Search ENSDF for the photon keystone: level restoring pairs and the veto gateway

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 neutron/data/
 neutron/work/
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README.md

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 - *Status: the simulation half is settled, affirmatively.* The digital twin in [simulator/](simulator/) samples its exact Boltzmann law at 26 decays per independent sample and beats the silicon benchmark on energy iff the carrier is the 8.4 eV transition. What remains of Phase A is hardware: the same measurement on a bench, with exempt quantity sources, detectors at the boundary only.
 
 **Phase B. Settle the keystone.** Now two questions, one per sector.
-- **B1, photon sector.** Measure (σ_trig, β, C_in) for the best NEEC or IGE candidate (precision EBIT or Penning trap NEEC; resonant IGE of a mid energy isomer) and locate it on the keystone figure. The required cross sections per facility are tabulated in [gates/experiment_menu.md](gates/experiment_menu.md); the ongoing nondestructive Penning trap test of the ⁹³ᵐMo claim largely decides this sector.
+- **B1, photon sector.** Measure (σ_trig, β, C_in) for the best NEEC or IGE candidate (precision EBIT or Penning trap NEEC; resonant IGE of a mid energy isomer) and locate it on the keystone figure. The required cross sections per facility are tabulated in [gates/experiment_menu.md](gates/experiment_menu.md); the ongoing nondestructive Penning trap test of the ⁹³ᵐMo claim largely decides this sector. *The computational half is done, in [photon/](photon/):* the chart holds 34 releasing gateways of the NEEC class, listed and ranked, and no level restoring candidate that survives the areal density wall, so B1 is an experiment on that list and not a search for a better list.
 - **B2, neutron sector.** *Status: done, in [neutron/](neutron/).* Existence was already answered by library data; the architecture is now computed. The two region subcritical gate runs in OpenMC with the official ENDF/B-VIII.0 library, calibrated first against three handbook criticals, and yields the coupling matrix (0.9140 against a transport k of 0.9132), the absorber's transfer curve, the drain per driver neutron (1.49 with the gate open), the level restoring emission spectrum, the clock (Λ = 106 µs, 1/Λ = 9.4 kHz) and the temperature coefficient (-25 pcm/K). All of it is inherited by the photon sector, including the two findings that were not sought: an absorber programs a weight rather than a threshold, and the sector has no signal controlled inversion worth the name.
 - *Kill criterion B (the big one, now confined to B1):* if no compact state can be shown to satisfy the leak condition, Γ>1, *and* level restoration at any achievable flux, then nuclear computing at benchtop scale is permanently confined to the stochastic tier plus memory, a real but bounded result, and the amplifier tier remains a reactor scale curiosity. The theory's *high* ambition lives or dies here.
 
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 | [transport/](transport/) | Monte Carlo demonstrations of every routine gate (exact coincidence multiplier, absorption complement, measured Green's matrix, saturable sigmoid, Bernstein universality), the degree checker, and the compiler: the adjoint assembler that turns a target weight matrix into a material layout, three ways |
 | [simulator/](simulator/) | the digital twin: a Tier 1 machine run decay by decay, validated against exact enumeration, with decays per sample and energy per sample measured |
 | [neutron/](neutron/) | the keystone at reactor scale, computed: the two region subcritical gate in OpenMC with the official ENDF/B-VIII.0 library, calibrated against three ICSBEP handbook criticals; gain, the fission matrix and its eigenvalue check, transfer curves under two absorbers, the truth tables, the superposition check, level restoration spectra, the clock and gain bandwidth product, and the temperature coefficient that prices the veto |
+| [photon/](photon/) | the photon keystone searched for in ENSDF: every gateway of every isomer that holds a bit for a second, in observed and allowed classes, with its release cascade; every level restoring coincidence within rotor reach and the areal density wall each one meets; every isomer with a signal gateway and a veto gateway; the NEEC class ranked |
 | [transistor/](transistor/) | the reference transistor: one pinout at three scales, the valve, the datasheet with characteristic curves and maximum ratings; with four accompanying notes: [SEALED.md](transistor/SEALED.md) (the machine), [EMBODIMENT.md](transistor/EMBODIMENT.md) (the build, at assembly grade), [VALVE.md](transistor/VALVE.md) (the logic), [COMPONENTS.md](transistor/COMPONENTS.md) (the full inventory of a working computer, missing pieces simulated), [POWER.md](transistor/POWER.md) (the metabolism), and [SCALING.md](transistor/SCALING.md) (the trajectory) |
 
