Branches from coherence-graph fragmentation: a testable definition (paper + reproducibility suite)
TL;DR. I've been developing a definition of wavefunction branches as connected components of the coherence graph of ρ, partitioned by the Fiedler eigenvector of a coupling graph built from the Hamiltonian. Given five axioms (three of which are standard QM), all four of Riedel's criteria for quasiclassical branches follow as theorems, and the branches are stable under perturbation. The full pipeline is run end-to-end numerically with no Lindblad equation and no Born–Markov in the simulation — only exact unitary evolution + partial trace.
Github link: https://github.com/bnstlaurent-crypto/Defining-Wavefunction-Branching
Zenodo link: https://zenodo.org/records/19645822
A few questions I have:
Is there a principled way to derive the S/E split (A4) from the Hamiltonian alone — e.g., via locality, tensor-product structure selection à la Carroll & Singh 2020, or something else? I'm stuck on this problem and don't see a way through it well.
For k > 2 sectors, the paper uses sequential Fiedler bisection (each physical decoherence event is a k = 2 step). Is there a cleaner simultaneous multi-sector partition — or a counterexample where sequential bisection provably fails on a physical Hamiltonian?
Where does this sit relative to Wallace's decoherent-histories account? I argue in §6 that coherence-graph fragmentation is strictly stronger (it gives the partition, not just consistency), but Everettians who know that literature better than I do will see things I don't.
As always, tear me up fam!