The Baby-Monster gate is sewing data, not another character

Date: 25 October 2026

Status: multiplier reconstructed by Arf conjugation; the required order-23-twined genus-two amplitude family is not present in the reviewed corpus

Evidence: machine-readable source-gate ledger

Certificate: source-gate verifier

Result

Three established results meet at this gate:

1. cutting an Ising vector out of the Moonshine module produces the Baby-Monster super VOA \(VB^\natural\) of central charge \(47/2\);
2. its even algebra has exactly three irreducible modules \(VB^0,VB^1,VB_T\), with Ising fusion rules;
3. Monster \(2A\) fermionization is the pointwise product, on a shared spin structure, of one free Majorana factor and the fermionic Baby-Monster factor.

These facts identify the carrier but do not evaluate its genus-two amplitude vector. The fusion ring records which channels may meet. It does not supply the analytic conformal blocks, sewing coefficients, or order-23 insertions. The reviewed primary literature gives an explicit genus-two sewing formula for the free fermion, but not the order-23-twined ten-even-spin vector for \(VB^\natural\).

1. What is fixed

Yamauchi proves that \(VB^\natural\) is a simple SVOA, that \(VB_T\) is its irreducible twisted module, and that

Lin and Shao establish

The central-charge identity constrains the product anomaly. It does not, by itself, determine relative phases among ten genus-two spin sectors.

2. Why characters and fusion stop short

For a VOSA \(V\), epsilon-sewing has the schematic form

with sector and automorphism labels added in the twisted case. A genus-one character supplies only the vacuum insertion \(u=\mathbf1\). Fusion rules specify allowed intermediate modules, but not the complete torus one-point functions, dual-basis contractions, intertwining normalizations, or their order-23 insertions. Thus central charge, three vacuum characters, the Ising fusion ring, and the untwined aggregate Moonshine genus-two function are all insufficient individually.

3. Minimal direct construction packet

Let \(b\in\mathbb B\) be the order-23 element obtained from a \(46C/46D\) Monster root after quotienting the central \(2A\) involution. A direct sewing construction requires:

1. the \(b\)-action on \(VB^0,VB^1,VB_T\) and compatible intertwining spaces;
2. \(b\)-twined torus one-point functions for the homogeneous sewing states;
3. invariant bilinear forms and dual-basis contractions;
4. a convergent vector $Z^{(2)}_{VB,b}\lbrack\delta\rbrack(\Omega)$ on the ten even characteristics;
5. its monomial action under \(K=S^2R^{-11}\);
6. separating degeneration to the order-23 genus-one traces.

4. Exact alternative and resolved multiplier

The Arf/Fourier reconstruction replaces direct Baby-Monster sewing by sixteen order-23-twined Monster amplitudes with all flat \(2A\) backgrounds. Its signed \(16\times16\) kernel is orthogonal after \(1/4\) normalization.

The follow-on Arf-conjugation audit then fixes the Baby-Monster \(K\) multiplier before those functions are evaluated: it is the edgewise inverse of the free multiplier. The remaining source gate is therefore purely at amplitude and degeneration level.

Boundary

The absence claim is limited to the primary sources reviewed here and the local corpus as of the stated date. A general sewing formalism is not an evaluated Baby-Monster answer. Fusion and central charge are not promoted to an amplitude calculation.

Sources and corpus links

• Yamauchi, 2A-orbifold construction and the baby-monster vertex operator superalgebra
• Höhn, Self-dual Vertex Operator Super Algebras and the Baby Monster
• Lin and Shao, Duality Defect of the Monster CFT
• Tuite and Zuevsky, Genus Two Partition and Correlation Functions for Fermionic Vertex Operator Superalgebras I
• Tuite and Zuevsky, Part II
• Free-Majorana relation-defect multiplier
• Arf/Fourier Baby-Monster reconstruction
• Arf-conjugated Baby-Monster 0 multiplier
• Joined order-46 bridge