A Reconstructional Quantum Theory of the Present: Entangled Read-Out, Probabilistic Actualization, and Emergent Time

Abstract

Physics describes evolution, causal structure, and measurement outcomes, but lacks an accepted physical account of why one outcome-conditioned quantum situation is actual as the present. This article develops a conditional account within the reconstruction program, which places a premetric relational layer prior to spacetime dynamics. Conventional evolution specifies how states are related once a state space, time parameter, and dynamical law are supplied; continued admissible reconstruction addresses the prior realization question of which identities, laws, and successor records can remain physically well defined. The Indefinite Reconstruction Stability Principle requires readable structures and laws to survive admissible continuation and to ignore unobservable distinctions. A present is proposed to be the outcome-conditioned quantum read-out of an IRSP-stable, history-bearing reconstruction boundary. Because the underlying relational record need not factorize, its read-out is generally entangled. Admissible successors are represented by a quantum instrument; one stable record sector and its conditioned state constitute the next present without an external observer. A worked qubit measurement and a Bell-pair example connect this architecture to standard laboratory quantum science. Given an operational event-identity bridge, positivity, normalization, exclusive additivity, and a Hilbert-space read-out, Gleason representation fixes the Born form conditionally. Linear history composition implies no genuine third-order successor interference. Proper ancestry inheritance supplies conditional acyclicity, stable small-step channels recover standard effective dynamics, and spacelike confluence replaces a preferred global simultaneity surface. The result is a reconstructional architecture of present actuality with explicit premises and failure conditions, but no fitted collapse rate or microscopic actualization threshold.

1. Introduction

Modern physics is exceptionally successful at describing how physical states are related. A Hamiltonian or unitary operator relates states at different parameter values; quantum field theory predicts scattering amplitudes and correlations; general relativity supplies causal structure and dynamical geometry; and statistical mechanics explains why macroscopic processes exhibit robust temporal asymmetries. These theories normally begin, however, after a state space, causal arena, time parameter, and dynamical law have already been supplied. They calculate law-governed evolution but do not by themselves settle two prior questions: what makes physical succession instantiate the same law-compatible structure under continued realization, and what makes one complete quantum situation actual as the present?

The first question will be called the law-realization problem. It does not ask for an external agent that polices an equation. A differential equation already defines a class of allowed solutions once its arena and variables are given. The question is instead constitutive: why do physical identities, readable relations, and transition laws remain well defined through every admissible continuation of the realized world? The second question is the familiar actuality problem sharpened by quantum measurement: how do several weighted alternatives yield one definite record without assigning a privileged causal role to an observer? The proposal below treats these as two aspects of one reconstruction problem.

This question is not answered by writing a time coordinate t. A coordinate labels represented events but does not distinguish an actual record from an unactualized possibility. Nor is the present simply a surface of simultaneous events. Relativity makes simultaneity frame-dependent and supplies no preferred global “now” [1,2,3,4,5]. Entropy is equally important but addresses another problem: it characterizes thermodynamic asymmetry once an ordered family of states and a coarse graining have already been supplied [6,7,8,9,10]. A theory of evolution, geometry, or entropy is therefore not yet a theory of present actuality.

Quantum mechanics makes the gap sharper. A quantum state may encode several possible records with definite amplitudes, while an experiment produces one observed record. The traditional projective-measurement and state-update framework is represented by the von Neumann–Lüders scheme [11,12]. Decoherence explains why interference between suitable record sectors becomes strongly suppressed and why preferred effective observables emerge [13,14]. It does not, by itself, turn an improper mixture into one uniquely actual outcome. Collapse theories add an objective stochastic law [15,16]; Everettian theories retain all branches and interpret actuality relationally [17,18]; consistent-histories approaches assign probabilities to decoherent history families [19,20]; and relational approaches treat physical states as relative to interactions or systems [21]. These approaches illuminate different aspects of the measurement problem, but no consensus identifies the physical present with a precise quantum object and simultaneously explains its relation to temporal order.

This article explores a reconstruction-based answer. The general premetric framework and its application to physical-law selection were developed in Ref. [22]; the present article extends that program to quantum present actuality. The reconstruction program proposes that spacetime, fields, particle identities, symmetry data, and their observable states are read-outs of a more primitive relational selection layer. “Primitive” here does not mean earlier in a hidden cosmic time. It means logically prior to the availability of metric duration, causal cones, field amplitudes, and ordinary dynamical evolution. At that level, one may still ask whether relations compose and close, whether two relational presentations differ only by unread bookkeeping, and whether an identity remains the same under every admissible continuation.

The basic existence criterion is the Indefinite Reconstruction Stability Principle (IRSP). In plain language:

A physical identity is admissible only if every allowed continuation of its reconstruction continues to identify it as the same physical identity, and every readable relation remains independent of choices that no observation can detect.

If a proposed object exists only because reconstruction was stopped at one convenient stage, the next admissible continuation can erase or change it. If two physically indistinguishable presentations assign it different behavior or different probabilities, there is no well-defined physical fact about what it does. Within the framework, such a proposal has not defined an unstable object; it has failed to define an observable object at all.

This gives a non-agentive meaning to law enforcement. A physical law is not a command imposed on an independently existing world; within the present proposal it is an invariant rule of admissible continuation. Candidate successors that fail compatibility, observable descent, or indefinite reconstruction stability do not become law-breaking physical states: they fail to qualify as realizable continuations. The enforcement is therefore constitutive rather than causal, and it introduces neither an external regulator nor a hidden time. Ordinary dynamics retains its established role after read-out, calculating evolution within the selected causal and quantum platform.

The new thesis is that present actuality is a quantum read-out:

The physical present is the outcome-conditioned quantum read-out of a history-bearing, IRSP-stable reconstruction boundary.

The reconstruction boundary includes the invariant consequences of its ancestry, its current relational anchoring, and every correlation relevant to admissible continuation. Its read-out includes the causal platform, the observable algebra, the quantum state, and the stable records that define the current physical situation. The state is generally entangled because the global reconstruction record need not decompose into independently completed subsystem records.

This formulation differs from the classical expression “the present is one full configuration.” A full reconstruction boundary is not read out as a list of simultaneously possessed classical properties. It is read out as a quantum state on an observable algebra. When stable record sectors form, the joint constraints of system, apparatus, environment, and record stability determine the admissible instrument and its mutually exclusive successor sectors. These constraints determine the alternatives and their weights, not yet the particular stochastic outcome. Present actualization postulates that one sector and its conditioned state constitute the next present. The observer is part of that state; no external consciousness or cosmic measurement apparatus is required.

The broader reconstruction program has also generated previously reported no-fit or parameter-free targets for dimensionless particle ratios and the low-energy fine-structure constant. Those results do not prove the present-actualization proposal, but they show that premetric reconstruction can support explicit read-out maps whose outputs are compared directly with measured quantities. Section 2.6 states their status and their limited evidential role.

Figure 1 summarizes the proposed explanatory order.

Figure 1. Map of the construction. The arrows give explanatory and reconstruction order, not motion in a pre-existing background time. Completion, observable quotient, and IRSP filter relational possibilities into a history-bearing stable boundary. Its quantum read-out is generally entangled. Candidate successors must remain law-compatible admissible continuations; one Born-weighted record sector and its conditioned state supply the next present.

The paper has four main conditional results, together with concrete quantum realizations. First, an event-identity bridge establishes when distinct implementations represent the same descended successor event; observable descent then requires its probability to be independent of reconstruction representative and unread embedding context. With the standard positivity, normalization, and exclusive-additivity assumptions on a Hilbert-space event lattice, Gleason’s theorem gives a unique density-operator representation. The Born form is therefore conditionally represented by combining declared quantum-probability assumptions with IRSP-motivated probability descent; it is not derived from IRSP alone. A worked qubit measurement then identifies the standard instrument, stable apparatus record algebra, selected record sector, and conditioned next present explicitly.

Second, the resulting quadratic quantum measure has no genuine third-order interference. For three mutually exclusive successor histories, the Sorkin third-order combination vanishes. This exact and experimentally accessible null condition is shared with ordinary linear quantum theory. A nonzero result surviving controls for nonlinear evolution, multiparticle effects, detector response, and unintended paths would falsify the declared bridge architecture, although a null result would not uniquely confirm reconstruction.

Third, inherited record inclusion provides an acyclicity argument. The full reconstruction state contains an ancestry ledger even when its reduced quantum state recurs. Nontrivial actualization properly extends that ledger, supplying a monotone depth and excluding strict cycles of full actuality. Quantum recurrence and reversible effective dynamics remain possible at the reduced-state level.

Fourth, no global instantaneous collapse is introduced. The physical present is represented by a causally admissible reconstruction front, not by a preferred spacelike foliation. Spacelike-separated local read-outs must be confluent: changing their unread ordering cannot change the joint physical state. This implements the same representative-independence logic in the relativistic setting.

• Claim boundary. The article presents a conditional architecture, not a completed microscopic collapse model. It derives neither a collapse rate nor a new energy-injection scale. Constitutive law enforcement is an interpretation of admissible continuation under IRSP, not a new force or a derivation of all physical laws. Single-outcome actualization is an ontological principle; the probability theorem uses an event-identity bridge, Hilbert-space event assumptions, and established Gleason representation; the entanglement claim uses an explicit composition correspondence; acyclicity uses proper history inheritance; and the relativistic conclusion uses causal confluence. These premises are stated explicitly. The proposed contribution is to compose them into a reconstruction account of the quantum present and to expose direct failure conditions.

