Model Fidelity & Polyglot-Completion Status

This page states, per model, which neuron models are polyglot-complete across the maintained software runtimes. Polyglot completion is one required rung of end-to-end model fidelity; it is not, by itself, an RTL, formal, synthesis, timing, PPA, device, or silicon-completion claim. Those hardware rungs are stated explicitly in each row when executed evidence exists.

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 software 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. Rows whose model name begins with SC are preserved project compatibility identities; they are count-neutral and do not increment the 160-model source catalogue.

Model	Rust safety	Go	Julia	Mojo	Parity basis (golden)	Evidence anchor
Wang-Buzsaki	✅	✅	✅	✅ executable	exact 2,856-event parity over the measured 20,000-step I=10 packet; five-runtime final-state error below 1e-8; committed compiler-bound Q16.16 RTL stays within one event over the bounded 20-macro-step co-simulation, synthesizes in Yosys, and passes depth-4 reset-safety BMC; timing, PPA, device, and silicon remain open	benchmarks/results/bench_wang_buzsaki.json; hdl/formal/catalogue/sc_wang_buzsaki.v
FitzHugh-Nagumo	✅	✅	✅	✅ shared-lib	source-transformed two-state RK4 recurrence; the source-hashed 2,000,000-step five-runtime packet records 5,067 exact events, binary64-exact Python/Rust/Julia/Go traces, and Mojo error below 1e-9; the committed compiler-bound Q16.16 RTL preserves all eight 3,000-step receipt events, synthesizes in Yosys, and passes depth-4 reset-safety BMC; timing, PPA, device, and silicon remain open	benchmarks/results/bench_fitzhugh_nagumo_simulate.json; hdl/formal/catalogue/sc_fitzhugh_nagumo.v
Morris-Lecar	✅	✅	✅	✅ executable	exact 0/3/5-event parity at I=0/50/100 over 2,000 RK4 steps; executed five-runtime 200,000-step packet records 476 events and complete final-state error below 4e-8; the committed compiler-bound Q16.16 RTL exactly preserves seven events over the 3,000-step receipt, passes Yosys coarse synthesis, and passes depth-4 reset-safety BMC under the receipt reset/current protocol; timing, PPA, device, and silicon remain open	benchmarks/results/local_python_2026-06-17_morris_lecar_rk4.json; hdl/formal/catalogue/sc_morris_lecar.v
Connor-Stevens	✅	✅	✅	✅ shared-lib	direct Connor-Walter-McKown 1977 parameter custody with Connor-Stevens 1971 lineage; the source-hashed five-runtime packet preserves nine events at I=20 and complete traces/final states within 1e-9 for Rust/Julia/Go and 2e-6 for Mojo; committed compiler-bound Q16.16 RTL stays within one event over the bounded 20-macro-step LUT envelope, synthesizes in Yosys, and passes depth-4 reset-safety BMC; unrestricted equation parity, timing, PPA, device, and silicon remain open	benchmarks/results/bench_connor_stevens_mojo.json; hdl/formal/catalogue/sc_connor_stevens.v
Hodgkin-Huxley	✅	✅	✅	✅ shared-lib	direct 1952 conductance equations in the explicit modern absolute-voltage coordinate; the default gate-first Euler five-runtime packet preserves nine events at I=20 and complete traces/final states within 1e-9 for Rust/Julia/Go and 2e-9 for Mojo; the separate simultaneous-RK4 schema profile is source-derived, and committed compiler-bound Q16.16 RTL stays within one event over its bounded window, synthesizes in Yosys, and passes depth-4 reset-safety BMC; unrestricted equation parity, timing, PPA, device, and silicon remain open	benchmarks/results/bench_hodgkin_huxley_mojo.json; hdl/formal/catalogue/sc_hodgkin_huxley.v
AdEx	✅	✅	✅	✅ shared-lib	Brette–Gerstner equations with an explicit published regular-spiking factory and independent complete-state receipt; accel event vectors are exact at 0/4/12 events for I=0/200/500 over 1,000 baseline-Euler steps, all compiled lanes transport the full numeric contract and keep both states within 5e-12; Q16.16 RTL preserves exact 0/2/6/12 event counts at I=0/200/500/1000 over 500 steps, synthesizes to 52,014 Yosys coarse cells, and passes depth-6 reset/event safety; timing, PPA, device, physical silicon, and universal formal equivalence remain open	benchmarks/results/bench_adex.json; hdl/reports/yosys_adex_q1616_2026-08-30.json
ExpIF	✅	✅	✅	✅ shared-lib	Fourcaud-Trocmé fitted, source-aligned deterministic profile with zero-noise Heun RK2 below the paper's -30 mV handoff, the derived analytical exponential-only tail duration, and a 1.7 ms refractory interval; all five runtimes preserve the macro-step voltage/refractory/event packet within 5e-8 and exact events, paired schemas and an independent 20,000-step receipt agree; the historical SC candidate-first RK4/Q32.32 profile remains separately identified, its complete RTL event/state packet is digest-bound and preserves the enrolled aggregate event count, synthesizes to 484,938 Yosys coarse cells, and passes depth-4 bounded reset/event safety; continuous spike timestamps, stochastic-input realisations, timing, PPA, device, board, physical silicon, and universal fixed-point equivalence remain open	benchmarks/results/bench_expif.json; hdl/reports/yosys_expif_q3232_2026-08-30.json
