Model Fidelity & Polyglot-Completion Status

This page states, per model, which neuron models are polyglot-complete — the strictest completion bar SC-NeuroCore tracks. It is the single tracked, public answer to "which models can be considered full-fidelity / completed / implemented across the whole compute chain?".

The bar — what "polyglot-complete" means

A model is polyglot-complete only when every one of its four acceleration-language kernels implements the real model dynamics and each is proven against the Python reference:

1. Real dynamics in all four accel lanes — accel/rust/safety, accel/go, accel/julia, accel/mojo — the actual model (integrator and sub-stepping included), not a stub, a pasted comment body, a dummy return, or fake placeholder dynamics.
2. Proven parity — an executed test asserting each lane reproduces the Python golden. Where the right-hand side is exact arithmetic the parity is bit-for-bit; where gating uses transcendentals (exp/tanh/…) the declared stable observable is either event count or the complete continuous trajectory inside an explicit numerical tolerance.
3. Honest benchmark — a runnable, committed per-backend benchmark producing a real number (no fabricated figures).

This bar is stricter than, and must not be confused with, two weaker properties that most of the catalogue already has:

• Faithful Python reference — every catalogued model in the neuron model catalogue has a real, tested Python implementation. That is the ground truth, but it is not polyglot-completion.
• Real Rust engine acceleration — many models are accelerated by the engine/ Rust+PyO3 crate (the genuine performance path today). That is real and benchmarked, but it is the engine lane, not the four-language accel/ chain this page scores.

Legend

Mark	Meaning
✅	Real dynamics, executed parity test passes
🔶	Real dynamics but the lane is not yet in its final executable form (a maintained parity note, or a strengthening pass still open)
⬜	Stub / fake / unverified
—	Not applicable for this model

Polyglot-complete models

Every lane below carries the real model dynamics with an executed Python-parity proof. Every Mojo surface in this promoted set is now executable; no lane below is a fake stub or documentation-only parity note.

