TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/e-series-source-reconstruction-20261024/NATIVE-CLOCK-CONJUGACY.txt
Original file SHA-256: 5f208d8d32fdc77e774ec77b5a320f378cfc9e2c8793d4d3d439983aae583a45
Inclusive original lines: 102-159
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.

000102 | 4. Keep the WHOLE cyclic compiler, including sigma
000103 | 
000104 | Conjugating only J does not entitle us to freeze the old sigma. Indeed
000105 | kappa does not commute with the old sigma: the root e4+e5 in zero-based
000106 | coordinates has kappa eigenvalue-1, while sigma sends it to e0+e1 with
000107 | eigenvalue+1. All candidate sigma field phases leave this witness intact.
000108 | 
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000115 | 
000116 |     (22,20,19,24,19,20,22,20,19,24,19,20).               (4.1)
000117 | 
000118 | After toralization, use Section2 to carry the ninth power to kappa.
000119 | All remaining toral compiler possibilities are
000120 | 
000121 |     c_t=kappa sigma_t,    sigma_t=exp(2pi i w(0)),
000122 |     w=b/3,              b in E8/3E8.                  (4.2)
000123 | 
000124 | This is exhaustive: for any c_t with c_t^9=kappa and c_t^12=1, its
000125 | fourth power is sigma_t and c_t=kappa sigma_t. There are exactly3^8=6561
000126 | toral b choices. The certificate checks ALL of them against the full
000127 | character(4.1). Exactly480 match. Reflections in the52 actual U roots
000128 | generate ONE orbit containing all480 matches. Hence the entire original
000129 | cyclic compiler is conjugate to one explicit representative(4.2), with
000130 | 
000131 |     b=(0,0,0,0,1,0,1,0) modulo3
000132 | 
000133 | in the ordered integral basis. The standard coordinates w are printed
000134 | in native-clock-conjugacy-results.json. Its exact powers are
000135 | 
000136 |     c_t^9=kappa,      c_t^4=sigma_t,      c_t^12=1.
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000142 | 
000143 | 5. What has been removed, and what remains original source work
000144 | 
000145 | Within the full E8 field-automorphism category, a second unrelated quarter
000146 | clock class and a second unrelated cyclic compiler class are unnecessary:
000147 | the native class is exactly the carrier/glue class above. Its primitive
000148 | toral orientations are the same7560 flags already occurring in the
000149 | tetrahedral incidence geometry. The fixed-J local compiler extension is
000150 | the canonical C4 extension over its intrinsic fixed subnet.
000151 | 
000152 | The theorem gives existence of a conjugator, not a preferred one. It
000153 | does not construct a microscopic P1/QWZ-to-VOA bosonization B_N, choose a
000154 | state/physical time, or prove that the original scalar seam and carrier
000155 | parity are interchangeable microscopic operations. It does not keep the
000156 | Gaussian lattice Cartan and all named marks fixed: a full conjugacy must
000157 | transport them. Full marked-tuple equivalence requires its additional
000158 | intertwining conditions. The source gap found in
000159 | SCALAR-QUARTER-REPRODUCTION.txt remains the next physical obligation.