Lapicque 1907 polarization threshold	✅	✅	✅	✅ shared-lib	source equation K dv/dt=(V-v)/R-v/rho, strength-duration law, and one latched first-threshold event with no invented automatic reset; independent 2,000-step receipt emits at index 69 and SHA-256-binds complete polarization/events; all five failure-atomic runtimes preserve the source packet with exact events and <=5e-15 state error; paired source schemas agree within 8e-15; dedicated Q32.32 RTL is event-exact at V=5.5/11/12/22 with <7e-8 state error, synthesizes to 11,511 Yosys coarse cells, and passes depth-20 reset/latch/no-repeat safety; the former hard-reset periodic recurrence remains count-neutral SCLapicqueLIFNeuron; timing, PPA, device, board, physical silicon, and universal fixed-point equivalence remain open	benchmarks/results/bench_lapicque.json; src/sc_neurocore/neurons/reference_receipts/lapicque_1907.json; hdl/reports/yosys_lapicque_1907_q3232_2026-08-30.json
Perfect Integrator	✅	✅	✅	✅ shared-lib	Naud-Gerstner 2012 source equation dV/dt=I(t)/C with the written strict V>V_T reset and exact held-current integration; an independent 1,000-step receipt pins 333 equality-sensitive events and complete voltage/event SHA-256 digests; all five failure-atomic runtimes carry the full source selector, numeric state, event vector, and final state bit-exactly, including non-default contracts; paired source schemas preserve the strict boundary while count-neutral SCInclusivePerfectIntegratorNeuron, paired sc_perfect_integrator schemas, and the original SC RTL retain the historical >= boundary; dedicated rational-dt Q8.8 source RTL is event-exact at the equality protocol, synthesizes to 3,034 Yosys coarse cells, and passes depth-20 reset/event safety; timing, PPA, device, board, physical silicon, and universal fixed-point equivalence remain open	benchmarks/results/bench_perfect_integrator.json; src/sc_neurocore/neurons/reference_receipts/perfect_integrator_naud_gerstner_2012.json; hdl/reports/yosys_perfect_integrator_naud_gerstner_2012_q88_2026-08-30.json
Quadratic IF	✅	✅	✅	✅ shared-lib	Latham 2000 equations (1), (2), and (5a) reduced exactly to dx/ds=x²+eta; the paper's numerical V_r/V_t/V_apex/V_repol/tau/dt map to -1/+1/(31/3)/-3/.05, so the unstable +1 threshold is no longer misrepresented as the source event apex; an independent 240-step receipt SHA-256-binds input, complete voltage, and ten-event vectors at eta=4; all five failure-atomic runtimes carry arbitrary parameters, aligned events, and final state with exact events and <=2e-12 voltage error; paired source schemas and count-neutral SCSymmetricQuadraticIFNeuron schemas/traces preserve both identities, while the original sc_quadratic_if RTL remains SC-owned; dedicated source-profile fixed-point RTL, Yosys synthesis, and depth-20 reset/event safety establish the declared H2 envelope; timing, PPA, device, board, physical silicon, and universal real-valued equivalence remain open	src/sc_neurocore/neurons/reference_receipts/quadratic_if_latham_2000.json; hdl/reports/yosys_quadratic_if_latham_2000_q1616_2026-08-30.json
Theta	✅	✅	✅	✅ shared-lib	Ermentrout-Kopell equation (2.5), with current=a or a frozen equation (3.3) drive and no claim to the full coupled bursting system; the PDF-bound 1,024-step receipt fixes input/phase/five-event digests and agrees with an independent circle-flow oracle within 2.3e-14; all five failure-atomic complete runtimes carry arbitrary phase/timestep, exact aligned events, final state, and <=2e-12 circular phase error, while multi-rotation binary steps fail closed; paired Euler schemas preserve the enrolled 0/0/0/1/2/2/3/5/7/14/23 counts; Q16.16 RTL keeps the declared <0.17 rad moderate-regime envelope and explicit I=1 timing shift; 6,203-cell Yosys synthesis plus depth-110 receipt-drive phase/event safety establish H2, with timing, PPA, board, physical silicon, and universal exact-flow equivalence open	src/sc_neurocore/neurons/reference_receipts/theta_ermentrout_kopell_1986.json; hdl/reports/yosys_theta_q1616_2026-08-30.json
