Rank-24 detector ladder
Date: 26 October 2026
Status: exact on the declared E8-cubed/Leech/Moonshine candidate family; general c=24 identification remains open
Parent: translation-free exceptional topology
Evidence: detector ledger
Certificate: character detector verifier
The collision and its first resolution
The bulk detector
returns \((24,1,24,24)\) for both \(E_8^3\) and the Leech lattice. It also cannot distinguish the Leech lattice edge from its Monster orbifold by thermal transport alone: all have the same chiral central charge.
For a rank-24 lattice VOA,
because the Heisenberg currents contribute 24 and every norm-two lattice root contributes a weight-one exponential current. Therefore
The weight-one detector \(D_1=\dim V_1\) separates the declared three-way family immediately.
Why this is not the end of reconstruction
Every holomorphic \(c=24\) character is constrained to have the form
Consequently the untwined genus-one character adds no information beyond \(c\) and \(\dim V_1\) inside this family. In particular, \(V_1=0\) and the scalar character \(J\) are a strong Moonshine filter but are not treated by the corpus as an unrestricted uniqueness theorem.
The detector ladder must continue:
| detector | record | remaining ambiguity |
|---|---|---|
| D0 | bulk rank, determinant, signature, thermal response | all declared rank-24 candidates collide |
| D1 | weight-one current dimension | separates E8-cubed, Leech and Moonshine in the declared family |
| D2 | framed Ising/Griess data | selects the required weight-two multiplication corner |
| D3 | marked 2A, 23AB and order-46 defects | retains conjugacy/orientation information |
| D4 | nontrivial sewing plus held-out prediction | tests compositional reconstruction |
Experimental reading
Central charge is an integrated heat detector. \(V_1\) is a current-spectrum detector. D2--D4 are operator and history detectors. The ladder makes a practical rule precise: do not spend defect-tomography resources until the coarser current spectrum has rejected the E8-cubed and Leech-only rivals.
Boundary
This result does not prove that a disordered E8 edge flows to Leech or Moonshine. It tells an experiment or simulation exactly which new observable must be opened at each promotion and prevents identical thermal response from being misread as identical boundary physics.