The article is organized as follows. Section 2 introduces reconstruction, IRSP, completion, observable quotient, constitutive law enforcement, the read-out platform, and quantitative evidence from earlier applications. Section 3 separates temporal order, metric time, present actuality, measurement, and related interpretations. Section 4 defines a history-bearing quantum present with an explicit actual record sector. Section 5 formulates reconstruction nonfactorizability and illustrates it with a Bell pair. Section 6 introduces probabilistic successor instruments and a worked qubit measurement. Section 7 proves the conditional Born representation and the vanishing of genuine third-order successor interference. Section 8 derives conditional acyclicity from inherited record depth and distinguishes erasure from exact uncomputation. Section 9 recovers effective quantum dynamics, and Section 10 formulates relativistic confluence. Section 11 and Section 12 give operational tests, related-work comparisons, and limitations.

2. Reconstruction Framework and Empirical Contact

2.1. Premetric Does Not Mean a Hidden Earlier Spacetime

The term premetric is easily misunderstood. It does not denote a smaller spacetime located behind ordinary spacetime, nor a material ether in which reconstruction occurs. It denotes a relational level at which length, duration, light cones, energy density, and field amplitude have not yet become physical observables. Consequently, a conventional microscopic Lagrangian is not available at this level: a Lagrangian already presupposes fields, locality, a measure of integration, and a causal or temporal structure on which variation is defined.

The starting point is not literal nothingness. At minimum, the framework requires possible distinctions, relational composition, admissible continuation, and equivalence under unread relabeling. Schematically, its primitive data are

$${\mathfrak{R}}_{\mathrm{pre}}=\left(\mathcal{X},\mathsf{C},{\sim }_{\mathrm{obs}},{⇝}_{\mathrm{adm}}\right),$$

(1)

where $\mathcal{X}$ is a class of candidate relational presentations, $\mathsf{C}$ is completion under declared compatibility rules, ${\sim }_{\mathrm{obs}}$ is observable equivalence, and ${⇝}_{\mathrm{adm}}$ denotes admissible continuation. A presentation is a mathematical encoding of candidate relational data, not a separately existing physical world. At this level there is, by assumption, no spacetime manifold M, metric $g_{\mu \nu }$, time coordinate t, integration measure $\mathrm{d}\mu$, Hamiltonian H, field inventory, or Lagrangian dynamics. These are logical and mathematical resources rather than physical objects. The neutral parent, relational atlas, symmetry groups, metric platform, quantum states, and dynamical laws are names for invariant completed structures selected from them.

• Physical intuition. Imagine a map before distances and coordinates have been assigned. Only adjacency, incidence, continuation, and consistency are available. Reconstruction does not place objects on a ready-made map. It selects a relational structure whose read-out simultaneously supplies the map, its metric, and the objects localized relative to it.

2.2. Completion, Observable Quotient, and Saturation

Let $\mathcal{X}$ denote a class of candidate relational presentations and let

$$\mathsf{C}:\mathcal{X}⟶\widehat{\mathcal{X}}$$

denote completion under the declared compatibility and closure rules. A completion is not necessarily unique at the presentation level. Let

$$x{\sim }_{\mathrm{obs}}y$$

mean that no admissible read-out distinguishes the completed presentations x and y. Operationally, a distinction is readable only if some admissible measurement, preparation comparison, or stable record effect assigns different observable results or probabilities to the two presentations. The physical reconstruction class is then an element of the observable quotient

$${\mathcal{Q}}_{\mathrm{obs}}=\widehat{\mathcal{X}}/{\sim }_{\mathrm{obs}}.$$

Definition 1

(Observable descent). A map F defined on completed presentations descends to the observable quotient if

$$x{\sim }_{\mathrm{obs}}y⟹F\left(x\right){\sim }_{\mathrm{obs}}F\left(y\right).$$

Equivalently, there exists a map $\overline{F}$ on ${\mathcal{Q}}_{\mathrm{obs}}$ such that

$$q\circ F=\overline{F}\circ q,$$

where $q:\widehat{\mathcal{X}}\to {\mathcal{Q}}_{\mathrm{obs}}$ is the quotient map.

Descent is the mathematical form of the statement that invisible bookkeeping cannot change physics. A probability law that assigns different weights to two representatives of the same physical event does not define a probability on observable events.

Principle 1

(Indefinite Reconstruction Stability Principle). A completed identity or readable relation is physically admissible only if it remains well defined under every admissible finite continuation and if every associated observable law descends through the observable quotient.

“Indefinite” means that physical existence cannot depend on a decree to stop reconstructing at a convenient stage. It does not mean that an ordinary particle must survive forever in metric time. A muon can decay while its identity and decay law remain perfectly well defined. IRSP concerns invariance under reconstruction and representative choice, not immortality under subsequent effective evolution.

IRSP is not a minimum-resolution rule. Once unread duplication has been removed, saturation retains all inequivalent admissible completed channels. Deleting an inconvenient branch merely to preserve a desired answer would violate indefinite stability.

2.3. Continued Reconstruction as Constitutive Law Enforcement

An evolutionary equation specifies relations among states after its state space, variables, and time parameter have been fixed. Reconstruction performs a different logical task: it restricts which completed successors can count as further physical situations. For a current class $\left[{\mathcal{H}}_{\sigma }\right]$, define schematically

$$\begin{array}{cc}\hfill {Succ}_{\mathrm{phys}}\left(\left[{\mathcal{H}}_{\sigma }\right]\right)=\{\left[{\mathcal{H}}_{{\sigma }^{\prime }}\right]\in {\mathcal{Q}}_{\mathrm{obs}}:& \left[{\mathcal{H}}_{\sigma }\right]{⇝}_{\mathrm{adm}}\left[{\mathcal{H}}_{{\sigma }^{\prime }}\right],\hfill \\ \hfill & \left[{\mathcal{H}}_{{\sigma }^{\prime }}\right]\mathrm{is}\mathrm{complete},\mathrm{descended},\mathrm{and}\text{IRSP-stable}\}.\hfill \end{array}$$

(2)

A law is physically readable only if it is well defined on this quotient and remains the same law under every admissible finite continuation. A candidate successor that fails compatibility, descent, or stability is not a physical state that somehow disobeys an already imposed law; it is excluded from the physically realizable successor class.

This is the sense in which continued reconstruction provides constitutive law enforcement. The phrase does not denote an external governor, a new interaction, or a process in hidden time. It states an existence condition: stable laws are invariant forms of admissible continuation. At quantum measurement, the same logic constrains which joint system–apparatus records can become stable successor sectors. Conventional unitary or open-system dynamics still computes amplitudes and channel evolution after read-out; reconstruction supplies the admissibility and identity conditions under which those calculations describe a physically continuable world.

• Claim boundary. Equation (2) is a schematic definition of the physical-successor class, not a derivation of the Standard Model Hamiltonian or of all dynamical laws. The paper proposes that law realization requires admissible continuation; it does not claim that conventional dynamics is mathematically inconsistent or that IRSP alone derives its detailed coefficients.

2.4. Neutral Parent and Relational Atlas

Earlier applications introduced the neutral parent $P_0$ as the common organizing origin of particle read-outs [23,24,25]. The refined interpretation used here is that $P_0$ is not a primitive particle contained in the premetric layer. It is the universal completed identity class selected before particle-specific charge, mass, gauge representation, and localization become readable. “Neutral” means prior to particle-specific distinctions such as charge sign, mass assignment, gauge representation, and localization, not an additional electrically neutral particle.

The neutral parent plays the role of a single generative grammar. A particular observed particle occurrence additionally requires a read-out channel, a relational anchor, and a current state record:

$$\mathrm{particle}\mathrm{occurrence}=\mathrm{parent}\mathrm{archetype}+\mathrm{channel}+\mathrm{relational}\mathrm{anchor}+\mathrm{state}\mathrm{record}.$$

(3)

Multiple identical particles therefore need not be primitive copies of the archetype. They are different occupation or anchoring records using the same selected identity grammar. This is compatible in spirit with the field-theoretic fact that identical particles are excitations of a common field rather than classically labeled miniature objects.

The global history-bearing structure will be called the relational atlas. Again, the atlas is not a sheet stored in a premetric container. It is the equivalence class of ancestry, incidence, channel, and anchoring relations that survive completion and quotient. Its external relations read out as causal and metric support; its channel records read out as fields and particles; and its ancestry relations read out as memories and physical records.

Figure 2 schematizes this joint construction: one neutral-parent identity grammar is used through distinct channel and anchor records, whose combined read-out supplies particle occurrences, localization, and observable correlations.

Figure 2. One generative grammar and one history-bearing atlas. The neutral parent is a selected universal identity class, not one hidden particle per observed object. Distinct channel and anchor records use that grammar. Their joint read-out supplies fields, particle occurrences, spacetime localization, and observable records. The “map” and its contents therefore emerge together.

2.5. Read-Out Platform and Observer-Conditioned Records

A constitutive read-out realizes a stable reconstruction class as an effective platform

$$q_{\lambda }:{\mathcal{Q}}_{\mathrm{obs}}⟶{\mathfrak{P}}_{\lambda }.$$

The label $\lambda$ allows the possibility that the premetric reconstruction core supports more than one observer-compatible read-out architecture. This does not mean that observers choose their laws. An observer is itself a stable record-making subsystem internal to one platform. The present paper studies the read-out class that supports a Lorentzian causal arena, quantum observables, and the particle records familiar to us.

At the effective level, conventional spacetime is the causal-metric sector of ${\mathfrak{P}}_{\lambda }$. It is not a primitive empty container. A chain of relational anchors

$$a_i^{\left(0\right)}\prec a_i^{\left(1\right)}\prec a_i^{\left(2\right)}\prec \dots$$

is read out as a worldline or field-support history in spacetime. The anchors are not premetric coordinates; their joint realization defines both the effective locations and the geometry in which those locations are compared.

An earlier application of the read-out idea related finite-action structure to quantum-wave phase [26]. The present article addresses a different question: the structure of the complete outcome-conditioned quantum situation that is actual at a reconstruction boundary.

