TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/original-local-source-variable-background-20261102/REFERENCE-SOURCE-COMPLETION.txt
Original file SHA-256: 5ddc9c63c5f20f42befba6ae32fc57fdecb61c4b70dd9ab2d7b26fe667380cbb
Inclusive original lines: 80-106
Line numbers below refer to the original source.
This bounded excerpt is source evidence; it is not a new proof/checker run.
Conversation metadata and personal execution details are omitted where indicated.

000080 | with its actual orientation. Do not use a one-slot symmetric pairing.
000081 | Therefore, for EACH actually supplied complete original source,
000082 |  Z_adm^U[J_new]=Z_adm[J],
000083 |  Z_ref^U[0]=Z_ref[0],
000084 |  Z_rel^U[J_new]=Z_rel[J].
000085 | This equality includes the original geometric, Higgs, gauge, fermionic,
000086 | ghost and eta factors whenever they belong to that given call.
000087 | It preserves the null-source factor, rather than resetting it to1.
000088 | Higgs/source jets commute with the fixed U and retain actual reference
000089 | variations. Exact equality at every compatible regulator passes to any
000090 | existing limit of that same family, with no extra limiting estimate.
000091 | If a source is only formal, this is the same formal coefficient identity,
000092 | not a proof of its analytic existence.
000093 | 
000094 | In particular it is unnecessary to first represent Z_rel as an expectation
000095 | in a separately supplied Gibbs reference state. That optional rewrite has
000096 | its own same-basis identity, as correctly stated in WEIGHT.txt. Its extra
000097 | matching condition is not a prerequisite for the direct full-source
000098 | transport just established. There is no global new omega_ref requirement.
000099 | Gauge fixing and ghosts also need not select new physical dynamics when
000100 | they are the original representation of the same gauge quotient.
000101 | 
000102 | The actual full state transports by its word algebra. With original
000103 | reflection, time and operations transported by U, every complete reflected
000104 | word and finite history has exactly the same expectation. The existing
000105 | full-moment OS theorem then gives an isometry of the reconstructed spaces
000106 | and their time evolutions. This uses full moments of Z/Z[0], not connected