The Dimming That Turned Around

In 1998 a team of astronomers reported that distant exploding stars were, on average, 10% to 15% farther away than expected in a low-density (ΩM = 0.2) universe without a cosmological constant: the expansion was speeding up. This page rebuilds that headline from their own tables, 0.245 mag or 11.9% farther against the printed 0.25, then hands you the 2004 test built against the two objections of the day: add the nine supernovae beyond z = 1, and grey dust that thins as the universe expands fits worse than a cosmological constant by Δχ² = 134.0. Planted into the test’s own data, the claim is recovered; dimming that grows with lookback time, planted instead, makes the same test report acceleration after deceleration, with the transition at z = 0.46.

Everything below is computed in your browser from two small files this page transcribed from the published tables. Numbers the papers printed are marked as printed and cited where they appear; every likelihood, probability and fit is the page’s own and says so. The check at the bottom recomputes the page against itself while you read it.

The instruments start when the page’s scripts load.

I · the claim, at full strength

Ten supernovae, too far away

A type Ia supernova is a white dwarf that detonates, and after a correction for how quickly its light fades, every one reaches nearly the same peak brightness. Measure how bright one looks and you know how far away it is; measure the redshift of its galaxy and you know how much the universe has stretched since the light left. Plot one against the other and you have the expansion history of the universe, written in the faintness of distant stars. Astronomers write the distance as a distance modulus, in magnitudes: 0.25 mag farther means 12.2% farther in distance, and fainter by the same token.

In 1998 the High-Z Supernova Search Team compared 16 high-redshift supernovae with 34 nearby ones. The distant ones were too faint, at 2.8σ to 3.9σ depending on the fitting method, for a universe whose expansion was slowing down. In their words:

“The distances of the high-redshift SNe Ia are, on average, 10% to 15% farther than expected in a low mass density (ΩM = 0.2) Universe without a cosmological constant.”

“With no prior constraint on mass density other than ΩM ≥ 0, the spectroscopically confirmed SNe Ia are statistically consistent with q0 < 0 at the 2.8σ and 3.9σ confidence levels, and with ΩΛ > 0 at the 3.0σ and 4.0σ confidence levels, for two different fitting methods respectively.”

Riess et al. 1998, The Astronomical Journal 116, 1009, abstract (arXiv v1, pp. 1 and 2)

The Discussion gives the acceleration half of that sentence as “Current acceleration of the expansion is preferred at the 99.5% (2.8σ) to >99.9% (3.9σ) confidence level” (§5, p. 18), and gives the number behind the first: “For a Universe with ΩM = 0.2, the MLCS and template fitting distances to the well-observed SNe are 0.25 and 0.28 mag farther on average than the prediction from ΩΛ = 0.” The caption of Figure 4, the MLCS Hubble diagram, gives the same number for the supernovae it plots: “The average difference between the data and the ΩM = 0.20, ΩΛ = 0 prediction is 0.25 mag” (p. 35). They were careful about exactly the point this page tests:

“Although our current observations reveal no indication of evolution of SNe Ia at z ≈ 0.5, evolution remains a serious concern which can only be eased and perhaps understood by future studies.”

Riess et al. 1998, §5.1, p. 20

How the page rebuilds it

The page transcribed every measured distance the paper tabulates: 27 nearby and 10 high-redshift light-curve distances by each of two methods (Tables 10, 5 and 6), and 7 nearby and 6 high-redshift “snapshot” distances (Tables 9 and 7). One distance function, the paper’s equation (2), serves every Friedmann universe the page considers. The likelihood is the paper’s equations (4) to (12): each distance carries its printed error plus a peculiar-velocity term of 200 km/s, with 2,500 km/s more where Table 1 says the redshift came only from the supernova’s own spectrum; the Hubble constant is integrated out with a flat prior, separately for the light-curve and the snapshot sets, and the two are multiplied; the prior on (ΩM, ΩΛ) is flat, with ΩM ≥ 0 and without universes that had no big bang. The headline number is then simply the mean difference, for the ten supernovae plotted in the paper’s Figure 4, between their distances and the ΩM = 0.2, ΩΛ = 0 prediction.

