TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/original-admissible-source-closure-20261025/JOINT-LIFT-NATIVE-CLOCK-CONNECTION.txt
Original file SHA-256: edd2cdaea4c4debd337b4850d48da95de68e9367d780b9e3f0a96755588a45c8
Inclusive original lines: 176-211
Line numbers below refer to the original source.
This bounded excerpt is source evidence; it is not a new proof/checker run.
Conversation metadata and personal execution details are omitted where indicated.

000176 | 7. Why identifying the clutch angle with clock time gives a different test
000177 | 
000178 | For the pure diagonal primitive weak loop k=(0,0,0,1,0), consider the
000179 | ADDITIONAL comparison assumption
000180 |   Q_m=exp(pi i ad(h(k,m))/2).
000181 | Modulo4, sum m=2 gives64 possible quarter actions. Their full characters,
000182 | ordered(1,-1,i,-i), and numbers of residue classes are exactly
000183 | 
000184 |   (60,60,64,64):8; (70,66,56,56):18; (82,54,56,56):24;
000185 |   (92,28,64,64):8; (134,2,56,56):6.
000186 | 
000187 | The eight native classes are permutations of(2,2,2,0) or(1,1,1,3).
000188 | The old minimum m_A=(0,0,-1,-1) and old3+1 m_B=(0,0,0,-2) miss this
000189 | full quarter test. The latter has the right square but the wrong quarter.
000190 | The least h norm in these eight residue classes is12, with exactly24
000191 | integer lifts: permutations of(-2,-2,2,0) and(-3,-1,1,1).
000192 | The minimum proof is unbounded: norm<=12 bounds every beta in[-sqrt11,
000193 | sqrt11]; alternatively three beta in the even residue pattern start at
000194 | -3/2, the fourth at1/2 and the sum constraint forces cost4 above7.
000195 | 
000196 | For the whole cycle use C_m=exp(-2pi i ad(h)/12), so C_m^9=Q_m.
000197 | Every such pure weak C_m fixes the24 D4 root currents on the four
000198 | unwound coordinates plus8 Cartans. Its fixed dimension is>=32, whereas
000199 | the actual native compiler has22. Thus NONE of the1728 mod12 m classes
000200 | works, even under full inner conjugacy. The entire class of toral weak
000201 | loops k=(0,0,0,a,1-a) has20736 mod12 possibilities and also no matches.
000202 | For that larger class a fixed count22 CAN occur, so the full character
000203 | is essential. This does not exclude the separate clock of Sections4-5.
000204 | 
000205 | There is also an immediate marked obstruction for ANY integer k of sum1:
000206 | If Q_m fixed the ORIGINAL D5 adjoint pointwise, every k_i+-k_j would be
000207 | 0mod4. Therefore all k_i would be0mod4 or all2mod4. Their sum could not
000208 | be1mod4. Thus a determinant-quarter action cannot be the central glue
000209 | quarter of its own fixed original D5+A3 marking. Matching the unmarked
000210 | clock class is insufficient for that stronger source identification.
000211 |