SEP 37 — Shot noise on by default, and an integrator and tolerances chosen for each interface#


SEP	37
Title	Shot noise on by default, and an integrator and tolerances chosen for each interface
Author	John Travers
Drafting agent	Opus 5.5 (2026-10-26); Opus 5.5 (2026-10-26, revision after review)
Status	Final
Review status	Reviewed
Reviewers	John Travers (human); GPT-6 (AI)
Type	Change
Created	2026-10-26
Resolution	Accepted 2026-10-26 by John Travers, with the 10 % tie margin of §5.2, after his human review, the GPT-6 AI review and the response to it, with decisions D1–D7 recorded in Part III (LupoLab/solprop#30). Final 2026-10-27 by John Travers after phases 0–3 and his decisions D8–D11 on the defaults (Part II, “Closing”). The proposal lands with its implementation’s single pull request.
Requires	SEP 16 (the multistep family and its work–precision qualification); SEP 30 (the benchmark suite); SEP 31 (field planes and coupled stages)
Supersedes	—
Superseded-by	—
Implementation	Opus 5.5 (AI) for John Travers, branch `feature/sep-0037-noise-and-stepper-defaults` (LupoLab/solprop#30): phases 0–3 implemented 2026-10-27, the defaults decided by D8–D11
Manual pages	Noise; choosing a stepper: the defaults; fixed schedules; processing: the noise floor

Part I — Proposal#

Revised on 2026-10-26 after the GPT-6 AI review. The response to the review (Part III) says what changed for each finding; the maintainer’s decisions are recorded there as D1–D5.

1. Abstract#

Every solprop run is noiseless unless it asks for noise, every interface steps with Multistep() by default, and the default tolerances differ between interfaces for reasons that are only partly written down. This SEP changes those defaults, using models and methods solprop already has. It is not a noise-physics project. It proposes:

noise="input" as the default: one photon per mode with a random phase, added to the input field. This is the seed of the supercontinuum literature, and the one the author’s group has used for years. The modified model stays available, with its limitations documented.
A default integrator for each prop_* interface, chosen by a rule fixed in this SEP and never dependent on the physics a run switches on.
Default tolerances for each interface, set by a stated convergence protocol.
Lifting the input-noise refusals that exist only because nobody built them: the TDSE response, coupled flows and explicit interior launches.

Where noise cannot be carried, a run that did not ask for noise falls back to none. The fallback is recorded and printed. Tests and worked examples fix their seeds.

Success is judged in four ways:

the default resolves as specified at every entry point;
each lifted refusal passes its stated checks;
the chosen integrators win their comparison under the rule;
the tolerances meet the protocol’s budgets.

2. Motivation and scope#

A noiseless default hides itself. A user who does not pass noise= gets no shot noise. Nothing is printed, and the run record says so only on inspection. Spontaneous processes then do not start: modulational instability, Raman scattering from noise and the shot-to-shot incoherence of a supercontinuum. Coherent dynamics seeded by the pulse itself look cleaner than they would in an experiment.

The least bad model solprop knows how to implement is the input model. It is what the literature uses [1, 2] and what the author’s group has run for years. Its known limits are stated in §4.1. The modified model is not provably better (§4.2):

With a unitary linear operator, the two models are the same equation. That holds whatever the nonlinear response is, Raman and plasma absorption included.
They differ only where the linear operator is not unitary. That means propagation loss, which every default capillary run has, plus the absorbing collars and the normalisation along a varying guide. There the modified model’s extra term is not reservoir noise, and it can be worse than the input model.
Its saved field leaves out the seed. That changes what a spectrum or a coherence computed from the output means.

So the input model is the default, and the modified model stays an option.

One default integrator does not suit every interface. Multistep() became the default everywhere with SEP 16 (ADR-045). The evidence was strongest where the source is expensive: 5.5 to 5.8 times faster than IP-DOPRI5 on the full resonant-dispersive-wave capillary, and 2 to 3 times on a soliton-to-continuum launch. The same record has IP-DOPRI5 ahead on the single-mode GNLSE window on numba_cpu, by 1.2 to 1.4 times, and the preliminary measurements of §3.4 find RK further ahead once noise is on. A default that changed with the physics switched on would be fragile, and the author rejects it. A default for each interface is not fragile in that way, because the user chooses the interface and the interface fixes the equation solved.

The default tolerances are only partly explained.

prop_gnlse asks for rtol = 1e-8 and atol = 1e-14 √W. These were set with the first driver, and no reason was recorded. They suit noiseless soliton recurrence, which is an occasional study; a user who wants it can ask for a tight tolerance. The GNLSE is used mostly for supercontinuum, where a looser tolerance is enough.
prop_capillary and prop_waveguide ask for 1e-6 and 1e-10 √W, the values Luna.jl documents. The docstring justifies them by the cost of a modal step. Production practice is looser still: rtol = 1e-5 is common, and runs with the TDSE response use 1e-3 to 3e-3.
prop_radial, prop_free and prop_planar have no default tolerance at all. Their SimulationSettings require a controller from the caller.

In scope:

the defaults of every prop_* interface and of the Simulation.from_* constructors behind them: noise model, integrator and formulation, rtol and atol;
the input-noise refusals that are not grounded in physics or numerics (§3.3);
a floor-subtracted spectrum in processing, which gives an input run the clean spectrum of the modified model’s readout (§5.5);
seeds for the test suite and the worked examples;
the manual’s account of noise, cost and stepper choice.

Out of scope:

Changes to the modified model. It is kept as it is, with no new work. Its own refusals (interpolated planes, field planes, coupled flows) stay, and so do its readout and its transport along a varying guide; they are recorded on the roadmap. Whether to keep or remove it is decided when SEP 7 settles whether gain media need its separate noise-injection path (D7).
New noise physics. No half-photon vacuum, no Langevin terms for loss or Raman, no thermal phonon occupation, no Gaussian amplitude for the draw and no technical (pump) noise.
Noise on the hybrid planar grid, which needs a transverse normalisation decision first, and noise under single precision, which binary32 cannot hold (§3.3).
Default changes elsewhere, such as grids, save planes, absorbers or Raman.

3. Context#

3.1 The noise models#

Shot noise describes the draw:

one photon per active bin, mode and polarisation, with a deterministic modulus and a uniform random phase;
masked to the active band on both grids;
one generator stream per seed.

The same draw serves both models:

input adds it to the field at the launch. It then propagates with the field under the full linear and nonlinear operators.
modified (ADR-008) keeps the draw apart from the propagated field. It advances the draw by the unitary part of the cumulative linear operator, \(N(z) = N_0\,e^{i\,\mathrm{Im}\,\Phi}\), and passes the full field \(\psi + N\) to the nonlinear response at every stage. The saved field is \(\psi\), without the draw.

The realisation and its seed are stored with the output. A seed of None draws from the operating system and records what it drew. A seed fixes the realisation. It does not make adaptive runs on different backends agree bit for bit (SEP 25).

3.2 The defaults today#

Interface	Noise	Integrator	`rtol`	`atol` (√W)
`prop_gnlse`	`None`	`Multistep()`	1e-8	1e-14
`prop_capillary`	`None`	`Multistep()`	1e-6	1e-10
`prop_waveguide`	`None`	`Multistep()`	1e-6	1e-10
`prop_radial`, `prop_free`	`None`	`Multistep()`	caller’s controller	caller’s controller
`prop_planar`	not carried	`Multistep()`	caller’s controller	caller’s controller

3.3 Where noise is refused today, and what this SEP does#

Where	Refuses	The reason given today	This SEP, for the input default
`precision="single"`	both models	binary32 rounding swamps a one-photon seed (SEP 33)	an accuracy limit: kept; the default falls back to none
the TDSE response	both models	noise left out of the initial qualification (SEP 12)	a scope choice: lifted for `input` (§6)
an interior launch, `initial_z > 0`	both models	none recorded	lifted for an explicit `input`; the default takes no new draw (§5.1)
a coherent wall, the taper coupling, a split block, a moving solid guide	both models	the draw’s transport through a nonunitary coupled flow is not measured	that question is the modified model’s alone; lifted for `input` (§6)
the hybrid planar grid	both models	no photon measure is declared for slab amplitudes	needs a normalisation decision: kept; the default falls back
a general modal guide with a diagonal metric	both models	a one-photon draw is not defined in that basis; nothing builds one	kept; the default falls back
interpolated save planes	`modified`	the draw is added outside the interpolant (SEP 14)	not affected by the input default
`processing.field_plane`	`modified`	the noise phase is not reconstructed into a plane (SEP 31)	not affected by the input default

Only the single-precision refusal rests on numerics. The planar and diagonal-metric refusals rest on a missing definition. The rest are scope choices or concern the modified model only.

