In a compression-based account of charge, five distinct objects share the single name “charge”: a global conserved charge , an einselected reduced record , a -odd Yang–Lee ordering operator , a decaying Gaussian occupation , and a trajectory charge-transfer count . We separate them inside an instrumented, charge-conserving open quantum process and ask which relations are invariants of the full process and which are only diagnostics of a monitoring scheme or of the no-jump conditional slice. In minimal completely-positive models we establish: (i) [THM] if every jump commutes with and , charge-diagonal monitoring makes the reduced record an exact fixed point, and [CALC] its survivor -algebra is the two-dimensional diagonal (charge-sector) algebra; a charge-violating perturbation makes it a finite-lifetime metastable record whose lifetime rises with the monitoring rate in the strong-monitoring (Zeno) branch. (ii) [THM] -covariance does not imply charge conservation — amplitude damping is covariant yet lowers the occupation. (iii) [CALC] the asymptotic () stationary fixed-point -algebra obeys a three-way classification: for a bare record; with unchanged charge centre when a non-abelian seed survives (intra-sector protected structure); and a refined centre when a second abelian label survives. Charge labels all asymptotic survivors iff the stationary and there are no nonzero-frequency peripheral modes; the weaker excludes neither intra-sector survivors nor rotating (nonzero-frequency) peripheral modes, which are counted separately from . (iv) [CALC] a genuine finite-time trajectory Lee–Yang zero of a two-site transport counting statistics exists (complex Newton root, residual , winding number one); we do not call it an edge. The two strongest results are negative: [NEG] the no-jump effective Hamiltonian is not a representation invariant of the physical generator — at an exceptional point the eigenvalue splitting opens from to under a redundant Lindblad representation that leaves fixed to , so the exceptional point itself is not a process invariant; and [NEG] in the stated model, at a no-jump exceptional point no non-analyticity of the physical scaled cumulant generating function is detected in the scanned range. One minimal model simultaneously instantiates three charge objects () and two derived dynamical objects (); and remain comparison entries supplied by other minimal models / companions. In that model the conserved record and the zero-generating transferred charge are different objects: the ledger and language are unified, but a direct, representation-invariant bridge from the record to the dynamical Lee–Yang zeros is not established. We do not derive , a dynamic exponent , or any universality class.
In a compression-based account of charge, five distinct objects share the single name “charge”: a global conserved charge , an einselected reduced record , a -odd Yang–Lee ordering operator , a decaying Gaussian occupation , and a trajectory charge-transfer count . We separate them inside an instrumented, charge-conserving open quantum process and ask which relations are invariants of the full process and which are only diagnostics of a monitoring scheme or of the no-jump conditional slice. In minimal completely-positive models we establish: (i) [THM] if every jump commutes with and , charge-diagonal monitoring makes the reduced record an exact fixed point, and [CALC] its survivor -algebra is the two-dimensional diagonal (charge-sector) algebra; a charge-violating perturbation makes it a finite-lifetime metastable record whose lifetime rises with the monitoring rate in the strong-monitoring (Zeno) branch. (ii) [THM] -covariance does not imply charge conservation — amplitude damping is covariant yet lowers the occupation. (iii) [CALC] the asymptotic () stationary fixed-point -algebra obeys a three-way classification: for a bare record; with unchanged charge centre when a non-abelian seed survives (intra-sector protected structure); and a refined centre when a second abelian label survives. Charge labels all asymptotic survivors iff the stationary and there are no nonzero-frequency peripheral modes; the weaker excludes neither intra-sector survivors nor rotating (nonzero-frequency) peripheral modes, which are counted separately from . (iv) [CALC] a genuine finite-time trajectory Lee–Yang zero of a two-site transport counting statistics exists (complex Newton root, residual , winding number one); we do not call it an edge. The two strongest results are negative: [NEG] the no-jump effective Hamiltonian is not a representation invariant of the physical generator — at an exceptional point the eigenvalue splitting opens from to under a redundant Lindblad representation that leaves fixed to , so the exceptional point itself is not a process invariant; and [NEG] in the stated model, at a no-jump exceptional point no non-analyticity of the physical scaled cumulant generating function is detected in the scanned range. One minimal model simultaneously instantiates three charge objects () and two derived dynamical objects (); and remain comparison entries supplied by other minimal models / companions. In that model the conserved record and the zero-generating transferred charge are different objects: the ledger and language are unified, but a direct, representation-invariant bridge from the record to the dynamical Lee–Yang zeros is not established. We do not derive , a dynamic exponent , or any universality class.
