# T_DM_NULL — Pre-registered analysis recipe

**Test:** Direct dark-matter null tracker. Anti-prediction: DCT
predicts σ_SI = 0 exactly; ΛCDM expects WIMP cross-section in 10⁻⁴⁵
to 10⁻⁴⁸ cm² range; continued null detections extend agreement with DCT.

## Null hypothesis (ΛCDM)

Particle dark matter exists as a WIMP with `σ_SI ~ 10⁻⁴⁵ – 10⁻⁴⁸ cm²`
at `m_χ ~ 100 GeV` (range across canonical WIMP models — neutralino,
heavy neutrino, etc.). The expectation is that direct-detection
experiments should make a positive detection within their
sensitivity-time-product budget.

## Alternative hypothesis (DCT)

DCT-DM-01 Eq. 12: `σ_SI = 0` exactly. There is no particle dark matter
in DCT. All "dark matter" phenomenology is gravitational, sourced by
the Brans-Dicke scalar field gradient `(1 − P)·∇²Φ`.

## Falsifier signature

A positive WIMP detection at any current-or-near-future direct
detection experiment at >5σ falsifies DCT's dark-sector treatment.

## Public dataset

- LZ Collaboration 2023, *PRL* 131 041002 — current best limit:
  `σ_SI < 9.2 × 10⁻⁴⁸ cm²` at `m_χ = 36 GeV/c²` (90% CL).
- XENONnT 2023 — `σ_SI < 2.58 × 10⁻⁴⁷ cm²` at `m_χ = 28 GeV/c²` (90% CL).
- PandaX-4T 2023 — `σ_SI < 3.3 × 10⁻⁴⁷ cm²` at `m_χ = 40 GeV/c²` (90% CL).
- DAMA/LIBRA — claims signal at 13σ but excluded by all other DM
  experiments using xenon / argon / silicon / germanium.

## Statistical method

Tracker model: each year, the strongest WIMP exclusion limit is
recorded. The DCT prediction `σ_SI = 0` is consistent with every
exclusion to date. The "agreement" is one-directional: DCT predicts a
hard zero; data reports an upper bound; agreement extends the joint
Bayesian preference for DCT-no-DM over ΛCDM-with-DM.

For the joint Bayesian, use a uniform prior `σ_SI ∈ [10⁻⁵⁰, 10⁻⁴⁰] cm²`
on the ΛCDM hypothesis and a delta function `σ_SI = 0` on the DCT
hypothesis.

```
log10 BF(DCT/LCDM) = log10[ Δ_LCDM_excluded / Δ_LCDM_full ]
                   ≈ log10[ (10⁻⁴⁰ − σ_SI_excl) / (10⁻⁴⁰ − 10⁻⁵⁰) ]
                   ≈ 0  (this is the wrong way to compute it)
```

A more honest metric: the `(σ_SI_excl) / (canonical_WIMP_expectation)`
ratio. For LZ 2023, σ_excl = 9.2e-48 vs canonical neutralino ~ 10⁻⁴⁵
gives a factor 100 below canonical. This is the "extending agreement"
direction: DCT prediction `0` is an order of magnitude below LZ 2023's
upper bound, so LZ 2023 cannot exclude DCT, while it does exclude
several canonical neutralino models.

## Decision rule

- All current direct-detection experiments report null → **NEUTRAL +
  extending agreement** (DCT-consistent, but not a discriminator).
- A 5σ positive WIMP detection at any experiment → **FALSIFIED**.

## Cross-validation

XENONnT, PandaX-4T, and LZ are independent experiments using different
target nuclei (xenon for the first two; xenon for LZ also). Three
independent collaborations all report null detection, supporting the
robustness of the null.

## What could go wrong

- Several non-WIMP candidates (axion, sterile neutrino, etc.) would
  not show up in WIMP detectors but would also be inconsistent with
  DCT's "no particle DM" prediction. The test is specifically against
  WIMP DM, not against all forms of particle DM.
- A "DAMA-like" signal claim has been contested and not reproduced;
  the test treats DAMA/LIBRA as not-confirmed pending independent
  reproduction.

## Recipe disposition

DCT prediction is a hard zero. Test produces a tracker output with
the year, experiment, exclusion limit, and a comparison to canonical
WIMP expectation. Classification: **NEUTRAL + extending agreement** in
the sense that data is consistent with DCT but does not measure DCT
directly.