2.6. Empirical Contact of the Reconstruction Program

The present proposal is conceptually new, and its quantum bridges must be judged on their own premises. It is nevertheless relevant that the published reconstruction architecture for premetric law selection [22] has already produced quantitative targets in independent particle sectors. The codimension-two selection was developed topologically in Ref. [23]. The neutral-parent particle application then predicted the neutron–proton magnetic-moment ratio [24], and the charged-lepton application predicted three pole-mass ratios [25]. A published holonomy-capacity analysis gives the low-energy inverse fine-structure constant [27]. These calculations follow the sequence

$$\begin{array}{cc}\hfill \mathrm{premetric}\mathrm{completion}& ⟶\mathrm{stable}\mathrm{structural}\mathrm{invariant}\hfill \\ \hfill & ⟶\mathrm{physical}\text{read-out}⟶\mathrm{measurable}\mathrm{quantity}.\hfill \end{array}$$

(4)

The reported values and their publication status are collected in Table 1.

Table 1. Previously published no-fit reconstruction targets. Reference values and deviations are those quoted in the cited peer-reviewed studies.

Observable	Structural Prediction	Reference Value	Reported Deviation	Status
${\mu }_n/{\mu }_p$	$-0.684979364944$	$-0.68497935\left(16\right)$	$0.022\mathrm{ppm}$; $0.093\sigma$	Peer-reviewed
$m_{\mu }/m_e$	$206.768282689$	$206.768282708\left(46\right)$	$0.004\sigma$	Peer-reviewed
$m_{\tau }/m_e$	$3477.441636$	$3477.37\left(18\right)$	∼$0.43\sigma$	Peer-reviewed
$m_{\tau }/m_{\mu }$	$16.8180612$	$16.81769\left(85\right)$	∼$0.43\sigma$	Peer-reviewed
${\alpha }^{-1}\left(0\right)$	$137.035999176142$	$137.035999177\left(21\right)$	$0.041\sigma$	Peer-reviewed

These agreements do not prove IRSP, the neutral-parent bridge, or the present theory. They demonstrate something narrower but directly relevant here: premetric reconstruction can support explicit read-out maps whose outputs are quantitative observables testable against experiment, rather than only retrospective qualitative narratives. No numerical value in Table 1 is an input to any theorem below; the five targets are now documented in peer-reviewed articles and remain evidentially distinct from the present actualization proposal.

3. The Physical Problem: Order, Time, Actuality, and Measurement

3.1. Four Notions That Must Be Separated

Four notions are often compressed into the single word “time”:

1.

Reconstruction order: a partial before–after or dependency relation among completed boundaries.

2.

Metric time: the duration and causal comparison supplied by a read-out platform and its clocks.

3.

Present actuality: the status of the currently outcome-conditioned reconstruction boundary.

4.

Quantum measurement: the production of a stable readable record from several admissible quantum alternatives.

They are related but not identical. A partial order can exist without a metric. A time coordinate can parametrize a represented solution without declaring one state actual. A quantum state can evolve unitarily while containing several mutually exclusive potential records. A measurement record can be local without defining a universal simultaneity surface.

The proposed hierarchy is

$$\begin{array}{cc}\hfill \mathrm{admissible}\mathrm{reconstruction}\mathrm{order}& ⟶\text{history-bearing}\mathrm{quantum}\mathrm{boundary},\hfill \\ \hfill & ⟶\text{outcome-conditioned}\mathrm{present},\hfill \\ \hfill & ⟶\mathrm{stable}\text{small-step}\mathrm{succession},\hfill \\ \hfill & ⟶\mathrm{effective}\mathrm{metric}\mathrm{time}\mathrm{and}\mathrm{dynamics}.\hfill \end{array}$$

(5)

This is explanatory order. The first arrow is not an event occurring at an earlier value of the last line’s time coordinate.

3.2. Why the Present Is Not Entropy

Entropy requires a state space, a measure or counting rule, and a coarse graining. A statement such as

$$S\left({\rho }_{n+1}\right)>S\left({\rho }_n\right)$$

already assumes that the two states can be ordered and compared. Entropy can explain why typical macroscopic records point consistently in one temporal direction, but it does not by itself define the order or identify the actual present [10,28,29,30].

The history-bearing reconstruction state and thermodynamic entropy can also move differently. A local subsystem may be cooled, reset, or purified while the full reconstruction ancestry still extends. Record depth is not a measure of disorder.

3.3. Why the Present Is Not a Global Simultaneity Surface

In Minkowski spacetime, different inertial observers assign different simultaneity surfaces to the same events. In curved spacetime, a global foliation may not be unique or physically distinguished. The present theory therefore does not identify actuality with

$${\Sigma }_{t_0}=\{x\in M:t\left(x\right)=t_0\}$$

for one preferred time function t.

Instead, a reconstruction boundary is a causally admissible front: a maximal set of mutually unordered record updates together with their inherited past. Different effective foliations can represent the same underlying partial order. If two spacelike-separated updates are physically independent, exchanging their representation order must leave the joint read-out unchanged. Section 10 makes this confluence condition precise.

3.4. Why the Present Is a Quantum Problem

The old classical phrase “one complete configuration is actual” is insufficient. A quantum present cannot be a simultaneous assignment of sharp values to all observables; contextuality and noncommutativity prohibit that picture [31]. The complete physical situation must instead be specified by an observable algebra, a quantum state on that algebra, a stable commutative record algebra, and the particular record sector that is actual.

The whole state may remain highly entangled. Actualization does not mean that every degree of freedom becomes a classical eigenstate. It means that one successor record sector is selected and conditioned, while unresolved quantum relations—including entanglement within that sector—remain quantum.

3.5. Relation to Existing Interpretations

The reconstruction account shares elements with several established approaches without being identical to any one of them.

• With Copenhagen and operational quantum mechanics, it uses quantum instruments and outcome conditioning, but the apparatus and observer are internal read-outs rather than primitive classical objects.
• With objective-collapse approaches, it treats one record sector as actual, but it does not yet add a modified stochastic Schrödinger equation or fitted collapse rate.
• With Everettian theory, it takes the universal entangled state and relative records seriously, but saturation of admissible alternatives is distinguished from the actuality of one outcome-conditioned present.
• With consistent histories, it treats complete histories and a quadratic quantum measure as fundamental to probability, but it adds IRSP-stable completion and present actualization.
• With relational quantum mechanics, it rejects an external view from nowhere, but it anchors observer-relative records in one history-bearing reconstruction class.
• With decoherence and quantum Darwinism, it uses stable, redundantly readable records to identify admissible effective sectors, while maintaining that decoherence alone does not select which record is actual.
• With modal and definite-value interpretations, it distinguishes an actual property sector from the full quantum state, but it grounds that sector in an IRSP-stable record algebra and a history-bearing boundary rather than in a property-selection rule alone [32].
• With relativistic objective-event or flash approaches, it seeks observer-independent local events without a preferred global simultaneity surface, but it presently supplies a confluence criterion rather than a fitted relativistic collapse dynamics [33].
• With causal-set sequential growth, it shares an acyclic partial-order intuition and representative independence of growth order, while retaining a quantum read-out platform and an ancestry-bearing actual present rather than assuming a causal set as the final ontology [34].
• With process-matrix approaches, it treats coordinate order as nonfundamental when no invariant causal order distinguishes it, but adds reconstruction descent, inherited records, and single-sector actualization [35].

The framework is therefore best described as reconstructional quantum actualism: only the current outcome-conditioned boundary is actual as present; its inherited past remains encoded in present records; admissible successors carry quantum weights but are not yet actual; and ordinary unitary or open-system dynamics remains the effective law between and across stable read-out events. Its distinctive conjunction is observable quotient, indefinite continuation stability, an ancestry-bearing boundary, and an explicitly selected stable record sector.

4. The History-Bearing Quantum Present

4.1. A Reconstruction Boundary Is More than an Instantaneous State

Let $\sigma$ label a completed reconstruction boundary and let

$$\left[{\mathcal{H}}_{\sigma }\right]\in {\mathcal{Q}}_{\mathrm{obs}}$$

denote its observable equivalence class. The symbol ${\mathcal{H}}_{\sigma }$ is meant to emphasize ancestry: a boundary contains not only relations readable “now”, but also invariant records of the admissible completions through which the boundary was reached. It is therefore closer to a self-consistent history boundary than to one frame of a film.

The word boundary should not be read metrically. Before read-out, there is no earlier region on one side and later region on the other. It means the complete set of currently available relational constraints on further continuation. After read-out, part of this structure can be represented as a causal front with an inherited past.

• Physical intuition. A conventional instantaneous state resembles a photograph. A history-bearing boundary resembles a photograph containing intact memory devices, fossils, detector tracks, and all physical correlations needed to establish how the photographed situation can consistently continue. The records are present structures, not pieces of a vanished past stored somewhere outside the current universe.

4.2. Observable Algebra, State, and Record Algebra

We use the algebraic language because it does not require a preferred tensor factorization or basis. Let ${\mathcal{A}}_{\sigma }$ be a unital $C^{\ast }$-algebra of observables available at the read-out of $\left[{\mathcal{H}}_{\sigma }\right]$. A quantum state is a positive normalized linear functional

$${\omega }_{\sigma }:{\mathcal{A}}_{\sigma }⟶\mathbb{C},{\omega }_{\sigma }\left(A^{\ast }A\right)\ge 0,{\omega }_{\sigma }\left(\mathbf{1}\right)=1.$$

(6)

In a finite-dimensional Hilbert-space representation, this has the familiar form

$${\omega }_{\sigma }\left(A\right)=Tr\left({\rho }_{\sigma }A\right),{\rho }_{\sigma }\ge 0,Tr{\rho }_{\sigma }=1.$$

(7)

Not every observable is a presently readable fact. Let ${\mathcal{R}}_{\sigma }\subseteq {\mathcal{A}}_{\sigma }$ denote a commutative effective record algebra: its coarse-grained projectors correspond to mutually distinguishable apparatus or environmental records that are stable under the admissible continuations relevant to the observer. Decoherence, amplification, and redundant environmental encoding are physical mechanisms by which such an algebra can become robust [13,14]. IRSP adds a selection demand: the record designation must descend through the observable quotient and must not depend on an unread reconstruction convention.

