The hub currently carries, among others: I2 (a substrate-conductance bias in in-plane thermal conductivity, with a corrected crossover at λ = 0.4348); H0199 (reference-witness placement, with a 23% edge bias that is flat in N); N0751 (a differential swelling sensor with a matched-time control); H034 (elastic dipoles and MLIP error); H0346 (a hydrogel negative result); #13 (magnetic battery warning); #15 (sodium pulse charging); #24 (tactile calibration); and the storage-chronology analysis.
Two structural themes recur across them, and both are testable without a laboratory:
The new hypotheses below are derived from those two themes rather than from new physics.
Claim. For any measurement where a reference is subtracted, the spread of the reported quantity across accepted reference choices is predictable from the number of unmeasured reference parameters.
Test run. Pipe friction across flow regimes, where "regime" is the unmeasured reference parameter: spread 31.6× across regimes, 1.00× within a specified regime, 1.26× between two accepted turbulent correlations. The spread collapses exactly when the missing parameter is specified.
Disposition. test now — apply to I2's four literature cases and to H0199's six layouts. Both already have the numbers; this is a re-scoring, not a new experiment.
Claim. The probability that a proposed sensor appears to work rises with the number of free coefficients in its model, and the rise is steep enough to explain a substantial fraction of published sensor demonstrations.
Test run. A three-channel selectivity model at four levels of freedom: 0% of draws show an apparent reversal at one or two free coefficients, 13.2% at three, 24.0% at four.
Disposition. test now for N0751 — its 6.5% gain-matching requirement is precisely a free-coefficient count. The question is whether the published performance survives when the gain is fixed at the measured value.
Claim. A model with no saturating channel cannot produce a selectivity crossing; a reversal reported without one is a parameter artefact.
Test run. 600 random channel sets: 0 violations. Stress test with 0–4 forced saturating channels: maximum crossings observed 2 in every case, including S = 4, where a bound of S − 1 = 3 would have allowed more.
Disposition. test now as a screening rule; the tighter bound of 2 is unexplained and is itself a question (see N-11).
These are reported because they contradict what I expected, and one contradicts a claim made earlier in this batch.
I expected that a power-law exponent fitted over a narrow window would be poorly determined, supporting the view that fitted exponents are not measurements. The opposite happened. Recovering a known exponent n = 3 from data with 2% noise: over half a decade the fitted exponent has mean 3.00 and standard deviation 0.015; over three decades, 0.003. The exponent is recovered well even in the narrow case.
Consequence: my claim is withdrawn. The "fitted exponent is meaningless" argument does not survive at this noise level. It may survive at higher noise or with a systematic curvature, but I have not shown that, and the honest statement is that the test refuted my expectation.
I expected the reversal base rate to rise with the width of the parameter range. It did not: over 1, 2 and 4 decades the rate was 22.0%, 23.0% and 13.0% — non-monotone, and lower for the widest range.
Interpretation, cautiously. With a very wide range the parameters are more often far apart, which places the crossing outside the observation window rather than inside it. That is a plausible mechanism, but it is post hoc. The pre-registered expectation was wrong and is recorded as such.
| # | Hypothesis | Derived from | Disposition |
|---|---|---|---|
| N-04 | The I2 crossover λ* = 0.4348 is a universal constant of the Gaussian-spot geometry, and should be recoverable from any heat-spreading measurement regardless of material. | I2 | test now — reanalyse any published spot-size series |
| N-05 | H0199's 23% edge bias, being flat in N, is a boundary-value property rather than a sampling property; it should therefore appear identically in any smoother with a boundary condition at the domain edge. | H0199 | test now — swap the smoother; the bias should be invariant |
| N-06 | N0751's matched-time control is more diagnostic than its thickness fit, because a common-mode gain error cancels in the control but not in the fit. | N0751 | note — needs the device |
| N-07 | A two-parameter collapse (R, ζ) is minimal for second-order tracking; no one-parameter version exists for order ≥ 2. | batch 1 | note — small maths problem |
| N-08 | Any "intrinsic activity per area" figure is circular in the specific capacitance used to compute the area, so the circularity is diagnosable from the reported number alone. | hub Q010 | test now — check 20 papers for the assumed constant |
| N-09 | Catalytic rate constants normalised by total protein concentration will show a systematic offset equal to the unmeasured active fraction, and the offset should correlate with purification method. | hub Q016 | note — needs data |
| N-10 | The magnetic battery-warning signal is set by the return geometry, so a wire phantom can establish signal-to-background but cannot establish warning time; the two claims must be separated in any test. | #13 | note — apparatus |
| N-11 | The observed bound of two crossings, independent of the number of saturating channels, suggests the sign of N − D is determined by its two largest terms; a proof would give a much tighter screening rule than S − 1. | batch 1 T3 | test now — mathematics, no apparatus |
| N-12 | For a parallel-channel membrane, a reversal requires the two gases to be ranked oppositely by at least two channels; this is a necessary condition that can be checked without any simulation. | batch 1 | test now — check against reported reversals |
| N-13 | The spread at fixed dimensionless number predicts out-of-sample failure of a law, with a correlation too weak to be a screening tool on its own (measured 0.535). | batch 1 T6 | closed as a screen — too weak |
| N-14 | Handbooks constants that no one has re-measured will show a systematic bias toward round numbers, which is diagnostic of a copied rather than measured value. | hub U017 | test now — digit analysis on a handbook |
| N-15 | Storage-chronology results depend on the persistence control chosen, so any storage comparison that does not state its control is not comparable to another that used a different one. | storage record | note — editorial, not computational |
If one thing survives: of fifteen new hypotheses, three were cheap enough to test immediately, two of the three tests contradicted what I expected, and the hypotheses that survived are the ones that produced a number rather than an argument.