Model	Rust safety	Go	Julia	Mojo	Parity basis (golden)	Landed
Wang-Buzsaki	✅	✅	✅	✅ executable	spike count — 3 AP @ I=10, 20 macro steps (Gauss-Seidel)	0ebf4ea88
FitzHugh-Nagumo	✅	✅	✅	✅ shared-lib	bit-exact — 1 AP @ I=10/100 steps, 5-spike train @ I=0.5/2000 steps (RK4, exact RHS)	729e0a2ea
Morris-Lecar	✅	✅	✅	✅ executable	spike count — 0/3/5 @ I=0/50/100 over 2000 steps (RK4, tanh/cosh)	bc46a0fb5
Connor-Stevens	✅	✅	✅	✅ shared-lib	spike count — 0/2/9 @ I=0/10/20 over 100 macro steps (candidate-first RK4 with 100 sub-steps, exp); Mojo C ABI preserves every event and the six-state trace within 2e-6 over the enrolled envelope	this commit
Hodgkin-Huxley	✅	✅	✅	✅ shared-lib	spike count — 0/6/9 @ I=0/10/20 over 100 macro steps (gate-first baseline-Euler with 100 sub-steps, exp); Mojo C ABI preserves every event and the four-state trace within 2e-9 over the enrolled envelope	this commit
AdEx	✅	✅	✅	✅ shared-lib	accel event count — 0/4/12 @ I=0/200/500 over 1000 baseline-Euler steps; all compiled traces stay within 5e-12 of Python and transport the complete maintained numeric contract except the factory-default Rust engine boundary; existing Q16.16 RTL co-simulation retains its declared two-percent event-count envelope at I=1000 over 500 steps	this commit
ExpIF	✅	✅	✅	✅ shared-lib	accel event count — 0/0/2 @ I=0/5/20 over 1000 candidate-first RK4 steps; every compiled lane preserves the events and stays within 5e-8 of Python, with the factory-default Rust engine boundary stated separately; hand/TOML/JSON and Q32.32 RTL preserve the enrolled event counts, and the generated depth-4 Z3 job passes	this commit
Lapicque	✅	✅	✅	✅ shared-lib	accel event count — 0/0/71/200/500 @ I=0/0.5/2/5/20 over 1,000 exact constant-current RC steps; all compiled events are exact and traces stay within 2e-15 of Python, with the factory-default Rust engine boundary stated separately; hand/TOML/JSON events are exact and state error stays within 2e-15, Q16.16 RTL preserves the complete 0/83/500 event vectors at I=0.333/2.3/20.25 with voltage error below 0.04, and the generated depth-20 Z3 job passes	this commit
Perfect Integrator	✅	✅	✅	✅ shared-lib	bit-exact accel traces and event counts — 0/32/66/200/250/500/1000 @ I=0/0.333/0.7/2/3/5/20 over 1,000 candidate-first Euler steps; the Rust engine retains its factory-default boundary while Julia/Go/Mojo carry the complete numeric contract; hand/schema/Q8.8 RTL are event-exact with 66 events at I=0.7 over 1,000 steps, the quantisation boundary at I=0.333 is declared as 32/32/31, and the generated depth-20 Z3 job passes	this commit
Quadratic IF	✅	✅	✅	✅ shared-lib	exact accel events — 0/2/3/6/11/26/100/250 @ I=0/0.333/0.5/1/2/5/20/50 over 1,000 exact Riccati-flow steps, with every compiled trace within 2e-12 of Python; the Rust safety module is exercised independently and the engine retains its factory-default boundary; hand/TOML/JSON events remain exact with state error below 0.006, both schema formats reset inclusively at configured v_peak, Q16.16 RTL preserves the enrolled cycle-level event vectors with voltage error below 0.011, the I=0.1 timing boundary is declared, and the generated depth-20 Z3 job passes	this commit
Theta	✅	✅	✅	✅ shared-lib	exact accel events — 0/0/0/1/2/2/3/5/7/14/23 @ I=-1/-0.5/0/0.1/0.333/0.5/1/2/5/20/50 over 1,000 tangent-half-angle exact-flow steps, with every compiled trace within 2e-12 circular phase error; the Rust safety module is exercised independently and the engine retains its factory-default boundary; paired Euler schemas preserve the enrolled counts, generated Q16.16 RTL is count-exact across the vector with circular phase error below 0.17 rad at the declared moderate regimes, the I=1 one-cycle timing displacement is explicit, and the generated depth-6 Z3 job passes	this commit
DPI	✅	✅	✅	✅ shared-lib	exact accel events — 0/0/0/0/1/3/6/11/21 @ I=-0.1/0/1/2/3/5/10/20/50 over 1,000 simultaneous-Euler steps of the coupled Indiveri-Stefanini-Chicca (2010) current-domain equations; compiled states remain within 5e-13, the Rust safety module carries the complete 18-field contract and the engine retains its factory-default boundary; hand/TOML/JSON states remain within 1e-13, generated Q16.16 RTL preserves 13 events at I=5 over 5,000 steps with declared state/timing envelopes, and the generated depth-4 Z3 job passes	this commit
COBA LIF	✅	✅	✅	✅ shared-lib	exact 3,077-event parity over the controlled 200,000-step complete non-default contract; Rust/Julia/Go traces are exact and Mojo stays within 7.11e-15; hand/TOML/JSON preserve the complete four-state RK4 trace and six enrolled events exactly, generated Q24.24 RTL preserves all six event indices with voltage/conductance/timer errors below 1e-5/5e-6/3e-6/2e-6, the independent Brette-2007 DOI trace matches every feature within 1e-12, and the generated depth-4 Z3 reset-safety job passes	this commit
