# Gap-11 — Dark Matter

## What this gate must establish

This gate must show that the frozen 13D geometry supplies a viable dark-matter candidate — a stable, neutral state with the right relic abundance — without that candidate being fitted to the observed cosmological data. Concretely, it must produce a particle whose stability, production rate, and present-day abundance follow from the geometry's structure and a derived coupling, then compare the resulting abundance to the measured Ω_DM h² ≈ 0.12 only after the prediction is frozen.

## The geometry's role (load-bearing, not validation)

The candidate is not invented for the purpose: the boundary structure of the geometry's `S¹_Y/ℤ₂` factor localizes a ℤ₂-odd, zero-hypercharge state at a fixed point, and that same structure is what makes it stable (the ℤ₂-odd parity forbids decay; zero hypercharge keeps the coupling renormalizable). In the corpus's selection audit this state was picked out 17 of 18 times across five reweightings — a structural selection, not a fit to any abundance. Two viability gates are already banked: renormalizable stability (Y = 0) and a one-sided KK-overclosure pass across the inflaton band. The geometry thus carries the candidate's identity and stability; it does not, on its own, fix the one number the relic abundance depends on.

## Current honest status

**Status: OPEN** (recorded in the corpus as "conditional, blocked on a named gate"). This is a serious candidate / partial unification — **not validated**. Promotions: 0.

The single blocker is the **portal normalization** `N_portal`: the derived coefficient of the operator coupling the candidate to the Standard-Model bath, which must come from a wavefunction-overlap integral on `S¹_Y/ℤ₂` and **not** be tuned to reproduce 0.12. Until it is derived, neither the freeze-in relic integral (Ω_DM h²) nor the spin-independent cross-section σ_SI can be computed. The blocking objects are:

- **The portal operator identity** — the explicit coupling (Higgs-portal-like, Wilson-line/KK-mixing, or higher-dimension) is not yet named in the corpus, and its ℤ₂ charge must be checked against the stability gate.
- **The portal normalization `N_portal`** — a finite, compact geometric overlap integral; specifiable but unrun, and an owner/machine computation rather than a logical argument. An open ambiguity (whether the frozen `λ_p(0.12) ~ 10⁻¹¹` *is* this normalization) could narrow the block but is unresolved.
- **A frozen reheating temperature T_RH** — inherited-conditional from Gap-09 (reheating), currently a ~3-orders-of-magnitude band, itself cascading on Gaps 08 and 04.

A null-forecast is banked at **forecast grade**: σ_SI ≈ 10⁻⁵⁵–10⁻⁶⁰ cm², roughly 6–11 orders of magnitude below the neutrino floor. The falsifier is therefore one-sided — no null experiment can confirm the candidate; only a positive WIMP-like signal can adjudicate, and any such signal would kill the minimal candidate.

## What would close it

There is exactly one new derivation this gate needs of its own: evaluate the portal-normalization overlap integral on `S¹_Y/ℤ₂` (after naming the portal operator), then run the standard freeze-in Boltzmann quadrature for Ω_DM h² and compute σ_SI from the *same* coefficient — comparing to 0.12 only after the prediction is frozen. This requires a frozen Gap-09 T_RH band as input, so closure here is gated on Gap-09 (and transitively Gaps 08/04). Because the load-bearing adjudication is an experiment with a null-forecast far below current reach, the honest endpoint is asymmetric: the candidate can be **refuted** by a direct-detection signal but cannot be **confirmed** by any foreseeable null result.

## Sources

- Gaps & Walls Register, TOE programme (status vocabulary; OPEN/conditional grading): `…/Fable_Version/rendered/TOE/GAPS_AND_WALLS_REGISTER.md`
- Gap-11 dossier — decomposition, named missing objects, and tractability: `…/Fable_Version/rendered/TOE/gap_11_dark_matter/` (`00_decomposition.md`, `01_named_missing_objects.md`, `02_tractability.md`)
- Cross-gap dependency (T_RH band): Gap-09 reheating folder, `…/Fable_Version/rendered/TOE/gap_09_reheating_thermal_history/`
- Primary theory text: `toe.md` §IV / §V (the four-paper Fable TOE manuscript)

No external links are fabricated; abundance (Ω_DM h² ≈ 0.12) and σ_SI figures are quoted as recorded in the corpus, where they remain forecast-grade pending the portal-normalization derivation.