3.4 Preliminary measurements#

These were taken while drafting, at commit 1d4f099, on the native backend (what backend="auto" resolved to), on an Apple M5 Max laptop, with seed 1. They count accepted steps, and each wall time is a single sample. They are evidence about these cases, not a qualification, and phase 0 repeats them under §5.2’s rule.

Capillary worked examples cover SPM, soliton self-compression, four-wave mixing, XPM, ionisation blue shift and two supercontinuum ensembles (16–256 µm bores, µJ–mJ pulses). Each took the same number of steps, within 2 %, with and without noise.

The N = 3 GNLSE soliton tutorial (20 pJ, 100 fs, 500–2000 nm band, the tutorial’s grid) behaves very differently:

Integrator, `rtol`	No noise	`input`	`modified`
`Multistep()`, 1e-9	1126	73199	73199
`Multistep(formulation="interaction")`, 1e-9	5189	108759	108760
`RungeKutta()`, 1e-9	1800	21845	21845
`Multistep()`, 1e-6	467	—	18863
`RungeKutta()`, 1e-6	507	—	4193

The two models cost the same here. The manual’s “about eight times” for the modified model alone was quoted from Luna.jl and is not reproduced in this case.
atol made no difference. Values from 1e-14 to 1e-6 √W left the counts unchanged.
Scaling the draw changes the cost. Scaling it by \(s\) took the RK count from 21845 at \(s = 1\), through 8153 and 2219, to 1816 at \(s = 10^{-6}\), against 1800 without noise.

Accuracy was measured against an RK reference at rtol = 1e-11 with the same draw. The noise part is the run’s departure from the noiseless run.

Run	Steps	Field error	Error in the noise part
RK, adaptive, `rtol` 1e-9	21845	6e-10	1e-7
RK, adaptive, `rtol` 1e-7	8152	4e-6	6e-4
RK, adaptive, `rtol` 1e-6	4193	7e-5	1.1e-2
RK, the noiseless run’s schedule replayed	1800	3e-4	5.7e-2
`Multistep()`, adaptive, 1e-9	73199	5e-8	8e-6
`Multistep()`, adaptive, 1e-6	18863	2e-4	3.2e-2
`Multistep()`, the noiseless run’s schedule replayed	1126	5e-3	0.78

In this case the extra steps are needed: a schedule discovered without noise gets the noise part wrong. A replayed schedule for a noisy ensemble should therefore be calibrated with noise on, across more than the seed that discovered it.

4. Theory#

4.1 The input model and its known limits#

Where one photon per mode comes from. In the symmetrically ordered (Wigner) picture, which a classical field simulation implicitly uses, the vacuum carries half a photon per mode [3]. One photon per mode is instead the equivalent input noise of a phase-insensitive amplifier. Smith showed that the spontaneous Raman or Brillouin emission along a fibre, amplified by the gain remaining after each point, is the same at high gain as one photon per mode injected at the input and propagated by the stimulated equations alone [4]. The supercontinuum literature adopted this seed with a random phase on every spectral bin [1, 2].

What it gets wrong, and by how much:

Parametric processes. For modulational instability and four-wave mixing, which have no reservoir, the exact seed is half a photon. One photon overestimates spontaneous parametric power by a factor of two at high gain [3, 6]. Modulational instability enters a supercontinuum logarithmically, so this shifts its development length by about \(\ln 2/(2\gamma P_0)\), a few per cent of \(L_\mathrm{MI}\).
Linear loss. Under linear loss, the seed decays with the field instead of staying at the vacuum level. Spontaneous processes far into a lossy guide are then under-seeded by about the guide’s power transmission up to that point.
The floor. The seed sits as a one-photon floor under the whole spectrum.
Thermal seeding. Spontaneous Raman scattering at a shift \(\Omega\) is seeded at \(n_\mathrm{th}(\Omega) + 1\) photons on the Stokes side and \(n_\mathrm{th}\) on the anti-Stokes side, with \(n_\mathrm{th} = 1/(e^{\hbar\Omega/k_BT} - 1)\) [3]. For vibrational shifts (tens of THz) \(n_\mathrm{th}\) is negligible, but for the rotational lines of nitrogen at room temperature (0.36–5 THz) it is about 1 to 17. One photon per mode then under-seeds rotational Raman by up to an order of magnitude, and seeds its anti-Stokes side where thermal phonons would. Neither noise model in solprop includes this; a Raman Langevin term with the thermal factor would.
Statistics. The fixed-modulus draw has the right second moments but not the fourth moments of a vacuum mode. A gain mode that spans many spectral bins sums many independent phases and approaches Gaussian statistics anyway.

These limits are known and bounded. Each is either small where the model is used or visible to the user. Fixing them needs the half-photon vacuum with a Langevin term for each reservoir [3], which is new physics outside this SEP.

4.2 Why the modified model is not the default#

Write the linear operator as \(\hat D = \hat D_u + \hat D_r\), with \(\hat D_u\) its unitary part. Let the modified draw obey \(\partial_z N = \hat D_u N\), and let the modified field obey \(\partial_z\psi = \hat D\psi + \hat N(\psi + N)\), for any deterministic nonlinear operator \(\hat N\). Then the reconstructed field \(\chi = \psi + N\) obeys

\[ \partial_z \chi = \hat D\chi + \hat N(\chi) - \hat D_r N . \]

When \(\hat D_r = 0\), \(\chi\) is exactly the input model’s field. This holds to all orders in the seed, whatever \(\hat N\) contains, including a delayed Raman response and plasma absorption. A short probe on numpy_ref reproduced this identity to \(10^{-16}\), with and without Raman (Part III).
When \(\hat D_r \neq 0\), the two differ by the forcing \(-\hat D_r N\). That covers propagation loss, the absorbing collars and the real normalisation term along a varying guide. The forcing is correlated with the original draw. It is not newly sampled reservoir noise, and it does not follow the fluctuation–dissipation form of a reservoir [3].
It can be the worse of the two. Take a gain \(G\) followed by a passive transmission \(\eta\). The modified model’s corrected readout gives \([1 + \sqrt\eta(\sqrt G - 1)]^2 - 1\) spontaneous photons, against the true \(\eta(G - 1)\). With \(G = 4\) and \(\eta = 1/4\), that is 1.25 photons against 0.75.

So the modified model equals the input model where the linear operator is unitary. Elsewhere it is an approximation of unqualified accuracy. That is not “provably better and not worse elsewhere”, and it is not adopted as the default.

Its practical differences add to this. The saved field excludes the seed, and no processing function restores it, so spectra and coherence computed from the output describe \(\psi\), not \(\chi\). Several routes refuse it (§3.3). A draw held at constant internal modulus also gives a restored energy per bin of \(\hbar\omega\,w(z)/w(0)\) along a varying guide, where \(w\) is the power weight of the mode. All of these are documented and left on the roadmap.

solprop’s modified model is also not the published one [5]. It evaluates the full nonlinear response of \(\psi + N\) rather than the first-order expansion, it has no separate emission gain (solprop has no gain media), and it transports the draw by the dispersive phase rather than holding it fixed. The paper’s results therefore qualify the published model, not solprop’s variant.

4.3 What noise costs#

The controller holds the embedded difference below \(\mathrm{rtol}\,\lVert y\rVert + \mathrm{atol}\) on its internal state norm. A seed of one photon per bin over \(n\) active bins carries an energy of about \(n\hbar\bar\omega\), against the pulse’s \(U\). Its initial share of the norm is then about

\[ r \approx \sqrt{n\hbar\bar\omega / U} , \]

about \(10^{-2}\) for the 20 pJ soliton and \(10^{-4}\) to \(10^{-5}\) for µJ–mJ capillary pulses. This is a size diagnostic, not a step-cost criterion. Linear propagation of the seed costs nothing under an exponential integrator at any \(r\). A small seed can grow into a resolved instability. And the capillary runs above showed no cost even with \(r\) above rtol. The cost of noise is measured, not predicted.

