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Architecture, E8 and the electromagnetic fixed point
Machine checks for this section: v106_ review_ validation.py
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documents/tfpt_1_architecture_e8/sections/006-source.tex · lines 132 to 167
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- explicit file citation v106_review_validation.py
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Architecture, E8 and the electromagnetic fixed point
The relation in plain words. The fine-structure constant is not just ``a number near [formula in source] '': it is the one exponential engine behind three wildly separated scales. Take the same [formula in source] and divide the carrier into it: [formula in source] of it sets the electroweak scale, [formula in source] it sets the Hubble scale, [formula in source] it sets the cosmological constant. The three action ch
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documents/tfpt_1_architecture_e8/sections/006-source.tex · lines 168 to 228
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Architecture, E8 and the electromagnetic fixed point
The engine [formula in source] is not an input — it is the unique root of an explicit closure equation (the exact electromagnetic closure theorem). With [formula in source] , [formula in source] , [formula in source] and the seam response [formula in source] , where the coefficient is [formula in source] , so the fine-structure constant reads the flavor transport budget [formula in source] and the [formula in source]
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documents/tfpt_1_architecture_e8/sections/007-source.tex · lines 1 to 256
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Architecture, E8 and the electromagnetic fixed point
Eliminating [formula in source] between the electroweak and the cosmological-constant lines gives a direct relation between the two scales:
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documents/tfpt_1_architecture_e8/sections/007-source.tex · lines 257 to 281
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Architecture, E8 and the electromagnetic fixed point
The decuple bridge is one rung of a tower. Writing [formula in source] for the stripped electroweak unit, all three cosmological scales are powers of the same [formula in source] with binomial exponents (verified exactly): with residues [formula in source] and [formula in source] . . The exponents are the complete-graph counts of the five-slot carrier [formula in source] : [formula in source] So the cosmological cons
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documents/tfpt_1_architecture_e8/sections/007-source.tex · lines 282 to 301
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Architecture, E8 and the electromagnetic fixed point
On the comparison layer [formula in source] ; equating to the TFPT line gives So the Hubble rung is not an independent third hit: it is the square root of the vacuum energy plus a geometric cosmology factor. The genuine TFPT content is the single [formula in source] . (The numerical coincidence [formula in source] is just [formula in source] and is [formula in source] -dependent; not a claim. )
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documents/tfpt_1_architecture_e8/sections/007-source.tex · lines 302 to 314
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Architecture, E8 and the electromagnetic fixed point
The `` [formula in source] '' is the action [formula in source] ; the `` [formula in source] '' is the seam defect [formula in source] .
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documents/tfpt_1_architecture_e8/sections/007-source.tex · lines 315 to 339
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Architecture, E8 and the electromagnetic fixed point
In units of the electroweak action [formula in source] , the three rungs are the first three binomial coefficients of the five-slot carrier: The first two are automatic ( [formula in source] , [formula in source] ). The non-trivial content is the cosmological-constant charge: since [formula in source] . So the ``double overlap'' charge [formula in source] equals the number of carrier-slot pairs [formula in source] on
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documents/tfpt_1_architecture_e8/sections/007-source.tex · lines 340 to 360
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- explicit file citation v2_carrier_pascal.py
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Architecture, E8 and the electromagnetic fixed point
The [formula in source] in the action ladder is not merely a rank: it is the square root of the discriminant of the carrier (hypercharge) polynomial. For a general split [formula in source] the carrier polynomial is [formula in source] with discriminant Hence the action ladder is, exactly, The electroweak hierarchy therefore reads the discriminant of the hypercharge polynomial, tying the Standard-Model hypercharge de
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documents/tfpt_1_architecture_e8/sections/007-source.tex · lines 361 to 376
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Architecture, E8 and the electromagnetic fixed point
All scales sit on the integer lattice spanned by two generators — the gauge unit [formula in source] and the flavor unit [formula in source] — as [formula in source] : @llll@ scale & [formula in source] & [formula in source] & axis \\ [formula in source] & [formula in source] & [formula in source] & gauge \\ [formula in source] & [formula in source] & [formula in source] & gauge \\ [formula in source] & [formula in s
