TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/SZEGO-PRIMARY-SOURCE-REVIEW.txt
Original file SHA-256: 51c7b0639973a5dbd66e3e1d24942b96aa7000f6fa301dc4336b60c44e0b06da
Inclusive original lines: 1-35
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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000001 | PRIMARY SOURCE CHECK: GENUS TWO SZEGO FORMULA
000002 | 29 October2026. Targeted full-text review, not a new TFPT physical claim.
000003 | 
000004 | Eric D'Hoker, Martijn Hidding, Oliver Schlotterer:
000005 | Cyclic products of Szego kernels and spin structure sums.
000006 | Part I. Hyper-elliptic formulation.
000007 | JHEP05(2023)073, DOI10.1007/JHEP05(2023)073.
000008 | Published9May2023; arXiv2211.09069.
000009 | Publisher: https://doi.org/10.1007/JHEP05(2023)073
000010 | Full text read: https://inspirehep.net/files/3c360b43c44e559038c405631b0e3e07
000011 | Printed page8,section2.3, and printed page9,equations2.24-2.27
000012 | (PDF pages10-11, zero based).
000013 | 
000014 | Source result, paraphrased:
000015 | For genus two, an even spin is represented by a partition of six branch
000016 | points into two triples. Choosing square roots sA,sB of the corresponding
000017 | cubic polynomials with sA*sB=s gives the normalized Szego kernel
000018 |  [sA(x)sB(y)+sB(x)sA(y)]/[2(x-y)] * sqrt(dx/s(x))*sqrt(dy/s(y)).
000019 | The unwanted opposite-sheet pole cancels. The diagonal residue is one.
000020 | The paper also distinguishes the six odd spin structures from the ten even
000021 | ones. This is established primary mathematics, not a new kernel formula.
000022 | 
000023 | [OMITTED: non-scientific conversation or execution metadata]
000024 | [OMITTED: non-scientific conversation or execution metadata]
000025 | [OMITTED: non-scientific conversation or execution metadata]
000026 | [OMITTED: non-scientific conversation or execution metadata]
000027 | [OMITTED: non-scientific conversation or execution metadata]
000028 | [OMITTED: non-scientific conversation or execution metadata]
000029 | [OMITTED: non-scientific conversation or execution metadata]
000030 | 
000031 | Scope:
000032 | The primary reference supports the geometric Szego formula. It gives no
000033 | TFPT P1-to-APS operator map, no original choice of a reduced inverse,
000034 | and no physical state, reflection positivity or time identification.
000035 | No analogy with a string worldsheet is used as a TFPT spacetime claim.