5. Proposed interface#

5.1 Noise#

The default is noise="input" on every interface and constructor that carries noise. seed=None keeps its meaning. noise=None switches noise off explicitly. noise="modified" is unchanged, with its limits documented (§4.2).
A route that cannot carry noise falls back. These routes are single precision, the hybrid planar grid and a general guide with a diagonal metric. A run on one of them that omits noise resolves to no noise. The noise record stores the requested model (default), the resolved model (None) and the reason. The start-of-run summary prints the resolution, and Output.metadata carries it.
Fallback limits. The list of fallback routes is closed. A backend choice never changes the resolution: a backend that cannot run a resolved model fails as today, and that failure is never reinterpreted as unsupported noise. A run that passes seed= without noise= on a fallback route is refused, because the seed states an intent the fallback would discard.
An interior launch (initial_z > 0, an explicit spectrum) takes the spectrum as given under the default, with no new draw. This is recorded as a resolution, because the spectrum may already carry a realisation from an earlier run. An explicit noise="input" adds one draw at initial_z.
A coupled launch from a field plane (Simulation.with_input with a Launch) keeps today’s behaviour: the plane carries whatever the source run carried, and no second draw is added.

run = prop_capillary(150e-6, 1.0, "He", 0.5, lambda0=800e-9, energy=200e-6, fwhm=10e-15)
run.metadata.noise          # model='input', seed=<recorded entropy>, requested='default'
run = prop_capillary(..., noise=None)          # noiseless
run = prop_capillary(..., seed=20261026)       # reproducible realisation

5.2 Integrators#

Each interface gets its own default, chosen in phase 0 by this rule:

Cases: the standard suite’s core cases for that interface (SEP 30), on short windows, each with noise on and off.
Candidates: Multistep() in both formulations and RungeKutta().
Selection: take the candidate with the lowest median wall time at matched accuracy under §5.3’s protocol. Measure on one CPU thread and at the production width, on the suite’s declared machines.
Ties: a candidate within 10 % of the fastest counts as tied, and a tie keeps today’s default.

The resulting table, with its evidence, goes into the phase 0 report. It takes effect only once the maintainer approves it there, which is this SEP’s approval gate. The expectation is RungeKutta() for prop_gnlse and Multistep() for the modal and spatial interfaces. The default never depends on the responses switched on, and a user who wants another method passes integrator= as today.

5.3 Tolerances#

Each interface’s default rtol is the loosest of three levels, a factor of ten apart, that meets the budgets below on that interface’s canonical case:

Cases:
- prop_gnlse: the standard suite’s gnlse_raman_shock, which is the supercontinuum of Dudley, Genty and Coen [1]: 15 cm, 10 kW, sech, \(\beta_2\) to \(\beta_{10}\), Raman and shock.
- prop_capillary and prop_waveguide: one capillary case and one waveguide case of the suite.
- prop_radial, prop_free and prop_planar: one case each from the suite.
Protocol:
- one set of seeds shared across every tolerance level (paired seeds);
- a reference for each seed at a tolerance a hundred times tighter than the tightest level;
- comparisons on stored witnesses or short windows, so that no full-length run is needed in tests.
Budgets:
- the ensemble-mean spectral energy density, in decibels, within 0.5 dB of the reference wherever the reference is above −40 dB of its peak;
- the coherence \(|g_{12}|\) within 0.02, absolute, over the same region;
- for a noiseless case, the same spectral budget on the single run.

A noiseless soliton-recurrence study asks for its own tighter value, and the manual says so. A response does not set a default: the TDSE practice of 1e-3 to 3e-3 is recorded in the manual as a recommendation. atol is set with rtol on the same cases.

For prop_radial, prop_free and prop_planar, SimulationSettings gains a default for its controller. An explicit controller always wins, and an omitted one takes the interface’s default. The default records which applied.

5.4 What the user sees#

The start-of-run summary, delivered separately, prints the resolved noise model and seed, any fallback and its reason, the integrator and the tolerances. It is a prerequisite of phase 2: the noise default does not land before the summary does. The seed share \(r\) of §4.3 may be printed as a size diagnostic, but nothing warns on it.

5.5 A floor-subtracted spectrum#

processing.get_spectral_density and processing.get_spectrum gain a keyword noise_floor, either "keep" (the default) or "subtract". "subtract" removes the injected seed’s energy, exactly one photon per active bin and channel, from the spectral energy density, using the route’s own photon measure, the one noise.photons_per_bin inverts.

The equivalence. The draw has a fixed modulus, so this is exact for one realisation. Where the linear operator only changes the phase, the subtracted spectrum of an input run equals the modified model’s corrected readout \(|\psi + N|^2 - |N|^2\) for the same draw.
What it is not. It is not a photon-number estimator under loss. There the input seed has decayed, and the subtraction removes more than remains.
Signs and refusals. Values near the floor can be negative, by the interference term and the seed’s decay. The keyword returns them signed, and the plotting helpers mask non-positive values on a logarithmic axis. It refuses a run without noise, and a modified run, whose saved field holds no seed.

6. Implementation strategies#

The default and its resolution are driver settings, in solprop.driver.interface and solprop.driver.simulation. A sentinel default resolves per route, before translation, by the rules of §5.1. The noise record gains the requested model and the reason for any fallback, so the output schema version changes. Input noise is part of the initial state, so the kernel contract is unchanged, and so is every backend: no backend has an input-noise path of its own. The numba_cpu stash of the plasma statistics is disabled only under the modified model, so the default does not touch it.

Lifting the input-noise refusals:

Refusal	Work	Checks
the TDSE response	admit `input`, which only changes the drive field the atom sees	the drive at the entrance equals the pulse plus the draw, and the realisation is stored; the draw alone, with no pulse, gives the TDSE’s weak-field (linear-susceptibility) response within its documented weak-field accuracy; the active band lies inside the response’s declared window, as it must for the pulse alone
coupled flows	admit `input`: the draw enters as part of the entrance state, in the channel basis, and the flow propagates it like any field	the entrance basis is orthonormal in true power, else the run is refused, as `check_noise_basis` does for general guides; one photon per channel and bin at the entrance; exit energy equals the noiseless run’s plus the transmitted seed, within the flow’s certificate
explicit interior launch	add one draw at `initial_z`	photon number per bin at the launch is one; the default case takes no draw (§5.1)

The modified model keeps all its refusals.

7. Verification and validation#

Resolution. At every entry point, test four cases: noise omitted, noise=None, each explicit model, and seed= without noise=. Cover the routes that carry noise, the fallback routes and the interior launch, and check the stored record and the printed summary.
Lifted refusals, as in the table of §6.
The floor-subtracted spectrum. It equals the modified readout of the same draw to rounding, in a lossless Kerr and Raman case. It removes exactly one photon per bin from an unpropagated noisy input, leaving the pulse’s spectrum. It refuses as §5.5 states.
Integrators and tolerances, by the rules of §5.2 and §5.3.
Examples. Re-run every worked example whose result changes under the new defaults, with a fixed seed.
The input model itself is unchanged. Its existing tests (one photon per bin, phase statistics) stand.

8. Documentation#

Shot noise:
- the default and the fallback rules;
- the input model’s origin [4] and known limits (§4.1);
- an honest account of the modified model: its origin [5], solprop’s variant, where it equals the input model and where it differs, its readout and its refusals (§4.2);
- the cost as measured in solprop, in place of the quoted factor of eight;
- the floor-subtracted spectrum and what it is not (§5.5);
- what neither model does.
Choosing a stepper: the default for each interface and the evidence behind it.
Fixed schedules: calibrate an ensemble’s schedule with noise on, across seeds.
The docstrings of every prop_* interface and Simulation.from_* constructor: noise, integrator and tolerances, each with its reason, and the recommendations of §5.3.
The worked examples and tutorials: a fixed seed where noise is now on, and noise=None only where the lesson is noiseless.

9. Compatibility and impact#

Every default run becomes stochastic. Two runs of the same script differ by realisation unless they fix seed. Users who compared outputs must pass a seed, or noise=None.
Existing results change at the level of the seed, and more visibly where noise seeds a spontaneous process. Low-energy GNLSE runs become slower (§3.4).
Tests. About 65 test modules build runs without naming noise. Those comparing against a deterministic reference pass noise=None, and a few tests cover the default itself.
The output schema version changes for the extended noise record. Older files read as before, with the requested model taken as the resolved one.
Luna.jl defaults to its modified model. solprop’s default is the input model, and the differences page records why (§4.2).
Nothing is public yet, so no deprecation path is needed. The changelog records the change.

