Incoprea research · five refined hypotheses · 3 November 2026

0. What this is, and what it is not

This page converts five selected ideas into investigations that could produce a numerical answer without a laboratory. It is a test plan, not a result. The distinction matters on this site: a plan has no evidence level, and none is assigned.

Each investigation is required to produce four things, and to fail visibly if it cannot:

Negative results are to be published with the same weight as supportive ones. Four of the five tests below are designed so that "the established model already explains this" is the most likely outcome; that outcome is the point.

Status vocabulary for this package

All five are currently planned. That label is the honest one and it should not be read as progress.

1. The five, at a glance

The order is a judgement about what can fail fastest and cheapest, not about which idea is best.

2. Pressure-induced membrane selectivity reversal — recommended first

Original claim (preserved): a membrane combining more than one transport mechanism can show a pressure-dependent crossover in gas selectivity, with a reproducible reversal for certain gas pairs and pore geometries.

Refined, falsifiable form: for a membrane in which Knudsen, solution–diffusion and adsorption-assisted (surface) transport act in parallel, the permeance ratio α_ij(P) for a stated gas pair is non-monotonic in pressure and crosses unity at a pressure P* that moves predictably with pore radius, temperature and adsorption affinity. The test is whether any such crossing survives when the transport model is constrained by independently measured isotherms rather than fitted.

Baseline first

Each mechanism alone is monotonic: Knudsen selectivity is pressure-independent; solution–diffusion permeance is pressure-independent above the linear regime; a Langmuir surface term saturates. A crossover therefore requires the mixture — and specifically requires that the saturating channel dominate at low pressure while the non-saturating channel dominates at high pressure. This is arithmetic, not a discovery, and the baseline computation should show it explicitly.

Test plan

1. Implement the three mechanisms separately, each validated against its own limiting case (Knudsen slope −1/2 in molar mass; constant solution–diffusion; Langmuir saturation).
2. Combine them with a consistent permeance definition, and verify that the combined model reduces to each single mechanism as the others are switched off.
3. Sweep pore radius 0.4–20 nm, temperature 250–400 K, adsorption affinity over two decades, and pressure 1–50 bar, for CO₂/N₂, CO₂/CH₄ and H₂/CO₂.
4. Record every α = 1 crossing with the parameter values that produce it.
5. Re-run with the adsorption parameters taken from published isotherms for named materials, rather than scanned freely. A crossing that exists only in the free scan is not a prediction.
6. Compare surviving crossings against published mixed-gas measurements.

Decision rule and falsification

Advance only if a crossing survives step 5 (constrained isotherms), persists under ±20% parameter perturbation, and is not contradicted by an existing mixed-gas measurement. The hypothesis dies if every crossing vanishes once adsorption parameters are constrained — which is the most likely outcome and would itself be a useful negative result: "the reversal is an artefact of unconstrained fitting."

Deliverable: a pressure–temperature map with the regions where α crosses unity, flagged by whether the underlying parameters came from measurement or from a scan.

3. Cross-system response-time mismatch

Original claim (preserved): a dimensionless ratio between intrinsic response time and external forcing timescale helps predict loss of tracking performance across different dynamical systems; any universal threshold must be established, not assumed.

Refined, falsifiable form: define R = τ_response/T_forcing. For linear systems the tracking error is a function of R alone (the standard first-order Bode response), so the only testable content is whether a shared threshold survives across systems of different order, nonlinearity and noise. The claim is that a single curve predicts held-out systems; the baseline says the curve is order-dependent and therefore not shared.

Baseline first

For a first-order lag driven sinusoidally, |error|/|input| = 1/√(1+(ωτ)²) — a function of R only. For second order, a damping ratio enters and the collapse fails. The baseline computation must show the collapse failing for order ≥ 2 before any new law is proposed. If it does not fail, the "law" is the standard response function.

Test plan

1. Build thermal, electrical and mechanical models at first, second and third order.
2. Drive each with sinusoidal, step and irregular (AR(1)) inputs.
3. Compute tracking error, phase lag, dissipated energy and stability margin.
4. Test whether any of these collapses onto R across orders, after normalising by order-specific parameters.
5. Repeat with a saturating nonlinearity and with measurement noise.

Decision: advance only if a single normalised curve predicts held-out model families better than the order-specific baseline. Dies if the collapse requires a per-order parameter, because then R carries no cross-system information.

4. Enzyme substrate-competition switching

Original claim (preserved): competition between primary and secondary substrates creates a predictable transition in relative enzyme activity, characterisable by dimensionless concentration ratios.

