Hilbert 12: contracting ambient torsion and theta transport
Author: Komorebi P.
This research package continues the pure cubic experiment \(K=\mathbb Q(\beta)\), \(\beta^3=7\).
Contents
H12_Contracting_Ambient_Torsion_Research_Note.md: formal statements, proofs, analytic theta-return formulas, the complete mod-seven torsion dynamics and the exact distribution identity.h12_contracting_seven_packet_verify.py: integer and rational algebra of the seven-point packet, plus optional high-precision numerical theta-carry checks.h12_full_ambient_torsion_verify.py: all 343 period carries, all orbit lengths, the order-21 arithmetic action, and optional numerical tests of the rank-three distribution identity.H12_Contracting_Seven_Packet_Verification_Log.txt: accepted exact and numerical run.H12_Full_Ambient_Torsion_Verification_Log.txt: accepted exact and numerical run.SHA256SUMS.txt: hashes of the included files, excluding the hash file itself.
Reproduction
Requires Python 3 with SymPy and mpmath. The optional complete distribution numerical test also uses mpmath. NumPy is not required.
python h12_contracting_seven_packet_verify.py
python h12_full_ambient_torsion_verify.py
python h12_contracting_seven_packet_verify.py --numeric
python h12_full_ambient_torsion_verify.py --numeric
Verification boundary
The exact script assertions check algebraic and finite-group identities. The analytic distribution formula is proved from the convergent elliptic-gamma logarithmic series in the mathematical note. Its numerical replay is supplementary, not an interval certificate. No Lean compilation or independent external review is claimed for this package.
Open: The exact identity between the normalized elliptic-gamma special value and the constructed cubic class-field unit. This package does not solve Hilbert's twelfth problem, the complex cubic algebraicity conjecture, or the remaining polarized phase identity.