Montbrió–Pazó–Roxin source, runtime, and co-simulation fidelity

This page records the publication boundary, independent equation trace, five-runtime parity, failure atomicity, fixed-point envelope, and controlled benchmark used to promote the legacy-named ErmentroutKopellPopulation.

Primary-source boundary

Montbrió, Pazó, and Roxin (2015) derive an exact macroscopic description for the thermodynamic limit of all-to-all coupled quadratic integrate-and-fire neurons with Lorentzian-distributed excitability. Their equations (12a–b) close the dimensionless network dynamics in population rate (R), mean membrane potential (v), and source time (t'):

[ \frac{dR}{dt'}=\frac{\Delta}{\pi}+2Rv, \qquad \frac{dv}{dt'}=v^2+\bar\eta+JR+I(t')-(\pi R)^2. ]

Primary source: Montbrió, Pazó, and Roxin 2015. The public class name is a compatibility boundary only; attributing these equations to Ermentrout and Kopell (1986) would be incorrect.

Time-scale and solver convention

SC-NeuroCore restores a physical population rate and time scale with the exact change of variables

[ R=\tau r,\qquad t'=\frac{t}{\tau}. ]

Therefore (dR/dt'=\tau^2\,dr/dt) and (dv/dt'=\tau\,dv/dt). Substitution into the printed dimensionless equations yields the maintained flow:

[ \frac{dr}{dt}=\frac{\Delta}{\pi\tau^2}+\frac{2rv}{\tau}, \qquad \frac{dv}{dt}= \frac{v^2+\bar\eta+J\tau r+I(t)-(\pi\tau r)^2}{\tau}. ]

This is a change of variables, not a numerical modification. The paper defines continuous equations and does not require a particular solver. SC-NeuroCore uses simultaneous explicit Euler at dt=0.01 as its deterministic implementation contract and records that choice separately from the scientific source.

Independent reference trace

src/sc_neurocore/neurons/reference_trace_data/ermentrout_kopell_pop_eq12_euler_doi.json pins a 256-step trace with:

• a deterministic sinusoidal external drive;
• both post-update states;
• the DOI and exact equation/solver boundary;
• first, final, minimum, maximum, and mean features for both traces.

tests/test_reference_ermentrout_kopell_pop.py independently re-derives the two equations without importing production equation helpers, checks every recorded feature, and compares every Python production state exactly. The canonical interleaved little-endian float64 digest is 6bf2d0b8611cba646e5b575ed3253090e1e02955c75c01efac13e603578edae5. The deterministic drive is a parity protocol, not a paper-figure reproduction.

Numerical and atomic contract

Each scalar step:

1. validates all parameters, the complete current state, and external drive;
2. evaluates both derivatives from the same pre-update state;
3. evaluates both Euler candidates;
4. rejects a non-finite or negative-rate candidate;
5. commits both states together.

Public batch dispatchers validate both trace shapes, finiteness, non-negative rate, and both final-state receipts before mutating the model instance. Go computes into private scratch traces before writing its C outputs. Mojo runs a validation pass before its output pass. Rust returns owned traces only after the complete batch succeeds. Empty batches preserve both states.

Executable parity matrix

Runtime	Executed surface	Enrolled result
Python	scalar reference and atomic batch	reference
Rust engine	modular PyO3 scalar and batch	two traces/two final states within 1e-12
Rust safety	standalone rustc --test module	equation wiring, validation, atomic mutation, reset
Julia	JuliaCall batch	two traces/two final states within 1e-12
Go	generated C-shared ABI	two traces/two final states within 1e-12
Mojo	exported shared-library C ABI	two traces/two final states within 1e-10

The configured test begins from non-zero state values, changes every public parameter, supplies a varied 128-step drive, and compares both trajectories plus both final states. Explicit selection of an absent runtime fails rather than substituting the Python path.

Paired schema and Q32.32 co-simulation

The TOML and JSON schemas are structurally identical and their direct floating- point execution matches the hand model within 1e-13. One input edge carries one external-drive sample and advances both states simultaneously.

Generated Q32.32 Verilog compiles with Icarus and preserves the varied 64-step trajectory with maximum firing-rate and voltage errors below 2e-6. This is a bounded fixed-point co-simulation result, not exact RTL equivalence.

