Representation types of the supplied free realization; no selection from P1/P2 and no new spinor-CAR replacement.
Read the exact result, assumptions and evidence
Result
D5_1 has ten real vector fermions; S± each contain 16 complex Ramond/spin-field states. Using S+ as an ordinary CAR coefficient would give c=16 and Spin(10) level 4. The documented c=8 connection uses 10+6 real fermions and mixed spin fields of weight 5/8+3/8=1.
Required assumptions
Original oriented exterior carrier
Given E=C5=E3⊕E2, a Hermitian metric, volume orientation, S± and Y=(-1/3)^3⊕(1/2)^2. Internal carrier labels are not physical vacua; geometric seam reflection is not identified with carrier conjugation.
Supplied free D5+A3 realization
Compare the documented free D5_1+A3_1 realization with five plus three complex fermions and spin-field sectors; realization by the raw P1 source is not presumed.
Only fixed fold time and fixed 5+3 marking. Covariant marking transport is positively constructed; other sources or dynamical dictionaries are not excluded.
Read the exact result, assumptions and evidence
Result
After actual quarter conjugation the D5 projections of the time axis have distinct squared norms 129/256 and 137/256. Hence no orthogonal T satisfies T d_beta=d_beta and T O(P5)T^-1=P5. This excludes every Weyl correction in this fixed comparison.
Required assumptions
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.
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.
First 5+3 marking and Z4 character supplied
In the supplied E8 dictionary, D5 on the first five coordinates, D3 on the last three and k=2sum(p1..p5) mod4 are given for the first quarter domain. The other domain may transport these data covariantly; their original physical selection is not presumed.
Exact map of the supplied source and conditional E8 lift; first marking, source realization and physical event law are not derived from P1/P2. Both quarter domains remain explicit; no switch to another branch to solve a fixed-sector question.
Read the exact result, assumptions and evidence
Result
n→−n−1 forces j→7−j and O=−MRM^T with O(x)=(x4,−x5,−x6,x1,−x2,−x3,x8,x7). O d_alpha=d_(1−alpha); P5_beta=O P5_alpha O^-1 and k_beta=k_alpha∘O^-1 need no new marking choice. Sea state and positive time are transported; the E8 current lift assumes the existing extension.
Required assumptions
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.
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.
First 5+3 marking and Z4 character supplied
In the supplied E8 dictionary, D5 on the first five coordinates, D3 on the last three and k=2sum(p1..p5) mod4 are given for the first quarter domain. The other domain may transport these data covariantly; their original physical selection is not presumed.
Correction of the finite selection inference; no identification of I with the actual Calderon operator and no P1 countermodel.
Read the exact result, assumptions and evidence
Result
CAR.PAIR.01 counts complex-bilinear singlets. The Hermitian scalar <f,g> already exists on S+; CAR.PAIR.02's 'scalar iff sheet-odd' inference is false in this reading. The previous J_C includes reversion signs and is fully Spin(10)-equivariant.
Required assumptions
Original oriented exterior carrier
Given E=C5=E3⊕E2, a Hermitian metric, volume orientation, S± and Y=(-1/3)^3⊕(1/2)^2. Internal carrier labels are not physical vacua; geometric seam reflection is not identified with carrier conjugation.
Given chiral source. No selection from P1/P2, no equal responses within one fixed twist, and no identification with affine r0.
Read the exact result, assumptions and evidence
Result
n→−n−1, alpha→1−alpha gives C D_alpha C^-1=−D_(1−alpha). Particles become holes and conversely; normal charge reverses and positive excitation energy is preserved. The unique sea state maps to the other sea state without adding a zero vector within one domain.
Required assumptions
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.
Representation with metric/orientation; J_C is not yet the actual boundary/OS conjugation. Two carrier labels are not two vacua.
Read the exact result, assumptions and evidence
Result
J_C=∏(epsilon_i+iota_i)K is antiunitary, exchanges S± and reverses Y. Exactly Lambda0 and Lambda5 have Y=0. J_C dGamma(h) J_C^-1=tr(h)I−dGamma(h). It is fully Spin(10)-equivariant. Reuse CAR.PAIR.01's bilinear pairing; CAR.PAIR.02's Hermitian selection inference has been corrected and is not evidence.
Required assumptions
Original oriented exterior carrier
Given E=C5=E3⊕E2, a Hermitian metric, volume orientation, S± and Y=(-1/3)^3⊕(1/2)^2. Internal carrier labels are not physical vacua; geometric seam reflection is not identified with carrier conjugation.
Only the supplied affine dictionary. Backgrounds or time-dependent covariant symmetries have different premises; no general gauge-physics no-go.
Read the exact result, assumptions and evidence
Result
Mdelta=(-1/2,0,alpha/4,-1/2,0,(alpha-1)/4,-1/4,-1/4). The six (3,2) root energies are (0,1/2,1/2,1,1/2+alpha/4,1+alpha/4). K therefore does not commute with the fixed full SM action. The quarter phase is retained.
Required assumptions
Original oriented exterior carrier
Given E=C5=E3⊕E2, a Hermitian metric, volume orientation, S± and Y=(-1/3)^3⊕(1/2)^2. Internal carrier labels are not physical vacua; geometric seam reflection is not identified with carrier conjugation.
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.
Original carrier plus supplied E8 charge dictionary; no physical field identification.
Read the exact result, assumptions and evidence
Result
epsilon1 epsilon4 produces u1∧u4 in the carrier: Y=1/6 and source charge change0. Root operator, spinor carrier vector and affine root-current state have different types. The exterior unit is the internal nu^c label, not the affine vacuum.
Required assumptions
Original oriented exterior carrier
Given E=C5=E3⊕E2, a Hermitian metric, volume orientation, S± and Y=(-1/3)^3⊕(1/2)^2. Internal carrier labels are not physical vacua; geometric seam reflection is not identified with carrier conjugation.
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.
Restore fixed marking after quarter conjugation by Weyl correction
Unequal projection norms exclude the whole orthogonal correction class at fixed d_beta.
Consequence: Use the actually transported marking or supply a different source action derived from P1/P2; a larger phase scan does not change the invariant.
Actual quarter conjugation transports the supplied marking
Exact map of the supplied source and conditional E8 lift; first marking, source realization and physical event law are not derived from P1/P2. Both quarter domains remain explicit; no switch to another branch to solve a fixed-sector question.
No time-stabilizing orthogonal repair of the fixed marking
Only fixed fold time and fixed 5+3 marking. Covariant marking transport is positively constructed; other sources or dynamical dictionaries are not excluded.
The two conjugations are typed; the actual quarter source determines transport of the supplied marking. No fixed time-stabilizing repair exists. Original selection of the first marked field source remains with the common selector; no new spinor16 replacement source.
Original historical attempts linked to this question
These are original research records. Their reported verdicts are distinct from the reviewed results above.
seam joint conjugation 20261015
What joint particle-hole, sheet, charge, state and time action follows from the actual retained quarter source, and can its marking be derived covariantly?
Recorded verdict: EXACT_COVARIANT_QUARTER_TRANSPORT
Historical inventory; not independently reviewed by this export.