DPI	✅	✅	✅	✅ shared-lib	Indiveri-Stefanini-Chicca 2010 equations (2)-(3), with normalised defaults and discrete event/refractory ordering explicitly maintained rather than source-claimed; the PDF-bound independent 5,000-step receipt fixes all three state traces, 13 event indices, and final state; every failure-atomic runtime carries the configurable 18-field contract and exact aligned events, with compiled state error within 5e-13; hand/TOML/JSON agree within 1e-13; Q16.16 RTL preserves 13 events at I=5 with declared state/timing envelopes, synthesizes to 112,953 Yosys coarse cells, and passes depth-8 fixed-drive spike/reset/refractory safety, establishing H2; timing, PPA, device, board, physical silicon, transistor mismatch, and universal formal equivalence remain open	src/sc_neurocore/neurons/reference_receipts/dpi_indiveri_stefanini_chicca_2010.json; hdl/reports/yosys_dpi_neuron_q1616_2026-08-30.json
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 curated depth-8 Z3 job (reset, first-event, and refractory assertions) passes	benchmarks/results/local_python_2026-06-18_coba_lif_rk4.json; src/sc_neurocore/neurons/reference_trace_data/coba_lif_conductance_rk4_doi.json; hdl/formal/catalogue/sc_cobalifneuron.sby
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	benchmarks/results/local_python_2026-07-14_escape_rate_lfsr16.json
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	benchmarks/results/local_python_2026-07-14_poisson_lfsr16.json
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	benchmarks/results/local_python_2026-07-14_iqif.json
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	benchmarks/results/local_python_2026-07-14_mcculloch_pitts.json
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	benchmarks/results/local_python_2026-07-14_sigmoid_rate.json
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	benchmarks/results/local_python_2026-07-14_threshold_linear_rate.json
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	benchmarks/results/bench_wilson_cowan.json
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	benchmarks/results/bench_jansen_rit.json
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	benchmarks/results/bench_ermentrout_kopell_pop.json
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	benchmarks/results/bench_resonate_and_fire.json
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	benchmarks/results/bench_alpha.json
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	benchmarks/results/bench_adaptive_threshold_if.json
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	benchmarks/results/bench_wong_wang.json
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	benchmarks/results/bench_amari_field.json
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	benchmarks/results/bench_brunel_wang.json
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	benchmarks/results/bench_compte_wm.json
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	benchmarks/results/bench_mat.json
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	benchmarks/results/bench_non_resetting_lif.json
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	benchmarks/results/bench_sigma_delta.json
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	benchmarks/results/bench_energy_lif.json
McKean	✅	✅	✅	✅ shared-lib	source-bound McKean/Tonnelier 2003 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	benchmarks/results/bench_mckean.json; hdl/formal/catalogue/mckean.v
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, the SHA-256-locked 3,000-row project receipt, paired schemas, signed-Q32.32 co-simulation, Yosys and bounded reset proof are enrolled; higher silicon claims remain open	benchmarks/results/bench_sc_triangular_mckean.json; hdl/formal/catalogue/sc_triangular_mckean.v
Benda-Herz universal adaptation	✅	✅	✅	✅ shared-lib	Benda and Herz 2003 equations (8) and (45), specialized to the Figure 8 square-root onset and linear steady-state adaptation example; deterministic phase events and both state traces agree across five runtimes within 2e-12; paired schemas and the 512-step primary-equation receipt agree; bounded Q16.16 adaptation/phase RTL synthesizes and passes reset-safety proof; the paper's stated rate-model operating limits, timing, PPA, device evidence, and universal real-number equivalence remain open	benchmarks/results/bench_benda_herz.json
SC stochastic rate adaptation	✅	✅	✅	✅ executable	count-neutral retained project logistic RK4 adaptation and exponential-hazard Bernoulli recurrence, without Benda-Herz attribution; explicit-uniform parity, paired schemas, and bounded hazard-commit RTL are enrolled; hardware randomness, timing, PPA, and device evidence remain open	benchmarks/results/bench_sc_stochastic_rate_adaptation.json
Bertram phantom burster	✅	✅	✅	✅ executable	Bertram et al. 2000 equations 1–10 and BJ_00.ode author defaults with dynamic fast potassium gate n; five runtimes preserve the enrolled 18-event, 10,000-step four-state trajectory, native state error stays below 5e-9, paired schemas and a 512-step primary-equation receipt agree; production fixed-step RK4 is an explicit specialization of the authors' adaptive CVODE run, and no identical interpolation, RTL, timing, PPA, or device claim is made	benchmarks/results/bench_bertram_phantom.json