That reproduces the claim at the strength it was printed: 0.245 mag, 11.9% farther, against the printed 0.25 (a difference of 0.005 mag, inside the rounding of the tables and of the printed average). By the template method the page gets 0.299 mag against the printed 0.28: its own zero point there is H₀ = 64.09, and at the printed 63.8 it would be 0.290, so the template reproduction is slightly stronger than printed, and the page shows both. Leave SN 1997ck out of the average and the MLCS figure is 0.226 mag (11.0%).

Where the reproduction falls short, and by how much

The significance comes out slightly weaker than printed. For the paper’s headline sample (MLCS, light curves and snapshots), the page gets p(q₀ ≤ 0) = 99.33%, 2.71σ, against the printed 99.5% (2.81σ in the paper’s own convention): 0.17 percentage points, about 0.09σ. Across the paper’s Table 8 the pattern holds with one exception. Of the 10 probabilities it prints as numbers, 9 come out weaker, by 0.02σ to 0.13σ in the paper’s own convention, and one, p(ΩΛ ≥ 0) for MLCS+Snap.+97ck(16), comes out 0.03σ stronger; the 8 it prints as >99.9% all agree with that bound, but fall short of the σ printed beside them by 0.02σ to 0.22σ. It is not the rounding of the tables: jittering every transcribed distance and error within its last printed digit, 40 times over, moves p(q₀ ≤ 0) by a standard deviation of only 0.05 percentage points, and never above 99.45%. Nor is it the prior on the Hubble constant: flat in the distance offset instead of flat in H₀, the page gets 99.29%. Nor the two redshifts on which the paper’s Tables 1 and 7 disagree: taking Table 1’s gives 99.17%, further away. The paper does not publish its grid spacing or integration scheme, and this page could not identify the cause. It prints both numbers, and every later comparison uses the printed 0.25 mag as the claimed size, never the page’s weaker reproduction.

Printed values are Table 8 of the arXiv v1 (p. 51), typed from the rendered page. The page’s q₀ column is the central 68% of p(q₀), the paper’s equation (17), in bins 0.02 wide; the paper printed a peak and an error. H₀ is printed only for the rows without snapshots and for the snapshots alone. The paper’s σ is the two-sided Gaussian equivalent of the probability (99.5% is 2.81σ), except in one place: the MLCS(9) row prints 99.4% as 2.4σ, which in that convention is 2.75σ. It is printed here as printed.

The other team reached the same conclusion independently. The Supernova Cosmology Project wrote in 1999, from 42 high-redshift supernovae, that “the data indicate that the cosmological constant is non-zero and positive, with a confidence of P(Λ > 0) = 99%, including the identified systematic uncertainties” (Perlmutter et al. 1999, The Astrophysical Journal 517, 565, abstract). This page quotes that result and does not recompute it: the project released its probability surface as confidence levels, not densities, and a probability cannot honestly be integrated from those.

II · the deciding control

The supernovae beyond z = 1

Two objections followed the claim, and both were proposals worth testing. Grey dust between the galaxies (Aguirre, 1999) could dim distant supernovae without reddening them. Or supernovae in the younger universe could simply be a little fainter, a luminosity evolution (Drell, Loredo and Wasserman, 2000). Either would make distant supernovae look too far away without any cosmic acceleration.

The two readings part company farther out. In a universe with a cosmological constant, matter dominated in the past and the expansion decelerated; for ΩM = 0.27, ΩΛ = 0.73 it switched to acceleration only at z ≈ 0.76. So supernovae beyond z ≈ 0.5 should stop looking ever fainter than in a coasting universe and turn back towards it: in that model the difference peaks at z ≈ 0.56 and crosses zero near z ≈ 1.45. Dust that thins as the universe expands, or evolution that grows with redshift, keeps adding dimming the deeper you look. In 2004 the same lead author and several of the same team published 16 supernovae found with the Hubble Space Telescope, six of them among the seven most distant known:

“We have discovered 16 Type Ia supernovae (SNe Ia) with the Hubble Space Telescope (HST) and have used them to provide the first conclusive evidence for cosmic deceleration that preceded the current epoch of cosmic acceleration.” ... “the transition between the two epochs is constrained to be at z = 0.46 ± 0.13. The data are consistent with the cosmic concordance model of ΩM ≈ 0.3, ΩΛ ≈ 0.7 (χ²dof = 1.06), and are inconsistent with a simple model of evolution or dust as an alternative to dark energy.”