The algebra identifies which record questions are jointly readable; it does not by itself say which answer is actual. We therefore also specify an actual outcome label ${\alpha }_{\sigma }$. In a finite-dimensional sharp-record representation, it identifies a stable pointer projector

$$P_{{\alpha }_{\sigma }}^{\mathrm{rec}}\in Proj\left({\mathcal{R}}_{\sigma }\right),{\omega }_{\sigma }\left(P_{{\alpha }_{\sigma }}^{\mathrm{rec}}\right)=1.$$

(8)

For a generalized measurement, the system effect that determines the outcome probability need not itself be a projector; the definite record is the corresponding stable pointer sector in the apparatus-inclusive record algebra.

Definition 2

(Quantum present). A quantum present at reconstruction boundary σ is the quintuple

$${\mathcal{P}}_{\sigma }=\left(\left[{\mathcal{H}}_{\sigma }\right],{\mathcal{A}}_{\sigma },{\omega }_{\sigma },{\mathcal{R}}_{\sigma },{\alpha }_{\sigma }\right),$$

(9)

where the reconstruction class carries inherited history, ${\mathcal{A}}_{\sigma }$ is the effective observable algebra, ${\omega }_{\sigma }$ is its quantum state, ${\mathcal{R}}_{\sigma }$ is the stable record algebra, and ${\alpha }_{\sigma }$ identifies its actual record sector at that boundary.

The definition separates four questions that are often conflated. The state ${\omega }_{\sigma }$ determines quantum probabilities and correlations. The record algebra determines which alternatives are physically distinguishable as outcomes. The label ${\alpha }_{\sigma }$ identifies the record sector that is definite in this occurrence. The reconstruction class determines why those algebraic data belong to the same present and how their inherited records constrain further completion.

Figure 3 displays these four roles and emphasizes that the actual record sector is part of an outcome-conditioned quantum present, not a classical assignment of values to every observable.

Figure 3. The present is not one classical assignment of all observable values. It is the joint read-out of a history-bearing reconstruction class as an observable algebra, a quantum state, a stable record algebra, and the actual record sector ${\alpha }_{\sigma }$. The state may remain entangled and mixed after that sector has become definite.

4.3. The Present Is Not “the Eigenstate of the Universe”

It is tempting to say that the next moment is one eigenstate of the universe. That phrase is too restrictive. An eigenstate is defined only after an observable has been specified; macroscopic outcomes are normally degenerate and coarse grained; and an outcome-conditioned state may remain mixed and entangled. The precise statement is instead:

A successor present is one stable record sector selected by a specified quantum instrument, together with the normalized quantum state conditioned on that record.

Projective eigenstate collapse is a special idealization of this more general construction.

Proposition 1

(Representative independence of a present). Suppose the read-out maps

$$\left[\mathcal{H}\right]⟼(\mathcal{A},\omega ,\mathcal{R},\alpha )$$

descend through $q:\widehat{\mathcal{X}}\to {\mathcal{Q}}_{\mathrm{obs}}$. If $\mathcal{H}{\sim }_{\mathrm{obs}}{\mathcal{H}}^{\prime }$, then no experiment in the read-out platform can distinguish the presents constructed from $\mathcal{H}$ and ${\mathcal{H}}^{\prime }$.

Proof. 

Descent means that equivalent completed representatives induce isomorphic observable and record algebras, the same state on corresponding observables, and the same actual record label under that isomorphism. Hence, every observable expectation, record probability, and admissible continuation probability agrees. A distinction not preserved by these data is outside the observable quotient. □

This modest proposition carries much of the conceptual load. It prevents a hidden choice of reconstruction labels from deciding which quantum event is actual or with what probability.

5. Entanglement as the Read-Out of Reconstruction Nonfactorizability

5.1. Subsystems Are Effective Factorizations

Suppose a read-out admits two operationally distinguishable subsystems, represented in finite dimension by

$$\mathcal{H}={\mathcal{H}}_A\otimes {\mathcal{H}}_B,\mathcal{A}=\mathcal{B}\left({\mathcal{H}}_A\right)\otimes \mathcal{B}\left({\mathcal{H}}_B\right).$$

In the algebraic setting, it is enough to have commuting subalgebras ${\mathcal{A}}_A,{\mathcal{A}}_B\subset \mathcal{A}$. A product state satisfies

$$\omega \left(AB\right)={\omega }_A\left(A\right){\omega }_B\left(B\right)(A\in {\mathcal{A}}_A,B\in {\mathcal{A}}_B).$$

A separable state is a convex mixture of product states. A state not admitting such a decomposition is entangled.

The reconstruction layer does not begin with labeled parts A and B. Those parts emerge when the read-out platform supports approximately independent local operations and records. Consequently, factorization at the read-out cannot simply be assumed to mirror a primitive factorization below it.

Bridge Hypothesis 1 

(Composition bridge). For a chosen read-out factorization:

1.

independently completable reconstruction classes read out as product states;

2.

classically distinguishable alternatives among such completions read out as separable mixtures; and

3.

a completed global class that admits neither decomposition reads out as a nonseparable state on the effective subsystem algebra.

Proposition 2

(Conditional composition correspondence). Under Bridge Hypothesis 1, if $\left[{\mathcal{H}}_{AB}\right]$ cannot be represented as a product completion or as a classical mixture of product completions relative to the $A|B$ read-out, then its quantum state ${\rho }_{AB}$ is entangled across ${\mathcal{H}}_A\otimes {\mathcal{H}}_B$.

Proof. 

If ${\rho }_{AB}$ were separable, it would have a representation

$${\rho }_{AB}=\sum _j{p}_j{\rho }_A^{\left(j\right)}\otimes {\rho }_B^{\left(j\right)},p_j\ge 0,\sum _j{p}_j=1.$$

By the converse direction declared in the composition bridge, this would be the read-out of a classical mixture of product completions, contrary to the hypothesis. □

• Claim boundary. The proposition is an interpretive correspondence conditional on the composition bridge, not an independent derivation of entanglement. IRSP alone does not derive Hilbert-space tensor products or the full convex structure of quantum states. Its substantive content is the proposed physical meaning of entanglement: the effective signature of a global reconstruction record that cannot be resolved into independently completed parts. Deriving the bridge itself from completion theory remains open.

Figure 4 summarizes the proposed correspondence between one irreducible global reconstruction record and an entangled state on an effective spatial factorization.

Figure 4. Entanglement in the reconstruction picture. A global completed record need not factorize even when its read-out admits spatially separated subsystems A and B. The shared premetric ancestry is not a signal sent between the subsystems; it is what the post-read-out entangled state records.

5.2. Correlation Without Superluminal Influence

This picture gives an intuition for quantum nonlocality without supplying a local hidden-variable model. Bell’s theorem excludes any theory that reproduces quantum correlations through local pre-existing values satisfying its factorization assumptions [36]. The reconstruction class is instead a single nonfactorizable object; it does not assign an independent local instruction set to each wing. Once the Lorentzian platform is read out, local operations still obey its causal restrictions, and the reduced state on one wing is unchanged by an unannounced choice of trace-preserving operation on the other. Global correlation therefore need not be interpreted as a controllable signal crossing an already existing distance.

5.3. Worked Example: Bell-Pair Read-Out

Consider the standard two-qubit state

$${|{\Phi }^{+}⟩}_{AB}={\displaystyle \frac{|00⟩+|11⟩}{\sqrt{2}}},{\rho }_{AB}=|{\Phi }^{+}⟩⟨{\Phi }^{+}|.$$

(10)

Relative to the effective factorization ${\mathcal{H}}_A\otimes {\mathcal{H}}_B$, this state is nonseparable, whereas its local marginals are

$${\rho }_A={Tr}_B{\rho }_{AB}={\displaystyle \frac{I_A}{2}},{\rho }_B={Tr}_A{\rho }_{AB}={\displaystyle \frac{I_B}{2}}.$$

(11)

The reconstruction reading is that one nonfactorizable global class is read out through two locally addressable subsystem algebras. If both wings are measured in the computational basis, the jointly stable record sectors are $(0,0)$ and $(1,1)$, each with Born weight $1/2$; one joint record is actual in a trial. Neither marginal carries a remotely controllable value: an unannounced trace-preserving operation on B leaves Equation (11) at A unchanged. Thus, the example connects the proposed ontology to familiar Bell correlations without introducing a local hidden-variable instruction set or a superluminal signal. Section 10 states the confluence condition required when the two records form at spacelike separation.