10. Alternatives considered#

Keep None and document it. This is the status quo, and it is how the gap went unnoticed. Rejected, because noise is part of the physics being modelled.
modified as the default. It equals the input model where the linear operator is unitary, and it is of unqualified accuracy elsewhere (§4.2). It also changes what the saved field means, and it refuses more routes. Rejected for the default; it stays an option.
Refuse, rather than fall back, where noise cannot be carried. This is the reviewer’s preference, and it is honest, but every default single-precision run would then need noise=None. Rejected in favour of a closed, recorded and printed fallback (D2).
Removing the modified model now. It adds little physics (§4.2), and it carries refusals and a different saved field. But its separate injection path is what amplified spontaneous emission in a gain medium would need, with the noise seeing only the emission gain. The decision waits for SEP 7 (D7).
A half-photon vacuum with reservoir Langevin terms, or a Gaussian draw. This is the scheme that is exact for both kinds of seeding [3], but it is new physics, with a qualification of its own. Left for a later proposal.
An integrator that depends on the physics switched on. Rejected by the author as fragile.

11. Phases#

The phases are made on one branch, feature/sep-0037-noise-and-stepper-defaults, and land in one implementation pull request, as SEP 0 requires. Each phase is qualified and reported on its own.

Exploration and measurement. Record what each default and refusal was based on. Run §5.2’s rule and §5.3’s protocol on the stated cases, at today’s defaults and at the candidates. Report the integrator and tolerance tables for the maintainer’s approval.
Integrators and tolerances. Set the approved defaults and their docstrings, add the settings default and its precedence, and re-run the affected examples.
The noise default. Add the sentinel, the resolution rules of §5.1, the extended noise record, the docstrings and the noise guide. Seed the tests and examples, and pin the noiseless references. This phase follows the start-of-run summary.
Input noise on the TDSE, coupled-flow and interior-launch routes, with the checks of §6, and the floor-subtracted spectrum of §5.5.

12. Open questions#

The review’s questions are decided (D1–D5, Part III). Two remain, each with its destination:

Q1. Is the channel basis at the entrance of each coupled-flow route orthonormal in true power, so that the input draw is one photon per channel there? Phase 3; a route where it is not stays refused.
Q2. Does any standard-suite case for prop_planar exist on which to set its tolerance? If not, phase 0 adds one or leaves prop_planar without a default. Phase 0.

13. References#

J. M. Dudley, G. Genty and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135 (2006). doi:10.1103/RevModPhys.78.1135
C. Adamu et al., “Noise and spectral stability of deep-UV gas-filled fiber-based supercontinuum sources driven by ultrafast mid-IR pulses,” Sci. Rep. 10, 4912 (2020). doi:10.1038/s41598-020-61847-w
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Part II — Implementation record#

Phase 0 report — measurement#

Scope: phase 0, 2026-10-26/27, Opus 5.5 (AI) for John Travers. The source was commit 71a671d, measured on an AMD EPYC 7763 (Zen 3) cluster node with the native backend, LOCAL profile, GCC 16.2, FFTW 3.3.11 and OpenBLAS 0.3.34. Each arm took three timing samples at 1 and at 16 threads, with node-local environments. It cost about 3.7 h of wall time and 410 CPU-hours. The harness, the raw records and the full report are kept with the project’s development records.
Cases: the maintainer-approved tracking set:
- gnlse_raman_shock, gnlse_soliton;
- rdw, he_rdw_averaged, argon_blueshift (with its averaged and envelope variants), h2_raman_6ps_averaged, ctc;
- radial_filament_256, grin_nonlinear (a 0.02 m window), kerr_beam_192, planar.

Integrator rule (§5.2): the geometric mean over cases and noise arms of each candidate’s time over the fastest, with a 10 % tie margin.

Interface	ms (exponential)	msi (interaction)	rk	Rule’s choice
`prop_gnlse` (1 / 16 threads)	2.48 / 4.84	2.01 / 3.33	1.00 / 1.00	`RungeKutta()`
`prop_capillary`	2.15 / 2.26	1.45 / 1.47	1.15 / 1.09	split (see phase 1)
`prop_waveguide`	4.7–7.4	1.00	1.26–1.29	msi, inadmissible (see phase 1)
`prop_radial`	1.00	tie / 1.3	— / 2.4	`Multistep()`
`prop_planar`	tie	1.00 / tie	—	`Multistep()`

On the noisy gnlse_raman_shock case, RK at 1e-5 took 32 s against Multistep’s 141 s at 1e-6, at 1 thread. On the capillary, RK wins 8 of 14 rows at 1 thread and 11 of 14 at 16, but Multistep wins rdw (RK is 1.6–2.0× slower) and the noiseless ctc.

Tolerance protocol (§5.3):

Interface	Case	Passing levels	Proposed
`prop_gnlse`	`gnlse_raman_shock`, RK, 16 seeds	1e-7, 1e-8, 1e-9 (and 1e-6)	1e-7
`prop_capillary`	`rdw`, 16 seeds; noisy `ctc` check	RK 1e-5; ms needs 1e-6 (Δ\|g₁₂\| 0.043 at 1e-5)	1e-6 with ms
`prop_waveguide`	`grin_nonlinear`, 4 seeds	1e-5	1e-5
`prop_radial`	`radial_filament_256`, 16 seeds	1e-5	1e-5, atol 0
`prop_planar`	`planar`, noiseless	1e-5	1e-5, atol 0

atol was never binding: atol = 0 gave identical steps and errors on the GNLSE, rdw, ctc and grin_nonlinear. Q2 is answered: planar serves.

Not measured: kerr_beam_384 and noisy free space (kerr_beam_192’s steps do not depend on rtol over its window, so free space gets no default); grin_nonlinear beyond its window; the modified model; any machine but this one.
Anomalies: on most cases every candidate passes at the loosest level, 1e-4, so the comparison there is not accuracy-limited. Noise changes the capillary step count only on ctc (1.4–1.6×).

Phase 1 report — integrators and tolerances#

Scope: phase 1, 2026-10-27, Opus 5.5 (AI) for John Travers. The defaults below are provisional, pending the maintainer’s approval of the phase 0 tables (§5.2’s approval gate).
Delivered: src/solprop/driver/simulation.py:
- _interface_integrator gives RungeKutta() to from_gnlse and from_waveguide;
- DEFAULT_RTOL is 1e-7, the new CAPILLARY_RTOL 1e-6, WAVEGUIDE_RTOL 1e-5, and SPATIAL_RTOL 1e-5 with SPATIAL_ATOL 0;
- SimulationSettings.controller is optional, its other fields keyword-only, and _spatial_settings fills the radial and planar default. Free space refuses a missing controller, and a direct Simulation needs one.
The docstrings, the stepper guide’s table, ADR-055 and the changelog follow.
Deviations:
- Admissibility. The rule now chooses among the methods every route of the interface admits. The interaction-formulation Adams method won the waveguide case but refuses the coupled flows of the split block and the moving guide, so the waveguide default is RK, which is 4× faster than today’s default there.
- The capillary is held at Multistep() and 1e-6. The rule’s aggregate prefers RK with 1e-5, but the evidence is split: Multistep wins rdw and the noiseless ctc, the production workloads SEP 16 qualified it on. RK would also refuse default TDSE runs and move most of the capillary test references. The maintainer decides this.
Verification: the default lane and the slow lane on the cluster node (below, at Final), and the defaults checked by construction.
After the maintainer’s review (D9–D11):
- The capillary keeps Multistep() at 1e-6 for every representation (D11, which replaced D10’s representation rule).
- prop_free takes adaptive RungeKutta(), a default controller (FREE_RTOL) and no noise by default.
- A TDSE run takes no noise by default and warns when asked for it (D8).

Phase 2 report — the input-noise default#

Scope: phase 2, 2026-10-27, Opus 5.5 (AI) for John Travers, branch feature/sep-0037-noise-and-stepper-defaults.
Delivered:
- src/solprop/driver/simulation.py: NoiseSetting and the "default" keyword default on every Simulation.from_* constructor; _resolve_noise, called where each route draws; Simulation.noise_resolution, carried through with_input and derived runs; the planar route’s resolution; and SINGLE_PRECISION_NOISE, PLANAR_NOISE and INTERIOR_LAUNCH_NOISE.
- src/solprop/driver/interface.py: the same default on every prop_* interface.
- src/solprop/output/schema.py: NoiseResolution, and RunMetadata.noise_resolution at output schema 26, stored beside the hash.
- src/solprop/driver/summary.py: the noise row marks a default model and gives a fallback’s reason.
- src/solprop/backends/driver.py: the input draw is added at the run’s launch position rather than at z = 0.
- Tests: tests/driver/test_noise_default.py.
- Manual: docs/guide/media/noise.md, interior-launch.md, coupling.md, luna.md.
- Tutorials and worked examples now pass a fixed seed or noise=None.
Deviations from the proposal:
- The general guide’s diagonal metric is not a fallback route. Nothing builds such a metric, and its translation-time refusal stands.
- A seed beside noise=None is now refused on every route, as the spatial routes already did.
Decisions:
- The resolution is a dataclass, not a free mapping.
- It stays out of the configuration hash, because the resolved model is already in the hashed noise record.
- The direct Simulation(...) constructor, which takes a realisation rather than a model, keeps None as its default.
Verification:
- The full default lane on an AMD EPYC 7763 cluster node (64 workers): 14851 passed. The one failure is a numba licence cache-key test that passes on an Apple M5 Max laptop and fails only in that environment.
- The source doctests pass.
- The test suite keeps its noiseless references explicit: about 380 driver calls in tests/ now say noise=None.
Limitations: the native backend is unchanged here (input noise enters through the shared set_initial), and it was not built for these runs.