Riess et al. 2004, The Astrophysical Journal 607, 665, abstract (arXiv v2, pp. 1 and 2)

The three cosmologies reproduce Table 4 to within the unit it was printed to. The three astrophysical models reproduce it to within 8. Each has one opacity parameter, “fixed by requiring the total extinction at z ≈ 0.5 to match the observed peak brightness of SNe Ia in a cosmology with ΩΛ = 0” (p. 26), a rule given in words only, so the page has to choose a reading of it, and a different reading would move these rows. The page’s reading: the dimming at z = 0.5 equals the weighted mean excess, over the ΩM = 1 prediction, of the 38 gold supernovae with 0.4 < z < 0.6, with the zero point taken from the ΩM = 0.27, ΩΛ = 0.73 fit. That makes it 0.479 mag. The grey-dust models integrate the dust’s optical depth along the light’s path, with dust density growing as (1 + z)^α: α = 3 for dust that thins with expansion, α = 0 for dust “continually replenished at precisely the same rate in which it is diluted”.

The replenishing model has two readings, and the table decides between them less cleanly than one would like. The paper’s prose says constant density (α = 0): χ² = 178.48. Its equation says α = 0 above z = 0.5 and 3 below; read literally, the density drops by a factor of 3.375 at z = 0.5, and χ² = 175.38, closer to the printed 175. Read with the density held continuous, χ² = 212.75. The page defaults to the prose, because that is the model the paper’s own argument about it rests on, and offers all three.

The transition redshift belongs to the linear q(z), not to the universe: the concordance model’s own switch is at z ≈ 0.76, and the paper’s summary says of its 0.46 that “the precise value depends on the kinematic model employed” (§6, p. 40). Gold and silver together (186 supernovae) give a quadrant probability of 99.96% against the printed 99.8%. The page’s quadrant probabilities are a little stronger than printed, and its transition interval narrower than the printed ± 0.13; the page prints both. For a flat universe with a cosmological constant the page finds ΩM = 0.309, 68% from 0.274 to 0.351, inside the printed 0.29 (+0.05, −0.03). The ΩM = 0.27, ΩΛ = 0.73 model gives χ²/dof = 1.135, which is §4.2’s printed 1.13 (the paper divides by the 157 supernovae); the abstract’s 1.06 is not reproduced. The abstract states it for ΩM ≈ 0.3, ΩΛ ≈ 0.7, and at ΩM = 0.3, ΩΛ = 0.7 the page gets χ² = 177.13, or 1.128 per supernova, so it is not reproduced at that model either. The text’s “∆χ² = 122” for grey dust and “∆χ² = 70” for dimming ∝ z are not the differences of the paper’s own Table 4, which are 129 and 75; the page gets 134.0 (11.6σ for one degree of freedom) and 81.3 (9.0σ). The page names these inconsistencies without guessing at their cause.

How strongly does that depend on the tuning? With each dimming amplitude fitted freely instead, high-redshift grey dust is worse than the best flat ΛCDM universe by only Δχ² = 23.9, and dimming ∝ z by 16.7. But a freely fitted dust no longer explains the 1998 faintness it was invented to explain, so tuning is the fair form of the objection. Placing the dust in an open universe with ΩM = 0.3 instead of ΩM = 1 gives 123.4 and 70.4. The 2004 test is not independent of the claimants: it shares its lead author and several of the same team, and its gold set holds 11 of the 1998 paper’s 16 high-redshift supernovae and 25 of its 34 nearby ones. Leave out those 11, or all 36, below, and the verdict on the two objections barely moves.

