the two rails share a plane, not a group

Exact assertion

The modular calculation now goes further. Fricke invariance gives the mixed branches as \(T_{23}((\tau+r)/23)\), and Fourier projection filters coefficients by \(n\equiv ab\pmod{23}\), reconstructing all 529 module characters as 25 scalar types. Volpato's inversion yields positive seeds for the twelve even-\(l\) commutant characters, and exact phase bookkeeping gives \(Z^{\mathcal N}_{23}/\sqrt{23}=q^{-1}+2+2446q+115834q^2+2446684q^3+33295322q^4+\cdots\). Fifth-power exchange preserves \(ab\), so this scalar defect trace is orientation-blind. The complete \(C_{23}\times S_4\) insertion census now rules out every additional scalar one-insertion trace. The look-here calculation must instead retain a vector-valued/projective \(S_4\) action, a relation among several insertions, or sew at genus two; another scalar trace cannot name 23A versus 23B.

What this commits us to

The construction is admitted only after the named additional input is supplied. The page records the dependency instead of hiding it inside the conclusion.

Logical anatomy

Verification route

1. Recover the declared objects and assumptions from the controlling documents.
2. Check the calculation, construction, obstruction or stopping rule on those same objects.
3. Compare the source conclusion with the exact assertion above; do not strengthen its verbs or enlarge its domain.
4. Apply the status rule and retain every named external dependency.

What would move or defeat this claim

Show that the named input is inconsistent, insufficient, unavailable, or fails to imply the claimed construction.

Source map

Controlling documents

• READMEOpen controlling document →
• open topics v1Open controlling document →
• frontier exhaustion checkpoint v1Open controlling document →