Classical theories of identity presuppose state distinguishability over time. Quantum mechanics appears to challenge this. The present paper establishes that LP’s structural persistence condition IR = R / (F · I · C) ≤ 1 is compatible with and illuminated by quantum mechanics. LP requires distinguishability of states, not constituents — satisfied in quantum mechanics at the system level. Superposition is a regime of structural indeterminacy (IR > 1 at the outcome level). Measurement is IR-reduction through environmental coupling. v3 strengthens Section 4a: the proof chain LP identity preservation → state-space isometry → Wigner symmetry → unitarity replaces the weaker injective-CPTP argument of v2. Identity is not merely compatible with unitary evolution — it structurally requires it.
Classical theories of identity presuppose state distinguishability over time. Quantum mechanics appears to challenge this. The present paper establishes that LP’s structural persistence condition IR = R / (F · I · C) ≤ 1 is compatible with and illuminated by quantum mechanics. LP requires distinguishability of states, not constituents — satisfied in quantum mechanics at the system level. Superposition is a regime of structural indeterminacy (IR > 1 at the outcome level). Measurement is IR-reduction through environmental coupling. v3 strengthens Section 4a: the proof chain LP identity preservation → state-space isometry → Wigner symmetry → unitarity replaces the weaker injective-CPTP argument of v2. Identity is not merely compatible with unitary evolution — it structurally requires it.
Physical theories determine how states transform, but a same-system claim asks a different question: whether the transformed description concerns the same physical subject. La Profilée (LP) proposes a universal structural law of nature governing identity under transformation; here “universal” denotes a functional necessity claim about determinate same-subject judgments, not a derivation of domain-specific dynamics, constants, masses, or couplings. In LP, persistence is not an independent primitive alongside identity: it is diachronic identity, the positive consequence of preserving the relevant sameness relation through admissible transformation. This paper gives the physical identity formulation of that law and isolates a necessary dynamical condition: No Coreference Without Congruence. If two admissible representatives are identified as the same physical subject through the transformation under analysis, they must induce the same retained future; otherwise no representative-independent reduced evolution exists on the proposed identity quotient. Q1 certifies whether a determinate integrated bearer continues at all. Q2 is the identity verdict on that continuing bearer and, where the physical realization requires distinct carriers, is typed into Q2a, identity-class continuity, and Q2b, continuation-stable profile/history identity. A constrained bridge π_p:H_ℛ ⇀ Ā_ℛ relates those carriers, and Q2b ⇒ Q2a ⇒ Q1. The congruence requirement is stated for deterministic maps, linear quotients, CPTP channels, and quantum instruments. Greatest-fixed-point, bisimulation-like, and quotient-congruence techniques are established mathematical tools; the contribution is their typed integration into the physical identity law supplied by LP. Persistence is then a regime consequence of successful identity preservation, not a primitive used to define identity.
La Profilée is the structural architecture of determinate nature: Constitution identifies the whole, Transformation evaluates its existence and identity through change, and Coexistence evaluates relations among realized wholes. This paper applies the full architecture to quantum measurement without changing the quantum equations. Its physical subject remains definite outcomes, their relation to unitary evolution, the Born law, and the identity of the records that carry them. A physically completed coupling resolves an exhaustive exclusive record variable; LP determinability then gives one actual record value without an observer selecting it. Exclusive actuality does not entail projection of the globally retained quantum state. Rank-one calibration and repeatability fix the affirmative branch map. Statistical non-contextuality additionally requires identity of the complete input–event experiment and descent of its law to that identity class. Stable Boolean event frequencies then give the Gleason representation, and preparation faithfulness identifies its operator with the prepared state. Each inference is proved in the text. The argument determines the carrier and instrument before using these results. It proves that a unique instrument constitution does not select a run outcome, and that decoherence alone does not identify the physical record partition. Worked reversible-laboratory and relational cases distinguish an actual event from persistence of its record. Quantum recovery makes the distinction quantitative: a two-qubit copying channel preserves classical labels exactly, loses local full-qubit recoverability with optimal normalized diamond error one half, and preserves the full code jointly. Continuation-family and complementary-channel results connect those measurement records to information preservation, including evaporation. The resulting measurement theorem states its structural and physical requirements explicitly; it does not predict the individual outcome or infer multi-time consistency from a formal state–label pair alone.