Escape Rate	✅	✅	✅	✅ shared-lib	seeded exact 29-event parity over the configured 4,096-step complete contract: Rust/Julia/Go voltage traces are exact, Mojo stays within 2e-14, and every lane finishes at RNG state 45,999; the independent five-seed/full-period artifact pins event hashes, rate, and geometric-ISI statistics; hand/TOML/JSON preserve private RNG and failure atomicity; generated Q24.24 RTL reproduces the complete 65,535-bit event stream with 14,496 events and final seed 0xACE1; the depth-4 Z3 safety job passes; the controlled 200,000-step benchmark records 1,523 exact events and final RNG 46,746 in all five lanes	this commit
Poisson	✅	✅	✅	✅ shared-lib	seeded exact 918-event parity over the configured 4,096-bin rate/dt/RNG contract, with every runtime finishing at RNG state 45,999; the independent exhaustive artifact pins the 65,535-state event hash, 14,496-event rate, and geometric-ISI statistics; hand/TOML/JSON preserve private RNG and failure atomicity; registered and folded Q24.24 RTL reproduce the complete event stream, threshold, probability word, and final seed 0xACE1; the depth-4 Z3 safety job passes; the source-hashed 200,000-bin benchmark records 44,256 exact events and final RNG 46,746 in all five lanes	this commit
IQIF	✅	✅	✅	✅ shared-lib	bit-exact signed-integer parity for the pinned Wu et al. source tutorial: all five runtimes, the independent source recurrence, and paired TOML/JSON schemas reproduce 26 events and every one of 400 states; registered and folded Q32.0 RTL preserve the complete event/state vector with two signed Q0.3 shifts; the depth-4 Z3 safety job passes; the source-hashed 200,000-step benchmark records 13,333 events, final state 165, and trajectory SHA-256 b5c84ffb…a4f4 in every lane	this commit
McCulloch-Pitts	✅	✅	✅	✅ shared-lib	McCulloch and Pitts' 1943 all-or-none rule: a positive active-excitatory-afferent count threshold with absolute veto by any active inhibitory afferent, without later real-weight substitution or fake internal state; Python, Rust engine+safety, Julia, Go, Mojo, paired stateless TOML/JSON schemas, and the independent primary-paper truth table are bit-exact; registered and folded signed-Q32.0 RTL preserve every enrolled row using -1 only as the inhibition sentinel; the depth-4 Z3 safety job passes; the source/binary-bound 200,000-row benchmark emits 102,273 events and trace SHA-256 52a05b62…aee4 with zero mismatch in every lane	this commit
Sigmoid Rate	✅	✅	✅	✅ shared-lib	complete configurable exact-relaxation rate traces over 200,000 steps: Python, Rust, Julia and Go are byte-identical; Mojo remains within 3.08e-14, below the declared 5e-12 float tolerance; reset preserves tau, beta, theta and dt; paired schemas preserve the varied hand trajectory within 5e-12, and generated Q32.32 RTL keeps the 256-step rate trace within 0.016 through public outputs while remaining event-silent; the source/binary-bound five-backend benchmark is local non-exclusive evidence, and no formal, synthesis, timing, device, or PPA claim is made	this commit
Threshold-linear Rate	✅	✅	✅	✅ shared-lib	complete configurable algebraic rate traces over 200,000 evaluations: Python, Rust, Julia, Go, and Mojo are bit-exact for r=gain*max(0,I-theta); below-threshold, equality, and above-threshold branches are executed; reset preserves theta and gain; paired schemas match the hand transfer exactly, and generated Q16.16 RTL preserves all 193 public rate words from I=-4 through 8 in 1/16 increments while remaining event-silent; the source/binary-bound benchmark is local non-exclusive evidence, and no formal, synthesis, timing, device, or PPA claim is made	this commit
Wilson-Cowan	✅	✅	✅	✅ shared-lib	normalised coupled E/I population reduction with shifted sigmoid and candidate-first RK4; complete configurable 100,000-step Rust/Julia/Go trajectories and final rates remain within 1e-9 of Python and Mojo remains within 1e-8; reset preserves all dynamics parameters; native failures are atomic; paired schemas match the hand trajectory within 1e-15, and generated Q32.32 RTL keeps both public rates within 0.021 across the 96-sample mixed-drive trace while remaining event-silent; availability/refractory factors and independent inhibitory drive are explicitly outside scope; continuous rates are not spikes, and no formal, synthesis, timing, device, or PPA claim is made	this commit