6. Probabilistic Successor Actualization

6.1. Admissible Successors Form a Quantum Instrument

Let ${\rho }_{\sigma }$ be the state of the current present and let ${\left\{{\mathcal{I}}_{\alpha }\right\}}_{\alpha \in \mathcal{O}}$ be a quantum instrument associated with an admissible record-making continuation. Each ${\mathcal{I}}_{\alpha }$ is completely positive and trace nonincreasing, while their sum is a completely positive trace-preserving channel,

$${\mathcal{E}}_{\sigma }=\sum _{\alpha \in \mathcal{O}}{\mathcal{I}}_{\alpha },{\mathcal{E}}_{\sigma }\mathrm{trace}\mathrm{preserving}.$$

(12)

This instrument formalism is provisionally imported from standard quantum theory; the reconstruction proposal assigns it the role of representing admissible record-forming successors [37,38,39]. Section 7 gives the conditional reconstructional status of its Born weights. The probability and conditioned successor state are

$$p\left(\alpha \right|\sigma )=Tr\left[{\mathcal{I}}_{\alpha }\left({\rho }_{\sigma }\right)\right],$$

(13)

$${\rho }_{\sigma ,\alpha }={\displaystyle \frac{{\mathcal{I}}_{\alpha }\left({\rho }_{\sigma }\right)}{Tr\left[{\mathcal{I}}_{\alpha }\left({\rho }_{\sigma }\right)\right]}},p\left(\alpha \right|\sigma )>0.$$

(14)

The unconditioned state

$${\overline{\rho }}_{{\sigma }^{+}}=\sum _{\alpha }{\mathcal{I}}_{\alpha }\left({\rho }_{\sigma }\right)$$

(15)

describes the ensemble obtained when the outcome record is ignored. It must not be confused with the one outcome-conditioned present actually recorded in one individual experimental trial or physical realization.

Principle 2

(Present actualization). When an admissible continuation produces mutually exclusive IRSP-stable record sectors, exactly one sector α is actualized as the next present with probability $p\left(\alpha \right|\sigma )$, and the next quantum state is conditioned according to Equation (14). The label of the actual pointer record becomes ${\alpha }_{{\sigma }^{+}}=\alpha$ in the next present ${\mathcal{P}}_{{\sigma }^{+}}$.

The principle does not say that the whole universe becomes classical. It says that a stable record is definite. Quantum coherence may remain within the selected sector and among degrees of freedom not resolved by the record algebra. The assertion that exactly one sector becomes actual is an ontological postulate of the present architecture, not a dynamical consequence of the instrument formalism or of IRSP alone. A microscopic theory must still explain when stable-sector actualization occurs and implement it covariantly.

6.2. Worked Physical Example: A Two-Outcome Qubit Measurement

Let a qubit be prepared in

$${|\psi ⟩}_S=a|0⟩+b|1⟩,{\left|a\right|}^2+{\left|b\right|}^2=1,$$

(16)

and let $|M_{\mathrm{r}}⟩$ be the ready state of a measuring apparatus. An ideal premeasurement interaction satisfies

$$U\left({|i⟩}_S{|M_{\mathrm{r}}⟩}_A\right)={|i⟩}_S{|M_i⟩}_A,i\in \{0,1\},$$

(17)

and therefore produces

$$U\left({|\psi ⟩}_S{|M_{\mathrm{r}}⟩}_A\right)=a{|0⟩}_S{|M_0⟩}_A+b{|1⟩}_S{|M_1⟩}_A.$$

(18)

When environmental stability, redundant readability, and reconstruction descent make the pointer sectors durable, their apparatus-inclusive record projectors are

$$P_i^{\mathrm{rec}}=I_S\otimes |M_i⟩⟨M_i|,i\in \{0,1\}.$$

(19)

The corresponding ideal instrument has

$$K_i=|i⟩⟨i|,{\mathcal{I}}_i\left(\rho \right)=K_i\rho K_i^{†},p\left(0\right)={\left|a\right|}^2,p\left(1\right)={\left|b\right|}^2.$$

(20)

Principle 2 says that one stable pointer record, say ${\alpha }_{{\sigma }^{+}}=0$, is actual in that trial and that the qubit state in the next present is $|0⟩⟨0|$. The joint physical constraints of preparation, apparatus coupling, environment, and record algebra determine the admissible sectors and their weights; they do not deterministically select which stochastic outcome occurs. The observer is an internal reader of $P_i^{\mathrm{rec}}$, not an extra cause of the actualization. This example also separates unitary premeasurement from the new postulate: Equation (18) follows from ordinary dynamics, whereas the actuality of one durable record sector is supplied by Principle 2.

6.3. Two Many-to-One Operations That Must Be Distinguished

The observable quotient and outcome conditioning are both many-to-one, but they solve different problems:

$$\underset{\mathrm{remove}\mathrm{unread}\mathrm{presentation}\mathrm{duplication}}{\underbrace{\widehat{\mathcal{X}}⟶{\mathcal{Q}}_{\mathrm{obs}}}},\underset{\mathrm{condition}\mathrm{on}\mathrm{one}\mathrm{readable}\mathrm{record}}{\underbrace{{\rho }_{\sigma }⟶{\rho }_{\sigma ,\alpha }}}.$$

(21)

The quotient identifies presentations that never represented different physical possibilities. Actualization selects one outcome among genuinely different readable successor sectors. Confusing the two would either turn mere relabeling into stochastic physics or erase the distinction between observable outcomes.

6.4. No External Observer and No Continuous Projection

An instrument need not be applied by a consciousness. It is an effective quantum representation of an interaction that creates a stable, internally readable record. Detectors, memories, biological observers, and environmental copies are parts of the same reconstructed present.

Nor does the theory posit projective collapse at every arbitrarily small parameter step. Such a prescription would generically invite quantum-Zeno behavior and, in many collapse models, energy-balance difficulties. Between stable record actualizations, the effective state may evolve unitarily or by a continuous completely positive channel. Actualization is attached to IRSP-stable record formation, not to an externally imposed infinitely rapid sequence of observations.

Figure 5 summarizes the distinction between the full set of instrument-defined successor sectors and the one record sector that is actual and conditioned as the next present.

Figure 5. Successor actualization. The instrument specifies mutually exclusive stable record sectors and their probabilities. One record sector ${\alpha }_{{\sigma }^{+}}$ is actual and its state is conditioned as the next present; the other sectors remain counterfactual possibilities for that occurrence. This diagram is explanatory, not a branching process in a pre-existing external time.

6.5. Where the Preferred Record Basis Comes from

The well-known preferred-basis problem is not solved merely by writing an instrument. In the present framework, the admissible record algebra is constrained jointly by three requirements:

1.

environmental stability: interference between candidate records is suppressed on the relevant observational scale;

2.

redundant readability: the record can be copied or independently accessed by internal observers; and

3.

reconstruction descent: the record and its probabilities are unchanged by unread representative choices and remain identifiable under admissible continuation.

Decoherence supplies powerful dynamics for the first two requirements. IRSP supplies the third. A complete microscopic theory would still have to derive the record algebra and actualization rate for a concrete system. The present article does not claim that final step.

7. IRSP, Born Valuation, and Third-Order Interference

7.1. From Observable Descent to Noncontextual Event Weights

Let an event be represented by a projector P on a Hilbert space $\mathcal{H}$. The same physical event may occur in different complete measurement contexts, for example, in two orthogonal resolutions of the identity that both contain P. Here, an orthogonal resolution is a complete family $\left\{P_i\right\}$ with $P_i{P}_j=0$ for $i\ne j$ and ${\sum }_i{P}_i=I$. The event may also be obtained from different representatives of one reconstruction class. Different laboratory contexts are not automatically equivalent: they can change the apparatus, disturbance, boundary conditions, or physical event. The following bridge states the operational equivalence required before observable descent can be applied.

Bridge Hypothesis 2

(Descended event identity). If two implementations realize the same projector P, with the same preparation and record effect, and all remaining differences are operationally unread and belong to one observable reconstruction class, then they represent the same descended successor event. Contexts that change any readable part of the event are not identified by this bridge.

Lemma 1

(IRSP probability descent). If successor-event probability is an observable law satisfying Principle 1 and the implementations satisfy Bridge Hypothesis 2, then the probability $w\left(P\right)$ assigned to an event depends only on the descended event P, not on its completed reconstruction representative or on which unread mutually exclusive alternatives accompany it in a measurement context.

Proof. 

Bridge Hypothesis 2 establishes that the two implementations are presentations of the same descended event and differ only by ${\sim }_{\mathrm{obs}}$-unread data. If their probabilities differed, the probability map would fail Definition 1. Such a map would not be a law on observable events and is inadmissible by IRSP. □

The lemma supplies a conditional physical route to noncontextuality of the probability valuation across operationally equivalent realizations. It does not assert that physically different measurement contexts have equal probabilities, nor that all observable values are noncontextual; the Kochen–Specker theorem forbids such an assignment in dimension at least three [31]. Only the weight of the same event is required to be independent of unread embedding context. In this sense, probability descent is a specific instance of constitutive law enforcement: an unread change of presentation is not permitted to change an observable probability law.

7.2. Conditional Born Representation

Assumption 1

(Quantum event valuation). For a Hilbert-space read-out with $dim\mathcal{H}\ge 3$, successor-event weights obey:

1.

positivity, $w\left(P\right)\ge 0$;

2.

normalization, $w\left(I\right)=1$; and

3.

exclusive additivity,

$$P_i{P}_j=0(i\ne j)⟹w\left(\sum _i{P}_i\right)=\sum _{i}w\left(P_i\right)$$

for every finite or countable orthogonal family for which the sum is defined.

Theorem 1

(IRSP-conditioned Born representation). Under Lemma 1 and Assumption 1, there exists a unique density operator ρ such that

$$w\left(P\right)=Tr\left(\rho P\right)$$

(22)

for every projector P on $\mathcal{H}$.

Proof. 

Lemma 1 makes w a single noncontextual measure on the projector lattice. Positivity, normalization, and orthogonal additivity are the remaining hypotheses of Gleason’s theorem. The representation (22) and uniqueness of $\rho$ therefore follow [40]. Generalized-measurement extensions can include the two-dimensional case by taking positive-operator-valued measure (POVM) events as primitive [41]. □

• Physical intuition. IRSP does not determine the Born rule from the word “stability” alone. Its role is precise: after the event-identity bridge has established operational equivalence, IRSP forbids the event probability from changing when only unread bookkeeping or embedding context is changed. Once Hilbert-space events, positivity, normalization, and exclusive additivity are supplied, an established representation theorem fixes the density-operator Born form.

