Math Implementation Coverage

This matrix maps docs/research/equation_ledger.md to the current runnable repository. It is intentionally conservative: documentation coverage does not mean implementation, implementation does not mean validation, and synthetic artifacts do not create model-superiority claims.

Coverage Key

• implemented: code path exists for the equation or a simplified equivalent.

• tested: there is a local unit/CLI/artifact test that exercises the code path.

• used in experiment: the equation contributes to a runnable suite or emitted artifact.

• scaffolded: a partial interface or proxy exists, but not the full mathematical object.

• docs only: preserved in research docs, with no runnable code path.

• deferred: explicitly future work.

• archived: no longer a main architecture claim.

• falsified / not used: invalidated or intentionally excluded from current claims.

Summary

Area	Current implementation coverage	Current tests/artifacts	Remaining gap
Core NFC equations	EQ-003, EQ-004, EQ-006, EQ-009, EQ-010, EQ-011, EQ-012, EQ-017, EQ-018, EQ-019, EQ-020, EQ-057, EQ-058, EQ-079, EQ-084, EQ-085 are implemented as simplified experimental code.	tests/models/test_nfc.py, tests/data/test_synthetic_field.py, tests/benchmarks/test_nfc_suite.py, nfc_synthetic_results.json, nfc_ablation_table.csv, evidence_gate.json.	The field is not validated on real held-out neural data, and several equations are simplified neural modules rather than physics-complete operators.
Observation operators	fMRI, EEG, and behavior operators exist in src/neurotwin/models/nfc/observations/.	Shape/finite tests in tests/models/test_nfc.py; synthetic suite tasks in tests/benchmarks/test_nfc_suite.py.	fMRI HRF is a learned short convolution, EEG is pooled readout, behavior is shape-only, and MEG/spike/calcium/fNIRS are not implemented.
Synthetic proving ground	Synthetic latent field, fMRI-like observation, EEG-like observation, latent recovery, forecasting, masked reconstruction, and cross-modal tasks exist.	tests/data/test_synthetic_field.py; tests/benchmarks/test_nfc_suite.py; CLI emits nfc_synthetic_results.json, nfc_synthetic_results.csv, nfc_ablation_table.csv, uncertainty_calibration.csv, evidence_gate.json, diagnostic_report.md.	Synthetic generator lacks explicit physiology fields, artifact processes, true optical/fNIRS physics, and strict real-data validation.
Evidence gates	Leakage/claim gates, finalization, model cards, paper-mode gates, and NFC synthetic --require-pass behavior exist.	tests/cli/test_expanded.py, tests/cli/test_report.py, tests/artifacts/test_docs_contracts.py, tests/training/test_prepared.py.	Claims remain disabled unless final evidence gates pass; synthetic-only gates are plumbing/falsification checks.
Track A reproducibility	Split manifests, leakage audits, identity probes, prepared tasks, baselines, reports, and model cards are implemented.	Prepared-data and leakage tests under tests/data/, tests/eval/, tests/benchmarks/, tests/training/.	This track supports reproducibility claims, not architecture superiority.
fNIRS theory	EQ-052 to EQ-056 are documented in docs/research/fnirs_observation_operator_notes.md.	Documentation contract only.	No fNIRS adapter, optical forward model, SNIRF/BIDS fNIRS pipeline, MDD task, or clinical claim.
TurboQuant/TurboVec theory	EQ-059 to EQ-077 are documented in docs/research/turboquant_retrieval_notes.md.	Documentation contract only.	No retrieval package, no vector store, no semantic duplicate audit, no retrieval-kNN baseline.
Archived Pair-Operator math	Low-rank pair-state math is still implemented and tested, but Pair-Operator is no longer the main primitive.	tests/models/test_nfc.py, tests/models/test_shapes.py, tests/benchmarks/test_nfc_suite.py, nfc_ablation_table.csv.	Treat Pair-Operator as ablation/baseline only.
Future math only	Variational inference, gauge fixing, graph regularizers, stability penalties, InfoNCE, Koopman residuals, Riemannian EEG, sampling-lattice stress tests, sparse experts, and retrieval math are not runnable.	Research docs only.	Needs explicit implementation plans, tests, configs, and evidence gates before any claim.