Jansen–Rit	✅	✅	✅	✅ shared-lib	Jansen and Rit 1995 equation-(6) neural mass with the published C2*S(C1*y0) and C4*S(C3*y0) wiring; all five runtimes return seven complete traces plus six final states, with Rust/Julia/Go within 1e-11 of Python and Mojo within 1e-8; the independent 256-step DOI/Brian2-pinned trace is byte-exact, paired schemas match the hand model, and generated Q32.32 RTL preserves the enrolled trace within declared potential/derivative envelopes; the 0.1 ms Euler step follows the pinned implementation rather than the continuous paper equations; the EEG proxy is continuous and higher silicon rungs are not claimed	this commit
Montbrió–Pazó–Roxin	✅	✅	✅	✅ shared-lib	Montbrió, Pazó, and Roxin 2015 dimensionless equations (12a–b), restored through R=tau*r and t'=t/tau and exposed through the legacy compatibility class ErmentroutKopellPopulation; all five runtimes return both complete state traces and final states, with Rust/Julia/Go within 1e-12 of Python and Mojo within 1e-10; the independent 256-step DOI trace is byte-exact, paired schemas match the hand model, generated Q32.32 RTL preserves the enrolled trajectory within 2e-6, and a depth-4 catalogue job proves bounded reset and event-silence safety only; the Euler step is implementation scope, firing rate is continuous, and formal equivalence or higher silicon rungs are not claimed	this commit
Resonate-and-Fire	✅	✅	✅	✅ shared-lib	Izhikevich 2001 complex resonator with current-like x, voltage-like y, exact constant-input flow, sampled upward voltage crossing, and generalised source reset z=i*threshold; all five runtimes return three complete traces plus both final states, with Rust/Julia/Go within 1e-12 of Python and Mojo within 1e-10; the independent DOI trace and paired schemas preserve the same equations; generated Q32.32 RTL matches the complete enrolled event vector with state error below 1e-8 and alternating-drive stress below 5e-8; a depth-4 job proves reset safety only; the lookup-grid envelope, sampled timing, non-monotone high-drive response, H1 limit, and absence of formal equivalence or higher silicon evidence are explicit	this commit
Alpha-Synapse LIF	✅	✅	✅	✅ shared-lib	dual excitatory/inhibitory current-based alpha-synapse LIF: Rall 1967 alpha kernel in two-state cascades with exact piecewise-constant-input filter relaxation and exact alpha-current convolution (equal-tau limit in all production lanes), somatic spike resetting only v; all five runtimes return five complete state traces plus five final states over the 200,000-step benchmark, with Rust/Julia byte-identical to Python, Go within 3.8e-14, and Mojo within 8.9e-15 of the declared 1e-10 tolerance; failures are atomic and reset preserves configuration; the independent dual-drive DOI reference and paired schemas preserve the same equations; generated Q32.32 RTL at the enrolled grid-exact operating point tracks all five states within 1.95e-8 with the complete 24-event vector identical at two inhibitory levels; a depth-4 job proves reset safety only, and no formal equivalence, synthesis timing, device, or PPA claim is made	this commit
Adaptive-Threshold IF	✅	✅	✅	✅ shared-lib	composite reduced adaptive-threshold LIF: exact LIF membrane relaxation, the a=0 Mihalas–Niebur 2009 threshold-decay limit, and the Platkiewicz–Brette 2010 fixed post-spike threshold shift, with the voltage-dependent equilibrium, voltage coupling, and adaptation current explicitly outside scope; all five runtimes return three complete traces plus both final states over the 200,000-step benchmark, with Rust/Julia/Go byte-identical to Python and Mojo within 1.14e-13 of the declared 1e-10 tolerance; reset preserves configuration and failures are atomic; the independent DOI reference and paired schemas preserve the same equations; generated Q32.32 RTL at the enrolled grid-exact operating point tracks both states within 1.22e-8 with the complete event vector identical, every RTL spike resetting and shifting exactly; a depth-4 job proves reset safety only, and no formal equivalence, synthesis timing, device, or PPA claim is made	this commit
Wong-Wang	✅	✅	✅	✅ shared-lib	Wong and Wang 2006 Appendix two-choice reduction with simultaneous explicit-Euler NMDA gating and AMPA Ornstein-Uhlenbeck current states; all five runtimes consume the same explicit Gaussian samples and return six complete traces plus four final states, with Rust/Julia/Go within 1e-12 of Python and Mojo within 1e-9; the independent 256-step DOI trace is byte-exact, paired schemas match the hand model, and generated Q32.32 RTL preserves the enrolled trace within declared state/rate envelopes; the paper's 0.1 ms timestep is used and the author-code 0.5 ms discrepancy is recorded; rates are continuous and higher silicon rungs are not claimed	this commit
