TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/e-series-quarter-clock-20261023/PROOF.txt
Original file SHA-256: ac3e95975adb14c82815731b3d8aa0f6e1caf72d25fb749250a5b1bbcd269884
Inclusive original lines: 232-269
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.

000232 | The source gives the organizing identity I*beta_angle*c3=1 with I=4
000233 | and beta_angle=2pi, while explicitly retaining the open modular-response
000234 | identification. The rank/central-charge reading c3=1/(pi*8) agrees with
000235 | it in the native E8 case. The present exact lattice indices are
000236 |   E6+A2:m=3, retained exceptional rank r=6;
000237 |   E7+A1:m=2, retained exceptional rank r=7;
000238 |   D5+A3:m=4, resulting E8 rank r=8.
000239 | Consequently the TWO POSSIBLE arithmetic continuation prescriptions
000240 |   a_rank=1/(pi*r), a_index=1/(2pi*m)
000241 | agree at E6(1/6pi) and E8(1/8pi), but disagree at E7(1/7pi vs1/4pi).
000242 | These are diagnostic conditional prescriptions, not two derived source
000243 | laws. In particular, identifying m with the original modular Jones
000244 | index in every new slice is an additional hypothesis. The E6/E8
000245 | endpoint agreement cannot select either prescription, and no E7
000246 | physical coupling or scale has been predicted by this comparison.
000247 | The old E7 window was defined by the rank rule and hence is not an
000248 | independent measurement deciding between these prescriptions.
000249 | 
000250 | Furthermore, the supplied conformal embeddings retain complementary
000251 | central charges7+1=8 or6+2=8. Rewriting the SAME complete E8 source in
000252 | these windows keeps its total central charge8. Extracting an E7 or E6
000253 | subtheory and renormalizing its response is a further operation, not a
000254 | consequence of the branching dimensions. A NEW proposed E7 response
000255 | would therefore need its own explicit restriction/extension identity,
000256 | with complementary sectors and actual quarter/peripheral data retained.
000257 | This is a requirement on that additional interpretation, not an open
000258 | P1/P2-to-E8 compiler step. No additional coupling, state rule or
000259 | physical-origin program has been introduced in this investigation.
000260 | 
000261 | Additional original sources inspected:
000262 |   documents/tfpt_1_architecture_e8/sections/001-source.tex:70-80
000263 |     (P1 index and modular-response identity),
000264 |   documents/tfpt_3_e8_audit_bootstrap/sections/003-source.tex:326-352
000265 |     (uniform mu3 monodromy and ramification at infinity).
000266 | Independent analytic continuation review proved the192->240 cross-sum
000267 | closure, exponent2 glue obstruction, intrinsic root-line curve functor,
000268 | eight monodromy lifts, and cover/deck distinctions. All finite statements
000269 | are checked in the updated executable; cover descent is proved above.