RECEIPT 6/6; D1415 e90c511eba97e838; frames e48d97cdfcad03c5
WORKBOOK 709857476498f0df; Objects 188; CrossLinks 96; sheets 27
D1415 SELF-CHECK e7[133] braid[relation; (B1B2)^3 = I - 2P_act; rank P_act 24] gieseking[G = B1 O anti-symplectic; G^2 = B1 B2^-1] Z[commutes D_sol, D56] X[rank 28] :: PASS
EXACT SL8 model e=rho(E_6,8), f=rho(E_8,6); floating correspondence 9.405e-14
EXTENSION factor control: OC=CO on56 2.277e-14; homology C2 O2=-O2 C2 exact; CP factor only
GROUP B1        unipotent-type order=None radius=1.000000000000 symplectic H1=(2,+1)
GROUP B2        unipotent-type order=None radius=1.000000000000 symplectic H1=(2,+1)
GROUP B1B2      periodic       order=6 radius=1.000000000000 symplectic H1=(1,+1)
GROUP B1B2B1    periodic       order=4 radius=1.000000000000 symplectic H1=(0,+1)
GROUP B1B2inv   hyperbolic     order=None radius=2.618033988750 symplectic H1=(3,+1)
GROUP Wh        hyperbolic     order=None radius=2.618033988750 symplectic H1=(3,+1)
GROUP G         hyperbolic     order=None radius=1.618033988750 anti-symplectic H1=(1,-1)
GROUP O         periodic       order=2 radius=1.000000000000 anti-symplectic H1=(0,-1)
GROUP C56       periodic       order=2 radius=1.000000000000 symplectic H1=(0,-1) factor-only
GROUP CP        periodic       order=2 radius=1.000000000000 anti-symplectic H1=(0,+1) factor-only
CENSUS order length first, then A,a,B,b; inverse pairs A/a and B/b
CENSUS SHA256 7278fd639272cbbbc507fb6dc3ab3bc8054e3b160c1206df4c8d47eded1ded68
CENSUS totals56 {'unipotent-type': 340, 'periodic': 344, 'hyperbolic': 772} totalsH1 {'unipotent-type': 340, 'periodic': 344, 'hyperbolic': 772} disagreements 0
CENSUS length=1 periodic=0 unipotent-type=4 hyperbolic=0
CENSUS length=2 periodic=4 unipotent-type=4 hyperbolic=4
CENSUS length=3 periodic=12 unipotent-type=12 hyperbolic=12
CENSUS length=4 periodic=44 unipotent-type=20 hyperbolic=44
CENSUS length=5 periodic=64 unipotent-type=116 hyperbolic=144
CENSUS length=6 periodic=220 unipotent-type=184 hyperbolic=568
CENSUS negative-unipotent 168; min hyperbolic radius 2.618033988750
ARITHMETIC det+ minimum 2.618033988750; det- minimum 1.618033988750; regulator 0.481211825060; logWh 0.962423650119; golden printed discrepancy 0.000003650119
LIE e        centralizer=99 inertia=[36, 30, 33] tr2=0.000000000 dXrel=0.500000000000 levelDsol=0.000000000 levelD56=13.856406461
LIE f        centralizer=99 inertia=[36, 30, 33] tr2=0.000000000 dXrel=0.500000000000 levelDsol=0.000000000 levelD56=13.856406461
LIE h        centralizer=67 inertia=[37, 30, 0] tr2=24.000000000 dXrel=1.000000000000 levelDsol=0.000000000 levelD56=0.000000000
LIE r        centralizer=67 inertia=[36, 31, 0] tr2=-24.000000000 dXrel=1.000000000000 levelDsol=0.000000000 levelD56=19.595917942
LIE Z        centralizer=67 inertia=[36, 31, 0] tr2=-24.000000000 dXrel=0.000000000000 levelDsol=0.000000000 levelD56=0.000000000
LIE gauge_n  centralizer=67 inertia=[20, 15, 32] tr2=0.000000000 dXrel=0.000000000000 levelDsol=19.595917942 levelD56=19.595917942
LIE golden   centralizer=49 inertia=[28, 21, 0] tr2=12.000000000 dXrel=0.707106781187 levelDsol=3.598155613 levelD56=0.000000000
ORBIT e: A1, dimension34, Djokovic Table4 no.1; (tr,inv)=[32, 31]; triple so(6,6)
SPECTRA h: -1x12,0x32,+1x12; r: -ix12,0x32,+ix12; exp(pi*r) centre residual 1.202e-13
PENCIL exact k(theta)^2=-cos(2theta)*P; boundary pi/4 is sqrt(2)*e, rank12 square0
CONJUGATOR g=exp(pi/2*rho(E76-E67)): Z->r 5.371e-15, symplectic 0.000e+00, levelDsol 0.000e+00
CONJUGATOR does not preserve X: relative 1.000000000000; Z!=r 6.928203230276; [Z,r] 4.898979485566
GAUGE triple [Z,P]=Q, [Z,Q]=-P, [P,Q]=-Z; trace form diag(-24,24,24)
GAUGE null n=Z+P: Jordan 3^12 1^20, ranks24,12,0; dX 5.074e-16; orbit A2 dim66, Table4 no.7; (tr,inv)=[128, 31]
GAUGE INTERSECTION 2A1  Table4 no.2 dim52; partition8=[2, 2, 1, 1, 1, 1]; ranks56=[20, 2, 0]; central inertia=[22, 17, 42]; (tr,inv)=[64, 23]
GAUGE INTERSECTION A2   Table4 no.7 dim66; partition8=[3, 1, 1, 1, 1, 1]; ranks56=[24, 12, 0]; central inertia=[20, 15, 32]; (tr,inv)=[128, 31]
GAUGE INTERSECTION 2A2  Table4 no.21 dim84; partition8=[3, 3, 1, 1]; ranks56=[36, 20, 4, 2, 0]; central inertia=[10, 7, 32]; (tr,inv)=[256, 23]
GAUGE INTERSECTION A4   Table4 no.43 dim100; partition8=[5, 1, 1, 1]; ranks56=[40, 30, 20, 12, 4, 2, 0]; central inertia=[6, 3, 24]; (tr,inv)=[640, 15]
GAUGE INTERSECTION COMPLETE: zero plus Table4 {2,7,21,43}; minimal A1/Table4 no.1 absent
GOLDEN commutators [h,Z,e,r] ['0.000000000000', '0.000000000000', '1.732050807569', '2.449489742783']
GOLDEN spectrum -1x2,-1/2x16,0x20,+1/2x16,+1x2; centralizer49 inertia(28,21,0)
CONTROLS: e is NOT gauge; same 56 spectrum did not establish Z~r without the displayed g
WORKBOOK PAYLOAD Objects206 CrossLinks110 LANE_D1415=24 sheets32
Q7: internal causal type and arithmetic stretch do not establish the proposed physical readings.
D1415 COMPLETE
D1415-END-e00aa743a4ab
