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Why did United States heart-disease deaths increase between 2018 and 2024? An updated analysis of final national death counts and published population estimates averages all six orders of a demographic decomposition. Known-age deaths increase by 28135. Population size contributes 25981.4 deaths, age composition 26512.2, and age-specific rates -24358.5. Demographic contributions outweigh the negative rate contribution. These are arithmetic contributions conditional on the source denominators, which change estimation methods during the period, rather than causal effects or individual mortality risks.

• Published, Reproduced, Reviewed.Published, Reproduced, Reviewed: In the bundled CDC WONDER D158 final snapshot for United States residents with known age, 2018-2024 heart-disease deaths increase by 28,135. Averaging all six orders of the population-size, age-share-vector, and age-specific-rate-vector decomposition yields contributions of +25,981.4, +26,512.2, and -24,358.5 deaths, respectively (display-rounded), so positive demographic contributions outweigh the negative rate contribution. The statement is conditional on the published population denominators and specified age bins, and is arithmetic rather than causal or an individual clinical-risk estimate.

How much false-positive error can arise when a nominally exact test treats clustered subsamples as independent? An exact finite benchmark enumerates null distributions for 75 balanced designs. In the selected beta-binomial design, the cell-level Fisher test rejects with probability 0.21567065919813758, compared with 0.0436374106894531 for a test using the known clustered null. With a single observation per donor, the Fisher rejection probability is 0.021484375. These are exact probabilities conditional on the specified toy model. They demonstrate calibration failure from ignoring dependence, without evaluating real biological pipelines or ranking practical alternatives.

• Published, Reproduced, Reviewed.Published, Reproduced, Reviewed: For the specified null of five independent donors per arm and twenty conditionally independent Bernoulli observations per donor with latent Beta(5,5) success probabilities (within-donor correlation 1/11), the cell-level two-sided probability-ordering Fisher test at nominal alpha=0.05 rejects with exact-model probability 0.215670659198, versus 0.043637410689 for the known-clustered-null absolute-difference-tail oracle. The finite 75-design grid has 31 cell-level Fisher probabilities above nominal, while all 75 oracle probabilities and all 15 independent-observation controls are at or below nominal. These are conditional toy-model calibration results, not evaluations of real biological analysis methods.

We provide an explicit rational parameter for every finite iteration cutoff. Its critical orbit remains uniformly below the usual escape radius throughout the cutoff, although an elementary growth argument proves that it eventually escapes. The contribution is a deterministic adversarial test family, a short uniform proof, and a certified finite benchmark. Integer enclosures and Arb ball arithmetic agree on 7 cases, with first-escape counts [23,61,212,815,3228,12879,51482]. Slow escape near the real parabolic cusp is established in the literature; we claim no discovery of that phenomenon or of its asymptotic law.

• Published, Reviewed.Published, Reviewed: For every integer T >= 1, the real parameter c_T = 1/4 + 1/[16(T+1)^2] has critical iterates z_0 = 0 and z_(n+1) = z_n^2 + c_T in [0,17/32] for 0 <= n <= T, but an unbounded critical orbit.
• Published, Reproduced, Reviewed.Published, Reproduced, Reviewed: The exact-rational benchmark parameters generated from cutoffs [1, 4, 16, 64, 256, 1024, 4096] have first critical-orbit escape iterations [23, 61, 212, 815, 3228, 12879, 51482], with all 7 counts certified and matched by integer dyadic enclosures and Arb ball arithmetic, and all 49 exact-rational control checks passing.

Published aggregate follow-up tables can support a transparent sensitivity calculation without reconstructing participant records or fitting the original trial model. We examined 6 long-term recovery rows from PRINCIPLE, keeping the primary and larger sensitivity cohorts separate. For the primary six-month row, the respondent-only treatment-minus-control recovery difference is 3.071 percentage points. Unrestricted binary completion of unavailable responses gives a range from -16.54 to 21.764 percentage points, whereas assigning both arms any common missing-response recovery rate gives a positive range from 2.329 to 2.896 percentage points. These are conditional bounds, not confidence intervals. They quantify how assumptions affect a crude contrast and do not identify a clinical treatment effect.

• Published.Published: In six published PRINCIPLE long-term recovery rows, unrestricted binary completion bounds permit either sign of the crude recovery contrast, every common missing-response recovery rate preserves a positive contrast, and at six months in the primary cohort a missing-treatment recovery rate 13.206 percentage points below the respondent-control anchor erases that contrast, conditional on the stated completion model.

Can a simple electricity-use schedule transfer across years? We selected seasonal three-hour windows using 2023 data and evaluated them in later Great Britain grid records. Relative to midnight use, assigned average carbon intensity was 5.78% lower in 2024 and 13.15% lower in 2025. The schedule performed worse on 137 and 111 days, respectively. A single year-round window did not improve both years. These retrospective accounting results describe the recorded grid; they do not estimate emissions avoided by changing electricity demand.

• Published, Reproduced, Reviewed.Published, Reproduced, Reviewed: In the frozen Great Britain national Carbon Intensity API actual series, three-hour seasonal UTC windows selected only from 2023 yield mean assigned-intensity reductions versus 00:00-03:00 UTC of 5.778479% across 364 complete days in 2024 and 13.150070% across 365 days in 2025, compared with -9.430428% and 2.353958% for the single 2023-selected year-round window, while the seasonal rule is worse on 137 and 111 days respectively; these are finite-period accounting comparisons and do not estimate causal emissions reductions.