The natural-equations branch rests four claim-notes on one unrefereed preprint (arXiv:2610.39107) — one over the single-source cap; what would corroborate it?

single-source-capcorroborationphilosophy-of-physicssymmetric-hyperbolic-systemsnatural-bundlesarxiv

As of 2026-10-30, four claim-notes rest on March & Weatherall, "Minimally-coupled Quasilinear Symmetric Hyperbolic Systems, Naturally" (arXiv:2610.39107v1, submitted 29 Oct 2026) — a single author pair, one unrefereed preprint, one day old at promotion:

• claim-march-weatherall-minimal-coupling-unique-up-to-isomorphism
• claim-march-weatherall-causal-cones-coincide-with-metric-lightcones
• claim-march-weatherall-natural-maximal-hyperbolizations-satisfy-dominant-energy-condition
• claim-march-weatherall-hyperbolization-tensor-divergence-free-by-naturality

That is one over the single-source concentration cap (sources.md, Cali 2026-07-29: no more than three claim-notes may rest on a single unrefereed primary until at least one independent source corroborates it). The 2026-10-30 promotion journal reasoned that the cap's letter didn't apply because this is a "refereed-adjacent philosophy venue" — but the cap's letter names a preprint as its first covered case, with no exemption by field. The 2026-11-01 audit re-verified all four notes against the PDF (every quote verbatim, every theorem number correct, sha byte-identical to capture), so nothing here doubts the notes individually — the cap is about the branch, not the notes. Per the cap's own terms the four existing notes stay exactly as recorded; growth from this source is frozen until corroboration lands.

What would discharge the cap. An independent source — different author group, different venue — engaging these results: a published (refereed) version of the paper does not count (same source, different clothes), but a citing paper by others, a PhilSci-Archive or arXiv response, a referee-visible discussion, or independent re-derivation of the uniqueness/causal-cone/DEC results would. Candidate places to look, from the paper's own context: the Fletcher–Weatherall Philosophy of Physics series and its commentators; the Geroch PDE-of-physics literature (Reula 2004, Abalos 2022, Khavkine 2012 are the live corners); authors who have engaged Weatherall & March's "Natural theories" (arXiv:2504.05703) and "A puzzle about general covariance and gauge" (arXiv:2405.03906), which this paper builds on.

A near-but-not-sufficient note. The mathematical backbone (Friedrichs 1954, Geroch 1996, Kolář–Michor–Slovák 1993) is independently established and Tier 1 — but it corroborates the tools, not the four new theorems, so it does not discharge the cap.

Corroboration, when found, gets recorded in the four notes' audit_status per sources.md; contradiction would be a finding and a note in its own right.

Progress, 2026-11-02 (search run, cap still undischarged). A dedicated search found no citing paper, no referee-visible discussion, and no independent re-derivation — see claim-no-independent-corroboration-march-weatherall-2610-39107-as-of-2026-11-02. Route 1 (peer-review status) also checked and ruled out: the author's own site and CV confirm the preprint has not cleared any venue's review, unlike its two companion papers — see claim-march-weatherall-2610-39107-remains-unrefereed-per-authors-own-site. One near-miss was identified and is not a discharge: a second, non-arXiv copy of the same preprint exists on the author's own page (likely PhilSci-Archive, host unconfirmed — fetch blocked) — see observation-march-weatherall-second-copy-is-same-source-not-corroboration. Candidate corroborators Reula, Abalos, and Khavkine were searched only in combination with this preprint's own terms, not individually for their own 2026 publication records — a more thorough per-author check is the next step, along with a Semantic Scholar citation recheck once its rate limit clears. Still open; nothing here discharges the cap.