Phase 3 report — input noise on more routes, and the floor#

Scope: phase 3, 2026-10-27, Opus 5.5 (AI) for John Travers; merged into the implementation branch.
Delivered:
- Input noise beside the coherent wall, the taper coupling, the split block and the moving solid guide. The refusals in translate/problem.py and the shared backend admission list now name only the modified model.
- Input noise beside the TDSE response (translate/tdse_source.py, the seam check and the driver).
- An explicit input draw at an interior launch (phase 2’s set_initial rule).
- noise_floor on processing.get_spectral_density and the plotting helpers.
- Tests: tests/driver/test_coupled_input_noise.py, tests/driver/test_tdse_input_noise.py and tests/processing/test_noise_floor.py.
Q1, answered: every coupled route’s entrance basis is orthonormal in true power:
- the capillary HE₁ₘ (and TE/TM) sets, by Bessel orthogonality and per-mode power normalisation;
- the split block’s dense metric, a declared unitary rotation of a Poynting-normalised reference, which keeps the total per bin;
- the moving guide’s identity metric, whose Gram departure is gated along the path.
No route needed a named refusal.
Deviations:
- The unpropagated-floor identity keeps its interference term \(2\,\mathrm{Re}(\psi^*N)\), which for one draw is as large as the seed.
- get_spectrum refuses "subtract", since no amplitude has the signed density as its modulus squared.
Verification:
- At the entrance, one photon per channel and bin to 3e-13 on all four coupled routes.
- The exit-energy identity to between 1.1e-6 and 5.8e-5 of the seed’s exit energy (the Kerr cross-phase on the seed).
- numba_cpu matches numpy_ref to 3e-15.
- TDSE: the drive equals the pulse plus the draw to 2e-16, and the draw alone is 3.5e-11 of the intensity at which the weak-field response is certified.
- The floor-subtracted density equals the modified readout to 1.2e-15.
Limitations:
- A full TDSE weak-field run through the real atomic engine was not made: it needs the pinned Pyroraptor.
- The native backend admits input noise beside a coupled flow by the shared list but was not run.
- The coupled routes’ modal identity records still write no noise reference basis.

Closing#

Scope: 2026-10-27, Opus 5.5 (AI) for John Travers, one branch and one pull request (LupoLab/solprop#30).

The defaults as built (the defaults table):

Interface	Integrator	`rtol`	`atol`	Shot noise
`prop_gnlse`	`RungeKutta()`	1e-7	1e-14 √W	`"input"`
`prop_capillary`	`Multistep()`	1e-6	1e-10 √W	`"input"`; none with the TDSE response
`prop_waveguide`	`RungeKutta()`	1e-5	1e-10 √W	`"input"`
`prop_radial`	`Multistep()`	1e-5	0	`"input"`
`prop_free`	`RungeKutta()`	1e-4	0	none
`prop_planar`	`Multistep()`	1e-5	0	none (not carried)

Noise: the input model by default, with a recorded and printed fallback (single precision, the planar grid, an interior launch under the default, the TDSE response and Cartesian or line runs). Input noise is admitted beside coupled flows and the TDSE response, with the draw’s basis recorded on the coupled routes; the modified model keeps its refusals there. noise_floor="subtract" gives the floor-subtracted spectrum.
Verification: the default and slow lanes on the cluster node, the native suite, the pull request’s continuous integration, and the worked examples run under the final capillary default.
Follow-ups on the roadmap: a full-length TDSE weak-field run against a pinned Pyroraptor release; the native backend beside a coupled flow with input noise; the modified model’s future, decided with SEP 7.

Part III — History#

2026-10-26: Drafted, with the preliminary measurements of §3.4.
2026-10-26: Revised after the author’s comments. §4 now rests on the modified model’s origin and its exact equivalence to the input model without a reservoir, with a quantum reference for spontaneous modulational instability. The tolerance targets follow production practice. Q1 and Q8 are new, and the factor of two in parametric seeding is recorded as deferred physics.
2026-10-26: Human review by John Travers and AI review by GPT-6, recorded below.
2026-10-26: Revised after the review and the maintainer’s decisions D1–D5. The default is now input, with the modified model kept as an option. The refusal lifts cover input noise only, the fallback contract is complete, and the integrator rule and tolerance protocol are fixed. The response to every finding is at the end of Part III.
2026-10-26: Added the floor-subtracted spectrum (§5.5, D6).
2026-10-26: Recorded that the modified model is kept, with no new work, until SEP 7 settles whether gain media need its injection path (D7).
2026-10-26: Accepted by John Travers, with the 10 % tie margin of §5.2. Part I is frozen from this revision.
2026-10-27: The maintainer decided that a TDSE run carries no noise by default and warns when noise is asked for (D8): its runs are expensive, never repeated as noise ensembles, and mostly checked coherently. This is the one default that follows the physics switched on, by his decision.
2026-10-27: Phases 0 to 3 implemented on one branch (Part II). The integrator and tolerance tables are applied provisionally, pending the maintainer’s approval; the capillary’s integrator is held at Multistep() for his decision.

Human review — 2026-10-26#

John Travers confirmed that he has read the proposal and that his human review is complete. Recorded at his request; no acceptance decision or resolution of the AI findings below is inferred from that confirmation.

AI review — 2026-10-26#

Reviewer: GPT-6 (AI). Reviewed all of Part I at PR #30, revision 653ac95, against the current implementation, conventions, SEP 0 and the sources identified below. Recommendation: revise before acceptance. The motivation for measured defaults is sound, but the reservoir argument, observable definitions and qualification contract need correction or decisions. Reviewed records completed reviews, not acceptance. Part I and Part II are unchanged. All R1–R14 below remain open for the drafting agent’s response and the maintainer’s decision.

Findings and questions#

R1 — P1: The claimed reservoir distinction does not follow from the equations (§§2, 4.1, 10). The change of variables works for any deterministic nonlinear functional when the draw solves the full homogeneous linear equation. In particular, a delayed Raman response or nonlinear plasma absorption inside \(\hat N\) does not invalidate it. With unitary \(\hat D\), the two reconstructed fields remain identical even when that nonlinear response is dissipative. The Raman probe below confirms this in the existing implementation. Conversely, write \(\hat D=\hat D_u+\hat D_r\) and \(N'=\hat D_u N\). The reconstructed modified field \(\chi=\psi+N\) obeys \(\chi'=\hat D\chi+\hat N(\chi)-\hat D_rN\). The last term is a forcing correlated with the same initial draw, not newly sampled reservoir fluctuations. For pure loss with power coefficient \(\alpha\), its forcing covariance is proportional to \(\alpha^2\langle N(z)N(z')^*\rangle/4\), not to a delta function in \(z-z'\). Drummond–Corney [3], section VI.C (arXiv equations 75–77), specifies the latter for gain/loss and Raman noise. This does not preclude matching particular observables: the corrected readout in R3 gives the exact mean \(G-1\) for constant scalar gain from vacuum. It is not a general reservoir replacement. For example, follow that gain by a passive attenuator of power transmission \(\eta\), attenuating \(\psi\) while retaining the same unattenuated \(N\), with \(\langle|N|^2\rangle=1\). The corrected readout becomes \([1+\sqrt{\eta}(\sqrt G-1)]^2-1\), whereas the amplified spontaneous photons must become \(\eta(G-1)\). With \(G=4\) and \(\eta=1/4\), these are 1.25 and 0.75 photons. This is an analytic counterexample to the general claim, not a solprop amplifier simulation. Recommendation: state the actual algebraic condition for equivalence, distinguish physical reservoirs from their deterministic response, and describe the current modified model as an approximation with qualified scope. A constant restored floor alone cannot establish fluctuation–dissipation accuracy. What reservoir observables, beyond that floor, justify choosing this default?
R2 — P1: Separate the cited models from solprop’s variant (§§4.1, 8, 10). Chen–Wise [5], equations 2a–2c, keeps only terms first order in the noise and separates emission gain from net gain. Solprop evaluates the full nonlinear response of \(\psi+N\). Keeping the full response is mathematically justified for the exact change of variables in R1; this finding does not recommend replacing it with the paper’s truncated expansion. The differences include the nonlinear expansion and gain treatment, as well as phase transport and the draw distribution; the paper’s results cannot qualify this variant by attribution alone. Also, a truncated-Wigner treatment is not generally exact for nonlinear quantum propagation: [3], section VI, explicitly drops higher derivative terms at large photon number. Recommendation: enumerate these differences, identify which reference results actually apply, and limit the exact half-photon statement to the linearised Bogoliubov problem with the correct observable ordering. Keep a full reservoir model as separate physics work.
R3 — P1: Define the measured field before specifying spectra, coherence and conservation (§§4.1–4.2, 5.3, 7). The saved modified field is \(\psi\), whereas the identity concerns \(\chi=\psi+N\). The current processing.fields.get_spectrum reads the saved field through processing.axes._plane_field; it does not automatically add back the noise. Subtracting a noise amplitude also does not subtract a photon background from an intensity: the interference term remains. For a linearised sideband \(\chi_s=\mu N_s+\nu N_i^*\) and transported background \(uN_s\), with independent input phases and \(|u|=1\), the two predictions are

