Paper 9b: neutrinos and a baryon asymmetry I cannot yet derive

Paper 9b is the framework’s smallest paper and its most complete: one particle, one mass scale, one mechanism, with the arithmetic checked to the end. It is also, after the audit, the paper that lost its most impressive-looking number and survived anyway, which makes it the right paper to read as a model of what status labels are for.

The mechanism

Right-handed neutrinos are the standard explanation for why the observed neutrinos are so light: their Majorana masses sit at some high scale, the observed left-handed neutrinos get masses through the seesaw, inversely proportional to the heavy scale. The framework’s version imports the heavy scale from the substrate rather than postulating it. The topological mass gap from Paper 4, the Planck mass divided by the category dimension to the fourth, is 1.82 times 10 to the 12 GeV, and that is the Majorana scale. Feed it through the seesaw with Dirac masses of ordinary Yukawa size and the light neutrinos land near the observed milli-electron-volt range.

The virtue of this is economy. One number, already derived in the framework for other reasons, doing the neutrino job for free. No new scale, no new fields beyond the right-handed neutrinos every seesaw needs. The paper’s structure is a template: import a scale from a derivation, state the seesaw arithmetic, check against observation, stop.

The number that got cut

The original draft carried a second result, a lepton-flavour asymmetry coefficient kappa, printed as an exact value and used to predict the baryon asymmetry. The audit’s finding was blunt: the coefficient was back-solved. Take the observed baryon asymmetry, run the mechanism backwards, and the required kappa falls out; the paper’s exact value was that back-solved number dressed as a prediction. In the corrections series this is the post about solving for instead of deriving, and it is the clearest instance in the archive: a quantity whose every decimal place was determined by the answer it claimed to predict.

What is striking is that the paper survives the cut. Without kappa, there is no baryon asymmetry prediction, and leptogenesis is marked open in the framework’s ledger. What remains is the mass scale mechanism, which was never touched by the error, and the paper is now a clean single-claim document.

Why this paper matters beyond its size

Two reasons. First, it is the only place where the framework’s topological sector produces a number that connects to a measured quantity, neutrino masses, through a mechanism, the seesaw, that nobody disputes. The chain is short, every link is standard, and the only framework-specific input is a mass gap whose own status is benchmark. If the mass gap computation is ever done rigorously and lands near 10 to the 12 GeV, this paper upgrades from plausible to derived with no additional work.

Second, it is the demonstration that status labels work as intended. A paper that lost a third of its content to an audit, and whose remaining content is more credible for the loss, is the pattern the whole programme is trying to institutionalise. The version that would have been embarrassing is not the one with the back-solved coefficient. It is the one that kept it.

The next paper is the framework’s wager on the cosmic microwave background: Paper 10, the CMB feature.