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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

Same Chern class can carry the whole clock without selecting physical connection

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

Unbounded minimum proof in this toral class via exhaustive finite lower search. Norm is not energy;155 is neither physical-source count nor full E8 conjugacy-class count. Nullhomotopic color loop and clutch class select no connection or holonomy. In the ordinary circle CAR contract,the whole64 clutch has index0 rather than1;no identification of bosonic E8 VOA with CAR. The simpler parallel-clock closure makes this loop optimization unnecessary for mathematical compatibility.

Read the exact result, assumptions and evidence

Result

The toral diagnostic k_color=(-6,0,6),k_weak=(0,1),m=(-5,1,1,1),h=(k,3,3,3) has the same block Chern classes0,1 and complete native C12 character. Norm100 is minimal in the specified integer toral class:an existing candidate bounds every better search,all6939 allowed canonical tuples through100 are checked exactly;155 match,all at100. These classify marked weight representatives,not a physical selection. The entire joint64 carrier still has determinant winding0.

Required assumptions

  • Existing natural joint lift with given split connection

    Assume a GIVEN unitary E=E3+E2 and GIVEN block U3xU2 connection A_E. Use only the natural iota_m with sum m=-2 completely classified on22September and their derived connection A_Wm=rho_LambdaEven(A_E)+M_m tr A_E. This does not select A_E from P1;an independent nonabelian family connection is not silently assumed.

  • Additional direct-angle identification of determinant clutch with native clock

    Only for the diagnostic comparison evaluate a supplied diagonal integer loop k,sum k=1 and m,sum m=-2 as h=(k,-v_m) at the same angles:Q=exp(pi i ad h/2),C=exp(-2pi i ad h/12),C^9=Q. Pure weak k=(0,0,0,1,0);larger weak toral class k=(0,0,0,a,1-a). A transition is not connection holonomy or derived physical time.

  • Full unitary E8 field conjugacy with transported marks

    Start with the existing unitary E8 lattice VOA, original cocycle and actual chat,Jhat,sigmahat. Full inner unitary E8 automorphisms are allowed for this conjugacy comparison. Cartan, Gaussian V4, Y, P5 and other marks are transported rather than frozen. This category is explicitly larger than original sign lifts and implies neither a G31 splitting nor a preferred microscopic conjugator.

  • Smooth matrix clutch on original negative Fourier sea

    H=L2(S1,C^r),P=1_(n<0) tensor I_r and U=M_g for smooth g:S1→U(r). The existing bosonic branch has c1(det E2)=1,c1(det E3)=0 on the normal S2. A common physical identification of that clutch equator with the tangential source circle,C_Sigma and response is an additional map to prove.

  • 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.

Original evidence

  • JOINT-LIFT-NATIVE-CLOCK-CONNECTION.txt lines 212–273

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/original-admissible-source-closure-20261025/JOINT-LIFT-NATIVE-CLOCK-CONNECTION.txt

    edd2cdaea4c4debd337b4850d48da95de68e9367d780b9e3f0a96755588a45c8

  • check_joint_lift_native_clock.py lines 192–238

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/original-admissible-source-closure-20261025/check_joint_lift_native_clock.py

    eea4b77219cd9d3192a64e257e4e69cd57f68137cc1573ef4908bd8c3dbce3e1

  • joint-lift-native-clock-results.json lines 345–380

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/original-admissible-source-closure-20261025/joint-lift-native-clock-results.json

    8d86f0b905ae317362205fab66c49e0e240bd8fff8af30eaed2269f32a7c8de0

  • PROOF.md lines 80–87

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/source-joint-spin-family-lift-20260922/PROOF.md

    d3ae02543e90d840879808554816f923cc36cab52268a032d1ce29c2569f5bd2

finding:same-chern-clutch-native-compiler-does-not-select-physical-connection