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Conditional result

Trace-preserving charged bracket support forces the entire carrier marginal

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

Removes another unnecessary origin condition: full Killing orbit average is sufficient but unnecessary for carrier marginal. P1 must deliver actual normalized closed CP bracket process on the correct charged carrier. A single Ward current, non-TP postselected branch, extra Kraus directions or mere field availability do not automatically meet these conditions. No complete physical TFPT solution. Whole-CPTP theorem remains correct. Actual sector-resolved source branch only needs same carrier Kraus support and effect pI; its normalized carrier marginal is alreadyPhi. Do not demand an exclusively Hodge unread total process as general necessary physical premise.

Read the exact result, assumptions and evidence

Result

Every CPTP joint map End(H10⊗F5bar)→End(H10bar⊗F5) with all Kraus operators in actual span{C_m⊗A_ab} obeys Tr_Fout E=Phi∘Tr_Fin. For any family density, reduced carrier map is CPTP with Kraus space inC5; existing injective25-coefficient TP theorem forces Phi without SU5 covariance. Product operators span the full input algebra, extending equality to entangled inputs. Arbitrary coherent insertion metric and unknown family state cannot change this marginal if TP and support hold.

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 local E8_1 vacuum representation and explicit cocycle

    Positive level-one E8 lattice vacuum representation in orthonormal D5+D3 coordinates, declared simple-root cocycle, level-one Heisenberg Ward rules and internal quarter character v=(0^5,1/2^3). Insertions are separated. No raw-P1 pullback or physical time law is assumed or derived from this representation.

Original evidence

  • CARRIER-MARGINAL-RIGIDITY.txt lines 1–165

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/source_sewing_20261028/current/CARRIER-MARGINAL-RIGIDITY.txt

    dc784d62ca5e1d4c9e53baabaebb735c99a592e0ff0140e29056264f6382151c

  • CHARGED-SOURCE-SELECTION-ORIGIN-AUDIT.txt lines 1–200

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/source_sewing_20261028/sewing/CHARGED-SOURCE-SELECTION-ORIGIN-AUDIT.txt

    66d1d8916e664fb855f05d867d0bfedc27b905d59afc4f3b6aff9a22340ef67b

  • CHARGED-SOURCE-SELECTION-ORIGIN-AUDIT.txt lines 201–349

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/source_sewing_20261028/sewing/CHARGED-SOURCE-SELECTION-ORIGIN-AUDIT.txt

    66d1d8916e664fb855f05d867d0bfedc27b905d59afc4f3b6aff9a22340ef67b

  • CURRENT-FAMILY-AND-NORMALIZATION.txt lines 1–187

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/source_sewing_20261028/current/CURRENT-FAMILY-AND-NORMALIZATION.txt

    b6d6a57fe2ed89c27ac62c11f57dde2d222efd5727e1dc2055680e96ae263569

  • OPERATOR-VALUED-BRANCH-RIGIDITY.txt lines 1–90

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/bracket_process_origin_20261028/process/OPERATOR-VALUED-BRANCH-RIGIDITY.txt

    c81495ad22225fe5e4701d4edfa0f876089d222d79750f2765809e76c0951dd6

  • ORIGINAL-BRACKET-PROCESS-SUPPORT-AUDIT.txt lines 1–200

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/bracket_process_origin_20261028/original/ORIGINAL-BRACKET-PROCESS-SUPPORT-AUDIT.txt

    aa8b9463457b1d0373befc8bcf4fa5a43b6bad7d50d5e51b0a3f1d168b869c40

  • ORIGINAL-BRACKET-PROCESS-SUPPORT-AUDIT.txt lines 201–309

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/bracket_process_origin_20261028/original/ORIGINAL-BRACKET-PROCESS-SUPPORT-AUDIT.txt

    aa8b9463457b1d0373befc8bcf4fa5a43b6bad7d50d5e51b0a3f1d168b869c40

finding:tp-charged-bracket-support-forces-entire-carrier-marginal