# INCOPREA RESEARCH — EXPEDITION V
## THE HIDDEN DISCOVERY LABORATORY

**300 hypotheses · 30 decisive dossiers · 3 verification investigations · 5 volumes**

*Total: ≈ 261,000 words.*

---

## The question this expedition asks

Expeditions I–IV asked *what could exist*. Expedition V asks something narrower and harder:

> **Where does existing scientific knowledge leave a precise, experimentally resolvable gap — and
> which measurement would settle it?**

Every hypothesis here begins from a disagreement or an uncertainty between two credible accounts, states
both of them fairly, and specifies the test that separates them. **A hypothesis with no discriminating
test was rejected at generation**, not at review.

---

## Structure: six discovery programs

| Program | Method | Hypotheses |
|---|---|---|
| **A** | Model collisions — two credible models, one shared regime | H001–H050 |
| **B** | Measurement collisions — two methods, one mechanism | H051–H100 |
| **C** | The missing variable | H101–H150 |
| **D** | Causal mechanism competitions | H151–H200 |
| **E** | Frontier technique crossovers | H201–H250 |
| **F** | The simple decisive experiment | H251–H300 |

---

## Deliverables

| Volume | File | Scale |
|---|---|---|
| **A** — 300 hypotheses | `01_VOLUME_A/VOLUME_A_COMPLETE.md` | 12-section entries, ~199k words |
| **B** — 30 dossiers | `02_VOLUME_B/VOLUME_B_COMPLETE.md` | 13-section dossiers, 58k words |
| **C** — 3 investigations | `03_VOLUME_C/VOLUME_C_COMPLETE.md` | derivation + computation |
| **D** — disagreement atlas | `04_VOLUME_D/ATLAS.md` | model pairs, missing variables, cheap tests |
| **E** — overlap register | `05_VOLUME_E/OVERLAP_AND_ORIGINALITY.md` | what was compared, what was not |

---

## The three investigations

| | Hypothesis | Result | Status |
|---|---|---|---|
| **C1** | 1/f noise: number or mobility fluctuation? | Both scale as 1/N — a geometry series at fixed carrier number is the only clean discriminator ($-1$ vs $0$ slope) | Computational model result |
| **C2** | Laplace pressure displaces a droplet's transition | $\Delta T=2\gamma T_m/(\rho\Delta H r)$; $\Delta T\cdot r$ constant separates it from chemistry; 0.33 K resolution needed at 20 vs 40 nm | Derivation + computation |
| **C3** | Butler–Volmer vs Marcus at high overpotential | BV is exactly linear in Tafel; Marcus peaks at $\eta^*=\lambda$ and reverses sign | Derivation + computation |

**All three are theory/computation. No empirical claim is made** — no data were available, and none is
simulated in place of data.

**C3 corrected its own hypothesis:** H007 quoted a 1100× separation at 0.6 V; the computed separation is
$10^5$–$10^6$ and depends strongly on $\lambda$ and $\alpha$. The sign test survives; the magnitude claim
does not.

**C1 corrected my own first calculation twice** — the Lorentzian amplitudes did not sum to 1/f, and I had
conflated trap density with carrier density. Both were caught by the output disagreeing with the expected
result.

---

## What is different about this expedition

1. **A disagreement must exist.** Every entry names two accounts and states where they diverge. Entries
   whose accounts coincided under the proposed test were discarded — several batch authors report doing
   exactly that.
2. **The test must be cheap where possible.** Program F is 50 questions answerable with a filter, a
   second gas, a wider tube, or reanalysis of published data.
3. **Pre-registered decision rules.** Every dossier section 8 fixes a threshold before data.
4. **An explicit overlap register**, including two duplicates found after assembly and documented rather
   than hidden.

---

## The duplicate problem, stated plainly

Program F was written by two agents running concurrently that could not see each other's files. Two
questions were therefore asked twice:

- **H255** ≈ **H284** (BET range dependence)
- **H256** ≈ **H276** (calibration curvature: stray light vs aggregation)

Both are documented in Volume E §3. The corpus therefore contains **298 distinct questions, not 300**.
They were retained rather than replaced, because finding genuine replacements would require generating
more candidates, and the brief prefers a documented shortfall to fabricated novelty.

---

## Reproducing

```bash
cd 06_SUPPORTING && python3 build_volume_a.py
cd ../03_VOLUME_C/C1_noise_mechanism && python3 c1_noise.py
cd ../C2_laplace_shift && python3 c2_laplace.py
cd ../C3_bv_marcus && python3 c3_bv_marcus.py
```

Deterministic; numpy only.

---

## Limitations

- **No literature search was performed.** Every prior-art statement is against this corpus only, and is
  marked unverified. Do not cite any entry as a novel claim without checking it.
- **Volume A is a question index, not evidence.** The entries state what is unresolved and how to settle
  it; they do not establish anything.
- **The 30 dossiers refine the questions, not the answers.** Their value is the decision rule and the
  error budget.
- **The three investigations are model results.** None is an empirical finding.