ij)

Define the root residual

\[ R_\theta(z;x)=z-T_\theta(z;x). \]

At a regular equilibrium, differentiating \(R_\theta(z^\star;x)=0\) gives

\[ \frac{\partial z^\star}{\partial x} = \left(I-\frac{\partial T_\theta}{\partial z}\right)^{-1} \frac{\partial T_\theta}{\partial x}. \]

This identity explains why the forward residual, the conditioning derivative, and the adjoint linear solve must be diagnosed separately from the task metric.

What Is Preserved

• receiver-autonomous nonnegative typed admission and source emission carriers
• anchored directed Jacobi relaxation whose system is an M-matrix
• centralized optimum comparison and numerical convergence certificate

What Can Be Replaced

Each item below is an explicit control rather than an undocumented modification:

• replace admission/emission policy or typed evidence precision
• compare every distributed solve to the centralized optimum and M-matrix certificate
• nodes
• typed fields
• carrier sparsity
• asynchronous iteration budget

Constructor and Shape Contract

silva_mesh_inference(config: 'SolverConfig | None' = None)

The transition must preserve the declared equilibrium-state shape even when the encoder, branch operators, constraints, solver, and readout are replaced. Test the transition by itself before testing the complete root solve.

Progressive Experiment Ladder

1. Equation and tensor contract

Objective: Make the state, conditioning variables, operator, and readout explicit.

Procedure:

• Write and evaluate the family equation: z_i_star=(b_i+sum_j w_ij z_j_star)/(lambda_i+tau_i+sum_j w_ij)
• Declare every tensor axis, boundary, mask, graph, or physical unit.
• Check the transition output has exactly the same shape as the equilibrium state.

Acceptance checks:

• finite transition values
• shape-preserving state update
• all conditioning variables affect the intended branch

Evidence target: contract-verified.

2. Primitive mechanism reconstruction

Objective: Build the retained source mechanism from replaceable modules.

Procedure:

• receiver-autonomous nonnegative typed admission and source emission carriers
• anchored directed Jacobi relaxation whose system is an M-matrix
• centralized optimum comparison and numerical convergence certificate

Acceptance checks:

• primitive modules expose trainable parameters and gradients
• mechanism-specific invariance or constraint check passes
• direct transition evaluation is deterministic under a fixed seed

Evidence target: compact-verified.

3. Public abstraction equivalence

Objective: Verify that the assembled family evaluates the same transition as its primitives.

Procedure:

• Copy the primitive module parameters into the public family constructor.
• Evaluate one transition and one complete equilibrium with identical inputs.
• Compare outputs, residuals, and parameter gradients with declared tolerances.

Acceptance checks:

• transition outputs agree
• equilibrium residual is finite and decreases
• primitive and assembled gradients agree on the compact case

Evidence target: compact-verified.

4. Compact real or analytic task

Objective: Exercise training, evaluation, diagnostics, and serialization end to end.

Procedure:

• make_mesh_gaussian_dataset gives a seeded carrier graph with a centralized reference solution.

Acceptance checks:

• record centralized agreement error
• record M-matrix certificate
• record carrier connectivity
• record spectral gap
• checkpoint reload reproduces the recorded prediction
• result record contains data and configuration fingerprints

Evidence target: compact-verified.

5. Official-data subset

Objective: Validate the complete source data path before spending the full budget.

Procedure:

• Generate topology, typed observations, precisions, admission/emission policies, lineage, and seeds as a versioned case table.
• Freeze preprocessing, split logic, metric code, and checkpoint format.
• Run a deterministic subset large enough to expose batching and memory failures.

Acceptance checks:

• dataset receipt and checksum are stored
• resume and evaluation paths reproduce the same subset metric
• memory and runtime are measured rather than estimated

Evidence target: subset-verified.

6. Source-scale reproduction or declared extension

Objective: Run the cited protocol, or change it explicitly as a SILVA extension.

Procedure:

• Generate topology, typed observations, precisions, admission/emission policies, lineage, and seeds as a versioned case table.
• Run distributed relaxation and the centralized solve for every case, retaining the M-matrix and spectral-radius certificates.
• Sweep connectivity, asymmetry, noise, anchor density, latency, and forwarding while reporting agreement and communication cost.
• paper synthetic lineage/carrier cases, source-novel forwarding policy, and noise model
• connectivity, asymmetry, anchor-density, latency, and confidentiality probe sweeps
• centralized Bayes optimum, spectral gap, recovery error, and communication accounting

Acceptance checks:

• all required artifacts are archived
• reported metrics use the cited evaluation protocol
• every architectural or training deviation is listed
• claims match the achieved evidence status

Evidence target: planned.