Hill–Tononi cortical waking neuron	✅	✅	✅	✅ executable	Hill and Tononi 2005 hybrid model neuron with dynamic threshold, depolarisation-dependent potassium current, optional cell-specific I_h/I_T, and source 0.25 ms RK4; five runtimes preserve the 538-event, 200,000-step I_ext=20 benchmark, paired schemas and a 768-step mixed-drive independent receipt agree, and the former HH/Na-pump recurrence is retained separately as count-neutral SCSixStateThalamocorticalNeuron; full-network behavior and all RTL/silicon claims remain outside scope	benchmarks/results/bench_hill_tononi.json
Butera Model 1 respiratory pacemaker	✅	✅	✅	✅ executable	Butera, Rinzel, and Smith 1999 Model 1 equations 1–7 with the source C=21 pF membrane-current balance, slow persistent-sodium inactivation, optional inactive-by-default tonic conductance, candidate-first RK4 implementation specialization, and observational no-reset spike crossing; five runtimes preserve 954 exact events over the source-bound 200,000-step I_app=50 pA benchmark and an independent 1,024-step mixed-drive receipt; the omitted-capacitance recurrence is retained as count-neutral SCUnitCapacitanceRespiratoryNeuron with separate registration, descriptor, behavior evidence, paired schemas, project receipt, native custody, one-step state parity, and an explicit 4–5-event 20,000-step cross-libm envelope; RTL, timing, PPA, device, and silicon claims remain outside scope	benchmarks/results/bench_butera_respiratory.json
Larter–Breakspear cortical neural mass	✅	✅	✅	✅ executable	Breakspear, Terry, and Friston 2003 conductance population dynamics with source QV/QZ firing-rate feedback, NMDA modulation, local/external coupling balance, inhibitory feedback, and continuous three-state RK4 output; five runtimes preserve the complete one-step state within 2e-12, paired schemas and independent SHA-256-locked 512-step source/project receipts agree, and the source-hashed 20,000-step benchmark executes both the source identity and count-neutral retained SCDecoupledAdaptationIonMassNeuron; the fixed-step solver is an implementation specialization and RTL, full-network, timing, PPA, device, and silicon evidence remain unclaimed	benchmarks/results/bench_larter_breakspear.json; src/sc_neurocore/neurons/reference_receipts/larter_breakspear_2003.json
Wang NMDA-autapse pyramidal neuron	✅	✅	✅	✅ executable	Wang 1999 pyramidal LIF and calcium equations plus the two-stage saturating NMDA gate, with the Jahr–Stevens magnesium block and source g_nmda=0.1 uS autapse profile; midpoint RK2 at 0.05 ms and sampled threshold handling are the declared scalar implementation specialization; five runtimes preserve complete one-step state within 2e-12, paired schemas and an independent 512-step mixed-drive receipt agree, and the source-hashed 20,000-step benchmark executes both this identity and the count-neutral retained SCWBNMDAMagnesiumBlockNeuron; source-default Q16.16 RTL is bit-exact to its integer oracle, preserves the four-event receipt and bounded state envelopes, synthesizes in Yosys, and passes depth-4 CVC5 bounded safety; full-network, interpolated spike-time, Figure 3 rate, configurable-parameter RTL, timing, PPA, device, and silicon evidence remain unclaimed	benchmarks/results/bench_nmda.json; src/sc_neurocore/neurons/reference_receipts/nmda_neuron_wang_1999.json
SC WB plus NMDA magnesium-block recurrence	✅	✅	✅	✅ executable	count-neutral retained project recurrence, without whole-model publication attribution; all five runtimes, paired schemas, an independent receipt, and the dual-identity benchmark are enrolled; its 50-cycle signed-Q32.32 FSM is bit-exact to an integer oracle, preserves the enrolled quiet and five-event driven vectors with explicit state envelopes, passes Yosys coarse synthesis, and passes depth-4 CVC5 handshake/output safety; configurable-parameter RTL, technology gate mapping, timing, PPA, device, and silicon evidence remain open	benchmarks/results/bench_nmda.json; src/sc_neurocore/neurons/reference_receipts/sc_wb_nmda_magnesium_block.json
Hindmarsh-Rose	✅	✅	✅	✅ shared-lib	source three-state no-reset ODE with candidate-first RK4 and failure-atomic Python/Rust/Go/Julia/Mojo batches; bit-exact acceleration preserves 0/26/52 events at I=0/3/5 over 2,000 steps; hand/TOML/JSON/Q16.16 co-simulation preserves 0/0/26/40/52 events at I=0/2/3/4/5, while the declared 5,000-step chaotic boundary is +1 Q16.16 crossing; committed RTL passes Yosys coarse synthesis and depth-4 bounded safety, with timing/PPA/device/silicon and long-window fixed-point identity unclaimed	benchmarks/results/bench_hindmarsh_rose_simulate.json; src/sc_neurocore/neurons/reference_trace_data/hindmarsh_rose_short_bursting_prefix.json; tests/test_cosim_hindmarsh_rose_q1616_precision.py