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documents/tfpt_1_architecture_e8/sections/008-source.tex · lines 1 to 28
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Architecture, E8 and the electromagnetic fixed point
The gravitational normaliser [formula in source] has a transparent exact form. Writing [formula in source] , So [formula in source] is the exact leading value (the inverse of the [formula in source] family/gauge compression that sits in the seed [formula in source] , so [formula in source] ), and the deviation is precisely the small topological seed correction [formula in source] , i.e.\ [formula in source] . Gravity
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documents/tfpt_1_architecture_e8/sections/008-source.tex · lines 29 to 46
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- explicit file citation v1_e8_glue.py
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Architecture, E8 and the electromagnetic fixed point
Machine checks for this section: v60_ lambda_ metrology_ branch.py
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documents/tfpt_1_architecture_e8/sections/008-source.tex · lines 47 to 118
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Architecture, E8 and the electromagnetic fixed point
Machine checks for this section: v6_ bootstrap.py v14_ carrier_ uniqueness.py
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documents/tfpt_1_architecture_e8/sections/008-source.tex · lines 119 to 144
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Architecture, E8 and the electromagnetic fixed point
In the series [formula in source] is a downstream scale grammar, not a primitive cause: the boundary kernel fixes [formula in source] , the carrier rank, families and admissibility without [formula in source] upstream. Three levels.
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documents/tfpt_1_architecture_e8/sections/008-source.tex · lines 145 to 153
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- explicit file citation v5_e8_cascade.py
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Architecture, E8 and the electromagnetic fixed point
Coxeter/gauge typing of the lcm–gcd pair. Writing [formula in source] and [formula in source] , the relations become [formula in source] and [formula in source] : the local SM algebra is the gcd of the Coxeter double-period and the [formula in source] rank-occupancy, and the [formula in source] root count is their lcm. Likewise the EW exponent reads [formula in source] (Coxeter principal part plus a rank singlet). \
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documents/tfpt_1_architecture_e8/sections/008-source.tex · lines 154 to 170
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Architecture, E8 and the electromagnetic fixed point
with [formula in source] the number of non-empty occupation words of the [formula in source] carrier code.
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documents/tfpt_1_architecture_e8/sections/008-source.tex · lines 171 to 179
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Architecture, E8 and the electromagnetic fixed point
Identify [formula in source] with the even-weight binary code on five bits. A transition [formula in source] has flip [formula in source] , even and nonempty, so [formula in source] ; per state there are [formula in source] flips, giving and the [formula in source] undirected flips match the [formula in source] [formula in source] root pairs ( , counting). This makes the atlas conjecture testable: a genuine root map
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documents/tfpt_1_architecture_e8/sections/008-source.tex · lines 180 to 240
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Architecture, E8 and the electromagnetic fixed point
Use the universal root-system identity [formula in source] (Coxeter number [formula in source] ). With the carrier values [formula in source] and [formula in source] , The Coxeter number of [formula in source] is exactly three families times the cosmological pair action: each family contributes one [formula in source] -decuple ( [formula in source] ) to the Coxeter period. Equivalently the action ladder is a Coxeter
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documents/tfpt_1_architecture_e8/sections/008-source.tex · lines 241 to 261
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Architecture, E8 and the electromagnetic fixed point
The number of positive [formula in source] roots equals the master hypercharge moment: so the second hypercharge moment of one family is the positive-root half-system. The whole integer chain then reads off [formula in source] : The [formula in source] slice is then [formula in source] : one [formula in source] phase slice of the [formula in source] root atlas is exactly the full flavor transport budget. \ (arithmeti
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documents/tfpt_1_architecture_e8/sections/008-source.tex · lines 262 to 277
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Architecture, E8 and the electromagnetic fixed point
The three hard carrier atoms — weak rank [formula in source] , color rank / family count [formula in source] , carrier rank [formula in source] — generate the [formula in source] data cyclotomically, without taking [formula in source] as input. Set where [formula in source] is the Coxeter number and [formula in source] the rank. Then the standard [formula in source] , [formula in source] give Moreover the [formula in
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documents/tfpt_1_architecture_e8/sections/008-source.tex · lines 278 to 303
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