A charged quantum subsystem is generally not dynamically closed once the electromagnetic degrees of freedom are traced out; its reduced dynamics is then a completely positive semigroup whose dissipator has a charge-dependent rate, . We read this semigroup as a lossy compression and ask a narrow question: of the internal unitary structure , which directions does the loss turn into permanent classical records, and which does it leave untouched? The reading that answers it — charge as the abelian centre , flavour and colour as the non-abelian seed — is taken from the companion charge line; what this note adds is to turn that reading into a dynamical criterion and to fix its boundaries. The rate is charge-dependent: for a fixed monitoring coupling the inter-sector decoherence rate is (bare is its value against the reference; Fermi’s golden rule fixes the coupling). This classicalizes the charge-sector label — coherence between distinct charge sectors decays and the sector basis is einselected — while the interior of each fixed charge sector, including a nonzero-charge sector, can stay unitarily reversible in this electromagnetic channel; the non-abelian (flavour/colour) directions, being charge-preserving, sit inside that reversible interior. Calling the einselected label a record in the operational sense requires more than dephasing (a charge-resolving environment output for an accessible record, redundancy for a durable one). Finiteness of the resolution available to distinguish neighbouring sectors then restricts the record’s spectrum to a discrete lattice (integer-valued only after normalization by the lattice unit) — given a finite-resolution premise. We separate what is borrowed (einselection; that charge decoheres into a record; ; the reading and the maintenance and Wick-bridge results of the companion lines) from the two things this note contributes: an imaginary-chemical-potential entry that relocates the analysis from the Hermitian dilation to the reduced generator’s anti-Hermitian part (the dilation exists but is not load-bearing), and a distinction between two “centres” that keeps the account from re-deriving known superselection results. The number of generations is not addressed: that is seed, not theorem.
We identify and separate a preliminary gauge obstruction from three logically distinct source requirements for a counting field to activate a Yang–Lee-compatible charge-odd direction in the class of local charge processes studied here. Gate 0 asks whether the counted jump observable is only a boundary term: if its weights are exact, the tilted generator is related to the untilted one by a similarity transformation and the long-time spectrum is unchanged. Once a non-boundary count exists, three further conditions concern the source itself: a charge-odd source must be symmetry-allowed, real analyticity together with charge conjugation must pin it to the imaginary axis on the counting line, and the zero mode to which it couples must be dynamically live rather than a c-number in a fixed charge sector. The last statement is a state-source inertness condition and is algebraically distinct from Gate 0. A 3×3 factorial test of source permission against sector openness contains nine conditions, exactly four of which are live; they are precisely the four carrying both ingredients. A symbolic elimination independently reproduces the source structure and its phase. We then construct a tilted three-state chain in which these requirements are realised. Its tilted generator has an exact antiunitary symmetry, from which we derive and verify that the real part of the charge expectation vanishes on the unbroken branch and splits into an equal-and-opposite pair after the finite-size branch point. Finite-time Lee–Yang zeros of the moment generating function approach that certified branch point as 1/t²; a spectral-side prediction of the convergence amplitude agrees with the zero-side measurement to 2.7–5.2%, improving with size, and the second-order Jordan secular term is observed directly. Two independent finite-size procedures return a common critical-field estimate within 0.02%. We do not promote that agreement to proof of thermodynamic branch-point accumulation, which remains unresolved in the available size window. The same calculations establish, equally sharply, the boundary of what these signatures can decide. The 1/t² law and the associated fixed-size zero-density exponent −1/2 are generic kinematics of a second-order branch point and therefore cannot identify a Yang–Lee universality class. On a published benchmark with a known answer, the dynamical-exponent estimator remains 7.7–11.8% from the truth at the largest comparable sizes and a linear 1/L extrapolation overshoots by 17%. An observable-specific correction-amplitude zero is stable across sizes, explaining why the best-looking finite-size working point can be the worst point from which to extrapolate; a separate rank-one residual test is reserved for deciding whether it is an effective-action property. We therefore keep two inference levels separate. Source-level/static Yang–Lee compatibility does not by itself fix the stochastic-time dynamical exponent. The stronger spectral-CFT route used for a Virasoro-tower, Casimir-energy and central-charge reconstruction additionally requires z=1. Conditional on that gate, three spectral anchors would overdetermine the low-energy tower through target-value-free closure identities; only if those identities close are the lowest weight, effective central charge and central charge to be read out blind, with the velocities and tilt-induced drift cancelling.
Non-Hermitian criticality is often treated as a single phenomenon, yet two distinct objects travel under that name. An exceptional point is a finite-N spectral object—the coalescence of eigenvectors of a single operator; a Lee–Yang edge is a thermodynamic-limit c-number object—the accumulation of partition-function zeros. We show that which of these an imaginary coupling produces is set by the direction the coupling occupies. When the coupling multiplies a conserved charge, [Q, H] = 0, the deformation H − iµQ is normal for every complex µ: its spectrum is entire, its eigenvectors are µ-independent, and no exceptional point exists at any coupling strength or volume, while Lee–Yang zeros persist and can carry an edge. When the coupling lies on a symmetry-invariant but non-conserved direction, exceptional points appear, but the associated universality is the analytic continuation of the Hermitian thermal transition, not the Yang–Lee edge. Only on the order-parameter (symmetry-odd) direction do the two coincide, at the M(2, 5) edge. The direction of an imaginary coupling therefore sets how much genuine non-unitarity its spectrum acquires. We give the theorem, a three-arm criterion, exactly solvable and exact-diagonalization checks, and falsifiable kill conditions.
