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Read the result in its research context.

Follow the published construction into its registered claims, then explore reviewed research questions, attempts and the connections that remain open.

Established in scope

Complete P5 range for marked SM phase family and witness collision

In the question: Common clock sectors, quartic geometry and operational reconstruction

Only the stated internal phase family and particular comparison with the given old channel. Not P1 sewing, complete SM channel classification, original measurement, or a universal process.

Read the exact result, assumptions and evidence

Result

For the previously defined SM covariant family Phi o Ad(aP_CC+bP_CW+cP_WW) with unit phases, Tr(P5J)=|a+4b+c|²/6+|a+b|² and covers exactly [2/3,10]. This is not the global range of all SM covariant channels. The choice a=-1,b=1,c=(1+2i sqrt2)/3 has the same P5 value 2 as the old Psi channel, but P45 values 16/3 versus 4. Both preserve original populations; one Choi response does not identify the entire process under these conditions.

Required assumptions

  • Do not identify source types

    Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.

  • Given five-slot exterior source with retained complement index

    V=C5 with given oriented unitary slot basis and volume form,H=Lambda²V. C_m[kl,ij]=epsilon(m,i,j,k,l) are five distinct linear maps to conjugate target;their coherent sum is a different operation. Inner products and CAR grading remain explicit. No physical record,coupling or time iteration assumed from exterior algebra alone.

  • Fixed three plus two mark and typed original degree clock

    V=C5,P rank3 color projector,G_P=S(U3xU2),X=(-2,-2,-2,3,3),original U5=exp(2pi iX/5). Literal slot cycle c=(01234) is distinct and moves P. Covariant transport over Gr(3,5) concerns different marks,not full SU5 covariance within one fixed marked instrument. Continuous marks are not six old outer event marks or135 D8 frames.

Original evidence

  • P5-EXACT-SEARCH-RANGES-20261102.txt lines 1–87

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/admissible_pair_20261028/P5-EXACT-SEARCH-RANGES-20261102.txt

    d4c711f4cab8703bdaa555786aa99eeffc2f87db3606027f77d00d18887d68d2

  • check_p5_phase_range.py lines 1–107

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/admissible_pair_20261028/check_p5_phase_range.py

    0cb713cf339edd6f8c6a0b30a887f3235c4c4a583c8afaa0e3377fd8a4646927

  • p5-phase-range-results.json lines 1–42

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/admissible_pair_20261028/p5-phase-range-results.json

    33a73d1fe16bfa90a9e5e7d8d19d3b6bef2f44c4d2a05bf2039a991fc0f879af

finding:marked-sm-phase-p5-exact-range-and-response-collision