Source and logical dependency audit of the cited chain, not a universal impossibility theorem. An independent original derivation of the cross-identification or unique minimal algebra/bimodule classification could close the gap. E8 glue rank selection and fixed state for given transport are retained and not equated with local algebra selection.
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Result
Original minimization does not classify the minimal algebra/bimodule fiber. The joint discrete theorem imports Higgs rank2 and branch-Yukawa rank3; the master functional fixes d_disc*,P_adm and B_min before varying only ξ=(α,χ_geo,δ_ph,ρ_vac). The singleton fiber product presupposes discrete uniqueness with E3⊕E2,Y in the shared invariant tuple. Two exact conditional decoders exist: independent occupancy balance at g5 gives {b,s}={2,3}; independent Bγ=g/(g−1) with Y roots−1/b,+1/s gives s²=g−1, hence s2,b3. Their cited original proofs evaluate these equalities only on the fixed3+2 branch. Using them as upstream selectors adds a premise.
Required assumptions
P1/P2 remain declared starting axioms
This program checks which additional source, state, event, and observable structures follow from accepted TFPT principles; it does not revoke or replace P1/P2.
Do not identify source types
Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.
Exact field-type comparison in the same given source. No universal exclusion of E8 or future source/sector extensions.
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Result
Each of the four candidates acts on the eight original complex fields with two copies of every quarter phase. Their neutral bilinears form A3+4A1 with twenty roots and rank seven, rather than D5+A3 with fifty-two roots. The latter uses the stipulated spinor completion. The new marking changes neither K nor the known ground-state comparison and supplies no event instrument.
Required assumptions
Fully normalized time/charge family in the given E8 completion
The given chiral quarter source, its eightfold pushforward and stipulated even E8 completion supply K_alpha and the full additive U1 generator Q. Only characters in the real span of their torus vectors modulo E8 are searched; no P5 is supplied as a search variable or target projector. Physical identification of this completion and of a composed marking is not assumed.
Stipulated E8 quarter-fold dictionary
The existing Weyl lift M, affine E8 module, Q'=2(H3+H6) and K_alpha=L0+delta_alpha.H0 with alpha=1/4,3/4 are held fixed for comparison. This representation is not derived from P1/P2; an unbroken SM time action is not assumed.
Given chiral source in both quarter domains
D_alpha=-i∂theta on f(theta+2pi)=exp(2pi i alpha)f(theta), filled negative spectrum and relative particle/hole excitation time; alpha=1/4,3/4. This compares two conjugate domains, not opposite charges in one fixed domain or all P1 sources.
Given chiral source, fold, full normalized charge and stipulated E8 completion. Algebraic construction and Lean lattice theorem; no physical selection of W or source from P1/P2.
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Result
Full lattice saturation reduces the continuous source torus to sixteen four-torsion characters, twelve primitive and exactly four D5+A3 markings. P5 is reconstructed from neutral root moments; a control without M or a target projector finds the same four. W=exp(4πiK)exp(-iπαQ/2) realizes one while preserving quarter time; sheet transport gives W Zq. Compensation was previously known; complete classification and control are added here.
Required assumptions
Fully normalized time/charge family in the given E8 completion
The given chiral quarter source, its eightfold pushforward and stipulated even E8 completion supply K_alpha and the full additive U1 generator Q. Only characters in the real span of their torus vectors modulo E8 are searched; no P5 is supplied as a search variable or target projector. Physical identification of this completion and of a composed marking is not assumed.
Stipulated E8 quarter-fold dictionary
The existing Weyl lift M, affine E8 module, Q'=2(H3+H6) and K_alpha=L0+delta_alpha.H0 with alpha=1/4,3/4 are held fixed for comparison. This representation is not derived from P1/P2; an unbroken SM time action is not assumed.
Given chiral source in both quarter domains
D_alpha=-i∂theta on f(theta+2pi)=exp(2pi i alpha)f(theta), filled negative spectrum and relative particle/hole excitation time; alpha=1/4,3/4. This compares two conjugate domains, not opposite charges in one fixed domain or all P1 sources.
Global charge transports in the stipulated even completion; not local vertex insertions, an ordinary-local odd CAR/E8 inclusion or event dynamics.
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Result
On the even D8 Fock sector W4=Us Rc holds with the actual ordered CAR/E8 cocycle, Klein signs, all oscillators and current central term; Rc preserves Q,K and the quarter transition. The E8 extension and lift convention are explicitly given.
Required assumptions
Stipulated even E8 completion with actual Klein signs
Assume the E8 extension of the even D8 CAR sector constructed in seam-joint-ward-state, with original ordered cocycle, retained quarter transition and explicit P-lift convention. An ordinary-local inclusion of odd CAR fields is not assumed.
Applies exactly relative to the declared experiment alphabet and complete answer functional; no absolute ontology or physical TFPT source claim.
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Result
For a fixed experiment alphabet and complete answer functional r, u~v exactly when r(uw)=r(vw) for every allowed continuation w. The quotient is the minimal distinguishable process state relative to those answers; by itself it yields neither complex amplitudes, the Born rule, continuous time, a metric, nor E8.
Required assumptions
Declared complete answer functional
A fixed set of allowed experiments and the answer functional r for every finite experiment sequence are additional operational inputs; they define the future quotient only relative to that experiment alphabet.