Amari neural field	✅	✅	✅	✅ shared-lib	Amari 1977 equation-(3) single-layer field on a declared periodic finite grid, with source-level Heaviside activity and a local-excitation/distal-inhibition difference-of-exponentials kernel; all five runtimes return complete vector states and exact active-site fractions, with Rust/Julia/Go within 2e-10 of Python and Mojo within 5e-10; the independent 8-site DOI receipt and paired schemas agree, Q16.16 four-site RTL is bit-exact to its integer oracle and within 0.0025 of the float state, Yosys passes, and a depth-12 Z3 induction proves bounded safety only; the source/binary-bound benchmark is local regression evidence, and continuous-space convergence, persistent-bump defaults, timing, PPA, device results, and formal equivalence are not claimed	this commit
Brunel-Wang pyramidal cell	✅	✅	✅	✅ shared-lib	Brunel-Wang 2001 Methods 2.2–2.3 excitatory-cell membrane specialization with paper-default AMPA/NMDA/GABA conductances and midpoint RK2 at 0.1 ms; all five runtimes preserve the complete voltage/refractory/event receipt, the independent 256-step primary-equation oracle records ten exact events, paired schemas agree, and hand Q16.16 RTL preserves the enrolled event vector and synthesizes in Yosys; the source/binary-bound 200,000-step benchmark is local regression evidence only; network connectivity, Poisson input, synaptic-state kinetics, persistent activity, timing, PPA, device validation, and binary64 formal equivalence remain unclaimed	this commit
Compte working-memory pyramidal cell	✅	✅	✅	✅ shared-lib	Compte et al. 2000 pyramidal membrane plus incoming AMPA/NMDA/GABAA kinetics with source control-set conductances, separate event paths, and coupled midpoint RK2 at 0.02 ms; all five runtimes preserve six complete state traces and 812 benchmark events, with Python/Rust/Julia/Go byte-identical and Mojo within 3.6e-14; the independent 1,024-step primary-equation receipt records four exact events, paired schemas agree, hand Q16.16 RTL preserves that event vector within declared state bounds, Yosys passes, and a depth-4 CVC5 job proves bounded safety only; the source/binary-bound benchmark is loaded-host local regression evidence; firing-time interpolation remains outside this scalar cell, while the separately named SC-COMPTE-WM-NETWORK successor closes its own five-runtime behavior, paired-schema, and bounded ring-connectivity RTL/Yosys/formal evidence without merging identities or incrementing the neuron-model count	this commit
Kobayashi MAT*	✅	✅	✅	✅ shared-lib	Kobayashi, Tsubo, and Shinomoto 2009 Equations 1-3 with the source non-resetting membrane, forward-Euler voltage at 0.001 ms, exact two-timescale threshold histories, and a 2 ms absolute refractory interval; all five runtimes preserve the complete voltage/threshold/refractory trace within 2e-12 and exact events; the independent 10,272-step regular-spiking receipt records one event and SHA-256 3382c1a7…9de8; paired schemas agree; signed Q32.32 RTL is bit-exact to its integer oracle, preserves the Python event vector over the enrolled trace, synthesizes in Yosys, matches its optimized netlist cycle-for-cycle over that sequence, and passes a depth-12 CVC5 bounded-safety job; the separately named SCResettingMATNeuron retains the historical project RK4/reset recurrence with its own full runtime/schema/RTL evidence but does not add a literature-model count; timing, PPA, device, and universal equivalence claims remain open	this commit
Kobayashi MAT(1)	✅	✅	✅	✅ shared-lib	Kobayashi, Tsubo, and Shinomoto 2009 one-history specialization: source non-resetting forward-Euler membrane at 0.001 ms, exact 50 ms threshold-history decay, and 2 ms absolute refractory gating; all five runtimes preserve complete voltage/threshold/refractory trajectories within 2e-12 and exact events; the independent 10,272-step source receipt records event index 3945 and SHA-256 2ac13e42…2069c6; paired schemas agree; signed Q32.32 RTL is bit-exact to its integer oracle, preserves the enrolled event vector, synthesizes in Yosys, matches its optimized netlist on the checked sequence, and passes depth-12 CVC5 bounded safety; the separately named SCNonResettingAdaptiveLIFNeuron preserves the former project exact-relaxation/no-refractory recurrence with equivalent runtime/schema/RTL evidence but adds no literature count; higher silicon and universal-equivalence claims remain open	this commit