Data, Access, and Storage

Candidate datasets:

• synthetic carrier-chain mechanism cases
• noisy linear-Gaussian collective estimation

Authoritative routes:

• https://arxiv.org/abs/2606.19537
• https://github.com/sym-bot/mesh-memory-protocol

Access obligations:

• The reported linear-Gaussian cases are synthetic and can be regenerated from declared topology, precision, policy, and seed.
• No private node state is needed in a shared archive; store admitted typed observations and lineage separately.

Storage planning:

• Storage scales with runs * typed observations * nodes plus sparse carrier edges and lineage records.
• Stream policy sweeps because centralized matrices and distributed traces can be regenerated from the saved seed and parameters.

Preprocessing record:

• record dataset version, split, normalization, shape convention, and seed
• preserve masks, graph indices, boundaries, or physical units required by the domain

Metrics and Current Evidence

Required metrics:

• centralized agreement error
• M-matrix certificate
• carrier connectivity
• spectral gap
• messages

This family is verified through its listed mechanism tests and executed notebook. It is not included in a same-task comparison when another family does not share its input, state, output, and loss contract. The absence of a comparison row is therefore a scope decision, not missing implementation evidence.

Executed notebook paths:

• notebooks/package_api/32_silva_mesh_inference.ipynb

Mechanism tests:

• tests/test_emerging_equilibria.py

Compact Defaults

Option	Value
tier	'smoke'
config	SolverConfig(solver='picard', max_iter=12, tol=1e-05, alpha=1.0, history=3, ridge=0.0001, beta=1.0, stop_mode='relative', relative_eps=1e-08, anderson_batch_dims=0, track_residuals=True, reengage=True, backward_mode='implicit', backward_solver='gmres', backward_max_iter=20, backward_tol=1e-05, backward_stop_mode='relative', backward_relative_eps=1e-08, phantom_steps=1, phantom_tau=1.0, neumann_terms=5, shine_refine_steps=0, indexing=(), return_best=True)

Full Defaults

Option	Value
tier	'full'
config	SolverConfig(solver='picard', max_iter=60, tol=1e-05, alpha=1.0, history=6, ridge=0.0001, beta=1.0, stop_mode='relative', relative_eps=1e-08, anderson_batch_dims=0, track_residuals=True, reengage=True, backward_mode='implicit', backward_solver='gmres', backward_max_iter=80, backward_tol=1e-05, backward_stop_mode='relative', backward_relative_eps=1e-08, phantom_steps=1, phantom_tau=1.0, neumann_terms=5, shine_refine_steps=0, indexing=(), return_best=True)

Defaults establish a starting budget; the cited source protocol takes precedence whenever reproduction is the claim.

Source-Scale Checklist

• Generate topology, typed observations, precisions, admission/emission policies, lineage, and seeds as a versioned case table.
• Run distributed relaxation and the centralized solve for every case, retaining the M-matrix and spectral-radius certificates.
• Sweep connectivity, asymmetry, noise, anchor density, latency, and forwarding while reporting agreement and communication cost.

Benchmark-specific requirements:

• paper synthetic lineage/carrier cases, source-novel forwarding policy, and noise model
• connectivity, asymmetry, anchor-density, latency, and confidentiality probe sweeps
• centralized Bayes optimum, spectral gap, recovery error, and communication accounting

Required archived artifacts:

• machine-readable model and solver configuration
• dataset receipt with source revision, split, license, and checksum
• preprocessing and normalization record
• seeded training and evaluation log
• checkpoint and optimizer-resume state for trained experiments
• task metrics and equilibrium diagnostics in a machine-readable result
• runtime, peak-memory, device, precision, and dependency record
• declared deviations from the cited protocol

Reporting Rule

Report the achieved evidence status, not the intended one. A compact or subset run may validate the implementation and data path, but only a completed cited protocol supports a source-scale reproduction statement. Modified operators are valuable SILVA extensions when every deviation is named and measured.

Where to Go Next

Question	Page
Where are all family dossiers?	Family Dossier Index
How is a custom family assembled?	Advanced Extension Handbook
How are experiment stages represented in the API?	Research-Depth API
Which lab inspects every dossier?	Family Dossier Lab