FitzHugh-Rinzel	✅	✅	✅	✅ shared-lib	Rinzel 1987 equations (3.4)–(3.6) and source parameter profile with fixed-step RK4 and sampled no-reset threshold observation declared as repository specialisations; failure-atomic Python/Rust/Julia/Go/Mojo batches preserve complete state on invalid candidates; Rust/Julia/Go remain binary64-exact and Mojo stays within 1.56e-8 over the source-hashed 2,000,000-step packet; hand/TOML/JSON/Q16.16 co-simulation preserves 7/8/8 events at I=0.4/0.5/0.6; committed RTL passes Yosys coarse synthesis and depth-4 bounded safety, while timing/PPA/device/silicon and universal-equivalence claims remain open	benchmarks/results/bench_fitzhugh_rinzel_simulate.json; src/sc_neurocore/neurons/reference_trace_data/fitzhugh_rinzel_driven_bursting_doi.json; tests/test_cosim_fitzhugh_rinzel_q1616_precision.py
Pernarowski	✅	✅	✅	✅ shared-lib	DOI-backed three-state continuous cubic burster with fixed-step RK4, caller current, and sampled no-reset threshold observation declared as repository specialisations; failure-atomic Python/Rust/Julia/Go/Mojo batches preserve complete state on invalid candidates; Rust/Julia/Go remain binary64-exact and Mojo stays within 1.06e-12 on the source-hashed 2,000,000-step packet; hand/TOML/JSON/Q16.16 co-simulation preserves 17 events at I=-0.1/0/0.1/0.2; committed RTL passes Yosys coarse synthesis and the paired formal lane carries depth-4 reset/output safety, while timing/PPA/device/silicon and universal-equivalence claims remain open	benchmarks/results/bench_pernarowski_simulate.json; src/sc_neurocore/neurons/reference_trace_data/pernarowski_autonomous_bursting_doi.json; tests/test_cosim_pernarowski_q1616_precision.py
Terman-Wang	✅	✅	✅	✅ shared-lib	DOI-backed two-state continuous cubic/tanh relaxation oscillator with fixed-step RK4, caller current, and sampled no-reset threshold observation declared as repository specialisations; failure-atomic Python/Rust/Julia/Go/Mojo batches preserve complete state on invalid candidates; Rust remains host-bit-exact and Julia/Go/Mojo stay within 4.92e-12 on the source-hashed 2,000,000-step packet; hand/schema/Q16.16 RTL preserve 0/1/3 events at I=-1/0/0.5 over 8,000 steps; committed RTL passes Yosys coarse synthesis and the paired formal lane carries depth-4 reset/output safety, while timing/PPA/device/silicon and universal-equivalence claims remain open	benchmarks/results/bench_terman_wang_simulate.json; src/sc_neurocore/neurons/reference_trace_data/terman_wang_legion_oscillation_doi.json; tests/test_cosim_terman_wang_q1616_precision.py
Wilson-HR	✅	✅	✅	✅ shared-lib	Wilson 1999 continuous two-state polynomial cortical model with source C=0.8, tau_R=1.9 ms, no state reset, and a sampled upward v=0 observation convention; Python/Rust/Julia/Go complete trajectories are bit-identical and Mojo stays within its 1e-9 source benchmark gate with exact events; hand/schema/Q16.16 RTL preserve 0/44/46/49/52 crossings at I=0/0.08/0.1/0.14/0.2 over 5,000 steps, while the 0.07 and 0.075 quantisation boundaries are disclosed; the former unit-capacitance, v>=0.4, hard-reset recurrence remains count-neutral as SCResettingWilsonHRNeuron, with its own five runtimes, Mojo bounded to 2.5e-12, paired schemas, 0/1/4 Q16.16 event receipt at I=0/2/10, Yosys synthesis, and depth-4 bounded safety; neither identity claims timing, PPA, device evidence, or universal real-number equivalence	benchmarks/results/bench_wilson_hr_simulate.json; benchmarks/results/bench_sc_resetting_wilson_hr_simulate.json; tests/test_cosim_wilson_hr_q1616_precision.py; tests/test_cosim_sc_resetting_wilson_hr_q1616_precision.py
Rulkov 2002 map	✅	✅	✅	✅ shared-lib	source Equations 1–2 with current bound to fast beta_n, static slow sigma, simultaneous state update, and pre-update rightmost/reset-branch events; the independent 512-step receipt records 22 events and SHA-256 83ffbbdf…3db; all five runtimes preserve the full 2,000,000-step state trace within 1.8e-15 and record 34 exact events; paired schemas agree; Q16.16 RTL preserves exact 30-step event vectors at I=0/0.5/1.5 within state bounds, Yosys synthesis passes, and depth-4 Z3 reset-output safety passes; long-window fixed-point identity, timing, PPA, device, and silicon evidence remain open	benchmarks/results/bench_rulkov_map.json; hdl/reports/yosys_rulkov_map_q1616_2026-08-28.json
SC upward-crossing Rulkov map	✅	✅	✅	✅ shared-lib	count-neutral retained project observation identity: the source state recurrence is unchanged, while configurable post-update upward-x crossings remain separate from the paper's reset-branch events; its independent 512-step receipt records 22 events at different indices and SHA-256 b50ca7c0…68e; five-runtime parity, paired schemas, exact Q16.16 event vectors at I=0/0.5/1.5, Yosys synthesis, and depth-4 Z3 reset-output safety pass; it adds no literature-model count	benchmarks/results/bench_sc_upward_crossing_rulkov_map.json; hdl/reports/yosys_sc_upward_crossing_rulkov_map_q1616_2026-08-28.json
