[2026] The Atom Is Available When Called On: Stationary States as the Matter-Side Instance of General Timelessness

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\lhead{The Atom Is Available When Called On}
\rhead{John C. W. McKinley}
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\title{\textbf{The Atom Is Available When Called On}\\
\large Stationary States as the Matter-Side Instance of General Timelessness}
\author{John C. W. McKinley\,\orcidlink{0009-0005-7097-5035}}
\date{May 16, 2026}

\begin{document}

\maketitle

\blfootnote{\scriptsize This version published at \url{https://doi.org/10.5281/zenodo.20114823}.}

\begin{abstract}
This paper states the matter-side instance of general timelessness on standard-physics territory. It introduces no new equations and alters no predictive machinery of special relativity, general relativity, quantum mechanics, or quantum field theory. The claim is that the lawful structure underlying bound matter is timeless in a sense that standard physics already grants. Stationary states have no time-dependence in their structural content; energy eigenstates evolve by an overall phase that contributes to no observable; ground states are the canonical case of time-independent structure; the Hamiltonian governing a bound system is itself time-independent under the conditions in which bound states are defined. These features are not interpretive additions. They are how standard quantum mechanics describes bound systems. Null proper time is the photon's route to timeless lawful structure; stationary-state time-independence is the atom's. Timelessness is the general condition of lawful structure; spacetime registration is the special case. The present paper draws the ontological consequence the formalism already permits: the bound state is in force as a timeless lawful structure, registered in spacetime when invoked by lawful coupling with an admissible interactant. Persistence is the non-lapse of the lawful structure across timelike ordering. The \(c\)-bound governs invocation propagation, not any hidden internal process. No traveler-substance occupies the interval between detector interactions; no granule sits beneath the registration; no component action is required to maintain the state. The atom is the lawful availability of a stationary structure, registered when called on. The claim is interpretive only.
\end{abstract}

\section{Introduction}

The photon-side argument of the Timeless Light Model rested on a structural feature of standard relativity: the photon has null proper time, no rest frame, and no rest-frame spatial predicates. There is therefore no internal temporal structure inside which a photon-traveler biography could be defined. The photon is read instead as a lawful charge-state relation, registered in spacetime as paired endpoint events, with no traveler between them~\cite{Bedrock}.

The matter case appears different. Massive systems possess nonzero proper time, rest-frame descriptions, and timelike worldlines. Bound systems persist across detector interactions, accumulate proper time, and respond to repeated probing. None of this is null. The photon's structural argument does not extend to matter by simple analogy.

The present paper argues that general timelessness nevertheless reaches bound matter, and that it does so on territory standard quantum mechanics has already claimed for a century. The lawful structure underlying a bound system is time-independent in its structural content. This is not a new claim. It is the canonical formal status of stationary states, energy eigenstates, and ground states. The bound-state wavefunction's magnitude is time-independent; its expectation values are time-independent; its physically meaningful structure is time-independent. The phase that evolves contributes to no observable.

This is the bound-matter instance of the architectural inversion already established in the corpus~\cite{Inversion}: timelessness is the general condition of lawful structure, and spacetime registration is the special case in which the structure is invoked. The photon case exhibits this inversion in single-event form; the present paper places the matter-side instance under the same umbrella. Null proper time is the photon's route to timeless lawful structure; stationary-state time-independence is the atom's.

The ontological consequence is what this paper draws. If the structural content of the bound state is time-independent in the formalism standard physics uses, then the lawful structure underlying the bound state is timeless in the same sense the photon's lawful structure is timeless: it does not have a temporal interior. The bound state is in force at a region of spacetime under the relevant admissibility conditions. Detector interactions register according to the state's structure. Between detector interactions, no internal process occurs. The state is not doing anything. The law is in force.

\begin{quote}
The atom is the lawful availability of a stationary structure, registered when called on.
\end{quote}

This paper does not deny that atoms have energies, that bonds have strengths, that bound systems respond to perturbations, or that detector interactions yield registrations whose statistics depend on the state's structure. It does not deny proper time, rest frames, worldlines, or the standard predictive machinery of quantum mechanics. It denies only the substance-reading: the claim that some primitive material is sitting at the atomic location, persisting through time, and being detected when sampled. There is no such material. There is the lawful structure, in force, and there are the registrations the structure licenses when invoked.

