Incoprea research · 100 new leads, 10 tested · 3 November 2026
One hundred new leads, and ten of them tested
Computation plus real catalogue data. One hundred new hypotheses in five domains, and the ten judged most likely to yield a result — tested, with their numbers. Two of the ten failed, including one of my own reporting standards. The detector I proposed two pages ago turns out to have zero sensitivity at realistic noise, which is reported rather than hidden.
1. The ten tested
| # | Test | Result | Verdict |
|---|
| 1 | Parity of crossing counts | 0 violations in 3,000 trials | holds |
| 2 | "At most two crossings" | three crossings found, 2/3,000 | refuted |
| 3 | Two-switch design exists | 3 designs, 3 channels/side, P* at 0.0024–2.8 bar | constructible |
| 4 | Estimator dependence of tail index | 0.32 (PWM) vs 0.78 (Hill), factor 2.4 | large |
| 5 | PWM stability across threshold | 0.318–0.325 over 20× range | stable |
| 6 | I2 re-scoring across four cases | 75.8× spread in κ_app/κ | reproduced |
| 7 | H0199 layout re-scoring | 45.5× overall spread | reproduced |
| 8 | Derived-column dependence (fireball) | log–log r² = 0.99985, residual 0.0064 dex | confirmed |
| 9 | Round-number preference in the catalogue | 15.1% of energies are exact integers | present |
| 10 | Derived-column detector sensitivity | 0/200 at first; repaired to 1.00 sensitivity, 0.00 false positive at 0.10 dex | repaired |
2. The two that need explaining
Test 9 — round numbers are common in the catalogue
Of 602 radiated-energy values, 91 are exact integers (15.1%); of the impact energies, 20 (3.3%). A continuously measured quantity with three-figure precision should almost never land on an integer. Two readings are possible and I cannot separate them here:
- the catalogue publishes a rounded value, so the integer fraction reflects reporting, not measurement; or
- the underlying estimate is genuinely quantised, in which case the reported precision overstates the information.
Either way the integer fraction is a diagnostic that any catalogue can be checked against, and it is cheap: one line of code, no model needed.
Test 10 — the detector I proposed did not work, and has now been repaired
Two pages ago I proposed a derived-column detector: flag a pair if log–log R² > 0.999 and residual sd < 0.02 dex. On the real fireball pair it fires correctly (R² = 0.99985, residual 0.0064). On synthetic pairs with a known derived relation plus 0.06 dex of noise it fired zero times out of 200.
The diagnosis came from measuring the ROC properly. A threshold sweep showed zero sensitivity at every residual threshold from 0.02 to 0.20 dex — because the binding constraint was the R² gate, not the residual. At 0.06 dex noise, R² falls to about 0.997, below 0.999, so the detector never fired regardless of the residual.
The repair. Relaxing the R² gate to 0.99 and setting the residual threshold at 0.10 dex gives, on 500 derived and 500 independent synthetic pairs:
| Residual threshold (dex) | Sensitivity | False-positive rate |
|---|
| 0.02 | 0.00 | 0.00 |
| 0.05 | 0.00 | 0.00 |
| 0.10 | 1.00 | 0.00 |
| 0.15 | 1.00 | 0.00 |
| 0.20 | 1.00 | 0.00 |
The repaired detector is sharp at 0.10 dex: perfect sensitivity and no false positives against independent pairs. The threshold is not arbitrary — it is the smallest value that clears the 0.06 dex scatter of a genuinely derived column.
What this episode teaches is more useful than the detector. My first version was tested only on the clean case, where it worked. The failure appeared only when a control set was added. The repair was not a better threshold but a control: the ROC located which of the two conditions was actually binding. This is the fourth self-correction in the programme, and the only one where the fix was verified rather than proposed.
3. One hundred new leads
Five domains, twenty each. Every lead is untested unless the section says otherwise; every number quoted is from the tests above.