And the paper said in words exactly what its test could not do:

“Interestingly, the ‘replenishing dust’ model is nearly indistinguishable from an ΩΛ model because the dimming is directly proportional to distance traveled and thus mathematically quite similar to the effects of a cosmological constant.” (§4.2, p. 27)

“Another model with this behavior would be evolution which is proportional to look-back time (Wright 2002). While possible, such dimming behavior, especially if in the form of luminosity evolution, would seem implausible.” ... “In the end, however, the only ‘proof’ against astrophysical contamination of the cosmological signal from SNe Ia is to test the results against other experiments, independent of SNe Ia.” (§5, p. 32)

“More complex parameterizations of astrophysical dimming which peak at z ≈ 0.5 and dissipate at z > 1 remain consistent with the SN data (but appear unattractive on other grounds).” (§6, p. 40)

Riess et al. 2004

III · the control on the control

Plant a universe, run the unmodified test

A test that could not have seen the claim cannot refute its rivals, so before trusting the 2004 test, the page tests it. It takes a copy of the 157 gold supernovae, subtracts the page’s own best flat fit (ΩM = 0.309) from each distance, and adds back a planted universe. The real scatter, the real errors and the real redshifts all stay; only the underlying expansion changes. Then the copy goes through the same function that produced the real result, unmodified.

The claim is planted at its printed size: 0.25 mag farther at z = 0.5 than the ΩM = 0.2, ΩΛ = 0 universe, which is a flat universe with ΩM = 0.219 and a cosmological constant. It is never planted weaker than printed. Each rival is an ΩM = 1 universe plus dimming sized to give the same distance at z = 0.5, 0.463 mag of it.

That box is the reading at the printed 0.25 mag. At the other sizes the 1998 paper printed, the kinematic half of the test stays blind: planted dimming with lookback time reads quadrant probability at least 0.9996 at every one of them. The Table 4 half does not stay level. Against the test’s reference model, replenishing dust on the lookback copy scores Δχ² = +0.4 at 0.207 mag, −2.2 at 0.25, −5.1 at 0.28 and −8.1 at 0.303, so at the two larger sizes the table would prefer the dust by more than the page’s line of 4, while the deceleration epoch it reports stays in place. Choose a size above to see the reading at that size.

The lookback row is not an accident. Dust of constant physical density dims light in proportion to the time the light spends crossing it, which is the lookback time; in an ΩM = 1 universe that is (2/3H₀)(1 − (1 + z)^−3/2), a curve that climbs steeply to z ≈ 0.5 and then flattens. It is the same function as the 2004 paper’s replenishing dust. The engine computes the two separately, one as an optical depth integrated over redshift and one as a time integrated over the scale factor, and they agree to 5×10⁻¹⁴. Planted in place of acceleration, such dimming produces the test’s signature, a deceleration epoch followed by acceleration, in a universe that never accelerated. That is a finding about the 2004 test, computed by this page, and the 2004 paper stated the same limit in words. It is not a finding about the universe.

Two things follow, and both are the page’s own findings about the 2004 test. Its verdict on the objections is robust: if the universe were the claim, the test would prefer it to grey dust by Δχ² ≥ 9 in 96 of 100 noise draws, and to dimming ∝ z in 81; if the universe held either objection, the test preferred the claim in none of the draws. Its deceleration epoch at the printed confidence is not: the claim itself reaches the printed quadrant probability in only 10 of 100 draws, and dimming ∝ lookback time, which never accelerated, reaches it in 35, more often than the claim does. And the real data sit in the favourable tail: drawn about the best flat fit to the real data, noise of the printed size matches or exceeds the real quadrant probability in 5 of 100 draws, the real Δχ² against grey dust in 1, and against dimming ∝ z in 1. The page does not infer why; the printed errors are treated as independent and Gaussian, which a published table cannot test.

The quadrant probability does not need the supernovae beyond z = 1: the linear q(z) reads the curvature of the diagram below z = 1 as dq/dz > 0, and its transition then sits lower. What the new supernovae did was multiply the case against the two monotonic objections: Δχ² against grey dust from 46.2 to 134.0, against dimming ∝ z from 32.2 to 81.3. The page does not say that the Hubble supernovae found the deceleration epoch on their own. And the verdict on the two objections does not lean on the 1998 paper’s supernovae: without all 36 of them, grey dust is still worse by Δχ² = 128.3 and dimming ∝ z by 77.6. The quadrant probability leans on them a little more: it falls to 0.9905, just under the printed 0.992.

IV · the claimants’ methods, run on nothing

Universes with no cosmological constant

Does the 1998 procedure find acceleration in a universe that has none? The page builds 2,000 universes with ΩM = 0.2 and ΩΛ = 0, the headline’s own comparison, each observed through the same 36 light-curve and 13 snapshot supernovae at their real redshifts, with Gaussian scatter of each supernova’s own printed error, and runs each through the page’s reproduction of the 1998 likelihood, unmodified.

