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.
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.
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.
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.
A small quantum arrangement — a reader qubit Q₁ coupled to a remainder qubit Q₂ through one fixed gate, with declared operations on Q₁ only — has access to some distinctions of the remainder and not to others. This manuscript follows that arrangement through fourteen research units — thirteen with a model, exact proofs and an executable checker (with certified interval enclosures wherever a propagation is read), and one, the maintenance criterion, a definition with checked decision logic — and organizes what they establish around four distinctions. First, protecting an access restriction is different from preserving the distinctions a reader can use: a universal leakage bound and an exact one-gate value are proved; a reset-based maintenance pulse prolongs limited leakage at the price of previously accessible information, while a reversible pulse prolongs it and preserves the full declared input class. Second, meeting protection criteria does not identify a mechanism: a prepared finite clock-controller meets four declared criteria at four sizes, and so does a static field with the clock decoupled, and so does the clock's free mean field at the largest size. Third, restoring a supporting condition does not necessarily recover the capability: coupling alignment is shown to be a supporting condition of the capability, and a restoring process that improves alignment in six matched realizations meets the full restoration standard in one, misses it narrowly in one and fails in four, while useful access is preserved in none. Fourth, retaining a relation, delivering it to a reader and using it internally are different achievements, and a supplied design's advantage can reverse when its context changes without the comparison identifying the mechanism: a sector record restores access at three of four endpoints under an added permission; an internal coupling improves the primary endpoint without reaching the reference; a two-by-two of axis term and gating cell reverses both contrasts. Each result is stated with what it does not establish. No conclusion about self-maintenance, ownership or experience is drawn. The deposit is a technical manuscript, not peer-reviewed, that consolidates fourteen closed research notes and adds no theorem; the supporting proofs are in the notes. The package contains the manuscript (PDF and Markdown), the fourteen notes with two errata, every checker and its run record, the failure-path harness with its recorded outputs and a release adapter, the two earlier baseline notes, a claim-to-proof map, a correction ledger, a source lock and a manifest with the SHA-256 of every file. Every number printed in the manuscript was read by script from a packaged run record. Running checks/run_all.sh reproduces every checker's recorded summary line with the declared dependencies only (Python 3.11 or later; sympy 1.14, mpmath 1.3, numpy); the harness coverage, including the checkers it does not cover, is stated in §10 and Appendix A. Drafting and computation were AI-assisted under the author's direction. Archive SHA-256: 119d835b2d2e19463f3eb6478ea34ddbdf4deea220a5d6d6fe528dcf7061bedb.
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.
Boundary-Access Holonomy and the Quantum Reversible Quotient: A Finite-Distinction Framework for the Zero-Record-Holonomy Sector introduces FDS-Q0, an upstream quantum-foundations paper in the Finite Distinction Systems (FDS) program. The central question is why reversible quantum mechanics has a symmetric distinguishability structure at all. Standard finite-dimensional quantum mechanics is usually formulated after this symmetry has already been assumed: states live in complex projective Hilbert space, reversible dynamics is unitary, and distinguishability is symmetric inside the closed-system formalism. Q0 asks what finite boundary-access conditions make such a reversible symmetric sector available. The proposal is that standard Hilbert-space quantum mechanics is located as the zero-holonomy reversible quotient of a more primitive asymmetric finite-boundary access dynamics. A physical distinction is first directed, boundary-relative, capacity-limited, and record-sensitive: a system may export, preserve, erase, or recover a distinction differently across different boundaries. The central object is the boundary-access holonomy H∂, an operational obstruction to closing a directed access loop through system, apparatus, environment, record, and recovery channels. Q0 defines finite boundary-access systems, operational directed access, access asymmetry, boundary-access holonomy, and three holonomy sectors: coherent holonomy, record holonomy, and leakage holonomy. It gives a restricted access-category theorem showing that zero record holonomy makes the reversible quotient well-defined; in the restricted quantum-access category, the recovered-state kernel is symmetric. The paper explicitly does not claim to derive the full Hilbert reconstruction, the Born rule, objective collapse, hidden variables, quantum field theory, or all of quantum mechanics. The paper also supplies two minimal operational normal forms. First, a Mach-Zehnder stable-record model separates ordinary coherence overlap from stable accessible record holonomy, predicting that recoverable visibility can split at fixed overlap when stable record accessibility differs. Second, a QEC directed-leakage model treats leakage from the computational subspace as directed leakage into uncorrectable boundary sectors, predicting that logical failure can split at matched physical error when uncorrectable leakage differs. The compressed thesis is: H∂ = 0 ⇒ reversible Hilbert sector,H∂ ≠ 0 ⇒ record, decoherence, measurement, and maintenance sectors. Q0 supplies an upstream quantum-access layer for the FDS quantum sequence. Its immediate scientific task is to make boundary-access holonomy a calculable and testable quantity. Official website: distinctiontheory.orgPublic portal for the start guide, papers, claim status, failure registry, prior-art boundary, and citation resources. Canonical GitHub repository:https://github.com/yiningwu-research/Distinction-Theory