Hilbert 12 Ambient Cubic Fourier Attempt
Author: Komorebi P.
This package contains a new exact algebraic continuation of the pure cubic Hilbert 12 program together with an explicit meromorphic gamma candidate and numerical diagnostics.
Included files
H12_Analytic_Fourier_Resolvent_Research_Note.md— mathematical setup, proofs, conditional analytic targets, and scope.H12_Analytic_Resolvent_Verifier.py— exact SymPy polynomial audits and independent mpmath fifth-smoothed gamma series.H12_Analytic_Resolvent_Verification_Log.txt— accepted exact checks, gamma data, and negative control.
Reproduce
Requires Python 3 and sympy and mpmath.
python H12_Analytic_Resolvent_Verifier.py --exact-only
python H12_Analytic_Resolvent_Verifier.py --dps 64 --nbase 4000 --n10 19000 --n23 34000 --negative-control
All work is offline.
Established
- Exact order three Möbius action extending the Galois action on the cubic roots.
- An invariant quotient coordinate and a one parameter cyclic cubic pencil.
- Exact perfect square discriminant and the three deformed Fourier identities.
- A canonical rational analytic gamma candidate and an explicit scalar obstruction.
- An algebraic reduction to gamma chart orbit identities plus trace normalization.
- Numerical agreement at conductor three, with a separate negative control at one quarter.
Not established
- The analytic gamma chart orbit relations.
- The exact trace normalization of those analytic values.
- The vanishing of the gamma scalar obstruction at one third.
- The elliptic gamma/class field equality or Hilbert's twelfth problem.
The numerical log does not constitute an interval proof. The analytic series tail has a mathematical bound, but the floating point operations themselves are not directed interval computations. The first attempted numerical run had prematurely rounded 1/3. The accepted log was generated after correcting this precision issue.