Compute the neutron sector keystone: the two region gate in OpenMC at k < 1

[MaxFreedomPollard]

Closes #10.

What this adds

A new directory, neutron/, that computes the theory's neutron sector keystone instead of citing it: a two region subcritical gate in OpenMC 0.16 with the official ENDF/B-VIII.0 library, strictly at k below one, every number with its Monte Carlo uncertainty. The same code and data are first shown to reproduce three ICSBEP handbook criticals (Godiva, SHEBA-II, STACY) within their stated uncertainties, so the calculation is calibrated before it is pointed at the gate.

The unit is the reference transistor's third scale made concrete: two 72 litre tanks of 4.9 percent enriched uranyl fluoride solution (the LEU-SOL-THERM-002 benchmark composition), each at k ≈ 0.901 alone, 3 cm of water apart in a water bath, with a 1 mm cadmium sheet or a 2 cm boron carbide blade as the GATE, a Cf-252 point source in tank A as the SOURCE, and the fission rate in tank B as the DRAIN.

What it measures

• gain M = 1/(1 - k) of a tank alone (10.1) and of the pair (11.5); the transfer curve of the cadmium sheet in quarters and of the blade, with the Shannon entropy of the fission source on the record
• the fission matrix K_ij from the converged fission bank, one generation at a time, whose dominant eigenvalue (0.9140) reproduces the transport k of the pair (0.9132), plus an unsplit bank control: the "Green's function with gain on the diagonal" reading of coupled region kinetics is exact to within statistics
• the drain per driver neutron with multiplication on: 1.49 fission neutrons born in tank B per driver neutron entering tank A with the gate open, 0.92 through the cadmium sheet, 0.67 through the blade; the coincidence table and the superposition check; the point model (I - K)^-1 c against the full transport, with the gap explained by source importance
• the neutron budget of a fission neutron born in tank A (the fan out tax of theory Section 1.3 as a table)
• level restoration: the emission spectrum of tank B under three drives (moderated leakage from A, Cf-252 at the axis, 14.1 MeV at the axis) agrees to a total variation distance of 0.002
• the generation time (106 µs), the switching time Λ/(1 - k) (1.22 ms), the gain bandwidth product 1/Λ (9.4 kHz), and the prompt step response of the pair
• the temperature coefficient of the pair (-25 pcm/K, Doppler and scattering separated from expansion of the liquid): the only signal controlled inhibition the neutron sector has, priced

What it changes in the theory

Two clauses of theory Section 4 are corrected in place and the correction is carried into the README and the transistor note: an absorber between the regions programs a weight, not a threshold (the medium is linear; its AND is a perceptron AND with the comparator at the boundary), and "adding a veto absorber yields NAND" holds only if something other than a neutron signal moves the absorber, because every coupling in the neutron sector is excitatory and heat, the one inhibitory channel, is worth a fraction of the gain. The keystone search of Section 2 inherits inversion as a requirement.

Files

• neutron/gate.py, neutron/benchmarks.py, neutron/report.py, neutron/data.py: the model, the calibration, the report, the data fetcher
• neutron/tallies.json, neutron/benchmarks.json: the committed run (full budget, 106 minutes of wall clock on a laptop)
• neutron/results.md, neutron/README.md, figures/fig15_neutron_gate.{svg,png}
• README.md, theory/THEORY.md, transistor/README.md: the neutron sector paragraphs updated to point at the computed numbers, Phase B2 marked done, a new deliverables row, open problem 1 sharpened

Not in this PR: the CI wiring

Two workflow files belong with this work and are not here, because the
GitHub token available to me carries repo but not workflow scope and the
push was refused. They are ready to drop in:

• a one line addition to .github/workflows/build.yml, running python neutron/report.py so the existing job rebuilds neutron/results.md and figure 15 from the committed tallies (numpy and matplotlib only, no OpenMC, no data download);
• a new .github/workflows/neutron.yml that installs OpenMC 0.16 from conda-forge, caches and streams the official data archive once, and regenerates the tallies at a reduced budget on any change to neutron/, publishing them as an artifact.

Granting the scope once with gh auth refresh -s workflow is enough to add both.

Provenance

OpenMC 0.16.0 (conda-forge, Intel build under Rosetta on an Apple Silicon Mac); ENDF/B-VIII.0 official OpenMC HDF5 distribution (openmc.org), 53 files streamed from the 3.4 GB archive; benchmark geometries and atom densities from the MIT CRPG benchmark collection (MIT licence), verified against it to machine precision; handbook eigenvalues from JEFF Report 21, Appendix 2; Cf-252 Watt parameters from Fröhner's 1990 fit.

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