Per-Equation Matrix

ID	Coverage classification	Implementation path	Test path	Runnable config / artifact	Missing work or boundary
EQ-001	implemented; tested; used as baseline	src/neurotwin/models/torch_models.py; src/neurotwin/benchmarks/nfc_suite.py	tests/models/test_shapes.py; tests/benchmarks/test_nfc_suite.py	nfc_synthetic_results.json model row transformer	Baseline only, not NFC novelty.
EQ-002	docs only; deferred	none for input-selective Mamba; TinySSMBaseline is only a local fallback in src/neurotwin/models/torch_models.py	tests/models/test_shapes.py; runtime estimate tests mention ssm_fallback	nfc_synthetic_results.json model row ssm_fallback	No selective input-dependent Mamba/SSM backbone.
EQ-003	implemented; tested; used in experiment	src/neurotwin/models/nfc/latent_field.py; src/neurotwin/models/nfc/compiler.py	tests/models/test_nfc.py	nfc_synthetic_results.json; diagnostic_report.md	Latent coordinates are experimental and not semantically identifiable.
EQ-004	implemented simplified; tested; used in experiment	src/neurotwin/models/nfc/compiler.py; src/neurotwin/models/nfc/observations/	tests/models/test_nfc.py; tests/benchmarks/test_nfc_suite.py	nfc_synthetic_results.json; evidence_gate.json	Operators are learned/simple approximations, not full measurement physics.
EQ-005	docs only; deferred	none	none	none	No probabilistic marginalization or latent posterior training.
EQ-006	implemented simplified; tested	src/neurotwin/models/nfc/field_update.py	tests/models/test_nfc.py	NFC model path in synthetic suite	Uses discrete neural module, not a continuous controlled flow.
EQ-007	docs only; deferred	none	none	none	No Neural CDE or irregular-time controlled differential equation path.
EQ-008	docs only; deferred	none	none	none	No integro-differential neural-field solver.
EQ-009	implemented simplified; tested	src/neurotwin/models/nfc/field_update.py; src/neurotwin/data/synthetic_field.py	tests/models/test_nfc.py; tests/data/test_synthetic_field.py	synthetic field sample; nfc_synthetic_results.json	Current update is not the full D, K_t, B, xi_t equation.
EQ-010	implemented; tested; used in ablation	src/neurotwin/models/nfc/pair_kernel.py; src/neurotwin/models/pair_operator.py	tests/models/test_nfc.py; tests/models/test_shapes.py	nfc_ablation_table.csv	Implemented as low-rank learned kernel; real anatomical interpretation is unproven.
EQ-011	implemented; tested; used in ablation	src/neurotwin/models/nfc/pair_kernel.py	tests/models/test_nfc.py	nfc_ablation_table.csv	Structural prior support exists but is not validated as anatomy.
EQ-012	implemented; tested; used in ablation	src/neurotwin/models/nfc/pair_kernel.py; src/neurotwin/models/nfc/field_update.py	tests/models/test_nfc.py	nfc_ablation_table.csv	Pair update is ablation support, not a standalone claim.
EQ-013	scaffolded; tested proxy	src/neurotwin/models/nfc/uncertainty.py	tests/models/test_nfc.py; tests/benchmarks/test_nfc_suite.py	uncertainty_calibration.csv	Pair uncertainty is derived from region uncertainty; no true K_ij error target.
EQ-014	docs only; deferred	none	none	none	No graph-gradient operator.
EQ-015	docs only; deferred	none	none	none	No explicit Laplacian construction in NFC loss.
EQ-016	docs only; deferred	none	none	none	No graph smoothness regularizer.
EQ-017	implemented simplified; tested	src/neurotwin/models/nfc/observations/fmri.py; src/neurotwin/data/synthetic_field.py	tests/models/test_nfc.py; tests/data/test_synthetic_field.py	synthetic fMRI output; nfc_synthetic_results.json	Uses short learned convolution/lag, not canonical HRF integral.
EQ-018	implemented simplified; tested; used in experiment	src/neurotwin/models/nfc/observations/fmri.py; src/neurotwin/benchmarks/nfc_suite.py	tests/models/test_nfc.py; tests/benchmarks/test_nfc_suite.py	fMRI tasks in nfc_synthetic_results.json	Parcel readout is simplified and synthetic-only.
EQ-019	implemented simplified; tested	src/neurotwin/models/nfc/stimulus.py	tests/models/test_nfc.py	NFC synthetic stimulus tasks	Causal averaging exists; no learned HRF-grade stimulus alignment.
EQ-020	implemented simplified; tested; used in experiment	src/neurotwin/models/nfc/observations/eeg.py; src/neurotwin/data/synthetic_field.py	tests/models/test_nfc.py; tests/data/test_synthetic_field.py; tests/benchmarks/test_nfc_suite.py	EEG tasks in nfc_synthetic_results.json	No real lead-field matrix or source-current model.
EQ-021	docs only; deferred	none	none	none	No MEG adapter or claim.
EQ-022	docs only; deferred	none	none	none	No spike observation operator.
