TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/e-series-incidence-algebra-20261024/THEOREMS.txt
Original file SHA-256: e80821d422297cfdfce23e892c1b099cc23505ae22ae92f01dcf77d4062f0a5d
Inclusive original lines: 28-55
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.

000028 | 
000029 | The exact orbit construction gives
000030 | 
000031 |    E7 cuts                 120
000032 |    E6 cuts                1120
000033 |    D8 frames               135
000034 |    A3 tetrahedra          7560
000035 |    tetrahedron/E6 flags  30240
000036 |    E6/E7 flags            3360.
000037 | 
000038 | There are four E6 cuts per tetrahedron, 27 tetrahedra per E6 cut, three E7
000039 | cuts per E6 cut, and 28 E6 cuts per E7 cut. Each D8 compiler frame contains
000040 | 56 tetrahedra in the sense of the FULL D5+A3 flag. Each full flag determines
000041 | exactly one of the 135 D8 frames. Thus 135*56=7560 counts full compiler flags.
000042 | 
000043 | There are 616 A3 root subsystems INSIDE a D8, rather than only 56. The 56
000044 | coordinate D3's use three coordinates. A second type is an A3 chain using
000045 | four coordinates: C(8,4)*8=560. These second-type A3's have D4 complement
000046 | inside that D8, while their full E8 complement is D5. Consequently a bare
000047 | A3 normal lies in 11 D8 root systems: 135*616/7560=11. Requiring its actual
000048 | D5 core as well singles out its one compiler frame. This qualification is
000049 | essential when interpreting the map tetrahedra -> D8 frames.
000050 | 
000051 | The checker generates all 135 and 7560 actual orbits and checks these
000052 | incidences individually; the product identities alone are not its proof.
000053 | The original rank32 projectors, 128/96=4/3 and norms5/4+3/4 remain the
000054 | intermediate D8-polarized statements proved in COMPILER-CLOSURE.txt.
000055 | The rank quotient does not by itself rescale an independently defined scalar.