Komori and Maru leave proton decay to future work in one sentence. This paper takes that sentence as its question, and answers the half that follows from their own equations.
The obstruction. Their eqs. (43)–(47) and (76)–(79) force U(1)′ = T3L + Y − (B−L) identically, and all four dimension-6 |ΔB|=1 operators carry Y = B−L = 0. At one generation the surviving symmetry cannot forbid a single one of them.
What the anomalies demand. Of six channels, three force XQ = −1/6, which is exactly A = 0; two cannot cancel at all and require a Standard-Model singlet of U(1)′ charge −1. That singlet is necessary and not merely minimal, only the 28 supplies it, and so only rows (2) and (3) of their Table 1 can.
The bill, in eighths. The curvature of the Wilson-line potential at the symmetric point is exactly V″(0) = −π²ζ(3)D with D an exact rational per multiplet: a 48(+,+) is worth exactly 0 and an 84(+,+) exactly 5/4. Hosting a third lepton generation costs one 84, which takes case (3) from 9/8 to −1/8 and loses electroweak symmetry breaking. Case (2) is the only one of the five published rows that satisfies both necessary conditions at once — within the minimal extension considered, and at the level of the one-loop curvature.
The selection rule is a half-line, not a tuning. Protection fails if and only if qφ = |Aj|/n, a countable set with a maximum. And qφ = 3/2 — the charge of the 84's pure index-7 component, which every row of their table already contains — forbids all four operators to all orders in ⟨φ⟩/M, for every half-integer brane-quark charge, with no family dependence.
The instrument, and where it fails. The dimensionless invariant K = mh·αmin/√F″ must return one number on every row of any table of this kind. We do not reproduce their αmin column, and state that as an open question rather than a defect: the truncation, the transcription and every multiplicative repair are excluded at one loop, three independent transcription controls pass, and a sixth row is pre-registered with both candidate values so that the question does not depend on anyone answering it.
Two editions, English and Spanish. Every displayed number regenerates from the ancillary scripts and is literally greppable in the archived standard output beside them; eight gates enforce it.
2026-08-08extensionaffects the record: no
Part VI §7's modified potential, recomputed
- what
Part VI says, in its own words, that the potential modified by the escape is not recomputed
there. With the Part VII kernel present in the same instrument it is: the modified potential is
evaluated, the vacuum is re-minimised on it, and the result is displayed labelled measured,
carrying the Part VI §7 anchor band and marked explicitly as going beyond what the paper claimed.
- why
Part VI reached a sign, deliberately, and stopped there. The kernel that turns the sign into a
number was written for Part VII. Once both live in one instrument, refusing to run the second on
the first's output would be a presentation choice, not an honesty one.
- so
The record is unaffected: Part VI's statement that it does not recompute remains true of Part VI.
The site is where the recomputation lives, and it is labelled as this page's work, not the
paper's. Every absolute number in it inherits the open question about the published α column —
see the tool's own "what this cannot tell you" panel.
- check
- open the anomalies section; the recomputed value is labelled "measured" and carries the anchor band
2026-08-08noteaffects the record: no
The published α column is still not reproduced — and where the residual can no longer live
- what
Our α disagrees with the α published in Table 1 of arXiv:2503.04090 on every one of the five
rows, and not by a constant: the ratio runs 1.03× to 2.08× with no pattern in 8D, in A₄
or in the content. A constant would be a convention and could be absorbed; this cannot. Row (2)
is the only row that agrees, and the only one whose Higgs mass lands inside the 125–127 GeV
window — and it is the row this tool opens on, which it inherited rather than chose.
- why
Everything upstream of the α column reproduces. Their §3 was rebuilt from their own
eqs. (11)–(13) and (54) — structure constants, KK spectrum, all four branchings — and agrees;
their eq. (67) is proved rather than sampled; their eq. (68) is rederived; their Table 1 is
internally consistent with their own eq. (82). No rescaling reconciles the two columns: neither
a per-representation nor a per-channel factor, and a single common coefficient on the
antiperiodic sector fails by 18 % at best while also breaking the Higgs-mass column.
- so
No absolute number on this site (TeV, GeV) is citable until this closes. The three things that
escape it entirely — the mass ratio, the bill in eighths, and the two arithmetic laws — are
marked as such, because no normalisation enters any of them.
Two things have moved since. A discriminating sixth row is registered in advance in Part VI, so
whoever computes such a row next can read our answer off in print rather than by asking us. And
Part VII adds a second, independent published anchor — von Gersdorff, Irges and Quirós,
arXiv:hep-th/0204223, whose five-dimensional single-parity model on S¹/Z₂ is exactly the Δ = 0
corner of our formula — and it reproduces our criterion, its three critical flavour numbers and
one of its two published minima exactly. That does not close the gap. It relocates it: the residual is no longer free to
sit in the potential itself.
- check
- the tool's header states the band on every page; the five rows are in the hierarchy section