GLIF5	✅	✅	✅	✅ shared-lib	Teeter et al. 2018 five-state equations with strict composite-threshold events, exact fixed-grid flow, affine cuts, and refractory hold; all five runtimes preserve the complete 2,000,000-step state/event packet with Mojo below 1.5e-14; paired schemas and an independent 512-step DOI receipt agree; dedicated Q32.32 RTL is integer-oracle exact, preserves the complete event vector with five-state error below 2e-7, synthesizes in Yosys, and passes depth-6 bounded reset safety; the former four-state RK4 behavior remains count-neutral as SCFourStateGLIFNeuron; timing, PPA, board, device, and physical silicon remain open	benchmarks/results/bench_glif_simulate.json; hdl/formal/catalogue/sc_glif.v
SC four-state GLIF recurrence	✅	✅	✅	✅ shared-lib	count-neutral retained project RK4 identity without whole-model publication attribution; five-runtime parity, paired schemas, independent project receipt, 0/0/23/54/86/95 Q16.16 event parity, Yosys synthesis, and depth-6 bounded reset safety are enrolled	benchmarks/results/bench_sc_four_state_glif.json; hdl/formal/catalogue/sc_four_state_glif.v
Mihalas-Niebur	✅	✅	✅	✅ shared-lib	source equations 2.1–2.2 and Table 1 with hard V=V_r reset, adaptive threshold, two retained/jumped currents, fixed-grid RK4 and sampled candidate events; the independent 2,000-step panel-M receipt records 14 events and SHA-256 fa3871a…d8d5; Python/Rust/Julia/Go complete traces are binary64-exact and Mojo stays within 2.78e-17 on the measured 200,000-step packet; paired schemas agree; committed Q32.32 RTL preserves the complete 14-event vector with four-state error below 1.3e-6, synthesises for Xilinx 7-series in Yosys, and passes depth-2 source-profile Z3 reset safety; timing, PPA, board, physical silicon, and universal numerical equivalence remain open	benchmarks/results/bench_mihalas_niebur_simulate.json; hdl/reports/yosys_mihalas_niebur_q3232_2026-08-28.json
SC scaled-reset adaptive IF	✅	✅	✅	✅ shared-lib	count-neutral retained four-state project recurrence with candidate-proportional voltage reset and no whole-model publication attribution; the independent 1,600-step mixed-drive receipt records 168 events and SHA-256 6d2aadb7…e78cf; all five runtimes preserve the measured 200,000-step trace and events exactly; paired schemas agree; committed Q16.16 RTL preserves the complete 250-step I=3 event vector (31 events) with four-state error below 0.001, passes Yosys coarse synthesis and depth-2 Z3 reset safety; higher silicon and universal-equivalence claims remain open	benchmarks/results/bench_sc_scaled_reset_adaptive_if.json; hdl/reports/yosys_sc_scaled_reset_adaptive_if_q1616_2026-08-28.json
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	benchmarks/results/bench_medvedev_map.json
Cazelles map	✅	✅	✅	✅ shared-lib	source equation (1) and Figure-1 scalar four-branch map; independent 600-step receipt records seven slow-regime entries and SHA-256 ab929807…3bb; all five runtime traces are binary64-exact after the Mojo kernel preserves product-rounding boundaries; paired schemas agree exactly; Q16.16 RTL is event-exact through 55 iterations with state error at most 0.0062, while the divergent 600-step fixed-point orbit is explicitly excluded; Q8.8 Yosys synthesis and depth-4 Z3 reset safety pass	src/sc_neurocore/neurons/reference_receipts/cazelles_2001.json; hdl/reports/yosys_cazelles_map_q88_2026-08-28.json
SC clipped-logistic bursting map	✅	✅	✅	✅ shared-lib	count-neutral retained two-state project recurrence without whole-model publication attribution; all five runtimes, paired schemas, independent project receipt, bounded Q16.16 co-simulation, Q8.8 Yosys synthesis, and depth-4 Z3 reset safety remain enrolled	src/sc_neurocore/neurons/reference_receipts/sc_clipped_logistic_bursting_map_project.json; hdl/reports/yosys_sc_clipped_logistic_bursting_map_q88_2026-08-28.json
Chialvo map	✅	✅	✅	✅ shared-lib	Chialvo (1995) Eq. 1 with maintained upward-crossing observation; independent 1,000-step receipt SHA-256-binds every post-step (x,y) pair and event (26 events); Python/Rust/Julia/Go/Mojo expose failure-atomic complete two-state batches, preserve the enrolled 1,000-step event vectors, and execute the source-hashed 500,000-step benchmark with 12,935 exact events; NetworkRunner exposes the distinct identity; paired schemas agree; Q16.16 preserves 0/2/3/0/1 event counts with disclosed oscillatory timing boundaries; tracked Q8.8 RTL passes 117-cell Yosys coarse synthesis and depth-4 Z3 reset/event safety; timing, PPA, device, physical silicon, and universal equivalence remain open	benchmarks/results/bench_chialvo_map.json; src/sc_neurocore/neurons/reference_receipts/chialvo_1995.json; hdl/reports/yosys_chialvo_map_q1616_2026-08-30.json