This paper proposes a structural principle that explains how physical reality emerges from quantum configuration space. While quantum mechanics accurately describes systems as superpositions of possible configurations, it does not by itself explain why only certain configurations persist as physical reality under interaction. We introduce stability as a necessary condition for persistence, derived from the requirement that physical systems must produce consistent relational outcomes under repeated interaction. Configurations that fail to satisfy this requirement cannot be empirically identified and therefore cannot constitute elements of physical reality. Within this framework, quantum states define structured configuration spaces, interaction imposes consistency constraints, and stability acts as a selection mechanism. Measurement is reinterpreted as stability-based selection rather than collapse or branching. A concrete analysis of a decoherence scenario demonstrates how incompatible correlation structures fail to persist. The framework distinguishes between state-level stability, governing the persistence of configurations, and sequence-level stability, governing coherence across change. While the present work focuses on physical persistence, this distinction provides a foundation for extending the same principle to identity and higher-level structures. This work does not modify the formalism of quantum mechanics, but provides a structural account of how probabilistic configuration spaces give rise to persistent physical reality.
This preprint develops a thermodynamic admissibility condition on the persistence of quantum identity in open systems. Standard quantum mechanics allows extremely large spaces of possible system histories, but only a small subset remains experimentally realisable once irreversible entropy production is taken into account. This work formalizes this as an admissibility constraint: any quantum system that preserves a stable, trackable identity over time must satisfy a finite budget on cumulative irreversible dissipation. No new forces, variables, or dynamics are added; the constraint is purely structural and compatible with existing open-systems formalisms. The paper connects this requirement with decoherence, spectrum broadcasting, quantum Darwinism, and the emergence of classical objectivity. It frames identity persistence as a pre-dynamical condition—necessary before predictions about evolution or measurement outcomes are meaningful. This structural account clarifies why only certain histories are physically realisable, how objectivity arises under irreversibility, and how thermodynamic bookkeeping parameters (such as an “identity budget”) implicitly constrain experimental practice. The result provides a unifying, thermodynamically grounded framework linking dissipative quantum processes, system architecture, and long-term identifiability.
The mathematical structure of quantum theory is usually postulated rather than explained—Hilbert spaces, operators, and probabilistic structure—without explaining why this arena should exist in the first place. In this work we address a more primitive question: starting from the absence of any prior structure, what conditions must be satisfied for coherent persistence to be possible at all? We begin from a state of zero determination (the Void), understood not as physical emptiness but as the absence of admissibility constraints. From this starting point, we show that the possibility of persistence forces a minimal triadic structure consisting of reference, transformation, and return. This structure enables self-verification without external supervision and distinguishes genuine continuity from accidental resemblance. The requirement of self-verifying persistence forces deviation to be representable quantitatively and to compose across histories. This necessity leads uniquely to a linear vector space structure. Stability further imposes a knife-edge viability condition: identity-preserving and identity-violating contributions must equalize at closure. From this condition, an inner product and norm are forced, yielding Hilbert space geometry and operator representations as consequences of viability rather than axioms. Within this framework, familiar features of quantum kinematics—such as uncertainty, unitary evolution, and probabilistic weighting—arise as structural necessities rather than postulated rules. The present work establishes the kinematic foundations of coherence, deriving the mathematical arena of quantum theory from the requirement that something persist at all. Applications to mass relations, symmetry, temporal ordering, and composite systems are developed separately.Version 1.0. This preprint establishes the structural foundations of Coherence Algebra and derives Hilbert space from self-verification and persistence.
This paper derives Schrödinger evolution as a structural consequence of coherent persistence rather than as a postulate of quantum mechanics. Starting from minimal requirements for viable propagation—linearity, norm preservation, and continuity—we show that admissible evolution must be unitary and generated by a self-adjoint operator. The resulting Schrödinger equation describes reversible propagation within the space of viable states, while irreversible selection arises separately from the return operation. This separation clarifies the relation between unitary dynamics and measurement without introducing collapse mechanisms or stochastic dynamics. Schrödinger evolution thus emerges as the unique form of continuous, coherence-preserving propagation compatible with structural closure and return, completing the dynamical layer of the Structural Coherence framework.