\[\langle|\chi_s|^2\rangle=(|\mu|^2+|\nu|^2)n_0,\qquad \langle|\psi_s|^2\rangle=(|\mu-u|^2+|\nu|^2)n_0.\]

Thus \(1+2|\nu|^2\) is the target for the reconstructed field, not the saved modified spectrum, when \(n_0=1\). At the entrance these are already \(n_0\) and zero. Chen–Wise v5, Appendix 2, equation A8 explicitly prescribes \(|\psi+N|^2-|N|^2\) for the constant-gain example. With \(\psi=(\sqrt G-1)N\), its ensemble mean is \(n_0(G-1)\), giving the correct spontaneous mean for \(n_0=1\) even at low gain. That estimator must be distinguished from both the raw saved spectrum and the classical MI target containing the seed; for vacuum MI, the symmetrically ordered half-photon calculation instead subtracts one half from the mean reconstructed intensity. Likewise, \(\int|\psi|^2dt\) need not be conserved in a lossless Kerr run; the probe below has a relative change of \(1.75\times10^{-7}\) while the full-field energy changes only at rounding level. Recommendation: name the field and its power/flux metric for every observable, specify any reconstruction API and its Fourier convention, and derive the appropriate conservation test. The quantum result \(|\nu|^2\), the classical one-photon result and any normally ordered estimator are distinct targets. For the MI reference, also supply its SI scaling, pump frame, undepleted-pump range and the finite \(K\to0\) limit; a lossy pump needs a separately derived reference.
R4 — P1: An exact continuous identity is not an adaptive rounding contract (§§3.4, 4.2, 7; Q1). numpy_ref.passes.error_norm scales by the propagated state, which is \(\chi\) for input noise and \(\psi\) for modified noise. Its denominators can differ, so acceptance, step sizes and Adams order/history can differ. Equal step counts in one example are evidence about that example, not a consequence of the identity. Further, a physically lossless fibre still has numerical absorption by default; the spectral collar is part of the linear exponent and is omitted from the draw’s transport. Recommendation: establish a rounding comparison with matched methods, prescribed steps and Adams histories/orders, constant metrics and disabled absorbers. Derive its budget from operations, transforms and conditioning, not step count alone. Test independent adaptive runs against a converged reference with an accuracy envelope, as SEP 25 requires. Add separate boundary tests rather than calling a default-collar run lossless. The small RK probe is not qualification of the other routes, Adams formulations or compiled backends.
R5 — P1: Phase-only transport does not preserve photons in a changing metric (§§3.3, 4.1, 6–7). Conventions §4 divides a modal draw by \(\sqrt{w(0)}\), with \(w=\operatorname{Re}n_\mathrm{eff}\), while observations multiply by \(\sqrt{w(z)}\). Transporting that internal draw only by phase therefore gives a restored energy per bin of \(\hbar\omega\,w(z)/w(0)\), not \(\hbar\omega\), even in a lossless guide. The real normalisation term \(-\tfrac12\log[w(z)/w(0)]\) is not physical absorption. A varying radial admittance has the corresponding issue. This case is not confined to the coupled-flow refusal. Recommendation: explicitly distinguish metric transport from dissipation, add varying-index/admittance cases to phase 0, and decide whether this SEP changes that transport or restricts its default/claims. A physical photon-floor assertion needs the local flux metric, not just an unchanged internal modulus.
R6 — P1: Specify a composable stochastic transport before lifting coupled-flow refusals (§6, phase 5). The unitary polar factor of a nonunitary propagator generally does not compose: \(U(F_2F_1)\ne U(F_2)U(F_1)\). A rule that takes a polar factor per numerical step can therefore change the noise when the step schedule, a save plane or a restart changes. For example, the passive contractions \(F_1=\operatorname{diag}(1,1/2)\) and \(F_2=\left(\begin{smallmatrix}3/4&1/4\\1/4&3/4\end{smallmatrix}\right)\) each have unitary polar factor \(I\), but the factor of \(F_2F_1\) differs from \(I\) by 0.1564 in Frobenius norm (a direct two-by-two numerical check). Preserving a total noise norm does not establish the correct correlations or the covariance in a nonorthogonal power metric. Recommendation: derive the transport in a declared physical basis, specify its dependence on the continuous path and any reservoir approximation, and test composition, subdivision, basis changes and restart covariance. Retain the refusal until that derivation exists; if reservoir increments are needed, acknowledge the new physics rather than treating this as merely missing plumbing.
R7 — P1: A coupled or interior launch must preserve the noise decomposition (§6, phase 3; Q6). Restoring \(N\) into a source plane and then drawing a new modified seed at the receiving launch adds a second background to the next nonlinear evaluation. Restarting the shifted field with a new independent seed instead loses the existing correlations. Merely saying that the draw starts at \(z>0\) does not define a continuation. Simulation.with_input(Launch) currently clears implicit noise specifically to avoid a second floor. Recommendation: define whether a plane carries the full field, the shifted field plus its draw, or an explicitly converted representation; preserve the same draw and its phase origin through identity coupling and continuation. Test a split run at multiple positions against the unsplit run, plus lossy coupling and regridding under the chosen model. Audit the saved-output and seam changes this requires: §6 cannot yet promise an unchanged SCHEMA_VERSION, or an output change limited to a fallback note.
R8 — P2: The fallback contract is incomplete and can silently change the experiment (§§5.1, 5.4, 6; Q2). Changing only precision, interpolation or the response can turn default noise off; changing a backend must not do so. A metadata note is not visible in a run with progress disabled, and the start summary this depends on is expressly outside the SEP. With an explicitly supplied seed but omitted noise, a fallback must not silently discard the user’s seeding intent. Field-plane extraction happens after propagation, so the source cannot resolve a different default based on an unknown future use. Recommendation: prefer an actionable refusal requiring explicit noise=None on unsupported configurations; no published compatibility constraint is cited here. If fallback is chosen, specify requested and resolved model, reason, seed handling and durable metadata, and make its user notification a delivery prerequisite. Test omission, explicit None, explicit models and supplied seeds at each entry point; never catch a backend construction error and reinterpret it as unsupported noise.
R9 — P1: Fix a convergence protocol before selecting defaults (§§5.3, 7, phases 0–1; Q3–Q4). Naming the Dudley–Genty–Coen review [1] does not select a unique simulation: the exact parameters, figure/case, grid, length, responses, spectral region and observable are needed. A relative tolerance on coherence is ill-defined near zero, and relative spectral error is ill-defined in empty bins. Comparing independent seed ensembles can hide integration bias inside sampling error; a one-standard-error pass threshold would also fail frequently by chance. Recommendation: declare paired seed sets, a refined deterministic reference for each seed, three refinement levels, held-out ensemble members, signal floors, absolute coherence and suitable spectral error measures, and an explicit confidence rule. Choose observable-specific accuracy budgets before the measurement, with the same protocol across interfaces, and separate integration, grid, model and Monte Carlo errors. Validate reused schedules across seeds, not only the seed that discovered them. Use bounded windows/stored witnesses for tests and timings; put any necessary full supercontinuum study in a permitted gallery workflow.
R10 — P2: The norm ratio is a heuristic, not a step-cost criterion (§§3.4, 4.3, 5.4, 6; Q5). Pure linear propagation can be integrated exponentially without additional source error at any \(r/\mathrm{rtol}\). Conversely, an initially tiny perturbation can grow into a resolved instability. The controller uses its chosen band and the internal state norm, not generally a whole-band physical-energy norm; spatial measures, varying indices, mode and polarisation counts matter. The quoted capillary estimate \(10^{-4}\) also exceeds its quoted \(10^{-6}\) tolerance despite the reported small step-count change. Recommendation: label \(r\) as an initial size diagnostic with stated assumptions, and measure the actual controller norm if it is printed. Do not trigger a warning or infer zero cost from this ratio alone. Supply the revision, backend, seeds, grids, measured windows, norm definitions, wall-time samples and uncertainty behind §3.4 before using it to choose a default. Accepted steps alone do not establish runtime, especially once the modified-noise statistics path disables the Numba stash.
R11 — P1: Planar noise requires a transverse normalisation decision (§§3.3, 6, phase 4). An energy per unit width is in J/m, while a photon’s energy is in J. A slab metric alone cannot turn one into the other. The existing LineGrid manual explicitly chooses one photon per column and bin per metre of y; that is a declared convention, not a width-independent quantum vacuum prescription. Recommendation: decide whether planar noise adopts that same convention or introduces a finite quantisation/effective width, derive its amplitude and units, and document what changing that width does to fluctuations. Test a matching line or finite-width reference with the same measure. Keep the refusal until that choice is made; do not classify the missing physical measure as purely mechanical.
R12 — P2: TDSE/PPT agreement is not an independent noise qualification (§6, phase 6). The two responses can have different spectra, memory and ionisation, so “within the response difference” supplies no defined bound. Noise also broadens the atomic drive and may probe frequencies beyond the response’s qualified window. Recommendation: name the TDSE limits and observables that are checked independently (zero drive, weak-field response and a deterministic perturbed-drive reference), specify bandwidth and convergence budgets, and retain the common supplied realisation through the atomic source. Treat PPT as a comparison in a stated shared regime, with a quantified model discrepancy, rather than the acceptance oracle. If that cannot be specified now, defer this lift.
R13 — P2: Resolve the API and acceptance boundary before implementation (§§5.2–5.3, 6, 11). prop_radial, prop_free and prop_planar take a caller’s SimulationSettings, whose controller is currently required; defaulting the tolerances needs a public signature/precedence design. The scope includes planar and general modal constructors, but the proposed tolerance list does not cover them explicitly. Phase 0 says to revise before review, while the concrete integrator/tolerance table is postponed to phase 1 after acceptance would freeze Part I. Phase 3’s “independently mergeable” also needs reconciliation with SEP 0’s single implementation PR. Recommendation: complete phase 0, record the default matrix and the rules for omitted settings versus explicit controllers, and request a response review before acceptance. Alternatively freeze a fully specified selection rule with approval gates. Keep all implementation phases on the one branch/PR, or explicitly split the later physics proposals and retain their roadmap work. Reassess schema impacts after R5–R7 and R11 have decisions.
R14 — P2: A Gaussian draw is a separate model choice, not just a seed migration (§§4.1, 9; Q8). Fixed modulus and circular Gaussian draws share second moments but have different fourth moments: for mean occupation \(n_0\), \(\langle|N|^4\rangle=n_0^2\) and \(2n_0^2\), respectively. That changes nonlinear statistics as well as individual realisations. The relevant basis matters: for \(c=\sum_k u_kN_k\), independent equal-occupation phase draws and \(\sum_k|u_k|^2=1\) give \(\langle|c|^4\rangle=n_0^2(2-\sum_k|u_k|^4)\). A single amplified temporal mode can combine many spectral bins and approach Gaussian statistics; it is not necessarily a single fixed-modulus draw. Determine the projections onto the actual gain modes before inferring an error in pulse-energy tails from the spectral-bin fourth moment. Changing the draw also changes the existing exact-per-bin photon test and the declared-basis sampling contract. Recommendation: retain the current distribution for a defaults-only change, with its limitations stated, or explicitly extend the scope and qualify both the distribution and the observables. In the latter case record the distribution and its version, preserve old-file/restart interpretation, and test moments, tails, transformed covariance and sampling uncertainty. A seed alone must not be claimed to guarantee bitwise reproducibility across backends or adaptive histories (SEP 25).