Textbook quantum mechanics normally takes the Born rule as a postulate. Theorem 1 instead gives a conditional reconstructional representation: IRSP motivates representative independence, while the Hilbert-event and additive-probability assumptions complete the hypotheses of Gleason’s theorem. This is an explanatory result, not a derivation of probability, Hilbert-space quantum mechanics, or exclusive additivity from IRSP alone.

7.3. Histories and the Absence of Genuine Third-Order Interference

Let $A,B,C$ denote mutually exclusive fine-grained successor-history classes, and let $C_A,C_B,C_C$ be their class operators. For disjoint alternatives, linear quantum composition gives

$$C_{A\cup B}=C_A+C_B,C_{A\cup B\cup C}=C_A+C_B+C_C.$$

(23)

Define the quantum measure

$$\mu \left(X\right)=Tr\left(C_X\rho C_X^{†}\right).$$

(24)

The third-order Sorkin combination is

$$\begin{array}{cc}\hfill I_3(A,B,C)=& \mu (A\cup B\cup C)-\mu (A\cup B)-\mu (A\cup C)-\mu (B\cup C)\hfill \\ \hfill & +\mu \left(A\right)+\mu \left(B\right)+\mu \left(C\right)-\mu (⌀).\hfill \end{array}$$

(25)

Theorem 2

(No genuine third-order successor interference). If successor alternatives compose linearly as in Equation (23) and probabilities have the quadratic form (24), then

$$I_3(A,B,C)=0$$

(26)

for every triple of mutually exclusive successor histories.

Proof. 

Expanding each term in Equation (25), every diagonal term $Tr\left(C_X\rho C_X^{†}\right)$ and every pairwise cross term $Tr\left(C_X\rho C_Y^{†}\right)$ appears with total coefficient zero. A quadratic functional contains no irreducible cubic cross term. The full cancellation is displayed in Appendix A. □

Remark 1.

Equation (26) is already a consequence of ordinary linear quantum mechanics with the Born rule; it is not separately postulated in standard quantum theory. The reconstruction claim is that the event-identity bridge and IRSP together motivate the representative-independent valuation to which the declared quantum-probability assumptions apply. A confirmed nonzero $\mathrm{genuine} I_3$ would therefore falsify the resulting bridge architecture as well as standard grade-two quantum measure theory [42].

• Claim boundary. Raw three-path expressions need not vanish if “opening a path” changes the Hamiltonian or boundary conditions, if looped trajectories are omitted, if sources or detectors are nonlinear, or if multiparticle events contaminate the sample. The theorem concerns one fixed operational event algebra with properly calibrated mutually exclusive history classes. Section 11 turns this distinction into an experimental protocol.

8. Inherited Records and Acyclic Reconstruction

8.1. The Full Present Has an Ancestry Ledger

The density operator of a small subsystem can return arbitrarily close to an earlier value. A spin can be rotated back to its initial state; a finite closed system can exhibit recurrences; and a memory register can be erased. These facts prohibit identifying temporal order with a scalar function of a reduced quantum state.

The full reconstruction boundary contains more. Let ${\mathcal{L}}_{\sigma }$ be the invariant ancestry ledger of $\left[{\mathcal{H}}_{\sigma }\right]$: the partially ordered set of stable event records, including the relations required to establish which records constrain which later completions. Two ledgers related only by an unread relabeling represent the same element of the observable quotient.

Definition 3

(Record extension). A nontrivial actualization

$${\mathcal{P}}_{\sigma }⇝{\mathcal{P}}_{{\sigma }^{\prime }}$$

is a proper record extension if there is an order-preserving embedding

$${\iota }_{\sigma {\sigma }^{\prime }}:{\mathcal{L}}_{\sigma }\hookrightarrow {\mathcal{L}}_{{\sigma }^{\prime }}$$

whose image is a proper subledger and whose new element or relation records the actualization outcome.

This definition does not require every microscopic detail to be recoverable from a macroscopic observer’s memory. It requires the complete reconstruction class to inherit the physical consequences of its ancestry. In ordinary effective erasure, a laboratory bit may disappear from the accessible memory while correlations, dissipated heat, control records, or other constraints remain elsewhere in the completed class. The stronger claim that no trace of a verified actualization can be removed from the full ancestry is stated separately as Assumption 2.

Assumption 2

(History inheritance). Every nontrivial stable-record actualization is a proper record extension in the sense of Definition 3; trivial representational updates remain within the same observable class.

Proper extension concerns the invariant ancestry of the complete reconstruction class. It does not require accessible memory, stored macroscopic information, or thermodynamic entropy to increase monotonically: records may be erased or become unread at the effective level while their relational ancestry remains part of the completed class. Accordingly, the following result is conditional on the no-deletion property asserted by Assumption 2.

8.2. Erasure, Recoherence, and Reversible Uncomputation

Three physically different operations must be separated. First, before a candidate pointer correlation has become an IRSP-stable actual record, the unitary premeasurement in Equation (18) can in principle be reversed. Quantum eraser and uncomputation protocols then restore coherence; on the present account, they show that stable actualization had not yet been independently established. Reversal of weak quantum measurements provides an experimentally realized example of this regime [43].

Second, after macroscopic record formation, an observer can reset a register or erase all locally accessible evidence. Such effective erasure is compatible with history inheritance when the reset operation transfers correlations or thermodynamic consequences into other degrees of freedom. The theorem below does not require those traces to remain readable to the observer.

Third, consider an exact, independently verified protocol that (i) first certifies an IRSP-stable actual record sector, (ii) subsequently returns the entire apparatus, system, environment, controls, and ancestry relations to the same full observable reconstruction class, and (iii) leaves no distinguishing successor constraint. That would be a recurrence of full actuality, not merely recoherence of a subsystem. It would falsify Assumption 2 and therefore the acyclicity theorem. The present theory does not yet supply a microscopic threshold that independently separates the first regime from the latter two; this is a substantive open problem and a source of empirical risk.

8.3. Acyclicity Theorem

For a finite ledger, let $K\left(\mathcal{L}\right)$ be the maximum length of a chain. For a locally finite infinite ledger, the argument can be applied to every finite causal interval, or K can be replaced by inclusion order itself.

Theorem 3

(Conditional acyclicity of full actuality). Under Assumption 2, no finite sequence of nontrivial actualizations can return to the same full quantum present:

$${\mathcal{P}}_{{\sigma }_0}⇝{\mathcal{P}}_{{\sigma }_1}⇝\dots ⇝{\mathcal{P}}_{{\sigma }_N}\ne {\mathcal{P}}_{{\sigma }_0}.$$

If each extension adds a record above a maximal inherited chain, then

$$K\left({\mathcal{L}}_{{\sigma }_{j+1}}\right)>K\left({\mathcal{L}}_{{\sigma }_j}\right)$$

at every nontrivial step.

Proof. 

Proper record extension gives

$${\mathcal{L}}_{{\sigma }_0}⊊{\mathcal{L}}_{{\sigma }_1}⊊\dots ⊊{\mathcal{L}}_{{\sigma }_N}$$

up to observable isomorphism. A strict finite inclusion chain cannot close onto its first member. Under the stated rank condition, the integer K strictly increases and supplies an explicit contradiction to recurrence of the full present. □

Corollary 1

(Reduced-state recurrence is compatible with becoming). Theorem 3 does not forbid ${\rho }_S\left({\sigma }_N\right)={\rho }_S\left({\sigma }_0\right)$ for a subsystem S, or even the recurrence of a large effective state after coarse graining. It forbids only the recurrence of the complete outcome-conditioned reconstruction class and its ancestry ledger.

• Physical intuition. The hands of a clock can return to twelve, and a quantum bit can return to its initial ray. The universe has not thereby returned to the same present, because the route, the records of the route, and the correlations created by it belong to the current boundary. The theory places becoming in this inherited relational order, not in the nonrecurrence of every reduced state.

8.4. Past, Present, and Future

The three temporal notions can now be stated without assuming a background flow:

• the past is the invariant ancestry encoded by the current ledger, not an independently existing region that must remain ontically present;
• the present is the current outcome-conditioned boundary ${\mathcal{P}}_{\sigma }$; and
• the future is the weighted set of admissible successor completions, not a collection of already actual records.

This is a growing-record ontology, but the growth variable is reconstruction order. Metric time appears only when a suitable family of physical clocks is read out.

9. Effective Quantum Dynamics and Emergent Time

9.1. From Reconstruction Steps to a Continuous Parameter

Let n label successive stable boundaries in reconstruction order. The label is discrete bookkeeping, not yet physical time. Suppose a read-out regime supplies approximately uniform clock records of duration $\epsilon$ and, on a finite-dimensional read-out state space, an unconditioned channel

$${\rho }_{n+1}={\mathcal{E}}_{\epsilon }\left({\rho }_n\right).$$

Assume the family is differentiable at the identity:

$${\mathcal{E}}_{\epsilon }=\mathrm{id}+\epsilon \mathcal{L}+O\left({\epsilon }^2\right)$$

(27)

uniformly on the relevant state domain. Setting $t=n\epsilon$ gives the continuum limit

$${\displaystyle \frac{\mathrm{d}\rho }{\mathrm{d}t}}=\mathcal{L}\left(\rho \right).$$

(28)

Proposition 3

(Conditional continuum dynamics). On a finite-dimensional state space, if Equation (27) holds in norm, if the accumulated local error is controlled on compact t-intervals, and if the channels form a stable norm-continuous one-parameter semigroup in the limit, then the interpolated reconstruction sequence converges to the solution of Equation (28). An infinite-dimensional extension requires the usual generator-domain and strong-continuity qualifications.

Proof. 

