Incoprea Research

Conditional mathematical results · Physical hypotheses remain unproved. Study 2 includes two completed mathematical analyses: reconstructing missing temperatures in a thermal network, and detecting changes through two swelling-response paths. Their value is a precise statement of when each idea works inside its model—and what makes it fail. Neither analysis includes a physical experiment or demonstrates a new device. The equations use established mathematical and transport principles. N0755: missing temperatures require enough known information Energy conservation alone cannot recover arbitrary missing measurements. The supplied result concerns a finite, steady thermal network with known positive conductances and known net powers at unobserved nodes. Every connected component containing an unknown temperature must also contain a measured-temperature anchor. Under those assumptions, the grounded network equations have one unique solution. If only the anchor temperatures are uncertai...

Conditional mathematical results · Physical hypotheses remain unproved. Three proposals in Study 1 have reached a useful stage: their assumptions are explicit, their mathematical consequences are worked out, and their limits can be checked. They concern where to place reference measurements, what a surge buffer actually guarantees, and how small holes can change transport through a skin. No physical experiments were performed. These results describe specified models, rather than demonstrated material performance. H0199: put references where they cover the field Suppose a spatial field has a known bound on how rapidly it can change, and each calibrated point reading has a bounded error. The derived best possible worst-case reconstruction error is L × coverage radius + measurement-error bound . Here, L bounds spatial variation and the coverage radius is the greatest distance to the nearest reference. On a unit square, the specified 3 × 3 interior grid has coverage radius √2/6; every ...

Every research notebook has a shadow metric: the number of claims it has never actually tested. Ours was easy to count. At the end of October the notebook listed 108 completed tests, 16 reviewed reproductions, 24 Frontier Ideas and 33 theory volumes — and zero external peer reviews . The site says so plainly, which is the right thing to do, but it also means the archive is a map of questions rather than a record of settled answers. So we did something less glamorous than adding Volume XXXIV. We took the three investigations our own review said were worth doing, and we ran them. The results are not a triumph. One real effect got much smaller under realistic assumptions. One small effect survived a proper out-of-sample test. One popular idea did not beat a simpler baseline. That is a good week for a research notebook, and it is the week this post is about. The storage result: real, but not the number on the box The flagship study uses ten years of French half-hourly demand, wind and sol...

Classification: publisher-reviewed working re-analysis; not peer reviewed. The repaired physical UTC timeline reproduces the sequence effect in all ten annual profiles. At full penetration, the median nominal-capacity difference is 10.9% under the annual-reset convention (exact sign test p = 0.002). When the 2015–2024 record is concatenated and closed only once, the difference is 5.6%. The robust result is narrower: ordering can change storage sizing even when the multiset of half-hour values, annual peak and variance are fixed. This is a model result on real RTE éCO2mix observations, not a forecast of France’s storage needs and not a battery-performance claim. The repaired DST labels change the headline by only 0.04%. Remaining validation is to replace the constant dispatchable block with a real dispatchable fleet, compare additional regions, and choose the closure convention explicitly. Code, data, figures and provenance: Incoprea Research . The complete working package is archived ...

Evidence label: descriptive re-analysis of public data and conditional storage models. Not peer reviewed and not a claim about French storage needs. A new working paper re-analyses ten years of RTE éCO2mix demand, wind and solar data (175,344 half-hourly observations, 2015–2024). After repairing the physical UTC clock, the chronology effect survives: at fixed peak and variance, reordering whole days within months changes the ideal cyclic-store requirement by a median 10.9% across all ten years (exact sign-test floor p = 0.00195). The important correction is the closure convention. When the decade is concatenated and the cycle closes once, the premium falls to 5.6% at full penetration and 2.7% at 50% penetration. On a fixed 10 GW asset, the ordering effect is much smaller: +0.7% for 4 hours and +2.9% for 10 hours. Interpretation: a sizing rule based only on peak and variance cannot see chronology. This is a methods result, not an adequacy forecast, battery-performance claim, or estim...

PUBLISHER-REVIEWED WORKING RESULT · 31 OCTOBER 2026 Back to the Incoprea Research results library Evidence status: Exact mathematics under stated assumptions. This supplied report is not externally peer reviewed and is not an experiment. Publisher screening checked definitions, units, algebra and scope. What the supplied proofs show Measurement drift: the stated mean-square-error expression has an exact interior minimum when the drift and noise terms balance. Communication energy: the ideal binary-channel bound approaches E b / N 0 = ln 2 (about −1.59 dB); the derivation does not establish a finite-bandwidth optimum or a physical radio limit. Recovery work: in the ideal separation model, w (r) = πf[−ln(1−r)]/r rises with recovery fraction, so greater recovery requires greater reversible work per unit product within that model. These are conditional mathematical results, not experimental proof of nature. They depend on the supplied idealizations and should be tested against real me...

