# Corrections, negative results, and superseded claims

This file records everything in the collection that changed during construction, every claim that failed a quantitative check, and every place where a hypothesis was narrowed rather than defended. It is deliberately kept separate from the hypotheses so that a reader can see what the evidence did to the original idea.

## 1. Two hypotheses were replaced before publication

**C38 (chemistry).** The original entry claimed that electrochemical ammonia synthesis rates near the detection limit are dominated by ambient and membrane-derived contamination. A check against the prior Incoprea corpus found an existing hypothesis making essentially the same claim ("Most reported electrochemical ammonia synthesis is contamination"). Rather than republish it with a new number, C38 was replaced with a different electrochemistry hypothesis: that scanning electrochemical microscopy assigns a finite rate constant to insulating regions because its feedback theory assumes a conductive substrate. The replacement has a different mechanism (diffusion-limited approach curve fitted with a conducting-substrate model), a different observable (tip-radius dependence of the apparent rate over a known insulator), and a different refutation.

**P20 (physics).** The original entry attributed the residual muon g−2 discrepancy to a scheme mismatch in the intermediate window between lattice and data. A prior Incoprea hypothesis already assigns the residual to lattice hadronic-vacuum-polarization systematics. The overlap was judged too close. P20 was replaced with a different precision-physics hypothesis: that optical-clock comparisons inherit an unmodelled self-gravity term from the apparatus mass. The replacement is testable with a ballast-variation experiment and does not depend on the g−2 literature.

## 2. A hypothesis failed its own quantitative check: R04 / B01

**Original claim.** Plate-reader OD600 compresses above ~0.3–0.6 because of detector saturation and stray light, suppressing fitted growth rates.

**What was computed.** A stray-light model, measured OD = −log₁₀(10^(−OD_true) + S), with the bias in fitted μ obtained from a log–log regression over four candidate windows (`R1_refinement_numbers.py`, section A).

**Result.**
- S = 10⁻³, window OD 0.2–1.0: bias **−0.1%**
- S = 10⁻², window OD 0.2–1.0: bias **−1.1%**
- S = 10⁻³, window OD 2.0–3.0: bias **−8.0%**
- S = 10⁻², window OD 2.0–3.0: bias **−23.4%**

**Conclusion.** Stray light cannot explain compression in the OD 0.3–0.6 range. The hypothesis as originally stated is **not supported**. It was narrowed: the mechanism is real but confined to OD > 1.5, and any sub-exponential growth below OD 1 must have a different cause. The entry in `hyp/04-biology.md` now carries the corrected numbers and names the surviving candidate mechanisms (detector nonlinearity, meniscus and fill volume, evaporation, physiological shift) along with the tests that separate them.

**Why it is kept.** A hypothesis that loses cleanly is the point of the collection. The failed mechanism was removed from the suspect list for the low-OD regime, which is a real gain.

## 3. A hypothesis was corrected in direction but not in kind: R21 / X33

**Original claim.** Inverse-variance weighting with variances estimated from the same data biases the weighted mean toward points whose noise fluctuated low.

**What was computed.** 40 000 Monte Carlo trials with four measurements and 2–30 degrees of freedom per variance estimate.

**Result.** The mean is unbiased (−0.000 to 0.005). The *spread* of the estimator exceeds its nominal value: 0.686 at 2 dof, 0.582 at 5, 0.539 at 10, 0.511 at 30, against a nominal 0.5. The quoted uncertainty is therefore 73%, 86%, 93% and 98% of the true spread.

**Conclusion.** The heading was wrong, the phenomenon is real. The refined entry now claims uncertainty understatement rather than mean bias, with the dof-dependent magnitude.

## 4. A hypothesis overstated its own effect size: R20 / X13

**Original claim.** Non-stationarity makes every estimated autocorrelation time too short, and hence every error bar too small, by a large factor.

**What was computed.** For a linear trend of amplitude a against noise σ, the ratio of the true standard error to the naive one is √(a²/12 + σ²)/σ.

**Result.** 1.01 at a/σ = 0.5; 1.04 at 1; 1.15 at 2; 1.53 at 4.

**Conclusion.** The effect is real but modest — under a factor of two even when the trend is four times the noise. The refined entry says so explicitly and restricts the claim to regimes where the trend dominates.

## 5. A claim about test power was softened after computation

In I1 the initial framing assumed that a broad distribution of relaxation times would be indistinguishable from a power law over a short window. Direct evaluation of the log-normal Laplace transform showed the opposite: a log-normal spectrum produces a strongly curved decay, and a 0.5-decade window is enough to reject a single power law at 1% noise when the window sits on the spectral knee. The investigation was rebuilt around the offset term instead, where the degeneracy is genuine and the Cramér–Rao bound actually diverges. The discarded framing is recorded here rather than deleted.

## 6. Numerical errors caught during development

- **I2, Hankel quadrature.** The first version of the validation integral was missing a factor of two and disagreed with the closed form by exactly 0.5 at every λ. The closed form was correct; the check was fixed. Agreement is now 2×10⁻¹³.
- **I3, spectral derivative.** The first harmonic-balance implementation divided the derivative of η by N, making the capacitive current 128× too small. The symptom was a fitted C_dl of 0.156 µF against a true 20 µF. Fixed by using the exact rfft/irfft derivative.
- **I3, Bessel comparison.** The first comparison used the thermal voltage RT/F where the Tafel parameter RT/(αF) was required, so the analytic and numerical curves differed by a factor of two in x. The identity was right; the comparison was wrong.
- **I3, Lin–KK.** The first Lin–KK implementation used an unbounded least-squares Voigt fit and reported a residual of 0.17 even for an exactly linear spectrum. Rather than use a fragile test, the final version compares the measured spectrum directly against the exact Debye form, which gives 10⁻⁷ and is unambiguous.
- **R1, DSC lag.** The first version double-converted scan rate and produced onset shifts of 12–200 K. Replaced with a time-constant formulation giving 0.4–6.7 K.
- **R1, TDTR.** The first sensitivity model was two series resistances, which is trivially degenerate at all frequencies. Replaced with a thermal-quadrupole multilayer model that includes the film's heat capacity and reproduces the expected frequency dependence.

## 7. Things that were not done

- No experiment was performed. No apparatus was built. No sample was measured.
- No published dataset was reanalysed directly. The reanalysis predictions in I2 and R03 are stated as tests, not as results.
- The arXiv records cited were retrieved through the arXiv API and their abstract pages returned HTTP 200 on 1 November 2026. Their content was read at abstract level; no claim in this collection depends on a number taken from a paper without saying so.
- The 300 hypotheses were checked against 358 prior Incoprea hypothesis titles with a string-similarity screen. Two overlaps were found and replaced (section 1). The similarity screen cannot catch semantic overlap with different wording, so residual overlap remains possible.