TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/dynamic_reconstruction_20261027/PETERSEN-POLAR-DECK-INTERTWINER.txt
Original file SHA-256: 0d2f283a3c6568bd77cc24f081c61dc706a7faef209138335336a1fbbd8007cd
Inclusive original lines: 401-468
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.

000401 | For even n the right hand side is
000402 | 
000403 |                 [    0        -5 sqrt(2)/2   -5 sqrt(2)/2 ]
000404 |                 [ -5 sqrt(2)/2  -5 sqrt(5)/3       0       ],
000405 |                 [ -5 sqrt(2)/2       0         5 sqrt(5)/3 ],
000406 | 
000407 | and for odd n it is its negative.  In either case its rank is two and its
000408 | squared Frobenius norm is 700/9.  Therefore the period two charge frame does
000409 | not satisfy
000410 | 
000411 |       Y_(n+1) M_lazy = M_lazy Y_n.
000412 | 
000413 | This is a deliberately narrow conclusion.  v808 describes carrier
000414 | representation geometry, not an isolated particle dynamics.  The calculation
000415 | only says that one Petersen Markov walk, even with the exact alternating
000416 | frame, is not by itself a charge conserving physical time transport.  A
000417 | compensating sector or interaction would have to come from an actual source
000418 | operation; this calculation supplies none.
000419 | 
000420 | 10. The Perron reflection already has a named source candidate
000421 | ---------------------------------------------------------------
000422 | 
000423 | The matrix Z was not first invented by the polar decomposition.  The original
000424 | v409 lemma RES.COXETER.SYMMETRY.01 explicitly sets
000425 | 
000426 |       sigma = diag(1,-1,-1)
000427 | 
000428 | and calls it the seam sheet involution and the universal prime two parity
000429 | factor.  In the common target slot convention used above, this is exactly Z,
000430 | and hence
000431 | 
000432 |       K = sigma Delta.
000433 | 
000434 | Moreover sigma, Delta and M_lazy commute pairwise.  Algebraically, the missing
000435 | sign is therefore precisely the older marked prime two parity multiplied by
000436 | the v487 family deck, rather than an arbitrary new reflection.
000437 | 
000438 | The checked source does not yet identify their bases.  v409 sets sigma as a
000439 | three dimensional sheet involution but imports neither the v487 family space
000440 | nor M_lazy.  The earlier v97 bridge places the same numerical matrix SIG in
000441 | the generation coordinate basis.  Its actual cusp eigenvectors are
000442 | 
000443 |       e_0=(0,0,1),  e_(1/3)=(0,1,2),  e_(2/3)=(1,0,0),
000444 | 
000445 | and cusp conjugation in that basis is
000446 | 
000447 |       T_A = [[0,1,0],[1,0,0],[2,-2,1]],
000448 | 
000449 | not SIG.  v97 also labels the identification between the generation grading
000450 | and the A3 discriminant grading as the remaining proposed dictionary.  Thus
000451 | the exact equality K=sigma Delta is source backed only after choosing the
000452 | common slot convention; the original chain still lacks the intertwiner that
000453 | proves v409 sigma and v487 Delta act on that same marked three dimensional
000454 | space.
000455 | 
000456 | No stronger identification was found in the inspected classical Z3 or SU3
000457 | transfer lifts.  A pure Z3 clock has no nontrivial element of order two, and
000458 | the reviewed quantum lifts establish the transfer or unistochastic data but
000459 | do not name 2 Pi_Perron-I as a half period.  In their uniform basis the
000460 | canonical Perron reflection is
000461 | 
000462 |       2 Pi_uniform - I = (2/3) 11^T - I,
000463 | 
000464 | which becomes diag(1,-1,-1) only after an orthogonal eigenbasis choice.  This
000465 | is consistent with v808's explicit spectrum-not-basis scope and cannot supply
000466 | the missing source intertwiner by itself.
000467 | 
000468 | No repository or Atlas file was changed.