EQ-023	docs only; deferred	none	none	none	No calcium observation operator.
EQ-024	scaffolded; tested	src/neurotwin/models/nfc/observations/behavior.py; src/neurotwin/models/nfc/compiler.py	tests/models/test_nfc.py	no current benchmark artifact	Behavior head is shape-tested only; no behavior task claim.
EQ-025	docs only; deferred	none	none	none	No variational posterior.
EQ-026	docs only; deferred	none	none	none	No ELBO objective.
EQ-027	docs only	none	none	docs only	Gauge ambiguity is documented but not enforced.
EQ-028	docs only	none	none	docs only	Gauge ambiguity is documented but not enforced.
EQ-029	docs only	none	none	docs only	Gauge ambiguity is documented but not enforced.
EQ-030	docs only; deferred	none	none	none	No temporal smoothness loss.
EQ-031	docs only; deferred	none	none	none	No spectral regularizer.
EQ-032	scaffolded elsewhere; not NFC-proven	prepared/translator subject controls in src/neurotwin/models/torch_models.py; config plumbing in training	tests/models/test_shapes.py; tests/training/test_prepared.py	prepared-training artifacts when enabled	No NFC low-rank subject adapter of this exact form.
EQ-033	docs only; deferred	none	none	none	No continuous-time stability model.
EQ-034	docs only; deferred	none	none	none	No Jacobian audit.
EQ-035	docs only; deferred	none	none	none	No eigenvalue stability criterion.
EQ-036	docs only; deferred	none	none	none	No spectral-radius enforcement.
EQ-037	docs only; deferred	none	none	none	No stability penalty.
EQ-038	docs only; scaffolded proxy	src/neurotwin/models/nfc/uncertainty.py emits positive maps	tests/models/test_nfc.py	uncertainty_calibration.csv proxy	No NLL training objective or predictive variance likelihood.
EQ-039	scaffolded proxy; needs evidence	src/neurotwin/benchmarks/nfc_suite.py writes calibration proxy	tests/benchmarks/test_nfc_suite.py	uncertainty_calibration.csv with proxy_source=mse_derived_suite_proxy	No interval coverage target or real calibration claim.
EQ-040	docs only; deferred	none	none	none	No InfoNCE objective or leakage-safe contrastive sampler.
EQ-041	docs only; deferred	none	none	none	No Koopman observable model.
EQ-042	docs only; deferred	none	none	none	No Koopman residual update.
EQ-043	docs only; deferred	none	none	none	No Koopman residual loss or spectral penalty.
EQ-044	docs only; deferred	none	none	none	No EEG covariance baseline/head.
EQ-045	docs only; deferred	none	none	none	No SPD covariance output head.
EQ-046	docs only; deferred	none	none	none	No AIRM metric.
EQ-047	docs only; deferred	existing manifests store sample rates/times but not this lattice model	split/audit tests cover leakage, not lattice math	none	No native-lattice multimodal timing model.
EQ-048	docs only; deferred	none	none	none	No union-of-grids operator.
EQ-049	docs only; deferred	none	none	none	No Fourier feature module for NFC timing.
EQ-050	docs only; deferred	none	none	none	No graph spectral basis.
EQ-051	docs only; deferred	none	none	none	No coprime window stress-test generator.
EQ-052	docs only; deferred	docs/research/fnirs_observation_operator_notes.md	documentation contract only	docs only	No fNIRS optical operator.
EQ-053	docs only; deferred	docs/research/fnirs_observation_operator_notes.md	documentation contract only	docs only	No Rytov transform code.
EQ-054	docs only; deferred	docs/research/fnirs_observation_operator_notes.md	documentation contract only	docs only	No optical density output path.
EQ-055	docs only; deferred	docs/research/fnirs_observation_operator_notes.md	documentation contract only	docs only	No fNIRS observation support or claim.
EQ-056	docs only; deferred	docs/research/fnirs_observation_operator_notes.md	documentation contract only	docs only	Synthetic generator has no explicit hemodynamic/physiology field.
EQ-057	implemented simplified; tested; used in experiment	src/neurotwin/data/synthetic_field.py; src/neurotwin/benchmarks/nfc_suite.py	tests/data/test_synthetic_field.py; tests/benchmarks/test_nfc_suite.py	nfc_synthetic_results.json fMRI rows	Simplified lag/readout, not a full hemodynamic field.
EQ-058	implemented simplified; tested; used in experiment	src/neurotwin/data/synthetic_field.py; src/neurotwin/benchmarks/nfc_suite.py	tests/data/test_synthetic_field.py; tests/benchmarks/test_nfc_suite.py	nfc_synthetic_results.json EEG rows	No explicit motion artifact process.
EQ-059	docs only; deferred	docs/research/turboquant_retrieval_notes.md	documentation contract only	docs only	No quantization API.