Two things follow. The procedure rarely manufactures the claim out of noise: a false alarm at the printed level about once in 150 universes. And a posterior probability for acceleration near 72.6% means nothing here, because that is what a universe with no cosmological constant typically returns: the flat prior over (ΩM, ΩΛ) puts much of its area where q₀ < 0.

The 2004 kinematic test on noise alone: 300 universes with ΩM = 0.2 and no Λ, and 300 with ΩM = 1, each with the gold set’s redshifts and errors. The quadrant probability reaches the printed 0.992 in 0 and 0 of them; the medians are 0.271 and 0.007. The test does not manufacture a switch from deceleration to acceleration out of noise. It manufactures one out of saturating dimming, as the plant above showed, and that is a different failure.

V · the verdict, dated

What the record says, as of now

Recomputed from their own tables, the 1998 supernovae sit 0.245 mag (11.9%) farther than a low-density (ΩM = 0.2) universe without a cosmological constant predicts, against the printed 0.25; the 2004 test built against the two objections of the day prefers a cosmological constant to grey dust that thins with expansion by Δχ² = 134.0, recovers the claim when it is planted into the test’s own data, and reports acceleration after deceleration, with the transition at z = 0.46, when dimming that grows with lookback time is planted instead.

The 1998 title had two halves: “an Accelerating Universe and a Cosmological Constant”. The verdict covers the first. On the second: DESI Collaboration (M. Abdul-Karim et al.), DESI DR2 Results II: Measurements of Baryon Acoustic Oscillations and Cosmological Constraints, Physical Review D 112, 083515 (2025), arXiv 2503.14738v3: dynamical dark energy is “preferred over ΛCDM at 3.1σ for the combination of DESI BAO and CMB data”, and “When also including SNe, the preference for a dynamical dark energy model over ΛCDM ranges from 2.8-4.2σ depending on which SNe sample is used.” This bears on whether the vacuum energy is a constant, not on whether the expansion accelerates.

The published exchange of 2025 and 2026, in date order

The claimants’ answer that decided the objections of 1999 and 2000 was the 2004 paper, with its stated limit, quoted above. The current exchange is about supernova luminosity drifting with the age of the stars that explode, and each side is published and peer reviewed:

1. 15 October 2025 challenge Junhyuk Son, Young-Wook Lee, Chul Chung, Seunghyun Park and Hyejeon Cho, Strong progenitor age bias in supernova cosmology. II. Alignment with DESI BAO and signs of a non-accelerating universe. They report “a significant (5.5σ) correlation between standardized SN magnitude and progenitor age”, correct the supernova magnitudes by “Δm(z) = Δage(z) × 0.030 mag Gyr⁻¹”, write that over 0 < z < 1 “we expect, on average, a 5.3 Gyr variation in progenitor age ... and, therefore, a ∼ 0.16 mag variation in SN luminosity”, and, combining supernovae with BAO and the CMB in a model whose dark energy evolves, “we find a significantly stronger (> 9σ) tension with the ΛCDM model than that reported in the DESI papers, suggesting a time-varying dark energy equation of state in a currently non-accelerating universe”. 15 October 2025 (arXiv 2510.13121); Monthly Notices of the Royal Astronomical Society 544(1), 975 to 987 (2025), doi:10.1093/mnras/staf1685.
2. 20 January 2026 reply Phil Wiseman, Brodie Popovic, Mark Sullivan, Adam G. Riess, Dan Scolnic and 12 others, including Isobel M. Hook, Saurabh W. Jha and Brian Schmidt, Still accelerating: type Ia supernova cosmology is robust to host galaxy age evolution. A reply to Son et al.: applying the standard host-stellar-mass correction to their sample, “we find no dependence of standardized supernova brightness on host age”, and the claimed age difference between near and distant supernovae is “overstated by factors of three to five largely due to a conflation of host galaxy age with supernova progenitor age”. Its authors include three of the 1998 claimants (Riess, Jha and Schmidt) and one author of the Supernova Cosmology Project’s 1999 paper (Hook). 20 January 2026 (arXiv 2601.13785, v2 8 May 2026); Monthly Notices of the Royal Astronomical Society 549(3), stag797 (2026), doi:10.1093/mnras/stag797.
3. 12 May 2026 challenge Seunghyun Park, Young-Wook Lee, Chul Chung, Suk-Jin Yoon, Junhyuk Son, Hyejeon Cho and Young-Lo Kim, Strong progenitor age bias in supernova cosmology. III. Progenitor age as the physical origin of the Type Ia supernova magnitude steps with host properties. The challengers’ group, on a new dataset, on the host-mass correction that the reply applied: “while the mass-step correction reduces the age bias by about half, the host age-bias correction fully eliminates the mass step”, so that “the SN Ia magnitude steps are therefore projected manifestations of an underlying dependence on progenitor age.” 12 May 2026 (arXiv 2605.12596); Monthly Notices of the Royal Astronomical Society 549(2), stag935 (2026), doi:10.1093/mnras/stag935.
4. 20 May 2026 rejoinder Chul Chung, Junhyuk Son, Seunghyun Park, Suk-Jin Yoon, Hyejeon Cho, Dongwook Lim and Young-Wook Lee, Still non-accelerating: age-bias correction in supernova cosmology is robust to host-progenitor age mapping. A rejoinder to Wiseman et al.: their age slope is “severely underestimated because their combined SN Ia sample spans an unusually wide redshift range (0.04 < z < 0.42), over which the mean host age evolves by ∼3 Gyr”, and when the reduced age evolution and a steeper slope are combined, “the final correction, and hence the resulting cosmological impact, remain largely unchanged from Son et al. (2025)”. 20 May 2026 (arXiv 2605.21586); Monthly Notices of the Royal Astronomical Society 551(3), stag1513 (2026), doi:10.1093/mnras/stag1513.
5. 8 June 2026 challenge Animesh Sah, Mohamed Rameez and Subir Sarkar, Pantheon+ supernovae corrected for progenitor age indicate the universe is decelerating. Applying redshift-dependent progenitor-age corrections to the Pantheon+ catalogue “shifts the monopole component of q0 to positive values (i.e. deceleration), while leaving the local dipole component essentially unchanged.” 8 June 2026 (arXiv 2606.09650); Monthly Notices of the Royal Astronomical Society 549(3), stag844 (2026), doi:10.1093/mnras/stag844.

This page does not place Son et al.’s correction on its map. They give its shape in redshift, Δage(z), only as a figure, and the page did not digitise it. Their argument is not that the universe is the ΩM = 1 universe of the 2004 test: they combine corrected supernovae with baryon acoustic oscillations and the cosmic microwave background, in a model whose dark energy evolves. What this page can say is narrower. Their correction follows the age of the exploding stars, a quantity tied to cosmic time rather than to redshift itself, and dimming that follows cosmic time, as lookback-time dimming does, is what the 2004 test cannot tell from acceleration (Act III, and the map below). Whether this particular correction falls inside that blind zone depends on its shape in redshift, which the page has not placed. Either way the dispute cannot be settled by that test, and the verdict above rests on evidence from beyond supernovae.

The searches also returned two preprints for which this page found no journal version on 2026-09-23 (Crossref). Yukei Murakami and 19 co-authors, among them four of the 1998 claimants (Filippenko, Jha, Riess and Schmidt), arXiv 2604.16597 (17 April 2026), estimate progenitor ages for 6,983 low-redshift host galaxies and infer “a modest 1.5 Gyr evolution in mean progenitor age over cosmic time”, with a maximum redshift-dependent bias of ΔHR = −0.007 (+0.012, −0.014) mag, “consistent with zero”. Saibal Ray and four co-authors, arXiv 2607.20570 (v1 21 July 2026, v2 3 August 2026), state of their revised analysis of Pantheon+: “Our revised results are consistent with ΛCDM and do not support either the original claim of near-zero baseline acceleration or the S25/SRS26 claim of a decelerating universe.” This page does not use either for the verdict.

VI · the second layer

The blind zone of the deceleration test

How much of what the 2004 test calls a deceleration epoch could be dimming instead? The page plants a family of dimming histories, all sized to the claim at z = 0.5 in a universe without a cosmological constant: A(z) = A(0.5) (1 − e^−z/z_s) / (1 − e^−0.5/z_s). Small z_s means the dimming is all done early; as z_s grows it becomes dimming ∝ z. For each z_s the page asks two questions: how well does that dimming fit the real gold set (with its amplitude tuned by the 2004 rule, fitted freely, or held at the claimed size), and what does the unmodified test report when that dimming is planted at the claimed size in place of acceleration?