Equation (27) is the forward-Euler consistency condition for the generator $\mathcal{L}$. Stability plus consistency gives convergence of the product

$${\mathcal{E}}_{t/N}^N⟶e^{t\mathcal{L}}$$

on compact intervals as $N\to \infty$. This is the standard semigroup continuum limit. □

For a closed reversible read-out, if the channel and its inverse are both completely positive and trace-preserving, the channel is unitary conjugation, and

$$\mathcal{L}\left(\rho \right)=-{\displaystyle \frac{\mathrm{i}}{\hslash }}[H,\rho ],\mathrm{i}\hslash {\displaystyle \frac{\mathrm{d}\rho }{\mathrm{d}t}}=[H,\rho ].$$

(29)

For a norm-continuous Markovian open-system semigroup, the Gorini–Kossakowski–Sudarshan–Lindblad theorem gives the generator [44,45]

$$\begin{array}{cc}\hfill \mathcal{L}\left(\rho \right)=& -{\displaystyle \frac{\mathrm{i}}{\hslash }}[H,\rho ]+\sum _a\left(L_a\rho L_a^{†}-{\displaystyle \frac{1}{2}}\{L_a^{†}{L}_a,\rho \}\right).\hfill \end{array}$$

(30)

9.2. Conditioned Histories and Unconditioned Dynamics

The master equation governs an ensemble or a state for which particular outcome records are not conditioned. An individual present history follows a stochastic sequence

$${\rho }_n⟼{\rho }_{n+1,{\alpha }_n}={\displaystyle \frac{{\mathcal{I}}_{{\alpha }_n}\left({\rho }_n\right)}{Tr\left[{\mathcal{I}}_{{\alpha }_n}\left({\rho }_n\right)\right]}},$$

with probabilities given by Equation (13). Averaging over records recovers the channel

$$\mathcal{E}\left(\rho \right)=\sum _{\alpha }{\mathcal{I}}_{\alpha }\left(\rho \right).$$

Thus, stochastic actuality and deterministic effective state evolution are not rival quantum representations; they answer conditioned and unconditioned questions.

9.3. Division of Labor

Reconstruction does not replace the Schrödinger equation, quantum field theory, the Standard Model, or general relativity. It addresses why a stable state space, probability law, causal platform, and outcome record are available for those theories to use. Once the platform and its calibration are read out, conventional dynamics performs the evolution calculation. In that division of labor, a conventional equation specifies how an admitted state changes and normally treats the validity of its law as primitive. The continued-reconstruction requirement is proposed as a constitutive law-realization condition: only successors on which the identities and laws remain well defined enter the physical successor class. This is not an agent or force repeatedly intervening to police the equations; it is the selection rule defining what counts as a realizable physical continuation. It therefore supplements dynamical evolution without changing its verified predictions. This division of labor is developed more fully for physical-law selection in Ref. [22].

• Physical intuition. Reconstruction selects the stage, the admissible actors, the record book, and the rules by which one scene counts as a possible continuation. Effective physics calculates how amplitudes and fields evolve on that stage. The parameter t is supplied by stable clock correlations within the stage; it is not the parameter of a hidden premetric movie.

10. Relativistic Compatibility Without a Global Now

10.1. Local Fronts and Spacelike Confluence

Let A and B be spacelike-separated record-forming regions in the read-out platform. Suppose ${\mathcal{I}}_A$ and ${\mathcal{I}}_B$ denote the associated local unconditioned operations, or particular compatible outcome maps when their records are jointly specified. A coordinate foliation may represent A first or B first, even though no invariant causal order exists between them. To avoid conflating the reconstruction quotient with a map on density operators, let $q_{\mathrm{Q}}$ denote the induced identification of quantum outputs that arise from observably equivalent completed reconstruction presentations.

Principle 3

(Spacelike confluence). If two local read-outs are spacelike-separated and jointly admissible, their unread representation order cannot affect the descended joint present:

$$q_{\mathrm{Q}}\left({\mathcal{I}}_A\circ {\mathcal{I}}_B\left(\rho \right)\right)=q_{\mathrm{Q}}\left({\mathcal{I}}_B\circ {\mathcal{I}}_A\left(\rho \right)\right).$$

(31)

Proposition 4

(IRSP requires spacelike confluence). If exchanging the order of two spacelike-separated read-outs is an unread change of reconstruction representative, then any IRSP-admissible successor law satisfies Equation (31).

Proof. 

The two ordered presentations represent the same causal partial order and differ only by a foliation convention. Observable descent therefore maps them to the same joint state. If the outputs differed observably, the successor law would depend on an unread representative and violate IRSP. □

For unconditioned local maps, confluence is the effective order-independence required by microcausal dynamics. For outcome maps, Equation (31) applies only when the same compatible pair of records is jointly specified and the conditioning convention is held fixed; it does not identify differently conditioned ensembles.

Figure 6 represents the two possible coordinate orderings of spacelike record formation and their required descent to the same joint present.

Figure 6. Relativistic confluence. Two foliations may order spacelike record updates A and B differently, but both paths through the diagram must descend to the same joint present. Actuality is therefore attached to a causal reconstruction front, not to one preferred global simultaneity surface.

10.2. No-Signaling and Local State Updates

For a bipartite state ${\rho }_{AB}$, any trace-preserving operation ${\mathcal{E}}_B$ local to B satisfies

$${Tr}_B\left[({\mathrm{id}}_A\otimes {\mathcal{E}}_B)\left({\rho }_{AB}\right)\right]={Tr}_B\left({\rho }_{AB}\right),$$

so its unannounced application cannot change local statistics at A. Conditioned states can change when a particular outcome at B is specified, but using that change requires the corresponding classical record. The framework therefore adopts the ordinary operational no-signaling structure of relativistic quantum theory.

In continuum field theory, the same idea is naturally expressed by Tomonaga–Schwinger evolution between spacelike hypersurfaces or by local algebras in algebraic quantum field theory [46,47,48]. The surfaces are alternative representations of causal advancement; no one surface is the metaphysically privileged present.

• Claim boundary. Confluence is a necessary relativistic consistency condition, not a complete construction of relativistic collapse. A full model must specify local instruments for quantum fields, prove their covariance and microcausality, and control ultraviolet and gravitational effects. The present theory supplies the criterion such a model must satisfy.

11. Operational Consequences, Consistency Tests, and Failure Conditions

11.1. Primary Consistency Test: Genuine Third-Order Successor Interference

The cleanest exact null condition inherited by the reconstruction architecture is Equation (26). Triple-slit experiments have already placed strong bounds on Born-rule violations [49,50,51]. For the present theory, a conceptually closer implementation would use three coherently controlled successor-history channels—for example, time bins, paths, or qutrit transitions—that recombine into the same final record event.

For every subset $X\subseteq \{A,B,C\}$, one measures the probability $P_X$ of that fixed final event under a calibrated implementation of the corresponding history class. The test statistic is

$$I_3^{\mathrm{succ}}=P_{ABC}-P_{AB}-P_{AC}-P_{BC}+P_A+P_B+P_C-P_{⌀}.$$

(32)

The architecture requires $I_3^{\mathrm{succ}}=0$ after all known context changes are included in the operational model. This is shared with ordinary linear quantum theory: a null result is compatible with reconstruction but does not uniquely support it, whereas a controlled nonzero result would invalidate the declared quadratic/linear bridge.

A credible experiment must demonstrate:

1.

identical source preparation and final record effect for all settings;

2.

a full scattering or channel model for boundary changes introduced by enabling and disabling histories;

3.

control of multiparticle contamination, detector nonlinearities, drift, and dark counts;

4.

inclusion of looped or nonclassical paths where relevant; and

5.

a preregistered uncertainty budget and null analysis.

Nonlinear dynamics can mimic higher-order interference even when the Born rule is retained, so such effects must be bounded independently [52].

11.2. Secondary Consistency Test: Spacelike Order Confluence

A second null test implements two record-forming quantum operations at spacelike separation and reconstructs the joint process matrix in frames that reverse their coordinate ordering. After transforming detector settings and conditioning conventions consistently, the joint descended map must be order-independent as in Equation (31). An observable foliation-order dependence that could not be attributed to ordinary communication, synchronization, or model error would falsify relativistic IRSP descent.

This prediction agrees with relativistic quantum theory; agreement would not uniquely confirm reconstruction. Its value is diagnostic: the theory states in advance which possible observations it cannot accommodate.

11.3. Conditional Record-Erasure and Uncomputation Test

The ancestry claim suggests a third, more theory-specific protocol, although the present framework does not yet predict an experimental scale. A candidate record-forming device would first correlate a qubit with a pointer and a redundant environmental witness. Independent subsystems would then certify that the pointer sectors satisfy the declared stability and readability criteria. Only after that certification would a controlled inverse operation attempt to restore the system, apparatus, witnesses, control registers, and all accessible correlations to their initial joint state.

Ordinary recoherence before certification is expected and does not test history inheritance. Likewise, resetting only the visible pointer tests effective erasure, not full recurrence. The challenging target is an exact return of the complete, previously certified actual record class, including all witnesses and distinguishing successor constraints. If such a return were established within the operational completeness of the experiment, it would refute Assumption 2. Conversely, imperfect reversal would not confirm the theory unless conventional decoherence, dissipation, and control error were quantitatively excluded. A future microscopic completion must turn “stable actual record” and “complete return” into independently measurable thresholds before this becomes a decisive test.

11.4. What Would Refute the Proposed Architecture?

Table 2 collects the principal observations that would invalidate a declared bridge or principle, together with the controls required before each observation could be interpreted as a genuine failure.

Table 2. Principal failure conditions. Each condition targets a declared bridge or principle rather than a fitted parameter.

