Established in scope
Actual polar mark reconstructed from simplex and clock
In the question: Historical: common source, state and event selection
Positive polar rule and physical interpretation remain inputs. One mark orbit does not prove every anisotropic source invariant or select a physical state. The mark remains distinct from all15 matching-response projectors.
Read the exact result, assumptions and evidence
Result
In consistent original N coordinates P2(q)=F_sigma-c_q c_q*, c_q=[n2+n3+n4-3(sqrt(6)-1)n_q/5]/sqrt(3). For q=5 this is the actual existing mark without SM charges. All three clock-fixed points form one mark orbit under actual native reflection lifts commuting with sigma4. N=O C^T, O=-rho_C(reverse), transports all labels together.
Required assumptions
- Actual native G31 event representation
Use the actual original Hamming/E8/J matrices and60 reflections, their four-dimensional action, characteristic P64=O2(G31), and existing S6 quotient. These are accepted mathematical core data, not a physical source derived from P1 in this round.
- Symmetric quartic and actual erasure intertwiner
Use Sym^4 of the native four-representation, the actual five codeword sums, and the existing one-register erasure intertwiner. The symmetric tensor rule and its physical selection are not silently inferred from the full tensor product.
- Original simplex and positive polar rule
Use the actual W6 simplex and raw metric, unchanged native three-clock and original positive polar prescription at one of its three marked fixed points. The prescription and its physical selection are not derived from P1.
Original evidence
- MARKED-CLOCK-LIFT.md lines 31–85
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/joint-native-algebra-selection-20261016/MARKED-CLOCK-LIFT.md
da0d56aeb94f078f496a0748911ad559fa5835d77757fc7d1879c2eb70123468
finding:original-polar-mark-clock-centralizer-orbit