The canonical sc_ermentroutkopellpopulation.sby job runs depth-4 BMC over the same Q32.32 generated RTL. It proves asynchronous reset clears spike_out and, after the first sampled clock, the public spike output remains zero because this population model has no binary event semantics. It does not claim equation equivalence, synthesis, timing, or H4 evidence.

Controlled benchmark

benchmarks/bench_ermentrout_kopell_pop.py measures the same complete deterministic-drive batch through all five public dispatchers. It rejects an unpinned run, any unavailable runtime, a standalone Rust-safety failure, trace/final-state drift, or an invalid run size. The committed JSON binds raw timing samples, source hashes, exact loaded Rust/Go/Mojo binaries, tool versions, affinity, load, and every parity delta.

The recorded run used logical CPU 10, five 50,000-step samples after a 1,000-step warm-up, and the exact isolated Rust wheel built for this source tree. Its one-minute load average was 23.65, so the timings are deliberately classified as non-exclusive diagnostics. The record separately identifies the JuliaCall runtime (1.11.9) and PATH Julia CLI (1.12.6), the Go shared library's embedded builder (1.26.3) and PATH Go CLI (1.24.0), and the pinned Pixi Mojo builder (0.26.2) and PATH Mojo CLI (1.0.0b1).

Runtime	Median call	Median ns/step	Maximum trace difference	Trace mismatches
Julia	3.844 ms	76.875	0	0
Mojo	4.088 ms	81.761	2.220e-16	0
Go	4.571 ms	91.429	0	0
Rust	4.703 ms	94.058	0	0
Python	170.959 ms	3,419.182	0	0

Python, Rust, Julia, and Go share interleaved-trace SHA-256 0e9c59cbe73cb9019d309fc484fa67c838ae503d0c9f9f7a6825bb6fa857cb7b. Mojo has a distinct byte digest because of its bounded final-bit difference. The complete JSON evidence SHA-256 is 7c5c1ac6acd7e3593dd7289612d1a8687f361d1b52c6d564ca8b95961036206e.

The record is one-logical-CPU, non-exclusive local regression evidence. It is not a production, cross-host, cross-framework, or hardware performance claim. The timing table is reproduced in Benchmark Comparison.

Boundaries

• The output is a continuous population firing rate, not a binary spike.
• The Euler step is an implementation choice, not imposed by the paper.
• The deterministic input protocol does not reproduce a published figure.
• The exact reduction does not model finite-size fluctuations, delays, adaptation, or sparse connectivity.
• Q32.32 co-simulation reaches H1 only.
• No synthesis, timing closure, formal equivalence, device resource, or PPA result is claimed.

Reproduction

Keep temporary and build outputs on a writable working volume:

Bash

WHEEL_SITE=/path/to/isolated-wheel-site
BUILD_ROOT=/path/to/writable/build-root
TMPDIR="$BUILD_ROOT/tmp"
mkdir -p "$TMPDIR" "$BUILD_ROOT/bin"

TMPDIR="$TMPDIR" \
  rustc --edition 2021 --test \
  src/sc_neurocore/accel/rust/safety/ermentrout_kopell_pop.rs \
  -o "$BUILD_ROOT/bin/mpr_safety_tests"
"$BUILD_ROOT/bin/mpr_safety_tests"

TMPDIR="$TMPDIR" \
PYTHONPATH=$WHEEL_SITE:src:. .venv/bin/python -m pytest -q \
  tests/test_model_ermentrout_kopell.py \
  tests/test_ermentrout_kopell_pop_dynamics.py \
  tests/test_reference_ermentrout_kopell_pop.py \
  tests/test_cosim_ermentrout_kopell_pop.py \
  tests/test_ermentrout_kopell_pop_backends.py \
  tests/test_bench_ermentrout_kopell_pop.py

taskset -c 10 env \
  TMPDIR="$TMPDIR" \
  PYTHONPATH=$WHEEL_SITE:src:. .venv/bin/python \
  benchmarks/bench_ermentrout_kopell_pop.py \
  --json benchmarks/results/bench_ermentrout_kopell_pop.json