The claim
Theory Section 2 says the photon sector keystone, if it is to cascade, must be self restoring or convertible, and names the convertible class as a search: pairs of isomers (A, B) in ENSDF whose cascade lines and gateway lines are mutually resonant. Open Problem 1 puts that search first. The neutron sector calculation (#10, #11) added a second requirement, a signal controlled inhibition, because the neutron medium has none. Nobody has run either search. The claim under test is that the nuclear chart, as evaluated in ENSDF, contains states satisfying them.
The test
From the adopted levels and gammas of every nuclide carrying an isomer with half life at least one second:
- enumerate every gateway of every isomer, in two classes: observed (ENSDF lists the gamma between gateway and isomer) and allowed (spin and parity permit E1, M1 or E2 and the line is unobserved, the class the 4.85 keV ⁹³ᵐMo gateway belongs to), and follow each gateway's release cascade through the adopted gammas to get the return probability, the photons per trigger, and the energy let go;
- compare every release line with every releasing gateway absorption, with both recoils and both thermal Doppler widths, allowing a rotor of up to 1 km/s to close the remainder (Moon, 1951); count matches, heterogeneous matches, and closed loops;
- for every match, compute the areal density of inverted nuclei the amplification condition demands from the gateway's integrated cross section, and the thickness of pure isomer it amounts to;
- count isomers with a signal gateway and a veto gateway whose cascades differ in whether they emit the signal line;
- list the NEEC class, every releasing gateway within 30 keV of its isomer, which is the target list for Phase B1.
Kill criterion: if no heterogeneous match exists within rotor reach, the convertible class is empty and Section 2 must say so. If matches exist but every one demands an areal density beyond any inverted solid, the class exists as energies and not as amplifiers, and Section 1.1's wall is confirmed with the chart's best case in it. If no isomer has a veto gateway, the photon sector shares the neutron sector's inversion problem.
Which part of the theory it touches
Theory Sections 1.1 (the areal density requirement) and 2 (level restoration and its three classes); README Open Problem 1 and the roadmap's Phase B1; the candidate table of Appendix C.
The claim
Theory Section 2 says the photon sector keystone, if it is to cascade, must be self restoring or convertible, and names the convertible class as a search: pairs of isomers (A, B) in ENSDF whose cascade lines and gateway lines are mutually resonant. Open Problem 1 puts that search first. The neutron sector calculation (#10, #11) added a second requirement, a signal controlled inhibition, because the neutron medium has none. Nobody has run either search. The claim under test is that the nuclear chart, as evaluated in ENSDF, contains states satisfying them.
The test
From the adopted levels and gammas of every nuclide carrying an isomer with half life at least one second:
Kill criterion: if no heterogeneous match exists within rotor reach, the convertible class is empty and Section 2 must say so. If matches exist but every one demands an areal density beyond any inverted solid, the class exists as energies and not as amplifiers, and Section 1.1's wall is confirmed with the chart's best case in it. If no isomer has a veto gateway, the photon sector shares the neutron sector's inversion problem.
Which part of the theory it touches
Theory Sections 1.1 (the areal density requirement) and 2 (level restoration and its three classes); README Open Problem 1 and the roadmap's Phase B1; the candidate table of Appendix C.