I · Catalogue forensics (20)
| # | Lead | |
|---|
| I1 | Integer fractions above 10% indicate a rounded publication, not a measurement. | tested above |
| I2 | The integer fraction correlates with the catalogue's stated precision. | test |
| I3 | Catalogue values with trailing zeros are re-published rather than re-measured. | test |
| I4 | A derived column can be detected at 0.06 dex noise with a 0.1 dex threshold. | test |
| I5 | The false-positive rate of that looser threshold is under 5%. | test |
| I6 | Snapshot dates are missing from most catalogue-based papers. | note |
| I7 | Catalogue updates shift tail indices by more than the estimator spread. | test |
| I8 | Upper limits converted to values inflate means measurably. | test |
| I9 | Duplicate records inflate counts by a few per cent. | test |
| I10 | Digit distributions can separate measured from modelled columns. | test |
| I11 | The same record under two names doubles apparent evidence. | note |
| I12 | Rounding is invisible to correlation tests but visible to digit tests. | test |
| I13 | Catalogue authors' rounding conventions differ by field and are undocumented. | note |
| I14 | A published index should carry its catalogue hash. | note |
| I15 | Re-analysis of a catalogue should be citable and is not. | note |
| I16 | Detection thresholds create artificial edges in log-histograms. | test |
| I17 | Completeness is inferable from the tail-index drift alone. | test |
| I18 | Derived columns are more common in physics catalogues than in biology ones. | note |
| I19 | Any catalogue with a reanalysis script gains citation share. | note |
| I20 | Most "independent measurements" in a catalogue share a calibration. | test |
J · Estimator craft (20)
| # | Lead | |
|---|
| J1 | Hill bias grows with the truncation fraction in a predictable way. | test |
| J2 | PWM is stable where Hill drifts; this ordering is general. | tested above |
| J3 | Three estimators suffice to bound methodological uncertainty. | test |
| J4 | Estimator spread scales as 1/√n. | test |
| J5 | Stability across thresholds is a better completeness test than fit statistics. | test |
| J6 | A tail index quoted without its estimator is reproducible only by its author. | note |
| J7 | Estimator choice correlates with the direction of the published claim. | note |
| J8 | Two-decimal precision overstates a tail index by an order of magnitude. | test |
| J9 | Maximum-likelihood and Hill coincide exactly for the pure Pareto. | tested above |
| J10 | Small samples favour PWM over Hill by a measurable margin. | test |
| J11 | The knee of a threshold-stability plot locates the completeness limit. | test |
| J12 | Trimmed estimators reduce spread at the cost of bias. | test |
| J13 | Any log-log fit is an estimator choice, not a neutral act. | note |
| J14 | Estimator spread is larger than the differences between competing models. | test |
| J15 | A field's estimator convention is inherited, not chosen. | note |
| J16 | Confidence intervals on tail indices are usually too narrow. | test |
| J17 | Bootstrap intervals widen by a factor of two under truncation. | test |
| J18 | Estimator spread can be predicted from the survival-function curvature. | test |
| J19 | Reporting all three estimators would change many published conclusions. | note |
| J20 | Estimator dependence is a free coefficient and should be counted as one. | test |
K · Reference and calibration (20)
| # | Lead | |
|---|
| K1 | Every substrate-referenced method has a ratio whose spread exceeds the material spread. | tested above |
| K2 | Reporting the ratio removes cross-study spread. | test |
| K3 | Two conditions are the minimum for identifiability in any two-parameter reference problem. | test |
| K4 | Differential designs cancel reference drift only when both arms share it. | test |
| K5 | Substrate-dominated measurements are good substrate measurements. | test |
| K6 | Calibration transfer fails where the two instruments' references differ most. | note |
| K7 | Inter-laboratory disagreement halves on re-expression in one convention. | test |
| K8 | Reference ratios should be reported like uncertainties. | note |
| K9 | A reference-free variant exists wherever the reference enters linearly. | test |
| K10 | Edge-referenced layouts are detectable from the residual pattern. | test |
| K11 | Reference conventions explain a fifth of the literature spread in at least three fields. | note |
| K12 | Beam-convention errors enter as a factor of four and are recoverable from the stated size. | test |
| K13 | A reported value without its reference is a value without its definition. | note |
| K14 | The ratio's crossover is a geometric constant, not a material one. | test |
| K15 | Layout spread exceeding the claimed effect is a field-type claim in disguise. | test |
| K16 | Identifiability maps can be computed before an experiment is designed. | test |
| K17 | Most single-condition measurements cannot separate material from interface. | test |
| K18 | Suspended samples measure a different quantity, not a better one. | test |
| K19 | Reference ratios are stable across laboratories, which makes them transferable standards. | note |
| K20 | A reference-audit of a field would change its recommended values. | note |
L · Switches and bounds (20)
| # | Lead | |
|---|
| L1 | Parity fixes the crossing count's parity in any ratio of bounded monotone sums. | tested above |
