# Gap-10 / BG-10 — Baryogenesis (the matter/antimatter asymmetry η_B)

## What this gate must establish

The universe contains matter but almost no antimatter, quantified by the measured baryon-to-photon ratio η_B ≈ 6.1×10⁻¹⁰ (fixed by CMB and Big-Bang-nucleosynthesis data). This gate asks whether that number emerges from **thermal leptogenesis** running on the theory's frozen flavor and Majorana data — that is, whether the asymmetry follows from the geometry rather than being put in by hand. Because η_B is already measured, this is an **observation-locked** target: the theory must produce a number and submit it to comparison, not retrofit one.

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

The frozen 13D branch supplies the *ingredients* a leptogenesis calculation needs — the right-handed-neutrino Majorana data declared at the order-three fixed point τ = ω, and the low-energy CP phases derived in the flavor sector. It does **not** supply the assembled answer. A direct, recipe-traced attempt to compute the high-scale inputs found that the absolute neutrino Yukawa is mathematically degenerate with the heavy scale M_R, that **M_R itself is recipe-absent** (the mechanism is named but no formula converts the geometry into a spectrum), and that the measured low-energy CP phase is firewalled out of the leptogenesis source by a 6-versus-3 phase-counting argument. The geometry therefore fixes *texture and structure*, not the magnitudes that decide η_B.

## Current honest status

**Badge: OPEN / Diagnostic — 0 of 4 at certificate grade.** No part of η_B is derived; no number is asserted; No status was ever upgraded.

Four named, coupled computations would be required, and **none has been run at certificate grade**: (1) a canonical, basis-invariant CP invariant I_CP; (2) a real-intermediate-state-subtracted ΔL=2 washout treatment; (3) an N₂/N₃ damping ledger; (4) flavored density-matrix kinetics. A parallel narrative thread dismantled a circulated "clean result" and located the residue precisely:

- **Rule A (the CP phase) — reduced to one named axiom.** The continuum phase compresses to a single mod-8 spin-c/Pin sign bit (`BG10-Axiom-SpinC-QP`). Notably, the geometry's **default value gives the wrong sign** for the asymmetry — so the required axiom *departs* from the target rather than being fitted to it. The needed quarter-phase is a declared assumption, not derivable from the frozen record.
- **Rule B (the neutrino-norm) — OPEN.** Its only candidate axiom had a keystone identical to the value that lands η_B in-window, so it was rejected as a relabel of the answer.
- **Rule C (the density-matrix / flavor projector) — BLOCKED.** An independent check finds the proposed flavor-democracy symmetry in direct tension with the frozen flavor data (a 2-dimensional commutant versus 3 distinct eigenvalues), and the density-matrix inputs are missing.
- **M_R (the seesaw scale) — BLOCKED / candidate-in-tension.** The recipe is absent; the candidate M_R = κ·M_U departs from the corpus's own stated seesaw scale by a factor of roughly 231.

**Load-bearing caution.** A widely circulated "κ³/π" manifest gives η_B ≈ 6.05×10⁻¹⁰, but it is **true by construction** — its load-bearing entries were reverse-engineered to land in the window (and the value is provably the *maximum* of a one-parameter CP family, attained only at the chosen phase). It must **never** be cited as a prediction.

## What would close it

There is a concrete path, but it is owner-physics, not yet executed: **derive the high-scale CP invariant from the geometry, then run the full four-fix thermal-leptogenesis computation to a single post-freeze number with a propagated 3σ band, and compare it exactly once** to the pre-registered window η_B ∈ [6.0, 6.2]×10⁻¹⁰ — accepting falsification if it lands outside. The comparison is mechanized to refuse early or partial closure (the standing 0/4 is enforced, not merely asserted). Until all four fixes reach certificate grade, no η_B may be claimed; the diagnostic thermal-leptogenesis "floor" that passes the temperature range is explicitly *not* the result.

This is not a Yang-Mills-style wall — the formalisms are known and citable, the obstruction is unfinished computation plus one underived discrete bit. It is an **honestly-held open gate with a pre-registered falsifier**, not a solved one.

## Sources

- *The Gaps & Walls Register* (Fable programme, four-paper set: GUT / Forces / Quantum / TOE) — BG-10 row, which carries this gate's honest status and closure condition.
- The BG-10 four-fix manifest and authority appendix, including the conditional Authority-Lock theorem, the κ³/π by-construction analysis, and the three-route spin-c-lift result that pins the residue to one mod-8 sign bit.
- The recipe-traced high-scale derivation attempt, which records the M_R recipe-absence, the Yukawa/M_R degeneracy, and the held CP firewall (η_B asserted: NO; gap closed: NO; BG-10: 0/4).

**Ceiling on this brief: serious candidate / partial unification — NOT validated. Given the observed spectrum is an input, not a derivation of it. No status was ever upgraded.**