A charged quantum subsystem is generally not dynamically closed once the electromagnetic degrees of freedom are traced out; its reduced dynamics is then a completely positive semigroup whose dissipator has a charge-dependent rate, . We read this semigroup as a lossy compression and ask a narrow question: of the internal unitary structure , which directions does the loss turn into permanent classical records, and which does it leave untouched? The reading that answers it — charge as the abelian centre , flavour and colour as the non-abelian seed — is taken from the companion charge line; what this note adds is to turn that reading into a dynamical criterion and to fix its boundaries. The rate is charge-dependent, (Fermi’s golden rule): only the centre is einselected into an (effectively) unerasable superselection record, while the non-abelian directions stay unitarily reversible in this electromagnetic channel. Finiteness of the resolution available to distinguish neighbouring sectors then restricts the record’s spectrum to a discrete lattice (integer-valued only after normalization by the lattice unit) — given a finite-resolution premise. We separate what is borrowed (einselection; that charge decoheres into a record; ; the reading and the maintenance and Wick-bridge results of the companion lines) from the two things this note contributes: an imaginary-chemical-potential entry that relocates the analysis from the Hermitian dilation to the reduced generator’s anti-Hermitian part (the dilation exists but is not load-bearing), and a distinction between two “centres” that keeps the account from re-deriving known superselection results. The number of generations is not addressed: that is seed, not theorem.
We identify the internal algebraic structures that can survive Entropy-Activated Dynamics (EAD) compression and separate exact protection theorems from conditional Standard-Model realizations and parent-specific generation selectors. For a finite quantum Markov semigroup in the faithful Frigerio class, the protected observables form a finite-dimensional -algebra and coincide with the commutant of the Hamiltonian and jump family. A reset-semigroup construction realizes any prescribed matrix-algebra block, while a corrected stability theorem preserves the fixed algebra only under conditional-expectation-, symmetry-, or commutant-preserving perturbations; an arbitrarily small generic primitive perturbation can collapse it. The real algebra , its algebra bundle, the faithful unimodular group , and the usual hypercharge ray are therefore realizable and stable in named classes, not uniquely selected by the present EAD ontology. Patchwise overlap modules give an integer chiral index, a quasilocal dissipative realization, and an exact charge-one Fock restriction; however, number-conserving evolution cannot select the charge-one sector from a generic Fock mixture. An independent event-level collision parent has a unique stationary mode at three copies. The TS-80 parent-modulus classification then supplies the decisive correction: permutation-covariant positive collision parents contain a correlation modulus , with response . The independent point selects mode three, whereas the admissible correlated parent selects mode four; interacting parents introduce a second modulus and held-out families contain both modes. Hence family number is an integer protected-module invariant, but three-family selection is parent-specific and not universal. We also retain the sealed class-level exclusion of aligned single-scale localization textures, which produce a mixing exponent and obey after the declared extension. The paper does not derive a unique Standard-Model algebra, a unique microscopic gauge connection, observed gauge couplings, a universal value , or a successful Yukawa texture.
Two statements about lossy compression are often made as analogies rather than proved: that discarding information is “the same as” non-unitary evolution, and that the imaginary parameter of a critical partition function is “the same as” a dissipative flow. We make both precise. First, we show that an optimal lossy code induces a non-unitary evolution of its retained representation: the reduced dynamics is a completely-positive semigroup whose no-jump effective Hamiltonian is non-Hermitian, H_eff = H₀ − iμN̂, where N̂ counts the retained modes and μ is half the information-discard rate; the evolution is unitary if and only if the code is lossless, and the physical requirement that compression discards variance selects the amplitude-damping jump — which yields an imaginary chemical potential −iμN̂ — over dephasing, which would not. Second, we show by Wick rotation that this real-time loss is the imaginary chemical potential of a Euclidean partition function, i.e. a Yang-Lee setup: the discard rate is the Yang-Lee field, and the conserved charge becomes non-analytic at the Yang-Lee edge, driven by the compression loss. We then record an empirical corollary for learned representations: the leading value of the measured correlation exponent is a property of the measurement construction rather than of the data, so the informative quantity is the excess above it. Both results are reached with standard tools, but the identifications they establish — the discard rate of a compressor as an imaginary chemical potential, and as the imaginary field of a Yang-Lee edge — are, to our knowledge, new, and they replace two working analogies with proved statements.