Recommendations on the existing open questions#

These are reviewer recommendations, not maintainer resolutions.

Question	Context and recommendation
Q1 — identity	Make the corrected identity a phase-0 prerequisite. The short RK probe passes, including Raman; all routes, grids, Adams formulations and backends still need the R4 qualification.
Q2 — refusal or fallback	Prefer refusal requiring explicit `noise=None`; otherwise require the complete, visible resolution contract in R8.
Q3 — integrators	Treat RK for GNLSE and Multistep for modal/spatial routes as candidates only. Choose the table from matched-accuracy runtime evidence and define settings precedence (R9–R10, R13).
Q4 — accuracy targets	Use observable-specific budgets with one common convergence/confidence protocol. Fix the budgets, floors and case definitions before selecting tolerances (R9).
Q5 — norm warning	Print an optional size diagnostic; do not warn solely because \(r>\mathrm{rtol}\) (R10).
Q6 — coupled source	Do not change a source’s default based on future extraction. Preserve the refusal until the decomposition is transported; an interim input-noise source must be explicit (R7–R8).
Q7 — reservoir physics	Yes: a later proposal should derive the half-photon/Gaussian and reservoir terms, their ordering corrections and qualified regime. Do not call the current default a substitute for it (R1–R2).
Q8 — Gaussian amplitude	Defer for this defaults change unless the maintainer explicitly wants the broader stochastic-model change and its qualification in scope (R14).

Further decisions raised by this review are the observable/reconstruction contract (R3), the treatment of changing power metrics and coupled transport (R5–R7), the physical transverse width of planar noise (R11), and the scope of TDSE qualification (R12). Their recommendations are recorded beside each finding.

Follow-up checks — 2026-10-26#

Further derivation and source checks refine R1–R3 and R14 without changing the recommendation to revise before acceptance. The full nonlinear response preserves the stated change of variables; the published corrected estimator recovers the constant-gain mean but fails the gain-then-loss counterexample under persistent-seed transport; and Gaussianity must be assessed in the measured mode. These are review clarifications, not resolutions of the proposal’s open questions.

Evidence and limits of this review#

Inspected the driver defaults, noise drawing and phase transport, nonlinear stage injection, error-norm scaling, output/processing accessors, launch handling, refusal checks, the conventions and SEP process. No implementation was changed.
Ran four short NumPy-reference GNLSE simulations: input and modified noise, each with Raman off and on, using RK, ten uniform steps over \(10^{-3}\) m, 128 temporal samples, seed 37, \(\gamma=0.1\) W\(^{-1}\)m\(^{-1}\), \(\beta_2=-2\times10^{-26}\) s²/m, 800 nm carrier, 600–1200 nm limits, a 200 fs requested window, 30 fs Gaussian pulse, \(10^{-14}\) J energy, shock off and both absorber rates zero. The relative field defect \(\|\chi-(\psi+N)\|/\|\chi\|\) over saved planes was \(1.19\times10^{-16}\) without Raman and \(1.35\times10^{-16}\) with it. Full-field energy drift was at most \(6.7\times10^{-16}\); shifted-field drift was \(1.75\times10^{-7}\) and \(1.54\times10^{-7}\) respectively. These are counterexample probes, not a tolerance calibration, benchmark or cross-backend qualification.
Checked the relevant equations in Chen–Wise, arXiv:2410.20567v2, v5, including Appendix 2’s readout, and Drummond–Corney, arXiv:quant-ph/9912095v2, and the linearised MI discussion in Brainis–Amans–Massar, arXiv:quant-ph/0412096. The remaining cited papers were not independently checked in full. The draft’s performance tables, production-practice tolerances, full supercontinuum ensembles, all-route identity and proposed refusal lifts were not reproduced or qualified.
Independently derived the scalar gain/attenuation example in R1 and checked its arithmetic. Derived R14’s projected fourth moment by pairing the independent phases; an exact finite phase quadrature reproduces \(1\), \(3/2\) and \(7/4\) for one, two and four equally weighted bins with \(n_0=1\). These are analytic checks, not qualification of a particular transient Raman mode or its output statistics.