Yoon asynchronous pulse sigma-delta	✅	✅	✅	✅ shared-lib	Yoon 2017 sampled APSDM specialization bound to WO2016022241A1 equations 20-27 and 40: integrating prefilter, local exponentially decaying reconstruction, upper-threshold quantizer, and unipolar feedback events; all five runtimes reproduce complete state trajectories and the 200,000-step 199,839-event vector exactly on the measured host; the independent 512-step receipt records 276 events and SHA-256 4c22a86d…b5b8d99; paired schemas agree; signed Q32.32 RTL is exact to its integer oracle, synthesizes in Yosys, and passes depth-12 CVC5 bounded safety; SCSigmaDeltaAccumulatorNeuron separately preserves the former bipolar one-quantum project recurrence with equivalent runtime/schema/RTL evidence but adds no literature count; continuous-time event timing, device, timing/PPA, biological-fit, and universal-equivalence claims remain open	this commit
Fardet-Levina energy-based LIF	✅	✅	✅	✅ shared-lib	Fardet and Levina 2020 source equations and author-Brian profile: coupled voltage/energy RK4 at 0.1 ms, strict voltage-plus-energy gate, reset, and per-event energy subtraction; all five runtimes preserve the complete two-state trajectory within 2e-12 and exact events; the independent 512-step DOI receipt records eight events and SHA-256 fc0aa0c…23d3; paired schemas agree; pinned signed-Q32.32 RTL preserves the enrolled event vector within 2e-6, synthesizes in Yosys, and has bounded reset proof; SCNormalizedEnergyLIFNeuron separately retains the former project exact-flow recurrence without adding a source count; transition-property formal proof, timing, PPA, device, and universal-equivalence claims remain open	this commit
McKean	✅	✅	✅	✅ shared-lib	source-bound McKean/Tonnelier space-clamped Heaviside system with H(0)=1, simultaneous RK4, upward switching-line events, and no reset; the independent 512-step mixed-drive receipt records one event and SHA-256 19c575db…fff5; all five runtimes preserve events and the complete two-state trace within 2e-12; paired schemas agree; signed-Q32.32 RTL preserves the enrolled event vector within 2e-6, synthesizes in Yosys, and passes bounded reset proof; diffusion, traveling waves, timing, PPA, device evidence, and universal real-number equivalence remain open	this commit
SC triangular McKean-like recurrence	✅	✅	✅	✅ shared-lib	count-neutral retained project recurrence with three continuous voltage branches, recovery epsilon*(v-gamma*w), upward v_peak events, and no reset; no paper attribution; Python/Rust/Julia/Go/Mojo parity, independent project receipt, paired schemas, signed-Q32.32 co-simulation, Yosys and bounded reset proof are enrolled; higher silicon claims remain open	this commit
Hindmarsh-Rose	✅	✅	✅	✅ shared-lib	bit-exact accel — 0/26/52 @ I=0/3/5 over 2000 steps; co-sim exact hand/TOML/JSON/Q16.16 counts — 0/0/26/40/52 @ I=0/2/3/4/5 over 2000 RK4 steps; declared Q16.16 +1 crossing boundary over 5000 steps at I=2 through I=5; formal Q8.8 BMC depth 4	this commit
FitzHugh-Rinzel	✅	✅	✅	✅ shared-lib	bit-exact accel — 0/1/8 @ I=0/0.3/0.5; co-sim exact spike count — hand/schema/Q16.16 RTL 8 @ I=0.5 (3000 RK4 steps, cubic RHS)	498376221
Pernarowski	✅	✅	✅	✅ shared-lib	bit-exact accel — 7/17/27 @ I=0 over 2000/5000/8000 steps; co-sim exact spike count — hand/schema/Q16.16 RTL 17 @ I=-0.1/0/0.1/0.2 (5000 RK4 steps, autonomous cubic burster); formal Q8.8 reset-spike BMC depth 4	c384ac0cd
Terman-Wang	✅	✅	✅	✅ shared-lib	accel spike count — 0/1/3 @ I=-1/0/0.5 over 8000 steps; co-sim exact spike count — hand/schema/Q16.16 RTL 0/1/3 at the same operating points (RK4, cubic + tanh gate); formal Q8.8 reset-spike BMC depth 4	ce04dd6f9
Wilson-HR	✅	✅	✅	✅ shared-lib	bit-exact accel — 0/1/4 @ I=0/2/10 over 5000 steps; co-sim exact spike count — hand/schema/Q16.16 RTL 0/1/4 at the same operating points (RK4, polynomial RHS, hard voltage reset preserving recovery); formal Q8.8 reset-spike BMC depth 4	4d9810e2f
Rulkov map	✅	✅	✅	✅ shared-lib	accel: Rust/Julia/Go bit-exact, Mojo ULP-bounded, 0/4/34 @ I=0/0.1/0.5 over 2000 iterations; co-sim: hand/TOML/JSON exact and Q16.16 RTL ten-event short-window trajectory within 0.001 state error @ I=1.5/30 iterations; Yosys Q16.16 H2 synthesis + formal Q8.8 BMC depth 4	7d5889e10
GLIF	✅	✅	✅	✅ shared-lib	bit-exact accel — 0/54/95 @ I=0/30/50 over 1000 steps; co-sim exact hand/TOML/JSON/Q16.16 spike counts — 0/0/23/54/86/95 @ I=0/15/22/30/45/50 (four-state RK4, candidate-first adaptive reset); formal Q8.8 BMC depth 6	ecd799d58
Mihalas-Niebur	✅	✅	✅	✅ shared-lib	bit-exact accel — 0/142/333 @ I=0/2/5 over 1000 steps; co-sim exact hand/schema/Q16.16 RTL — 0/0/0/31/60/87/131/157/207/256 @ I=0/0.5/1/1.5/2/2.5/3.5/4/5/6 over 1000 RK4 steps; explicit I=3 boundary 111/111/112; formal Q8.8 BMC depth 3	081dd569c
Medvedev map	✅	✅	✅	✅ shared-lib	Source-derived slow-calcium first-return map: Rust/Julia/Go bit-exact and Mojo bounded to 5e-13, with exact 750-event parity at I=2 over 1000 iterations; hand/TOML/JSON exact and Q16.16 RTL preserves the complete 75-event vector at I=2 over 100 iterations with maximum u error below 0.007813; DOI feature trace + Q16.16 depth-4 Z3 BMC	this commit