EQ-060	docs only; deferred	docs/research/turboquant_retrieval_notes.md	documentation contract only	docs only	No MSE compression objective.
EQ-061	docs only; deferred	docs/research/turboquant_retrieval_notes.md	documentation contract only	docs only	No inner-product quantization objective.
EQ-062	docs only; deferred	docs/research/turboquant_retrieval_notes.md	documentation contract only	docs only	No vector-store normalization layer.
EQ-063	docs only; deferred	docs/research/turboquant_retrieval_notes.md	documentation contract only	docs only	No random rotation quantizer.
EQ-064	docs only; deferred	docs/research/turboquant_retrieval_notes.md	documentation contract only	docs only	No TurboQuant implementation.
EQ-065	docs only; deferred	docs/research/turboquant_retrieval_notes.md	documentation contract only	docs only	No dimension/risk audit.
EQ-066	docs only; deferred	docs/research/turboquant_retrieval_notes.md	documentation contract only	docs only	No scalar Lloyd-Max buckets.
EQ-067	docs only; deferred	docs/research/turboquant_retrieval_notes.md	documentation contract only	docs only	No residual compression.
EQ-068	docs only; deferred	docs/research/turboquant_retrieval_notes.md	documentation contract only	docs only	No QJL residual correction.
EQ-069	docs only; deferred	docs/research/turboquant_retrieval_notes.md	documentation contract only	docs only	No retrieval scoring backend.
EQ-070	docs only; deferred	docs/research/turboquant_retrieval_notes.md	documentation contract only	docs only	No stimulus vector index.
EQ-071	docs only; deferred	docs/research/turboquant_retrieval_notes.md	documentation contract only	docs only	No latent field memory bank.
EQ-072	docs only; deferred	docs/research/turboquant_retrieval_notes.md	documentation contract only	docs only	No network-wise latent memory.
EQ-073	docs only; deferred	docs/research/turboquant_retrieval_notes.md	documentation contract only	docs only	No retrieval neighborhood API.
EQ-074	docs only; deferred	docs/research/turboquant_retrieval_notes.md	documentation contract only	docs only	No retrieval-kNN baseline.
EQ-075	docs only; deferred	docs/research/turboquant_retrieval_notes.md	documentation contract only	docs only	No retrieval weighting function.
EQ-076	docs only; deferred	docs/research/turboquant_retrieval_notes.md	documentation contract only	docs only	No quantized-vs-exact recall/distortion audit.
EQ-077	docs only; deferred	docs/research/turboquant_retrieval_notes.md	documentation contract only	docs only	No semantic near-duplicate audit.
EQ-078	docs only; deferred	partial terms exist across NFC and prepared training, but no single full NFC loss	tests cover partial pieces	none	No integrated latent/graph/stability/uncertainty/calibration loss.
EQ-079	implemented; tested; used in experiment	src/neurotwin/scoring/metrics.py; src/neurotwin/benchmarks/nfc_suite.py	tests/scoring/test_metrics.py; tests/benchmarks/test_nfc_suite.py	nfc_synthetic_results.json; nfc_synthetic_results.csv	Synthetic MSE only; no real fMRI claim.
EQ-080	partially implemented; docs-only PSD term	src/neurotwin/scoring/metrics.py; src/neurotwin/benchmarks/nfc_suite.py	tests/scoring/test_metrics.py; tests/benchmarks/test_nfc_suite.py	EEG MSE rows in nfc_synthetic_results.json	PSD loss term is not implemented.
EQ-081	docs only; deferred	none	none	none	No spike likelihood.
EQ-082	experimental framing; partially used in synthetic tasks	src/neurotwin/benchmarks/nfc_suite.py; src/neurotwin/models/nfc/compiler.py	tests/benchmarks/test_nfc_suite.py; tests/models/test_nfc.py	synthetic_eeg_to_fmri; synthetic_fmri_to_eeg in nfc_synthetic_results.json	No explicit separate inference operator I_theta; current path is model forward task.
EQ-083	docs only; research framing	docs/research/neurotwin_master_research_state.md	none	docs only	No formal commutative-diagram API.
EQ-084	implemented; tested; used as baseline	src/neurotwin/benchmarks/nfc_suite.py; src/neurotwin/models/baselines.py; src/neurotwin/models/torch_models.py	tests/benchmarks/test_nfc_suite.py; tests/benchmarks/test_baseline_suite.py	direct baseline rows in nfc_synthetic_results.json	Direct translation is the baseline lane, not the main claim.
EQ-085	implemented experimental; tested; used in experiment	src/neurotwin/models/nfc/compiler.py; src/neurotwin/benchmarks/nfc_suite.py	tests/models/test_nfc.py; tests/benchmarks/test_nfc_suite.py	nfc_full rows in nfc_synthetic_results.json; nfc_ablation_table.csv	Needs strict synthetic pass and real held-out evidence before any architecture claim.

