TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/joint-native-algebra-selection-20261016/ORIGINAL-SEAM-STATE-FLAG-SELECTION.txt
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Inclusive original lines: 81-116
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This bounded excerpt is source evidence; it is not a new proof/checker run.
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000081 | 3. COMPLETE CHARGED CHARACTER AND THE CANONICAL GLOBAL PAIR
000082 | 
000083 | For each doubled physical root r=Tz, read the character exactly as
000084 |   chi_v(r/2)=i^[sum_(a=5..7) r_a mod4].
000085 | The root phase multiplicities are 52,60,64,64 for 1,-1,+i,-i. Cartan fields
000086 | are fixed by t_v, but this does NOT justify deleting the character from the
000087 | full source data: its named charged action has a smaller native stabilizer.
000088 | 
000089 | We impose chi_v(g alpha)=chi_v(alpha) on all240 roots. Since these span the
000090 | E8 lattice over Z, this is equality of the character on the entire lattice,
000091 | not a finite approximate sample. For the square/deck use the mod2 character.
000092 | 
000093 | Data                       native Stab  logical image   q-orbits
000094 | unmarked                   46080       720             6
000095 | halfway deck character     3072        48              {0,1}|{2,3,4,5}
000096 | oriented quarter character 64          16              {0,1}|{2,3,4,5}
000097 | 
000098 | Among ALL15 unordered global label pairs, exactly ONE is invariant under
000099 | either character stabilizer: {0,1}. The result is covariance-intrinsic and
000100 | transports with the source frame; {0,1} is its original chart name. It is a
000101 | pair of event labels, not a rank2 physical subspace or a proof of particles.
000102 | 
000103 | The root must lie outside this pair if it is to be used as S in P(q,S).
000104 | There are four such q, forming ONE orbit:
000105 |   (2,{0,1}), (3,{0,1}), (4,{0,1}), (5,{0,1}).
000106 | Thus the seam data canonically provide this four-element subfamily once
000107 | the globally invariant pair is retained. Saying that all60 flags remain
000108 | undistinguished would lose this positive result. Saying that precisely
000109 | one flag is selected would be false.
000110 | 
000111 | For completeness, the oriented-character action on ALL60 flags has orbit
000112 | sizes4,4,4,8,8,8,8,16. None is a fixed flag; no q is fixed. Supplying q=5
000113 | by hand leaves TWO invariant label pairs {0,1} and {2,3} in its complement.
000114 | The first is distinguished globally by the unrooted character orbit; the
000115 | rooted fixed-point condition alone is weaker. These are different tests.
000116 |