Cazelles map	✅	✅	✅	✅ shared-lib	accel: Rust/Julia/Go bit-exact, Mojo per-step ULP-bounded, 5/182/204 @ I=0/0.5/1.0 over 1000 iterations; co-sim: hand/TOML/JSON exact and Q16.16 RTL event-exact at I=0.5/1.0/2.0 over 30 iterations with state error below 0.0004; I=0.05 is excluded; formal Q8.8 BMC depth 4	22110c66d
Chialvo map	✅	✅	✅	✅ shared-lib	accel: all compiled lanes ULP-bounded to the source recurrence and event-count exact at I=-0.05/0/0.01/0.05/0.1/1.0 over 1000 iterations (0/26/30/0/0/1); pinned 500,000-iteration benchmark records 12,935 events in every lane; co-sim: hand/TOML/JSON exact and Q16.16 event counts 0/2/3/0/1 at I=-0.05/0/0.01/0.1/1.0 over 100 iterations, with stable-point x/y errors below 0.055/0.093 and oscillatory timing explicitly excluded; formal Q8.8 BMC depth 4	this commit
Aihara map	✅	✅	✅	✅ shared-lib	Aihara (1989) Eqs. 10–12: one internal state, logistic graded output, and source level waveform shaper; all lanes are within 5e-11 over the 64-step equation window, the measured 512-step Mojo chaotic envelope is below 2e-4 with exact events, and the source Figure 4 periodic benchmark records 120,000 exact events in all lanes; paired schemas and the primary-equation oracle agree, Q8.24 RTL preserves the first 12 events with state error below 0.01, and the depth-6 Z3 event-consistency job passes	this commit
Nagumo–Sato map	✅	✅	✅	✅ shared-lib	Nagumo and Sato's source one-state refractory map as reproduced by Aihara (1989): Python/Rust/Julia/Go complete traces are binary64-exact, Mojo stays within 5e-15, and all source level events are exact; the independent primary-equation receipt and paired schemas agree; Q16.16 RTL preserves the enrolled event vector with bounded state error; Yosys synthesis and the depth-12 Z3 induction job pass; the source-bound 200,000-step five-lane benchmark is local diagnostic evidence only	this commit
SC adaptive-threshold map	✅	✅	✅	✅ shared-lib	the retained two-state SC project recurrence, explicitly separated from publication identities: all five runtimes preserve complete x/theta receipts within 1e-10 and exact upward-crossing events; the independent project-spec receipt and paired schemas agree; Q8.24 sigmoid-LUT RTL preserves the 32-step I=0.4 event vector with x/theta error below 0.07/2e-6; Yosys synthesis and the depth-12 Z3 induction job pass; KilincBhattMapNeuron is a deprecated alias and is not counted separately	this commit
SC chaotic map	✅	✅	✅	✅ shared-lib	the preserved two-state SC engineering recurrence, with no Aihara or other publication attribution: five-runtime 512-step state parity stays within 1e-10 with exact events; the independent project-spec receipt and paired schemas agree; Q8.24 sigmoid-LUT RTL is bit-exact to its quantized 32-step alternating-drive oracle, preserves all 16 events, and stays within 0.009/0.0016 of binary64 x/y; Yosys synthesis and depth-12 Z3 safety induction pass; the source/binary-bound 200,000-step benchmark records 100,000 exact events in every lane	this commit
Courbage-Nekorkin map	✅	✅	✅	✅ shared-lib	accel: Rust/Julia/Go bit-exact, Mojo per-step ULP-bounded, 157/193/168 @ I=-0.3/0/0.3 over 1000 iterations; co-sim: hand/TOML/JSON exact, Q16.16 event-exact at I=-0.3/0/0.3 over bounded 30/20/30-iteration windows, and Q32.32 event-exact at all three inputs over 30 iterations with state error below 0.00003; autonomous Q16.16 30-iteration trace is an explicit 4/6-event boundary; formal Q8.8 BMC depth 4	63826b513
Izhikevich 2007	✅	✅	✅	✅ shared-lib	bit-exact — 0/3/14 @ I=0/100/400 over 2000 steps (RK4, quadratic v-nullcline, spike reset v→c / u+=d; Mojo ULP-bounded but the per-spike reset re-synchronises the trace so its counts always match)	75b32d935
Ibarz-Tanaka map	✅	✅	✅	✅ shared-lib	Ibarz et al. (2007), Eqs. 2–3: source four-branch fast map plus simultaneous slow update; accel reset events 9/33/195 @ I=0/0.2/1 over 1000 iterations, Rust/Julia/Go bit-exact and Mojo within 1.5e-8; hand/TOML/JSON exact, Q16.16 event-vector exact over the bounded 30-step I=0.2 co-sim with v/u errors below 0.003/0.0001; formal Q16.16 BMC depth 4	corrected source implementation
Ermentrout-Kopell	✅	✅	✅	✅ shared-lib	accel spike count — 0/20/64 @ I=-0.5/0.1/1.0 over 2000 steps (theta flow, forward Euler, modulo 2π); schema enrolment — hand/TOML/JSON exact, Q16.16 RTL spike counts 0/45/64 @ I=-0.5/0.5/1.0 over 2000 steps with circular phase error below 0.081/0.089/0.025 rad; generated integer C/Rust and Verilog event/state words cycle-exact over 240 steps at both current signs; formal Q8.8 safety BMC depth 4	2669a831f

