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.
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.
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.
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.
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.
STATUS (18 October 2026). The physics programme that motivated this work was concluded in October 2026 and its claim of a unified derivation withdrawn. The results in this paper do not depend on that programme and stand as stated. NOTE ON SCOPE (18 October 2026). Where this paper says that the Standard Model's matter content, charges or gauge structure are derived from, forced by or emerge from the eight-bit error-correcting cell, read encoded in or assigned to. The finite results themselves stand: the code, its constraints and the anomaly arithmetic are exact. But two things are premises of the framework, not consequences: the identification of codewords with particles, and the choice of the eight-bit [8,4,4] cell. In particular, the step from read/write balance to a single CSS code is not derived [R22]. The author's October 2026 review of the programme concluded that the framework's Standard-Model content is assigned rather than derived. No observation currently distinguishes the framework's account from the Standard Model itself. This revised note argues that, within the accepted complex quantum-error-correcting record substrate, the quadratic Born form arises from linear record writing, orthogonality of record sectors, and isometric normalization before any probability measure is introduced. Conditional uniqueness is treated separately through Gleason-type and refinement-stable record-sector routes. The 30 August 2026 additivity-audit revision cites Jiaxuan Zhang's analysis of five Born-rule derivations (arXiv:2603.06211) and makes the premise accounting explicit: a Gleason frame function includes orthogonal additivity, while Marko Lela's route begins with a non-negative extensive valuation on disjoint continuation bundles. The closed-record-pair route assumes neither measure-level object, but establishes the quadratic form rather than a standalone uniqueness theorem. The resulting open frontier is to obtain both form and uniqueness without importing measure-level additivity. The paper also records the minimal [8,4,4] record cell and the bare monitored service rate alpha_0 = 1/137, while retaining the deeper reconstruction question as open.
The Doplicher–Roberts reconstruction theorem converts one premise — every superselection sector has finite statistical dimension — into the full apparatus of a compact gauge group: conjugate sectors, para-Bose/Fermi statistics, and an integer charge lattice. In the companion framework [Dai-chg] that premise was priced as an identification. This paper — every component priced as theorem, identification, input, or open — upgrades it to a pair of theorems by deriving both finiteness properties of superselection from resource principles. Theorem A (maintenance law): a dense set of charge values admits no addition-consistent coarse-graining — composition is a free amplifier of sub-resolution differences — so any P3-maintainable value set is exactly a lattice λℤ, with the bonus bound λ ≥ δ (the charge quantum is no smaller than the world's resolution). Theorem B (writing law): an irreducible sector that a bounded, graded, adjoint-paired channel can write, and whose pair of label lines can both be relayed through vacuum pairs, possesses a conjugate and has d ≤ ‖W‖²/√|c₁c₂| < ∞; the relay amplitude is 1/d (probability 1/d²), and it is nonzero only on the conjugate-paired fusion channel — "a conjugate is the channel with a road home." Together: maintenance pins the ladder, writing caps the dimension, and the two laws supply the finiteness premise the Doplicher–Roberts reconstruction requires — returning Rep(G) for a compact G, given that the writable sectors form a DR-admissible subcategory. Three numerical campaigns in Cuntz-algebra models (predictions stated before each run) verify the finite-M structure — the zig-zag coefficient c = 1/d, the channel-resolved relay, and the braid sign — at machine precision. The d = ∞ death point is analytic rather than simulated: in standard normalization the pair-creation cost ‖R‖² = d = 1/c grows without bound as the zig-zag c → 0, diverging exactly where the boundedness axiom fails. One withdrawn formula is printed beside the live results.
Finite Determinacy (FD) was developed from a representational question: whether theuse of real numbers for physical quantities should be read as implying arbitrarily precisephysical determination. Replacing that idealisation by objectively finite determinationleads to bounded shared resolution depth for related records. Close finite-informationand relational antecedents in quantum foundations were identified subsequently and areacknowledged here; they were not the route by which the present framework was developed,and no historical priority is claimed for those principles. This companion paper asks whatdynamical restrictions follow once the resulting finite-record geometry is combined withexplicit finite-rate premises.For self-containment the paper first reproduces the common foundation: bounded jointdepth and split-invariant refinement give exponential resolution and a non-zero two-registerwidth-product floor; a homogeneous, finitely additive area regularity promotes that scalarconstraint to a local area measure; and a primitive tick/readout role asymmetry suppliesorientation, after which the two-member sector is symplectic. The positive symmetric formused for compatible complex structure remains an independent structural input. Dynamicsthen adds a universal pace ceiling rmax, a saturated intra-pair exchange ceiling |dv/du| ≤ L,and an inter-pair causal conversion c∗. In the quantum branch, explicit coherent-recordand record-faithfulness assumptions lead through Weyl–Heisenberg representation theoryto finite-step unitary evolution and the Schrödinger law-form. In the gauge branch, recordgeneratedtransport and holonomy lead, under a minimal local reversible continuum closure,to Yang–Mills curvature-square dynamics. In gravity, locality, reversibility and isotropy givea minimal hyperbolic principal part, while an explicit spatially relational continuum closureleaves two transverse-traceless modes.The proposed contribution is therefore not a new finiteness or relationality principle,nor an exclusive derivation of familiar terminal equations. It is an independently developedfinite-geometric route from the physical interpretation of real-number representation to acommon pre-Hilbert, pre-gauge and pre-metric substrate, followed by sector-specific dynamicalconsistency conditions.