Complete response classification
Eight irredundant generators for coherent complex Dirac matter; six when real Majorana masses are also allowed. The proof has no representation-size cutoff.
Featured research · Axion theory
From axion couplings to heavy-particle constraints.
Which heavy particles can produce a proposed axion coupling—and what does their existence require of gauge running? The featured paper gives a complete response classification for specified fermion classes and sharp conditional constraints, without assuming CHC.
Mingoo Kim · 2026-09-10 · Preprint v1.0 DOI 10.5281/zenodo.22684159
Featured paper · Axion theory
Which Axion Couplings Admit Heavy-Fermion Completions?
Global quantization does not decide which axion couplings heavy particles can generate. This paper classifies the complete gauge response of specified Dirac and Dirac–Majorana matter classes, determines their minimum contribution to gauge running, and derives conditional heavy-threshold bounds. The central classification requires no CHC hypothesis.
Exact anomaly–running compatibility
A necessary-and-sufficient integer test gives the complete minimal running frontier: at most 70 Dirac candidates, or nine with Majorana masses, for any anomaly vector.
Conditional threshold bounds
Published Standard Model inputs turn the arithmetic restriction into a heavy-mass bound. The stated benchmark is stronger than the componentwise triangle test, under the same validity assumptions.
The generators classify coupling responses, not unique particle spectra. Cosmological applications require separately specified interactions and thermal histories. This is a theoretical preprint, not an experimental detection.
Independent inverse-problem paper
Passive measurement is insufficient; two controlled interventions are globally identifying.
Complete flux spectra and nondegenerate persistent currents do not identify the individual site offsets and hopping magnitudes of a general Hermitian three-mode ring. They determine only three centered polynomial invariants and generically leave a two-dimensional family of indistinguishable Hamiltonians. Two calibrated attenuations of distinct labelled edges remove the ambiguity and recover the positive-hopping Hamiltonian globally by closed-form equations.
Exact result
- Complete phase-resolved spectra and currents compress five microscopic coordinates to three invariants.
- The passive inverse therefore has a generic two-dimensional family of indistinguishable Hamiltonians.
- One attenuation is locally identifying but can retain several global solutions.
Experimental remedy
- Attenuate two distinct labelled edges and reconstruct all positive hopping magnitudes and site offsets.
- Propagate invariant covariance and test residuals for cross-talk or control-induced site shifts.
- Complete cuts are D-, A-, and E-optimal under equal invariant noise.
Methods-and-theory paper
When does a proposed distinction reach observation?
The paper gives one decision theorem for separating reparameterization, unrestricted functional fitting, finite predictive closure, comparator-specific distinction, and noise-limited measurability. It then applies the criterion to canonical scalars, compact winding sectors, and a symmetric three-mode magnetic graph.
Central result
- The predictive codimension is the observable dimension minus the rank of the closed-model Jacobian.
- The rank gained by adjoining a named comparator counts the directions exposed by the model restrictions.
- Covariance whitening and declared perturbation units determine local power and required sample size.
Prospective test
- Twelve fixed nondegenerate phases.
- Independent spectrum and generalized-current measurements with full covariance propagation.
- One rejection threshold; agreement does not distinguish CHC from standard magnetic-graph theory.
Three source papers underlie the distinguishability criterion.
Papers 01, 46, and 47 establish the root branch, predictive-closure criterion, and finite holonomy realization.
CHC · Covariant core
Local equivalence, global distinction.
On every regular connected branch, the constrained action reduces locally to general relativity plus one canonical scalar. The compact branch remains globally distinct through its circumference and winding sectors.
CHC-MCL · Predictive closure
Prediction begins where nuisance freedom ends.
Action integrability, probability completion, passive memory, and positive predictive codimension are stated as common closure conditions. Unrestricted constitutive freedom is proved locally non-predictive when it spans the observable space.
CHC-MHB · Finite holonomy benchmark
One exact relation can be rejected directly.
A symmetric three-mode loop gives a scale-free spectral invariant. The same finite model fixes phase loading, causal response, loss, and resolved events; an open chain supplies the phase-null control.
Open paper 47
What v2.0 changes.
The revision increases formal control, not merely page count.
Archive 70 entries 72 papers: 70 revised and 2 added
Formal structure No complete series-wide inventory 477 theorem-like statements and 477 proofs
Microscopic closure Sector-local and incomplete One finite-closure criterion propagated through all 70 original manuscripts
Finite test No complete microscopic benchmark Exact compact-holonomy invariant with an open-chain null control
Reproducibility PDF archive and checksums Sources, scripts, structured outputs, audits, visual QA, and checksums
Strong results, declared limits.
Internal mathematical closure and physical selection are different standards.
Established within the stated models
- General relativity plus one canonical scalar on every regular connected root branch, with compact topology retained as a global distinction.
- Helmholtz and Cech conditions for action closure, CPTP completion for event probabilities, and KYP/Hankel criteria for finite passive memory.
- A functional-nuisance non-predictivity theorem and compatibility-manifold criterion for observable restrictions that survive profiling.
- An exact trimer spectrum and scale-free holonomy invariant, checked over 1001 control phases with an open-chain null.
Still required for physical selection
- Microscopic coupling maps fixed before the relevant data are inspected.
- Complete likelihoods with covariance and nuisance propagation for each physical application.
- Prospective held-out comparisons against relevant standard models.
- Independent mathematical review, experimental reproduction, and peer assessment.
Version 2.0 is not presented as a replacement for general relativity, quantum field theory, standard cosmology, detector theory, or open-system quantum mechanics.
Choose a reading depth.
Each route preserves the premises, proof boundary, and strongest conclusion.
Additional independent papers.
These three works develop adjacent philosophical, measurement, and benchmark questions outside both the flux-trimer paper and the 72-paper CHC archive.