Refined, falsifiable form: for mutually exclusive substrates, the relative rate is already determined by established kinetics:

v_i = E_T k_cat,i (S_i/K_m,i) / (1 + Σ_j S_j/K_m,j)

So the crossover in v₂/v₁ as a function of S₂/S₁ is fixed by the ratio of specificity constants, and is not a new prediction. The only testable content is a systematic departure from this form — for example from allosteric competition, substrate inhibition, or a second binding site.

Test plan

1. Extract k_cat and K_m for enzymes with at least two documented substrates (SABIO-RK, BRENDA).
2. Compute the predicted crossover from the equation above for each enzyme, with no fitting.
3. Locate published measurements that scan both substrate concentrations.
4. Measure the residual between prediction and measurement on held-out enzymes.
5. Test whether any extension (substrate inhibition, two-site model) reduces that residual out of sample.

Decision: advance only if an extension beats the conventional model on held-out enzymes. Dies if the conventional model already predicts within the stated uncertainty — in which case the hypothesis is a rediscovery and should be recorded as such rather than deleted.

5. Fog collection versus surface geometry

Original claim (preserved): the ratio of feature spacing to incident droplet diameter predicts collection performance, with an optimum that depends on wettability, airflow and droplet-size distribution.

Refined, falsifiable form: in a droplet-interception-and-drainage model, collection per unit area is non-monotonic in the spacing ratio s/d, with an optimum whose position moves with contact angle and wind speed. The claim is a shape prediction (a maximum exists, and it moves), not a performance number.

Test plan

1. Implement interception (aerodynamic capture efficiency as a function of droplet Stokes number) and drainage (gravity shedding above a critical mass), separately validated.
2. Sweep s/d from 0.1 to 10 for smooth, periodic and irregular patterns.
3. Vary contact angle 20–150°, wind 0.5–10 m/s, and a lognormal droplet distribution.
4. Score collected and drained water, not intercepted droplets — an intercepting surface that never drains collects nothing.
5. Report the optimum's position and the width of the region within 10% of it.

Decision: advance if the optimum is robust across a factor-two change in droplet distribution. Limit, stated up front: this can only rank designs. It cannot establish real-world collection efficiency, and no such claim will be made.

6. Cellular expression variability and drug response — recommended last

Original claim (preserved): after controlling for mean expression, cell identity and technical noise, biological expression variability carries additional information about drug sensitivity.

Refined, falsifiable form: adding noise-adjusted dispersion (not raw variance) to a model that already contains mean expression, lineage and technical covariates improves held-out prediction of drug response across cell lines. The critical control is that variability is measured within comparable populations; variance across unrelated lines is a different quantity and does not test the claim.

Why this one is last

The claim needs single-cell expression matched to drug response. Bulk expression plus drug response exists (DepMap, Sanger), but bulk data contain no within-population variability. If matched single-cell plus response data cannot be located, the correct outcome is inconclusive, not a substitution of bulk variance for single-cell variance.

Test plan

1. Establish whether a public dataset joins (a) per-cell expression, (b) a drug-response measurement for the same line or donor, and (c) enough cells per condition to estimate dispersion.
2. If it exists: compute mean, variance, coefficient of variation and a noise-adjusted dispersion (correcting for the mean–variance relationship).
3. Fit nested models: mean-only; mean + covariates; mean + covariates + dispersion.
4. Validate by holding out cell lines, never random cells.
5. Report incremental held-out accuracy with confidence intervals.

Decision: advance only if the dispersion term improves held-out accuracy consistently and the interval excludes zero. Dies if the improvement vanishes under line-level holdout, which is the standard signature of leakage.

7. Recommended order and effort

Effort assumes an AI coding agent and ordinary Python libraries, with no physical experiment.

8. Known versus potentially novel

No prior-art search has been performed for this package. Every "could be new" cell is unassessed and must not be quoted as a novelty claim. A literature check precedes any promotion of these tests.

9. What this package does not establish

• No result of any kind. All five are plans. None has been run.
• No novelty. No literature search was performed for the five claims.
• No data confirmed. Every data source named below is a pointer to be checked, not a dataset verified as suitable.
• No experimental support. Four of the five cannot produce experimental evidence at all without a laboratory; the fifth depends on data that may not exist.
• No ranking of importance. The order is about cost and speed of failure, not about which idea matters.

10. Sources and verification status

No dataset was downloaded, joined or inspected in preparing this page. No number above is a measurement.

Back to the research hub

Status: planning document, 3 November 2026. All five investigations are planned. No experiment was performed; no result, novelty or data suitability is claimed. Original hypothesis wording is preserved above each refinement. Negative and inconclusive outcomes are to be published with the same weight as supportive ones.