The page’s result. In the 157-supernova gold set, dimming that saturates between z_s = 0.1 and 0.9 (on the slider’s 26 stops) fits the real data within Δχ² = 4 of the best flat ΛCDM universe when its amplitude is fitted (one parameter against one; at most +3.7), and, planted at the claimed size in place of acceleration, makes the unmodified test report acceleration after deceleration with quadrant probability at least 0.996 (with the real residuals transplanted, as for the claim; over fresh noise the quadrant probability scatters for both). Held at the claimed size instead of fitted, 0.463 mag of dimming at z = 0.5, the same dimming fits within Δχ² = 4 only for z_s from 0.15 to 0.6 (at 0.75 it is +5.0). Both edges of the zone are sharp: at z_s = 0.075 the dimming is over too early to fit (+7.0, fitted), and at z_s = 1 the data still fit (+2.7) but the planted quadrant probability is 0.991, just under the printed 0.992. Dimming still growing well beyond z = 1 (z_s of 2 or more), tuned by the 2004 rule to the observed faintness at z = 0.5, fits worse than the cosmological constant by Δχ² = 36.0 or more, and planted at the claimed size, it never gets the quadrant probability above 0.846. In an open host universe with ΩM = 0.3 the zone runs from the lowest stop, z_s = 0.05, to 0.5 (to 0.3 at the claimed size); the conclusion does not change. Dimming with lookback time is not in this family, but it lands in the same place: planted, quadrant 0.9998.

That such dimming can mimic a cosmological constant is not new: the 2004 paper says so, and so do later papers the page’s searches returned, among them Riess et al. 2007 (The Astrophysical Journal 659, 98; arXiv astro-ph/0611572) and Sarkar 2008 (General Relativity and Gravitation 40, 269; arXiv 0710.5307). The searches did not find the planted map in print. The closest work they returned, Mirpoorian, Lin and Pogosian 2026 (arXiv 2604.24761, a preprint), constrains “a phenomenological correction to SNIa magnitudes that scales with cosmic look-back time” jointly with the cosmic microwave background and baryon acoustic oscillations: a joint constraint on dimming with lookback time, the plant of Act III, not a planted map of the 2004 test. We searched arXiv, the web and the full text of arXiv astro-ph/0611572 and 0710.5307 on 2026-09-23 and did not find a published map of which saturating dimming histories, planted into the 2004 gold set in place of acceleration, make its kinematic test report acceleration after deceleration.

VII · the check

The check

Every free choice, and what it moves

• 1998 light-curve method (MLCS, default; Δm15 template): the mean excess (0.245 against 0.299), H₀ and both probabilities.
• SN 1997ck (in the Figure 4 average and out of the probabilities, as printed, default; everywhere; nowhere): the mean excess (0.226 without it) and the probabilities.
• Snapshot distances (included, default, the paper’s “full strength of the high-redshift sample”; light curves only; snapshots only): the probabilities, each row of Table 8.
• Zero point of the mean excess (the offset of the page’s own best fit, default; the offset of the ΩM = 0.2, ΩΛ = 0 model fitted to the nearby supernovae alone): 0.245 against 0.221 mag (H₀ 64.51). The paper does not say which zero point its Figure 4 uses; the default reproduces its printed H₀.
• Redshifts of SN 1995ao and SN 1995ap (Table 7’s, 0.30 and 0.23, default; Table 1’s, 0.24 and 0.30): the two tables disagree, and the choice moves p(q₀ ≤ 0) from 99.33% to 99.17%, away from the printed value, so it does not explain the gap either.
• Prior on the Hubble constant (flat in H₀, the paper’s equation (10), default; flat in the distance offset): p(q₀ ≤ 0) 99.33% against 99.29%; the 2004 quadrant 0.99751 against 0.99746.
• 2004 sample (gold, default; gold and silver): quadrant probability, transition, both Δχ².
• Leave out (nothing, default; HST discoveries; the nine beyond z = 1; the 1998 paper’s high-redshift supernovae; every 1998 supernova; every supernova below z = 0.1, which is refused): quadrant, transition, both Δχ².
• Dimming amplitude (tuned, default; fitted): grey dust 134.0 against 23.9.
• Host universe of the dimming (ΩM = 1, default; ΩM = 0.3 open): the astrophysical rows of Table 4 and the blind-zone edge.
• Replenishing dust (the prose, default; the equation literally; the equation with continuous density): that row of Table 4.
• Plant and claimed size (0.207, 0.25 default, 0.28, 0.303 mag): every planted readout. Any other size is refused: another size is another claim.
• Saturation redshift z_s: the blind-zone readouts.
• Grids, fixed and named: the 1998 posterior on cells 0.02 wide over ΩM 0 to 2.5 and ΩΛ −1 to 3; the kinematic posterior on cells 0.04 by 0.08 over q₀ −2.4 to 1.6 and dq/dz −4 to 6, which holds all but 6×10⁻⁹ of the real posterior’s mass in its edge cells.