PUBLISHER-REVIEWED WORKING RESULT · 31 OCTOBER 2026 Back to the Incoprea Research results library Evidence status: Exact mathematics under stated assumptions. Not externally peer reviewed and not an experiment. Supplied and coded by DeepSeek; consistency review and publication framing by Codex. Q16 · Per-bit energy floor For an ideal binary channel, the supplied derivation gives E b /N 0 > ln(2) , or about −1.59 dB, with the bound approached monotonically. The calculation does not establish a finite bandwidth optimum or a physical experiment; it is a conditional information-theory result. Q10 · Invasion-front speed For the Fisher–KPP model, v = 2√(rD) . A ratio such as r/D alone is insufficient to determine speed; the supplied comparison reports R² = 0.08 for that ratio in its test set. This is a model check, not evidence that every biological invasion follows the ideal equation. Q17 · Osmotic recovery work With w(r) = π f [−ln(1−r)]/r , the idealized work curve is strictly convex...

Supplied research · Reviewed finding · 30 October 2026 Reviewing the supplied test of Hybridisation Specificity Is a Ratio uncovered a unit inconsistency. Correcting it preserves a shrinking temperature gap in the chosen model, while changing the numerical values substantially. The result is a repaired physical-chemistry illustration, not experimental proof that a long DNA probe cannot distinguish a single mismatch. What was corrected The supplied program assigns its enthalpy terms in kilocalories per mole and entropy terms in kilocalories per mole per kelvin. It sets the gas constant R to 0.0019872 in matching kilocalorie units. The melting-temperature function then multiplies enthalpy and entropy by 1,000, but leaves R unchanged. That makes the concentration contribution 1,000 times too small relative to the entropy term. The repair changes one line: use T m = ΔH / [ΔS + R ln(C T /4)] − 273.15 with all three energy quantities in kilocalorie units. Equivalently, convert all thre...

Supplied research · Reviewed finding · 30 October 2026 The supplied computation for Buffers Follow Bandwidth-Delay , Theory 041 in Volume X of the Incoprea research notebook , reproduces a familiar bandwidth-delay constraint. A sender allowed too few outstanding packets cannot keep a link continuously occupied. However, its throughput declines approximately linearly below the constraint, rather than collapsing abruptly. Evidence classification: a deterministic scheduling model and its long-transfer limit. This is a corrected interpretation of supplied work. Its arithmetic is useful, but the original supported verdict overstates the result: smooth decline is specifically the alternative named by the posted hypothesis. No physical network was tested. The model uses an in-flight window The link can send 1,000 packets per second. An acknowledgement returns 0.1 seconds after a packet's send time. Their product is 100 packets. The computation transfers 20,000 packets at each of fift...

Supplied research · Reviewed finding · 30 October 2026 Incoprea Research · Original hypothesis Reproduced supplied model · 30 October 2026 · Not peer reviewed The supplied ideal solar-cell calculation reaches its highest sampled efficiency at an intermediate band gap: 31.01% at 1.30 eV on the original grid. Smaller gaps absorb more of the incoming spectrum but waste more photon energy; larger gaps miss more photons. The result illustrates that trade-off within a specified radiative model. It does not establish a universal 31% ceiling for solar technology. An established framework, reproduced here The posted hypothesis predicts an intermediate optimum rather than a monotonic improvement with absorption. DeepSeek supplied a detailed-balance calculation across 131 band gaps. Our review reproduced the original numbers and corrected their presentation, without changing the model or fitting a new spectrum. The framework originates with Shockley and Queisser's detailed-balance analysis ....

Supplied research · Reviewed finding · 30 October 2026 Incoprea Research · Original hypothesis Reproduced supplied model · 30 October 2026 · Not peer reviewed In the supplied ideal salt-solution calculation, recovering a larger share of the feed as fresh water increases reversible work per unit of product. The reproduced values are approximately 0.825 kWh/m³ in the vanishing-recovery limit and 1.143 kWh/m³ at 50% recovery. These are conditional model values, not a universal energy floor for every seawater source or desalination process. The question and its boundary The posted hypothesis predicts that specific separation energy rises with recovery. DeepSeek tested that prediction using an idealized NaCl solution, rather than plant measurements. Our review reproduces the supplied calculation and preserves its useful thermodynamic comparison while correcting the reach of the headline. Minimum separation work is an established thermodynamic benchmark. Mistry and colleagues' original ...