TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/original-local-source-variable-background-20261102/CURRENT-ARGUMENT-MAP.txt
Original file SHA-256: d53d2cfc44cdfc84f3f36ab6a09248e97ab79f57c2d8c199cbaab29dab2d00f2
Inclusive original lines: 76-128
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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000076 | tfpt31 occupancy/bridge007:44-58 defines the graded geometric bundle and
000077 |  mathbbA_Sigma=(D_geo,D_rel,A_Sigma,geo),
000078 |  A_Sigma,geo:=B_rel directsum nabla_chi_geo.
000079 | It explicitly says these bundle data reorganize the primitive seed
000080 | package. Its next theorem identifies D_geo, not a compressed D_rel, as
000081 | the geometric Dirac anchor with the stated Clifford principal symbol.
000082 | 
000083 | Crucially the local-spectral-scale definition109-126 gives a REAL
000084 | profile-dependent action on that branch:
000085 |  chi_geo=Lambda exp(sigma),
000086 |  D_sigma,geo=exp(-sigma/2)D_geo exp(-sigma/2),
000087 |  S_rel[sigma,D]=Tr f((D_sigma,geo+B_rel)/Lambda)
000088 |               -Tr f(D_ref/Lambda)+i*pi*Delta_eta/2.         (2)
000089 | 
000090 | This is the concrete original operator realization to use; no new
000091 | choice of an A_Sigma operator is needed to manufacture it.
000092 |  paper-source:e9244069a9db317a185d62c7:44-141,
000093 |  documents/archive--paper-latex--tfpt-31/sections/
000094 |  007-subsection-occupancy-and-boundary-to-bulk-bridge.tex,
000095 |  SHA256 9c441d14de6a6c9586a4d2b077b160a4c5ce020d82243ff832300ff9554e6397.
000096 | 
000097 | The later tfpt42/45 source retains the explicit SAME geometric argument
000098 | K_sigma but changes the functional reading to canonical residues:
000099 |  Zcal_rel(s;sigma)=Tr_rel(|K_sigma|^(-2s)-|D_ref|^(-2s))
000100 |                   +i*pi*Delta_eta/2,
000101 |  E_D=Res_(s=1) Zcal_rel, Gamma_D^(4)=FP_(s=0) Zcal_rel.
000102 | It explicitly states D_geo=D_ref+D_rel=D, the geometric-anchor role,
000103 | and the same seed-to-geometric package reorganization. These are the
000104 | source45 metrology001:15-17,30-66,98-128 definitions.
000105 |  paper-source:10c47d481fd025831567f94b:30-150 and
000106 |  research-source:20271554929f9198008f7754:1-146,
000107 |  documents/archive--tfpt-45--source_extracts--05_metrology_source/
000108 |  sections/001-subsection-from-bridge-to-geometric-completion.tex,
000109 |  SHA256 f03609effe2abf6629a0057fa024c29fba0c59176072588599bfa1646f48939e.
000110 | The same wording appears in carrier006:286-406,
000111 |  paper-source:0718d9ef29b886f7d99dba6d,
000112 |  SHA256 179b2d568e897e059c2d1ef804bb9b06ee053483d366fc9d24189f1df44253b2.
000113 | 
000114 | Hence the original geometric route is supplied in both a profile-trace
000115 | version and a later profile-free residue version. Sharing K_sigma does
000116 | not make these two FUNCTIONALS equal. Keep the selected original version
000117 | and its trace, subtraction, eta and scale. Neither one is inferred from
000118 | the word relative alone.
000119 | 
000120 | 3. WHAT THIS SAYS ABOUT A_SIGMA AND THE BOSONIC DATA
000121 | 
000122 | A_Sigma,seed/geo is presented as bundle/superconnection package data,
000123 | not as a definition A=sum a[D,b] of a bounded represented inner one-form.
000124 | In particular it contains nabla_chi, which is covariant-derivative data.
000125 | A covariant derivative and its contracted operator realization cannot
000126 | be reduced to its local connection coefficient one-form by notation.
000127 | The original geometric reconstruction theorem fixes the full elliptic
000128 | principal symbol through D_geo before the later K_sigma is evaluated.