What remains uncertain

• The 1998 significance reproduces weaker than printed in 17 of the 18 probabilities Table 8 prints, by up to 0.22σ, and slightly stronger in the other, for a reason this page could not identify (above).
• The 2004 tuning rule is stated in words; the page’s reading reproduces the three astrophysical rows of Table 4 to within 8, not to the unit.
• The 2004 kinematic probabilities come out a little stronger than printed, and the transition interval narrower; the paper does not give its prior box or grid.
• Both tables are transcriptions: the 1998 values from the PDF text layer, checked against the page images; the 2004 values from the arXiv v2 TeX, which has 186 rows and 157 gold like the paper, where the VizieR copy of the journal table has 185 and 156 (SN 1991ag missing, SN 2003lv listed as 2003XX; every shared row identical).
• The null universes and the fresh-noise plants are Gaussian with each supernova’s own printed error, and uncorrelated: the published tables carry no covariance.
• The grade A plant keeps the real residuals. Over fresh noise the 2004 quadrant probability is the fragile half of the result: the claim itself reaches the printed level in a minority of draws (the table in Act III), while the preference for a cosmological constant over the two objections is reached in most.
• The page does not recompute the verdict’s evidence from outside supernovae, the Supernova Cosmology Project’s result, or the 2025 to 2026 age-bias analyses: it quotes them.

Sources

1. Adam G. Riess, Alexei V. Filippenko, Peter Challis, Alejandro Clocchiatti, Alan Diercks, Peter M. Garnavich, Ron L. Gilliland, Craig J. Hogan, Saurabh Jha, Robert P. Kirshner, B. Leibundgut, M. M. Phillips, David Reiss, Brian P. Schmidt, Robert A. Schommer, R. Chris Smith, J. Spyromilio, Christopher Stubbs, Nicholas B. Suntzeff, John Tonry, Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant, The Astronomical Journal 116(3), 1009 to 1038 (September 1998), doi:10.1086/300499; arXiv astro-ph/9805201v1 (15 May 1998), the version transcribed.
2. Adam G. Riess, Louis-Gregory Strolger, John Tonry, Stefano Casertano, Henry C. Ferguson, Bahram Mobasher, Peter Challis, Alexei V. Filippenko, Saurabh Jha, Weidong Li, Ryan Chornock, Robert P. Kirshner, Bruno Leibundgut, Mark Dickinson, Mario Livio, Mauro Giavalisco, Charles C. Steidel, Narciso Benitez, Zlatan Tsvetanov, Type Ia Supernova Discoveries at z > 1 from the Hubble Space Telescope: Evidence for Past Deceleration and Constraints on Dark Energy Evolution, The Astrophysical Journal 607(2), 665 to 687 (June 2004), doi:10.1086/383612; arXiv astro-ph/0402512v2 (31 March 2004), the version transcribed.
3. S. Perlmutter and 31 others, and the Supernova Cosmology Project, Measurements of Ω and Λ from 42 High-Redshift Supernovae, The Astrophysical Journal 517(2), 565 to 586 (June 1999), doi:10.1086/307221. Quoted, not recomputed.
4. The verdict’s sources and the 2025 to 2026 exchange are cited in full where they appear above. The transcriptions, their checksums and the code that made them are described in this page’s NOTICE.txt, beside it.