Which Way Is Forward? Anticharge in Antitime

Relativistic physics contains many paired descriptions: conjugate charge representations, opposite orientations of a worldline, the two signs of a spinor above a vector, left- and right-handed Weyl modules, and positive- and negative-frequency sectors. This paper asks whether part of that doubling is the representation of one elementary structure: observables can depend on the relative alignment of two orientations while remaining blind to their simultaneous reversal. The exact starting point is an oriented gauge line. After fixing a reference charge Q⋆, let q = ±1 denote the conjugate representation orientation and let t = ±1 denote the orientation of the line relative to an observer. Equivalently, each particle carries a charge arrow and a time arrow, the latter measured against the arrow along which records accumulate, and only their alignment is observable. Wilson transport and the worldline current depend on the binary character χ = qt, (q,t) ∼ (−q,−t), Q_obs = Q⋆χ. Choosing Q⋆ = −e, the lifts (++) and (−−) therefore have the electron charge, while (+−) and (−+) have the positron charge. Either half flip changes the particle class; the diagonal flip does not. The temporal sign is the choice of a time copy: time is doubled, two coincident copies with opposite orientations, left time and right time, and for observer time orientation u^μ and microscopic phase covector k_μ the relative sign t = sgn(−u·k) records which copy a phase runs on. Proper time counts up on both copies, and the names of the signs are conventional: exchange them everywhere and nothing has happened. A finite four-lift Hilbert carrier realizes the same algebra more sharply than a literal finite gauge quotient. Its operators I_q, I_t, D generate a group of order 16 with center {1, −1, χ, −χ}; the simultaneous reversal D is noncentral, while −1 = I_q^2 = I_t^2 is central. Relative to the microscopic complex structure I_q, D is an involutive real structure whose fixed carrier is {(a, b, b, a)}. On that real form the two half flips induce the same exchange of the χ = ±1 sectors, and χ is explicitly intertwined with the standard charged-Kähler charge operator. Equal ++/−− weight follows only for a D-invariant state or measure; it is not a kinematic population law. Under a minimal simple-bivector realization this full carrier is the complexified spin module of Cl(2,2), with χ equal to the negative split volume element; this makes the half-flip identity an exact Clifford relation. The standard relativistic structures surrounding this quotient are then derived independently. Charged Kähler theory separates a signed first-order generator from the positive Hamiltonian, L = Qh with h = |L| ≥ 0. A massive action gives the exact Compton phase density dφ/dτ = −mc^2/ℏ, and the rest-frame Dirac doublet exhibits the standard SU(2) → SO(3) factor of two in its projective clock. Feynman's switchback identity C S_F(p)^T C^−1 = S_F(−p) gives the exact propagator version of reversing a charged Dirac line without identifying the geometric half flip with Wigner time reversal. The T of the CPT theorem is the particle's own time arrow: on the arrows the theorem reads Θ = PT_g, parity times one arrow flip, and the C in its name is bookkeeping, the receipt for a charge conjugation hidden inside Wigner's time reversal, which is the arrow flip composed with that conjugation, so the charge flip is written twice and cancels. In the finite CAR bridge, particle and antiparticle modes have opposite charge but equal positive energy, and the neutral pair creator obeys [Q, a†b†] = 0 and [H, a†b†] = 2ε a†b†. Thus antimatter is not a negative-energy sector; a charged half flip is constrained by gauge charge while neutral pair production is allowed. The charge current is linear in the worldline tangent while the gravitational source T^μν = m u^μ u^ν is quadratic, so an arrow flip changes measured charge but never the sign of gravity: antimatter falls down, as ALPHA-g observed. The thermodynamic arrow admits the same relational treatment. For an arbitrarily oriented time parameter λ, define D_t = t d/dλ. The second law may be written D_t S_coarse ≥ 0. Under complete temporal reversal t ↦ −t together with S(λ) ↦ S(−λ), this inequality is invariant even though dS/dλ reverses sign. Hence a time-reflection-symmetric complete state can contain conjugate histories with opposite coordinate entropy rates while every internal record-forming observer sees entropy increase toward its own future. In a diagonal-invariant measure, equal lift weight gives an exact cancellation of signed entropy flux while the orientation-covariant entropy production remains nonnegative. This is the precise sense in which thermodynamic irreversibility need not imply an absolute fundamental arrow of time. The geometric completion is developed separately. The Grassmannian order-four map extends to a linear orthogonal transformation of the Klein carrier; its Pin lift exchanges half-spin modules. A doubled Lorentzian parent W^6,2 admits a transverse two-plane whose fixed-radius quotient produces the four-dimensional massive off-Klein shell rather than deleting the extra directions. The determinant square-root cover, transverse Spin(2) cover and free Dirac Compton phase are explicitly intertwined. The maximal compact subgroup of Spin_0(6,2) contains the central product (SU(4) × U(1)_⊥)/Z_2, fixing the primitive color-centralizer generator X = 3(B − L), but it cannot also supply a commuting weak SU(2). A Clifford audit shows why parity cannot be added as a third binary sign: Pγ_5P^−1 = −γ_5, so parity exchanges Weyl modules. Keeping the (q,t) orientation carrier separate from weak chirality leads to the orthogonal extension R^6,2 ⊕ R^4,0 = R^10,2. Its maximal compact group contains Spin(10) × Spin(2) modulo the common center; chirality multiplication gives the Pati-Salam family branching, and the Majorana-Weyl real structure in signature (10,2) packages a complex 16 and its conjugate opposite-Spin(2) partner into one real chiral object rather than two independent realities. The adjoint branching of one Spin(10,2) connection is also fixed: relative to the block reduction, its general local form has the (6,2) and weak block connections together with an off-diagonal (8,4) one-form whose compact content includes conjugate weak bidoublets and a colored partner. The exact theorems therefore support a sharply delimited hypothesis: complete reversal of system and the physical standards used to name charge, the time arrow and handedness may be a change of lift, while incomplete reversals are observable. The remaining obligations are dynamical: derive a positive physical action and interacting section, symmetry breaking and partner lifting, low-energy couplings, Yukawa/CP data, the many-body record arrow, and the operational observable algebra. Any observable that remains odd after the complete dictionary is applied falsifies the strong quotient.