TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/C4-DESCENT-FINITE-MONODROMY.txt
Original file SHA-256: b707e2d720a6dad3a74115b62f16d76077dfda3fe0d3eb8f0f8f76edaf5d7bd5
Inclusive original lines: 10-60
Line numbers below refer to the original source.
This bounded excerpt is source evidence; it is not a new proof/checker run.
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000010 | PROVED, BUT NOT NEW: the exact analytic closure of the v117 monodromy was
000011 | already present in the 28 September Gesamtsynthese.  The actual four point
000012 | connection descends by t=z^4 to a three point Fuchsian system with local
000013 | orders (4,3,2).  Its orbifold monodromy is therefore the faithful
000014 | three dimensional S4 representation.  With the original orientation the
000015 | order four generator is U^(-1), and the marked representation is conjugate
000016 | to the exact v117 pair (U^(-1),M0).  The numerical ODE comparison in v117 is
000017 | only a basis calibration, not the proof of finiteness.
000018 | 
000019 | The shorter gauge used below makes the residue at infinity semisimple with
000020 | no integral resonance.  It is meromorphically equivalent to the older
000021 | printed gauge, whose one possible resonance was explicitly cancelled.  The
000022 | two arguments prove the same result.
000023 | 
000024 | This positive C4 descent does not contradict the separately proved absence
000025 | of a rational inversion lift.  C4 is sufficient.  The connection is not a
000026 | D4 linearized connection.
000027 | 
000028 | 1. Recovered primary source
000029 | ===========================
000030 | 
000031 | The result is printed in:
000032 | 
000033 | [OMITTED: non-scientific conversation or execution metadata]
000034 | [OMITTED: non-scientific conversation or execution metadata]
000035 | [OMITTED: non-scientific conversation or execution metadata]
000036 | [OMITTED: non-scientific conversation or execution metadata]
000037 | [OMITTED: non-scientific conversation or execution metadata]
000038 | [OMITTED: non-scientific conversation or execution metadata]
000039 | 
000040 | Those lines contain the substitution t=z^4, the old gauge
000041 | diag(1,z,z^3), the three residue spectra, the infinity resonance check,
000042 | the triangle group argument, the marking U^(-1), the exact diagonal of M,
000043 | and the distinction between the A4 four puncture image and the extended S4
000044 | image.  They also continue to the signed permutation basis and the genus
000045 | two curve.  The present report only restores the part needed for the v117
000046 | analytic monodromy claim and checks it independently.
000047 | 
000048 | The active source modules against which it is reconciled are:
000049 | 
000050 |   source:80af15193155b4dcf60c
000051 |   verification/v116_resonance_uniqueness.py:1-170
000052 |   SHA256 e9cbeb665cf8c1a2bed3f34281be06aee4c661d784e7f13a5bd8e9be37f577ca;
000053 | 
000054 |   source:830238c9699fad6ae325
000055 |   verification/v117_monodromy_weyl_a3.py:1-206
000056 |   SHA256 55eca6a64144f6e49789f3f1bbe84e256764e7ce92b207044be693f8684d5df5.
000057 | 
000058 | The [N] status of the analytic identification still printed in v117 is
000059 | therefore stale relative to the older source.  The exact matrix properties
000060 | in v117 remain correct.