Each model carries a committed benchmark: a Go Benchmark* in the services lane for the conductance models (Wang-Buzsaki, Morris-Lecar, Connor-Stevens, Hodgkin-Huxley, FitzHugh-Nagumo), plus source-hashed executable closure benchmarks for Connor-Stevens, Hodgkin-Huxley, AdEx, ExpIF, Lapicque, Perfect Integrator, Quadratic IF, Theta, DPI, COBA LIF, Escape Rate, Poisson, IQIF, McCulloch-Pitts, Sigmoid Rate, Threshold-linear Rate, Wilson-Cowan, Jansen–Rit, Montbrió–Pazó–Roxin, Resonate-and-Fire, Wong-Wang, Amari neural field, Brunel-Wang, Compte working-memory pyramidal cell, and Kobayashi MAT*, and a committed benchmarks/bench_<model>*.py harness with its recorded per-backend result for the FFI-dispatched models (McKean, Hindmarsh-Rose, FitzHugh-Rinzel, Pernarowski, Terman-Wang, Wilson-HR, Rulkov map, GLIF, Mihalas-Niebur, Medvedev map, Cazelles map, Courbage-Nekorkin map, Izhikevich 2007, Chialvo map, Aihara map, SC chaotic map, Ibarz-Tanaka map, and Ermentrout-Kopell). A dedicated per-kernel benchmark harness for the Rust accel/rust/safety crate remains a tracked open lane item.

In progress

No model is mid-flight right now. The next remediation unit will appear here when it opens; see the internal working tracker for the queue.

The rest of the catalogue

Every other catalogued model has a faithful, tested Python reference (and most have the real Rust engine acceleration path), but its four accel/{rust,go,julia,mojo} kernels are stubs, fakes, or not yet verified — the polyglot-stub-remediation sweep is replacing them model-by-model. Those models are deliberately not ticked here: per-model status is promoted onto this page only after a unit is closed and verified at source, so this table never claims completion it has not proven. As of the latest landed commit that is fifty-four polyglot-complete models out of the 155-model catalogue; the remaining 101 source-model units are Python-faithful with an acceleration chain still under remediation.

How a model graduates onto this page

A model moves from "the rest" to polyglot-complete when a remediation unit delivers, and this page records, all of:

• real executable dynamics in accel/rust/safety, accel/go, accel/julia, and accel/mojo;
• an executed Python-parity test per lane (bit-exact, or spike-count with the transcendental caveat);
• an honest committed benchmark.

The internal working tracker for the sweep (with per-unit close-out detail) is docs/internal/POLYGLOT_STUB_REMEDIATION_BACKLOG.md (developer-local, not published). This page is its public, per-model summary.