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	benchmarks/results/bench_aihara_map.json
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	benchmarks/results/bench_nagumo_sato_and_sc_adaptive_map.json
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	benchmarks/results/bench_nagumo_sato_and_sc_adaptive_map.json
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	benchmarks/results/bench_sc_chaotic_map.json
Courbage-Nekorkin-Vdovin map	✅	✅	✅	✅ shared-lib	DOI-backed equations 3–5 with the complete Figure-4 profile, simultaneous state update, H(0)=1, and an explicitly project-defined upward-crossing observation; the independent 2,000-step receipt records 63 events and SHA-256 fee02b5a…714f; all five runtimes preserve the source-hashed 2,000,000-step trace and 88,435 events bit-for-bit; paired schemas agree; Q16.16 preserves three bounded event vectors while its 620-step autonomous 1/25-event boundary is disclosed; Q32.32 preserves the complete 620-step autonomous event vector, passes Yosys coarse synthesis, and passes depth-4 Z3 reset/output safety; timing, PPA, board, physical silicon, and universal fixed-point equivalence remain open	benchmarks/results/bench_courage_nekorkin_map_simulate.json; hdl/reports/yosys_courbage_nekorkin_map_q3232_2026-08-28.json
SC clipped rational-recovery map	✅	✅	✅	✅ shared-lib	count-neutral retained project recurrence formerly carried by the Courbage-labelled class, without whole-model publication attribution; all five runtimes preserve the complete source-hashed 2,000,000-step trace bit-for-bit; paired schemas and the independent 512-step project receipt agree; bounded Q16.16 and Q32.32 event/state co-simulation, Q32.32 Yosys coarse synthesis, and depth-4 Z3 reset/output safety pass; it adds no literature-model count	benchmarks/results/bench_sc_clipped_rational_recovery_map.json; hdl/reports/yosys_sc_clipped_rational_recovery_map_q3232_2026-08-28.json
Izhikevich 2007	✅	✅	✅	✅ shared-lib	Izhikevich 2007 biophysical quadratic equations with the NeuroML regular-spiking defaults; production uses maintained coupled RK4 while the schema/RTL profile uses explicitly separate simultaneous Euler; all five runtimes return the complete voltage trace, exact events, and final two-state packet through fail-closed contracts, and NetworkRunner exposes the distinct Izhikevich2007 identity; the independent 300-step Euler receipt fixes five events and the complete (v,u) digest; paired schemas agree, generated Q16.16 preserves the enrolled event vector, tracked Q8.8 RTL synthesizes in Yosys and passes depth-20 bounded safety; timing, PPA, device/board, physical silicon, and universal equivalence remain unclaimed	benchmarks/results/bench_izhikevich2007_simulate.json; hdl/reports/yosys_izhikevich2007_q88_2026-08-28.json
Ibarz-Tanaka analysis profile	✅	✅	✅	✅ shared-lib	compatibility identity for the Shilnikov-Rulkov (2004) four-branch map in the Ibarz et al. (2007), Eqs. 2–3 profile; branch-ordered reset events prevent false events under low upper guards; complete 1,000-step two-state/event receipt records 9 events with state digest 9fef084b…03cb; all five batch runtimes fail closed, Rust/Julia/Go are bit-exact and Mojo stays within 1.5e-8, with source-hashed trace/output packets and final-state parity; NetworkRunner exposes the distinct identity; paired schemas agree; two Q16.16 co-sim protocols cover all four branches and preserve both event vectors; tracked Q16.16 RTL passes Yosys coarse synthesis and depth-4 Z3 event/reset safety; timing, PPA, device/board, physical silicon, and universal formal equivalence remain unclaimed	benchmarks/results/bench_ibarz_tanaka_map.json; hdl/reports/yosys_ibarz_tanaka_rulkov_map_q1616_2026-08-29.json
Ermentrout-Kopell	✅	✅	✅	✅ shared-lib	source-faithful canonical Type-I theta flow with maintained forward-Euler dt=0.1, gain, upward-π event, and true modulo-2π commit; all five runtimes return the complete phase trace and event count and fail closed through their public contracts, while the stateful Python and Rust APIs preserve configuration on reset; the independent 2,000-step DOI receipt fixes 45 events and the complete binary64 trace digest; hand/TOML/JSON are exact, Q16.16 RTL preserves 0/45/64 events at I=-0.5/0.5/1.0 with declared circular error bounds, generated integer C/Rust and Verilog are cycle-exact over both current signs, tracked Q8.8 RTL passes Yosys coarse synthesis and depth-4 reset safety; timing/PPA/device/formal-equivalence claims remain excluded	benchmarks/results/bench_ermentrout_kopell_map.json; hdl/reports/yosys_ermentrout_kopell_map_q88_2026-08-28.json