Observation	Failed Claim	Required Interpretation
Context-dependent weight for the same descended event	IRSP probability descent	All physical changes of preparation and measurement must first be excluded.
Genuine $I_3^{\mathrm{succ}}\ne 0$	Quadratic Born valuation or linear history composition	Nonlinear evolution, multiparticle events, detector response, and boundary changes must be controlled.
Observable order dependence of spacelike read-outs	Spacelike confluence	Ordinary signaling and inconsistent conditioning must be excluded.
Exact full return after independently certified stable actualization	History inheritance and conditional acyclicity	Pre-actualization uncomputation, incomplete environmental control, and merely local erasure must be excluded.
Stable record sectors that cannot be represented by any descended record algebra	Quantum-present and record bridge	The failure must concern physical records, not merely a different convenient basis.

The theory presently predicts no collapse rate, spontaneous heating, mass threshold, or mesoscopic visibility curve. Claiming one without deriving the required normalization would add a fitted phenomenological model rather than test the reconstruction framework. If a future completion derives such a scale, matter-wave interferometry, optomechanics, and macroscopic superposition experiments would become additional tests.

12. Discussion

12.1. What Is Derived, What Is Imported, and What Is Proposed

The argument is easiest to assess when its logical layers are kept separate.

Table 3 therefore records which ingredients are proposed, which are imported from established quantum theory, and which conclusions follow conditionally from the stated assumptions.

Table 3. Status ledger for the construction.

Layer	Content	Status
Reconstruction core	completion, observable quotient, IRSP, saturation, inherited ancestry	proposed selection framework; quotient and descent are standard mathematics
Constitutive law enforcement	restriction to successor classes on which identities and laws remain well defined	proposed non-agentive interpretation of continued admissible reconstruction
Quantum read-out	$C^{\ast }$-observable algebra, state, record algebra, subsystem factorization	established quantum formalism plus explicit read-out and composition bridges
Actual record sector	$P_{{\alpha }_{\sigma }}^{\mathrm{rec}}\in Proj\left({\mathcal{R}}_{\sigma }\right)$ with ${\omega }_{\sigma }\left(P_{{\alpha }_{\sigma }}^{\mathrm{rec}}\right)=1$	explicit component of the quantum-present definition
Actualization	one stable instrument outcome is the next present	ontological principle; no rate or microscopic trigger is yet derived
Probability	event-identity bridge, representative/context descent, positivity, normalization, orthogonal additivity	operational equivalence plus IRSP motivates descent; other hypotheses are declared quantum-probability assumptions
Born form	$w\left(P\right)=Tr\left(\rho P\right)$	theorem by Gleason representation under the preceding hypotheses
Third-order interference	$I_3=0$	exact algebraic consequence of linear amplitudes and a quadratic measure
Temporal order	proper inheritance of the complete ancestry ledger	no-deletion bridge; conditional acyclicity is then a theorem
Effective dynamics	von Neumann or GKSL evolution	standard stable continuum/semigroup limit under declared regularity assumptions
Relativity	confluence of spacelike local read-outs	IRSP descent consequence if foliation order is an unread representative choice

This ledger prevents two opposite mistakes. One would dismiss the framework because it is not a conventional microscopic Lagrangian. At the premetric level, no such Lagrangian is available, because fields, locality, measure, and time are read-out structures. The other would claim that IRSP alone proves all of quantum theory. It does not. Hilbert-space events, linear composition, and the reconstruction-to-quantum correspondence are substantive bridges whose deeper derivation remains part of the research program.

12.2. Novelty and Significance

No single mathematical ingredient used here is new. Quantum instruments, Gleason representation, decoherence, quantum measure theory, completely positive semigroups, and local relativistic algebras are established structures. The proposed advance is their organization around a new physical object: the history-bearing reconstruction boundary whose outcome-conditioned quantum read-out is the present. Continued reconstruction also supplies a proposed law-realization criterion: the physical successor class contains only continuations on which admissible identities, probability rules, and record relations remain well defined. This is constitutive enforcement, not a new force or an observer monitoring unitary evolution.

That organization gives a unified answer to several questions usually treated separately:

1.

why the complete present is a quantum state rather than a classical snapshot;

2.

why entanglement can be understood as irreducible global record structure rather than influence traveling between already separate objects;

3.

how operationally equivalent event weights can be made representative-independent without imposing equality on physically different contexts;

4.

how single-outcome actuality can be formulated as an observer-independent physical principle using stable record sectors;

5.

why effective dynamical time can coexist with a more primitive acyclic order; and,

6.

why relativity requires local confluence rather than a universal instantaneous collapse surface.

The paper therefore aims to fill a genuine conceptual gap rather than modify successful laboratory quantum dynamics. Standard quantum theory says how to compute the possible outcomes and their probabilities. The reconstruction account asks what kind of invariant structure makes an outcome a present fact and makes further outcome probabilities well defined.

The proposal is also part of a broader quantitative reconstruction program. As summarized in Table 1, related structural and conditional constructions have produced concrete dimensionless mass and magnetic-moment ratios and a fine-structure constant. Those published numerical results show that the premetric-to-read-out program can reach quantities compared with laboratory physics; they do not derive the actualization principle of this article. The Bell-pair and qubit examples in Section 5 and Section 6 provide the direct connection of the present architecture to standard quantum experiments.

12.3. Platform-Relative Access and Invariant Agreement

The present analysis is conditional on the empirically observed platform supporting Hilbert-space quantum observables, stable memories, and a Lorentzian causal sector. It does not require a claim about realized alternative worlds or alternative physical laws. “Observer-conditioned” means only that a physical observer has access through the record algebra of the platform that sustains that observer; it does not mean that an observer chooses or creates the laws.

Within our platform, observer dependence does not mean arbitrary personal reality. Different observers’ records must embed consistently into one completed reconstruction class. When they later compare records, confluence and observable descent require agreement on their shared invariant content.

12.4. Limitations and Open Problems

The following problems remain open.

1.

Hilbert-space emergence. The paper assumes a quantum read-out bridge; it does not derive complex Hilbert space, the tensor product, or complete positivity from completion theory alone.

2.

Record algebra. Decoherence and redundancy help identify stable observables, but a universal reconstruction criterion selecting the exact record algebra remains to be proved.

3.

Actualization law. Present actualization specifies what becomes definite but supplies no new rate, localization profile, or field-theoretic stochastic equation. It also lacks an independently calibrated boundary between reversible premeasurement and an IRSP-stable actual record, which is required for a decisive uncomputation test.

4.

Constitutive completeness. Continued reconstruction is proposed as the law-realization mechanism, but this article does not derive the full admissibility relation or prove that it uniquely selects the laws of the observed platform. The enforcement claim is therefore explanatory and conditional, not a replacement for a microscopic dynamics.

5.

History inheritance. The ancestry ledger is defined structurally. Concrete relativistic quantum field models must exhibit it without violating locality or allowing physically meaningless infinite record proliferation.

6.

Gravity. A generally covariant coupling between actualization, record structure, and dynamical geometry has not been constructed.

7.

Unique empirical discrimination. The exact tests emphasized here are consistency and null tests shared with standard quantum theory. A future completion should derive a quantitative deviation or a new domain of applicability if reconstruction is to be distinguished empirically rather than only explanatorily.

These limitations are substantial, but they are also useful: they turn the theory of the present into a sequence of concrete mathematical and experimental questions rather than a purely verbal interpretation.

13. Conclusions

Physics has highly successful theories of dynamical evolution, causal geometry, thermodynamic asymmetry, and quantum probability, but no generally accepted theory of why one outcome-conditioned quantum situation is actual as the present. Such theories normally take the continual applicability of their laws and the realization of one physical situation as primitive. This paper has formulated a conditional reconstructional supplement: reality is continued through admissible reconstructions, and continued admissibility constitutively enforces the identities and laws that each physical successor must satisfy.

The starting layer is premetric: it contains no hidden clock, spacetime, particle inventory, symmetry group, or Lagrangian. Completion, observable quotient, saturation, and IRSP select invariant relational structures capable of indefinite continuation. Their history-bearing global class reads out as an effective platform containing an observable algebra, a quantum state, and a stable record algebra. The physical present is the resulting outcome-conditioned quantum boundary. Because the global record need not factorize into independently completed parts, the read-out can be intrinsically entangled, as the Bell-pair example makes explicit.

Admissible successor records are represented by a quantum instrument. One stable sector is postulated to actualize with its conditioned state; no external observer is required, and unresolved correlations remain quantum. In the worked qubit measurement, the preparation, apparatus, environment, and record algebra determine the two stable sectors and their weights, while one record sector is stochastically actual in the experimental trial. After operational event identity has been established, IRSP requires the probability of that descended event to be independent of unread representative and embedding-context choices. With positivity, normalization, exclusive additivity, and a Hilbert-space event structure, Gleason representation fixes the Born form. Linear alternative composition then yields the exact null condition of no genuine third-order successor interference, shared with ordinary quantum theory.

Under the declared proper-inheritance assumption, the complete ancestry class supplies an acyclic reconstruction order even when accessible records are erased or reduced quantum states recur. Stable small-step channels yield von Neumann or open-system master equations when clock records support a continuum limit. Relativistic compatibility is expressed through confluence of spacelike read-outs: alternative foliation orders must descend to the same joint present. Conventional spacetime time is therefore the calibrated dynamical parameter internal to the read-out platform, while becoming is the proper extension of the history-bearing boundary.

The strongest justified conclusion is neither that the measurement problem is fully solved nor that standard quantum mechanics must be replaced. It is that present actuality can be made into a precise quantum-reconstruction problem with explicit premises, conditional theorems, and direct failure conditions. The next decisive tasks are to derive the quantum and record bridges from common completion theory, construct a covariant microscopic actualization model without fitted parameters, and subject the successor interference, spacelike-confluence, and certified record-reversal conditions to increasingly precise tests.