No causal-set everpresent-Lambda Model 1 history among 83,760 noise sequences fits DESI DR2 BAO and Pantheon+ supernovae together

Version 3. Causal set theory heuristically predicts a cosmological constant that fluctuates over cosmic history (everpresent Λ). Three independent preprints have compared its stochastic Model 1 with DESI: with DR1 through fitted w0, wa; with DR2 for six supernova-selected histories; and with DR2 BAO alone. This short data note searches unselected Model 1 histories for a joint fit to DESI DR2 BAO and Pantheon+ supernovae. The analysis uses our reading of the recipe of Das, Nasiri and Yazdi (DNY): nodes a = i/n with n = 104 from z = 104, S0 = 0, and a sub-stepped quadrature of the four-volume. Our code does not reproduce DNY's published survival fractions on that discretisation. Steps of 0.002 in ln a come close to them, so the main search is repeated with those steps. Correction. Version 2 evaluated H(z) at the stored redshifts with the Λ of the next interval instead of the one in force. Version 3 fixes this, adds a regression test against an independent integrator, and repeats every run that depends on it. Replication. Of 20,000 noise seeds, refitting α and ωm for the best 200 gives one seed below ΛCDM on Pantheon+SH0ES (best Δχ2 = −0.88), where DNY's rate predicts about 3.6. This passes the replication criterion only in the form it took after a first failure. Main test. Of 540,000 draws on a grid in α and ωm, 257,130 survive (83,760 independent noise sequences). The best histories for each data set were refitted in α and ωm with their noise fixed (200 per data set; up to 3000). On DESI alone the best history reaches Δχ2 = 4.2 against ΛCDM. On uncalibrated Pantheon+ alone it reaches −4.4, with H0 ≈ 41 km/s/Mpc. On DESI+Pantheon+ the best is 67.8 (67.8 after refitting the best 3000). On DESI+Pantheon+SH0ES it is 47.8. Across conventions for DH (one point, or a window around each DESI redshift) these range down to 58.8 and 39.2. With steps of 0.002 in ln a they are 56.0 and 57.0. No survivor comes within Δχ2 ≤ 4 on either combination before the refit. The 95% upper limit, 3.6 × 10−5, is a rate per noise sequence averaged over the grid. It cannot separate Model 1 from the smooth Model 2, whose observed rate is 1.3 × 10−5. The verdict rests on the refitted minima. Robustness and caveats. Doubling the number of steps gives 72.1, 89.1 and 7.9 (DESI+Pantheon+, DESI+Pantheon+SH0ES, DESI), on a smaller sample. A second discretisation (logarithmic steps), whose registered replication failed and which is report-only, gives 66.5 (radiation-era starts) and 26.7 (later starts) for DESI+Pantheon+. No DESI+Pantheon+SH0ES search was run on it, but one history selected for DESI+Pantheon+ reaches 7.2 on that combination and 3.3 at ωb = 0.0212, which meets the Δχ2 ≤ 4 fit criterion; these are upper bounds on that combination's minimum, and the history starts its fluctuations at ai = 3 × 10−3, after the drag epoch, not at DNY's start. The registered step-size check failed. All results hold only for fixed choices: S0 = 0, a start at z = 104, and our grid ranges. The smooth Model 2 is not excluded by this rule. The plan and thresholds were committed before the runs they concern; the time stamps are our own git commits, not an external registry, and a disclosed pilot preceded the protocol. The archive contains the code, the data script with checksums, the protocol and its amendments, the review records and the files from which every number from our runs is generated. Version note. Version 3 fixes the H(z) error, repeats the affected runs, retitles the note (formerly "...cannot fit DESI DR2 BAO and Pantheon+ supernovae together"), moves the headline minima (DESI 1.2 → 4.2; DESI+Pantheon+ 74.1 → 67.8; DESI+Pantheon+SH0ES 54.0 → 47.8), withdraws the claim that Model 1 fits DESI alone, and adds a comparison with DNY's survival fractions, a log-step search, a DH convention check, deeper refits and scope statements. Version 2 (doi:10.5281/zenodo.23071404) cited three earlier preprints that version 1 (doi:10.5281/zenodo.23062385) missed, withdrew version 1's claim to be the first DESI test, and removed version 1's sentence "We found no test of Model 1 against DESI BAO". Both earlier versions remain available. The itemised changes of every version are in REVIEW_POSTPUB.md in the deposit.