Maintainer decisions — 2026-10-26#

John Travers, on the review. His guidance: no research project; the least bad noise model solprop knows how to implement; input has been used for years, so it, or anything provably better and not worse elsewhere, is an improvement.

D1 (R1–R3, R14; old Q1, Q7, Q8). The default is noise="input". The modified model is not provably better, so it stays an option, with its limits documented. Its readout, its transport along a varying guide, its coupled-flow transport, a half-photon vacuum and a Gaussian draw are all outside this SEP.
D2 (R8; old Q2, Q6). Where noise cannot be carried, a run that omits noise falls back to none, recorded and printed. The maintainer also asked why the TDSE should refuse input noise at all, since it is only part of the input field. It need not: that refusal is a scope choice of SEP 12 (D5).
D3 (R9; old Q4). The lean convergence protocol of §5.3: paired seeds, a tight reference for each seed, three levels, 0.5 dB on the mean spectrum above −40 dB, 0.02 absolute on \(|g_{12}|\), and the canonical cases named there. The maintainer approves the resulting table in the phase 0 report.
D4 (R11). Planar noise stays refused. The default falls back on the planar grid, and the roadmap item stays open.
D5 (R12). Input noise is admitted beside the TDSE response. The refusal was a qualification-scope choice: the atom is driven only inside its gated, edge-free window (SEP 26), and the seed’s band is the grid’s, which the propagated pulse fills anyway. The checks are those of §6.
D6. The maintainer asked for a floor-subtracted spectrum, which keeps the one benefit of the modified model’s readout that costs nothing (§5.5).
D8 (2026-10-27). A TDSE run takes no noise by default and warns when noise is asked for (TDSE_NOISE). TDSE runs are expensive, never repeated as noise ensembles, and mostly checked coherently, so noise there is the exception.
D9 (2026-10-27). The GNLSE and waveguide defaults (RK, 1e-7 and 1e-5), the radial and planar defaults (Multistep, 1e-5) and the TDSE, record and merge items are approved. A Cartesian or line run (prop_free) takes adaptive RungeKutta() by default, since the Adams history’s memory rules the multistep method out there, and no noise by default (FREE_NOISE), since such runs are slow and rarely about noise sensitivity. Its tolerance is set by a measurement on the suite’s free-space cases: FREE_RTOL = 1e-4, FREE_ATOL = 0. The suite’s 5.5 µm window cannot set a tolerance, so kerr_beam_192 was run to 1 and 3 mm (near self-focusing at 3 mm), kerr_beam_384 to 1 mm and line to its full length. The spectral budget never binds (worst 0.0017 dB at 1e-3, 3 mm), so the rule’s literal answer is 1e-3; 1e-4 is taken for a 2.5 times smaller field error (L2 6.6e-4 against 1.7e-3) at 18 % more steps. Against the suite’s 0.5 µm RK4IP schedule the adaptive march is 26 to 53 times faster; against a fixed step matched to its error it is about 1.6 times slower and takes about twice the memory. atol changed nothing. The documentation carries one table of every interface’s defaults.
D10 (2026-10-27). The capillary steps by its representation: RungeKutta() at 1e-5 (SINGLE_MODE_RTOL) for one resolved mode or a mode-averaged one, Multistep() at 1e-6 (CAPILLARY_RTOL) for two or more resolved modes or the TDSE response. The RDW measurement showed why. Going from one resolved mode to four, the Runge–Kutta march’s steps grow 3.7 times (484 to 1778) and the Adams method’s 1.2 times (1469 to 1802): the source beats at the modes’ phase mismatches, which the interaction-picture march resolves within its steps and the exponential Adams method carries in its propagator. The noisy comb-to-continuum case, the only one that matters there, is 1.3 to 1.6 times slower with the Adams method; that is the accepted cost. Replaced by D11 the same day.
D11 (2026-10-27). The capillary takes one default, Multistep() at 1e-6 (CAPILLARY_RTOL), for every representation, and D10’s rule is withdrawn. Re-running the worked examples under D10 showed that it did not carry beyond the one-mode RDW comparison it came from. On the cluster node, with the native backend, the Adams method at 1e-6 was faster than the Runge–Kutta march at 1e-5 on the Kerr-only single-mode examples (self-phase modulation 20.5 s against 32.1 s, soliton compression 15.2 against 20.8, four-wave mixing 10.8 against 13.4, cross-phase modulation 9.6 against 13.2) and on the dispersive Kerr four-wave-mixing scan (1202 s against 4327 s). The Runge–Kutta march won only on the long Raman (584 s against 160 s) and ionisation (44.5 against 21.3) examples. Re-measured warm on self-phase modulation against a tight reference, the Adams method at 1e-6 took 2.8 s for a field error of 4.2e-5, and the Runge–Kutta march at 1e-5 4.9 s for 2.6e-4. The guide names RungeKutta() as the faster choice for long Raman and plasma runs, and says that the dispersive Kerr policies cost more per step.
D7. The modified model is kept as it is, with no new work. Whether to keep or remove it is decided when SEP 7 settles whether gain media need its separate noise-injection path: amplified spontaneous emission needs the noise to see only the emission gain, as in Chen and Wise’s split, or a gain Langevin term (§2, §10).

Response to review — 2026-10-26#

Drafting agent: Opus 5.5. Part I is revised throughout.

R1 — accepted. The reservoir claim was wrong. §4.2 now states the condition exactly: the two models agree when the draw is transported by the full homogeneous linear operator, whatever the nonlinear response is. They differ by \(-\hat D_r N\) where the linear operator is non-unitary. That forcing is correlated with the original draw, not reservoir noise, and the review’s gain-then-loss counterexample is quoted. This finding, with D1, is why the default is now input.
R2 — accepted. §4.2 lists how solprop’s variant differs from the published model. §4.1 limits the half-photon statement to the parametric (linearised) case, and the reservoir model is left as separate work.
R3 — accepted, and largely dissolved by D1. The input model saves the full field, so every existing observable keeps its meaning. §4.2 records that the modified model’s saved field excludes the seed and that processing does not restore it. Reconstruction and the Bogoliubov comparison are no longer part of this SEP.
R4 — accepted. The exact identity is no longer a qualification contract. §3.4’s step counts are labelled as evidence about their cases, and the modified model is unchanged by this SEP.
R5 — accepted. The restored energy \(\hbar\omega\,w(z)/w(0)\) along a varying guide is documented in §4.2 as a limit of the modified model. The input draw is part of the state, so the full operator, including the normalisation term, carries it.
R6 — accepted. The modified model keeps its coupled-flow refusal. Under the input model there is no transport question: the draw is part of the entrance state, and the flow propagates it like any field. §6 lifts the refusal for input only, behind an entrance-basis check (Q1).
R7 — accepted. §5.1 defines the launches. A coupled launch keeps today’s behaviour, with no second draw. An interior launch under the default takes its spectrum as given, and an explicit input adds one draw. The schema change is now stated (§6, §9).
R8 — fallback kept (D2), with the full contract. The list of fallback routes is closed; backends never change the resolution; requested and resolved models and the reason are stored; the summary prints them and is a prerequisite of phase 2; and seed= without noise= is refused on fallback routes. The four-case test matrix is in §7.
R9 — accepted, in the lean form of D3. §5.3 names the cases, the paired seeds, the reference, the levels, the signal floor and absolute coherence. Witnesses and short windows are used for tests. Monte Carlo error is controlled by the pairing rather than a separate confidence rule, a simplification taken on purpose.
R10 — accepted. \(r\) is labelled a size diagnostic (§4.3), with no warning. §3.4 now gives its provenance: the commit, backend, seed, grids and single wall samples.
R11 — accepted; planar stays refused (D4).
R12 — accepted in part (D5). PPT is no longer an oracle. The TDSE check is now the weak-field response to the draw alone, plus drive equality and the band condition (§6).
R13 — accepted. §5.2 freezes a selection rule, with a tie margin of 10 % (a drafting choice for the maintainer’s approval) and an approval gate in the phase 0 report. §5.3 adds the settings default and its precedence. §11 puts every phase on one branch and one implementation pull request.
R14 — accepted. The draw’s distribution is unchanged (D1), and its limit is stated in §4.1.
Reviewer’s recommendations on Q1–Q8. Followed for Q1 (no qualification contract), Q3 (candidates only, chosen by rule), Q4 (one protocol), Q5 (diagnostic only), Q6 (no default changed by future extraction), Q7 (a later proposal) and Q8 (deferred). Not followed for Q2, by D2.