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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

Full Petersen populations allow the entire P5 range

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

Entire class of fixed finite one-step CPTP channels with the specified full populations, without SM covariance, derived P1 Choi identification, or multitime process. No physical no-go.

Read the exact result, assumptions and evidence

Result

Among all CPTP channels in the fixed given 10 to 10 dictionary with all 100 Petersen transition probabilities, Tr(P5 J) ranges exactly over [0,10]. The original Hodge channel attains 10. Dm obtained from Cm by flipping three signs is HS orthogonal to all five Cn, preserves each Kraus effect and all 100 populations; J0=(1/3)sum |Dm>><<Dm| is CPTP and unital and attains 0. Since 0<=P5<=I and Tr J=10 and mixtures preserve populations, all intermediate values occur. The concrete J0 is not SM covariant by an exactly checked SU3 commutator.

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.

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:petersen-population-full-cptp-p5-range-zero-to-ten