# INCOPREA RESEARCH — FRONTIER SCIENTIFIC DISCOVERY ENGINE **300 hypotheses · 30 refined dossiers · 3 pursued to result** This directory contains a complete run of the three-phase programme: generate 300 frontier scientific hypotheses, refine the strongest 30 into research dossiers, and pursue the best 3 to a defensible mathematical or computational result. --- ## Headline numbers | | Count | Words | |---|---|---| | Phase I hypotheses (H001–H300) | 300 | 120,402 | | Phase II dossiers (ranked) | 30 | 45,635 | | Phase III results | 3 | 4,700 + code | | **Total** | | **≈ 178,000** | --- ## The three Phase III results | | Hypothesis | Result | Status | |---|---|---|---| | **C1** | Transport precision in multi-terminal conductors | The thermodynamic uncertainty relation is the Cauchy–Schwarz inequality in the Onsager metric; the proposed slack law is **refuted** by an explicit counterexample family; a genuine violation exists in the sub-Poissonian thermal regime | Partial result: proof + refutation + counterexample | | **C2** | Stroboscopic sampling of entropy production | Sampling at $\Delta = n\pi/\Omega$ makes the reconstructed drift a scalar, so the current loses its rotational part **exactly** while the true entropy production is $4\Omega^2/\gamma$ | Formal proof (model-specific) + simulation | | **C3** | Mode counting in a square cavity | Distinct resonances are arithmetically suppressed: $N_{\rm dist}/N_{\rm tot} \sim (4K/\pi)(\ln X)^{-1/2} \to 0$, with the Landau–Ramanujan constant $K$ recovered numerically and an exact control that restores the ratio to 1.00000 | Formal proof + computation to $X = 10^7$ | Two of the three candidates were **partly wrong**, and the reports say so. Phase II did the same to the hypothesis set: all 30 selected entries were narrowed, and **at least 15 had their headline mechanism or central claim withdrawn or corrected** — see the corrections ledger in `02_PHASE_II_REFINED_30/PHASE_II_COMPLETE.md`. --- ## Directory map ``` 300 study 1/ ├── README.md ← you are here ├── 01_PHASE_I_HYPOTHESES/ │ ├── PHASE_I_OVERVIEW.md corpus construction, statistics, review findings │ ├── PHASE_I_COMPLETE.md all 300 entries, 120k words │ └── batches/B01…B30.md the 30 source batches ├── 02_PHASE_II_REFINED_30/ │ ├── SELECTION.md the 30 chosen, the rejects, and why │ ├── PHASE_II_COMPLETE.md ranking + corrections ledger + all 30 dossiers │ ├── scoring_A.md, scoring_B.md independent adversarial panel scores │ ├── build_phase2.py assembly + verification │ └── dossiers/D01…D30.md one dossier per hypothesis ├── 03_PHASE_III_DEEP/ │ ├── PHASE_III_COMPLETE.md synthesis of the three results │ ├── C1_transport_precision/ REPORT.md + c1_tur.py │ ├── C2_stroboscopic_null/ REPORT.md + c2_strobe.py │ └── C3_mode_counting/ REPORT.md + c3_weyl.py └── 04_SUPPORTING/ ├── STYLE_GUIDE.md the seven-part entry contract ├── PHASE_II_DOSSIER_CONTRACT.md the twelve-section dossier contract ├── build_phase1.py assembly + QA for Phase I ├── phase1_title_index.md 300-line index with testability type └── .venv/ numpy / sympy / mpmath environment ``` --- ## How the work was done **Phase I.** Thirty thematic batches of ten hypotheses, each batch constrained to a distinct scientific cluster and required to join at least four of its entries to a field that does not normally meet that cluster. Every entry uses a fixed seven-part form (title, hypothesis, connection, evidence, prediction, uncertainty, classification) with source-tier tags `[EST]` / `[OBS]` / `[SUG]` so that established results, published observation classes and suggested-but-unexamined sources are never conflated. No fabricated citations, DOIs or measurements appear anywhere; every number is a named constant or a labelled estimate. **Phase II.** Forty finalists were scored blind by two independent adversarial panels on mechanism, novelty, falsifiability, mathematical tractability, evidence availability and significance. The panels flagged 21 of 40 — a rate that indicates the screen worked. Their objections are recorded in `SELECTION.md`, including five hypotheses rejected outright as internally inconsistent or textbook. Thirty dossiers were then written to a twelve-section contract that required each author to narrow the claim, give it an equation and a dimensionless group, and confront the strongest competing explanation. **Phase III.** Three candidates were pursued to explicit statuses. Each report contains the exact claim, its foundations, the derivation, an independent numerical check, a stress test, and an honest outcome. All three computations are reproducible from the included scripts. --- ## What is genuinely new here The value of the submission is not that 300 ideas were produced. It is that: 1. **The screening is documented and adversarial.** Rejections, corrections and refutations are recorded rather than filtered out. Fifteen of thirty refined hypotheses had their central claim repaired or withdrawn during refinement. 2. **Three results are exact rather than suggestive.** A proof that the TUR is Cauchy–Schwarz; a proof that a specific sampling period erases dissipation identically; a proof that a square cavity's resolvable spectrum is deficient by an arithmetic factor that grows without bound. 3. **Each Phase III result comes with a built-in null.** Single-terminal driving saturates the transport bound; an irrational squared aspect ratio restores the mode count to exactly 1; the rotational fraction is machine-zero at half-integer periods. Predictions with a control that can fail are worth more than predictions without one. --- ## Reproducing the computations ```bash cd "03_PHASE_III_DEEP/C1_transport_precision" && ../../04_SUPPORTING/.venv/bin/python c1_tur.py cd "../C2_stroboscopic_null" && ../../04_SUPPORTING/.venv/bin/python c2_strobe.py cd "../C3_mode_counting" && ../../04_SUPPORTING/.venv/bin/python c3_weyl.py ``` Rebuild the Phase I and Phase II master documents: ```bash cd 04_SUPPORTING && .venv/bin/python build_phase1.py cd ../02_PHASE_II_REFINED_30 && ../../04_SUPPORTING/.venv/bin/python build_phase2.py ``` All scripts are deterministic (fixed seeds) and depend only on numpy. --- ## Known limitations, stated plainly - **Phase I is idea generation, not evidence.** The entries are mechanistic proposals. Their `[OBS]` tags name classes of observation, not verified datasets; a specialist would need to check each against the literature before treating it as prior art. - **Phase II refuted a lot.** Several selected hypotheses were wrong in their headline claim (H062, H124, H274, H285, H296) or in their proposed mechanism (H081, H227, H234, H241, H267). This is documented, not hidden, and it is the most useful part of the refinement. - **The three Phase III results are model results.** C2 and C3 are proved inside explicitly stated models; C1 is proved under standard linear-response assumptions. None is a claim about nature. - **C3's physical claim is open.** The counting deficit is mathematical; whether it explains measured mode deficits in real cavities requires the resolution-filtered calculation, which is specified but not done.