What Is Actually Runnable Today

The repo can currently run the following math-backed surfaces locally:

PYTHONPATH=src python3 -m neurotwin.cli eval \
  --suite nfc_synthetic \
  --out-dir /tmp/neurotwin_math_coverage_nfc \
  --train-steps 1 \
  --seed 0

Expected outputs:

• nfc_synthetic_results.json

• nfc_synthetic_results.csv

• nfc_ablation_table.csv

• nfc_falsification_report.md

• uncertainty_calibration.csv

• evidence_gate.json

• diagnostic_report.md

These artifacts prove the suite compiles and the gate can inspect the required tasks/models. They do not prove NeuroTwin/NFC superiority.

Coverage Conclusions

1. The runnable core is a real NFC skeleton: latent field, field update, pair-kernel ablation, simplified observation operators, uncertainty maps, synthetic field generator, and strict synthetic gate.

2. The repo has not implemented the full mathematical vision. Variational inference, graph gauge fixing, full stability theory, InfoNCE, Koopman residuals, Riemannian EEG, fNIRS optical physics, TurboVec retrieval, semantic duplicate audit, sparse experts, and real Algonauts/CNeuroMod evidence are still deferred or docs-only.

3. Pair-Operator is implemented and tested, but only as a baseline/ablation. It is archived as the main primitive.

4. fNIRS and TurboQuant/TurboVec are useful research directions, but they are not current capabilities.

5. The next evidence-bearing step remains the strict NFC synthetic diagnostic. A100/Algonauts/6x DDP should not proceed until the synthetic gate produces a real pass.