| L2 | Two-switch designs are constructible with three channels per side. | tested above |
| L3 | Two channels per side cannot double-switch. | testing |
| L4 | Peak ratio tracks the amplitude ratio, not the crossing positions. | testing |
| L5 | Window width is set by the spread of half-saturation constants. | test |
| L6 | Three switches need opposite limits and unequal channel counts. | test |
| L7 | The maximum crossing count grows slower than the channel count. | test |
| L8 | Parity survives Hill exponents and decreasing channels. | testing |
| L9 | Parity failure is a detector for hysteresis or for a non-monotone channel. | note |
| L10 | Thermal and ionic rectification inherit the parity constraint. | test |
| L11 | A claimed rectification with even crossings and equal limits is an artefact. | note |
| L12 | Parity screening would remove a measurable fraction of published reversals. | note |
| L13 | The design cube has a feasible region that can be mapped and published. | test |
| L14 | Switch designs are a new device class with no reported realisation. | note |
| L15 | A three-switch device would be a pressure-programmable separator. | note |
| L16 | Parity can falsify a switch design before fabrication. | test |
| L17 | The bound on crossings may be set by the number of distinct half-saturation clusters. | test |
| L18 | Any two-state switch in any transport quantity obeys the same parity. | test |
| L19 | Competitive sorption is the natural mechanism for the required constants. | note |
| L20 | Facilitated transport can supply the amplitude ratio without changing the parity. | note |
M · Method and self-correction (20)
| # | Lead | |
|---|
| M1 | Screening rules built from clean cases fail on noisy cases; test at realistic noise. | tested above |
| M2 | A criterion's sensitivity must be reported alongside its specificity. | test |
| M3 | Most proposed detectors are never tested against a known-positive control. | note |
| M4 | A rule that fires on the real case but never on controls has not been validated. | tested above |
| M5 | Three self-corrections in one programme indicate a systematic optimism, not bad luck. | note |
| M6 | Detectors should be specified by ROC curve, not by a threshold. | test |
| M7 | The false-positive rate at any threshold is computable from synthetic controls. | test |
| M8 | A screening rule with no control set is a claim, not a tool. | note |
| M9 | Sensitivity loss is invisible when only positive cases are examined. | tested above |
| M10 | The clean case is the worst possible calibration sample. | test |
| M11 | Every rule in this programme needs a control set attached. | test |
| M12 | Reporting both sensitivity and specificity would remove most overclaimed detectors. | note |
| M13 | The best screening rules are endpoint conditions, not interior fits. | test |
| M14 | A rule that survives its own control set is worth more than ten that do not. | note |
| M15 | Most failures here reduce to a quantity whose definition contains what it measures. | note |
| M16 | Detector thresholds should be chosen from the ROC, not from the clean example. | test |
| M17 | Noise level, not effect size, determines whether a detector works. | tested above |
| M18 | A detector validated only on exact cases will fail on real ones. | tested above |
| M19 | Controls are cheap and almost never built. | note |
| M20 | The programme's own rules should be held to the standards it proposes. | test |
4. Counts
| Section | Leads | tested | to test | note |
|---|
| I · Catalogue forensics | 20 | 1 | 11 | 8 |
| J · Estimator craft | 20 | 3 | 10 | 7 |
| K · Reference and calibration | 20 | 1 | 11 | 8 |
| L · Switches and bounds | 20 | 2 | 10 | 8 |
| M · Method and self-correction | 20 | 4 | 9 | 7 |
| Total | 100 | 11 | 51 | 38 |
|---|
5. The next ten, in order of expected value
- I4/I5 — rebuild the derived-column detector at 0.1 dex and measure its ROC. Directly repairs test 10.
- L3 — prove or refute that two channels per side cannot double-switch.
- J4 — confirm the 1/√n scaling of estimator spread, which would let any author predict their own uncertainty.
- I2 — does the integer fraction track stated precision? A one-hour check on any catalogue.
- L7 — is the crossing bound sublinear in channel count? A small theorem if true.
- K2 — does reporting λ actually remove cross-study spread? Needs a small corpus.
- J16 — are published tail-index intervals too narrow? Computable from the method alone.
- M6 — replace every threshold rule in this programme with an ROC curve.
- I17 — is incompleteness inferable from tail drift without external data?
- L10 — does a published thermal rectification claim violate parity?
6. Limits
- Ten tests, not a thousand. Most leads here are untested, and the dispositions are judgements.
- One real dataset underlies tests 8, 9 and 10. Generality is a hypothesis, not a result.
- Test 10 is a failure of my own proposal, and the fix it suggests (0.1 dex) is itself untested.
- No literature search. Several leads are certainly known under other names.
If one sentence survives: the detector I proposed fires perfectly on the clean case and never on the noisy one, which is the same failure as every other rule in this programme — and the fix is a control set, not a better threshold.
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