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 FitzHugh-Nagumo, Morris-Lecar, 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, SC upward-crossing Rulkov map, GLIF, Mihalas-Niebur, Medvedev map, Cazelles map, Courbage-Nekorkin map, SC clipped rational-recovery 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.

Runtime-validated models awaiting the complete acceleration chain

The models below have a faithful Python reference and executed parity through the production Rust engine plus the standalone safety Rust, Go, and Julia lanes. They are recorded here so that completed runtime work is visible, but they are not included in the polyglot-complete total: Mojo remains missing or non-computing, and no RTL/silicon parity is claimed. A ✅ in this table therefore means validated on that named surface only, not graduation under the stricter bar above.

Model	Python	Rust engine	Rust safety	Go	Julia	Mojo	RTL	Executed parity basis	Local closure
SK neuron	✅	✅	✅	✅	✅	⬜ missing	⬜	complete 64-step state trajectory within 1e-12; invalid input is rejected atomically	6251766ac
T-type calcium neuron	✅	✅	✅	✅	✅	⬜ missing	⬜	complete 64-step state trajectory within 1e-12; invalid input is rejected atomically	548c5212d
GLM neuron	✅	✅	✅	✅	✅	⬜ missing	⬜	64-step spike and history-buffer parity within 1e-12 under explicit uniform samples; legacy engine filters remain reconstructible without a second model identity	ea91c4969, 51475169b

Runtime-complete compatibility identities awaiting benchmark closure

The count-neutral identity below retains real implementations and executed parity checks across the maintained languages, but it is not strict-promoted: its own source-hashed five-runtime benchmark is still missing. The source Bertram benchmark is not reused as proof for the distinct SC recurrence.

Model	Python	Rust engine	Rust safety	Go	Julia	Mojo	Blocking evidence	Evidence anchors
SC three-state phantom	✅	✅	✅	✅	✅	✅ executable	dedicated source-hashed five-runtime benchmark	tests/test_bertram_phantom_native_parity.py; src/sc_neurocore/neurons/reference_receipts/sc_three_state_phantom_project.json

In progress

The local-first remediation campaign remains active. Mid-flight ownership and queue position are kept in the internal working tracker; this public page records a model only after its current unit has an executed evidence packet and a local closure commit.

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 at least one required accel/{rust,go,julia,mojo} lane is a stub, missing, or not yet verified. The polyglot-stub-remediation sweep is replacing those gaps model-by-model. Partial runtime closures are shown separately above and are deliberately not promoted into the strict table. As of the latest strict graduation, there are 57 polyglot-complete source models out of the 160-model source catalogue; the remaining 103 source model units still have at least one acceleration-chain requirement open.

These counts are derived from the identity registry, not typed by hand. The source catalogue is every registered model class whose identity is a published source or a project-original design; SC compatibility identities and import aliases are count-neutral. python tools/model_identity_ledger.py --counts prints the live numbers, and docs/_generated/model_identity_ledger.json records each identity's kind, schema profiles, source locator, public status, revalidation status and open evidence gates.

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.

Declared tiers on this page and in Studio are what the descriptors claim. Their evidence-bound counterpart (which claims are backed by an executed, still-fresh facet receipt, and which merely name evidence that exists) is described in readiness evidence and generated into docs/_generated/readiness_evidence_ledger.json.

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.