Architecture fidelity

Each cell has an architecture spec: equations, state layout, Jacobian class, Newton defaults, and an explicit fidelity label. Specs are the contract observers use to reimplement the recurrence by hand and compare against our sequential oracle within the numerics contract.

Labels

Label	Meaning
paper-faithful	Recurrence matches cited paper equations (up to documented notation). Parallel path is Alg. 1 on that \(f\).
paper-core	Core recurrence matches; block / conv / readout wrappers may sit outside the Newton cell.
research-variant	Intentional design choice that diverges from a named paper; deviations listed on the spec.
unverified	Shipped API; fidelity against a specific paper equation set is not yet audited.

Zoo status

Cell	Spec	Fidelity	Primary source
ParaGRU	yes	paper-faithful (mix='diag'); paper-faithful / Dreamer-style for mix='head' gates	Danieli et al. 2025 eq. 3.1a, 3.3
ParaLSTM	yes	paper-faithful	Danieli et al. 2025 eq. 3.1b, 3.3; Greff CIFG
ParaSLSTM	yes	paper-faithful (mix='diag'); Beck-style head mix documented	Danieli et al. / xLSTM sLSTM lineage
ParaNLRU	yes	research-variant vs linear Griffin RG-LRU	Griffin / RG-LRU + nonlinear slot (ours)
ParaM2RNN	yes	research-variant / paper-core	Mishra et al. arXiv:2603.14360
ParaCfC	yes	research-variant	Hasani et al. Nat. Mach. Intell. 2022 / arXiv:2106.13898 eq. (10); ncps CfCCell
ParaHopfield, ParaRWKV7, ParaTitans	pending	unverified	see cell catalog

How to challenge a cell

1. Read the spec’s Recurrence and Deviations.
2. Implement sequential step from the equations alone.
3. Run verify_agreement (or compare trajectories) against pararnn at the stated τ.
4. Open an issue with shapes, dtype, and report.to_dict() if agreement fails at recommended \(K\).

Template for new specs: TEMPLATE.md.