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+## The photon keystone, searched
+
+The neutron gate handed the photon sector a list: gain, level restoration, and a signal controlled inhibition. Section 2 of the theory supplement had already reduced level restoration to a search of ENSDF for pairs of isomers whose cascade lines and gateway lines are mutually resonant, and Open Problem 1 had put that search first. [photon/](photon/) runs it, and the inhibition search beside it, over the adopted level schemes of every nuclide carrying an isomer that holds a bit for at least a second: 415 isomers, every gateway above each of them in two classes (observed, where ENSDF lists the line, and allowed, where spin and parity permit an E1, M1 or E2 and the line is unobserved, the class the 4.85 keV gateway of ⁹³ᵐMo belongs to), and every release cascade followed through the adopted gammas.
+
+- **Level restoration exists as candidates the data cannot yet resolve.** With both recoils, both thermal Doppler widths, and a 1 km/s rotor allowed to close the remainder, the way Moon closed recoil in 1951, 12470 release lines are compatible with a gateway absorption within the quoted uncertainties of the three energies involved, 12402 of them between different nuclides and 3775 closed loops. But a rotor closes a few electronvolts and ENSDF quotes most energies to tens or hundreds, so the data can call only 0 of them resonant within reach: the median candidate is 475 times too coarsely known to decide. The first thing the search asks of an experiment is three energies to an electronvolt, not a cross section.
+- **Every candidate meets the areal density wall regardless.** Among candidates whose gateway width ENSDF actually measures, the least demanding (¹²⁷Ba feeding ⁵²Mn) asks for 1×10²⁴ inverted nuclei per cm², a solid 23 cm thick made entirely of the isomer. This is Section 1.1's wall with the chart's own best case in it: a Doppler broadened MeV resonance is barns wide, and no macroscopic quantity of any long lived isomer above 100 keV has ever existed. The convertible class is real as a set of energies and empty as a set of gates, whether or not any of its members turns out to be resonant.
+- **Inhibition is native to isomers.** 214 isomers offer a signal gateway and a veto gateway, two releasing paths whose cascades differ in whether they emit the signal line, so that a control opening the second empties the register without producing the signal. The operation the neutron sector could not perform, the photon sector performs by construction, at the same cross section price as its gain.
+- **Everything now rests on the NEEC class.** 34 releasing gateways sit within 30 keV of their isomer. Their triggers are electron capture resonances, not photon ones, and whether those are strong enough is the contested ⁹³ᵐMo question the roadmap already waits on. The census does not decide it. It writes down every state the answer will apply to.
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+![The photon keystone, searched](figures/fig16_photon_keystone.svg)
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+Two lines of the theory change as a result. The convertible class of Section 2 is no longer a conjecture but a table, and its entries fail Section 1.1 by orders of magnitude, so the photon sector amplifier cannot be found in the chart and must be engineered, which is what Phase B1's experiments have been for all along. And the inhibition that the neutron result added to the keystone's requirements is available in the photon sector without new physics, so it no longer belongs on the list of things the keystone must be discovered to have; it is a property of any isomer with two gateways, and the search that must still succeed is the one for gain.
+
+---
+
 ## Open problems and how to contribute
 
 1. **Keystone:** propose or measure a compact state meeting the leak condition with β>1 *in a level restoring or convertible class* (theory, Section 2). *This is problem number one.* A concrete, computable subproblem: search ENSDF for heterogeneous pairs of isomers whose cascade lines and gateway lines are mutually resonant (gate A's output pumps gate B and vice versa); the search space is already tabulated in `/gates`. The computed neutron gate ([neutron/](neutron/)) adds a second requirement that the photon sector had not been asked for: the state must also supply a *signal controlled inhibition*, because the only one the neutron sector has is heat and it is worth a fraction of the gain. A gate with gain but no inversion is a linear amplifier with a comparator bolted to its boundary, and the machine it builds is the Bernstein machine of Section 6 with better numbers, not a logic family.