Clock, Geometry, Matter, and Source Variables in the Causal-Fermion-Systems Baryogenesis Line: A Threshold Reanalysis of A Mechanism of Baryogenesis for Causal Fermion Systems

This note applies a minimal threshold framework to the causal-fermion-systems baryogen-
esis line, centered on Finster, Jokel, and Paganini’s A Mechanism of Baryogenesis for Causal
Fermion Systems. The framework separates three sector checks — clock, geometry, and
matter — and asks when asymmetry equations are actually writable. Two framework results
are used. First, retarded source laws are not admissible before a clock sector is active. Second,
baryonic variables are not admissible before a matter sector supplies the needed charge
basis. Applied to the CFS case, the first result is clarificatory and error-preventing rather
than corrective: although recent CFS ontology work describes spacetime as emergent from a
web of correlations, the 2022 baryogenesis calculation itself is carried out in a descendant
continuum regime with a smooth globally hyperbolic Lorentzian spin spacetime, a global
time function, a Cauchy foliation, a Dirac Hamiltonian, and an explicit particle/anti-particle
spectral split. In the present language the calculational regime is therefore post-threshold
with (IC , IG, IM ) = (1, 1, 1). The second result is not more corrective; it is more informative
about the framework’s range. The 2022 source paper already uses the right primitive variable:
not baryon number, but a fermionic occupation imbalance, signaled by the paper’s own
language of fermiogenesis, its fermion-number reading of Sakharov’s first criterion, and its
spectral-counting source observable. Later descendants broaden the label “baryogenesis”
while leaving the primitive observable spectral and fermionic. The threshold-safe rewrite
therefore keeps the source variable fermionic and postpones baryonic or leptonic specializa-
tion to a descendant charge map. The CFS case is thus a confirmation case rather than a
corrective one: the framework does not repair the 2022 mechanism, but it does make clear
why the original variable choice was disciplined and where later shorthand begins to outrun
the observable.