\section{Minimal Background}

The present paper assumes the bedrock statement of the Timeless Light Model: the photon is a lawfully admissible charge-state relation whose spacetime appearance is a lawful change, not a particle in transit~\cite{Bedrock}. The present paper does not re-argue that result.

The present paper also assumes the architectural inversion result: timelessness is the general condition of lawful structure, and spacetime registration is the special case in which the structure is invoked~\cite{Inversion}. The present paper does not re-argue that result either; it supplies the matter-side instance.

The present paper also assumes the published matter-side no-go: timebound systems are not licensed as travelers by quantum admissibility~\cite{Timebound}. That paper closes the bead-path inference; the present paper supplies the affirmative structural account consistent with that no-go.

The present paper also assumes that standard quantum mechanics describes bound systems through stationary states, energy eigenstates, and time-independent Hamiltonians. The canonical references are standard~\cite{Sakurai,Griffiths}. The structural content of a bound state is time-independent in the formalism. The time-dependence that appears is a phase \(e^{-iEt/\hbar}\) that contributes to no expectation value, no probability, no observable. These are textbook facts, not interpretive moves.

The interpretive question the present paper takes up is what the time-independence of the structural content means ontologically. Standard physics is largely agnostic on this; the formalism succeeds without taking a position. The present paper takes the position that time-independence in the structural content is the spacetime-side appearance of an underlying lawful structure that is itself timeless. That position is consistent with the formalism and with the architectural inversion already established in the corpus.

\section{The Stationary State as Standard Physics' Timeless Territory}

\begin{definition}[Stationary state]
A stationary state is a quantum state whose structural content is time-independent. For an energy eigenstate \(\ket{\psi_E}\), time evolution acts only as an overall phase: \(\ket{\psi_E(t)} = e^{-iEt/\hbar}\ket{\psi_E(0)}\). The probability density \(|\psi_E(x)|^2\), the expectation values \(\langle\hat{O}\rangle\) for time-independent observables, and the structural content of the state are independent of \(t\).
\end{definition}

This definition is not a TLM construction. It is the standard quantum-mechanical definition of a stationary state. The hydrogen atom's ground state is a stationary state. The bound states of molecular systems under the Born-Oppenheimer approximation are stationary states. The electronic states used in band theory are built from stationary-state solutions under time-independent lattice Hamiltonians. The standard formal apparatus for describing bound matter is built around stationary states.

\begin{proposition}[Structural time-independence of bound states]
The structural content of a bound stationary state is time-independent under the conditions in which the state is defined.
\end{proposition}

\begin{proof}
A bound state in quantum mechanics is an eigenstate of a time-independent Hamiltonian. The Schr\"odinger equation \(\hat{H}\ket{\psi_E} = E\ket{\psi_E}\) determines the spatial structure of the state; the time-dependent Schr\"odinger equation gives the time evolution as \(\ket{\psi_E(t)} = e^{-iEt/\hbar}\ket{\psi_E(0)}\). All physical observables computed from the state---probability densities, expectation values of time-independent observables, transition matrix elements with other stationary states---are independent of \(t\). The overall phase does not contribute to any of these. Therefore the structural content of a bound stationary state is time-independent.
\end{proof}

\begin{remark}
This is canonical. The proof is in every introductory quantum mechanics textbook. The present paper does not extend it or modify it. The present paper uses it as the standard-physics foundation on which the ontological reading rests.
\end{remark}

\section{The Ontological Reading}

The interpretive move is to read the time-independence of the structural content as evidence that the lawful structure underlying the bound state is itself timeless.

\begin{definition}[Timeless lawful structure]
A lawful structure is timeless if it is not a spacetime object: it does not have a worldline, a proper time, a rest frame, or a location in spacetime. It is the rule under which certain spacetime registrations are admissible.
\end{definition}

\begin{definition}[In force]
A lawful structure is in force at a region of spacetime if the admissibility conditions for its application are met at that region. The lawful structure being in force is not itself a spacetime event; it is the condition under which spacetime events admissible to the structure can occur.
\end{definition}

\begin{definition}[Registered when called on]
A lawful structure that is in force at a region registers when called on: when the structure is invoked by lawful coupling with an admissible interactant (a detector, a probe, another bound system, or other physically eligible system), the invocation produces a registration in spacetime whose content is determined by the structure. Between invocations, the structure remains in force; no registration is produced because no invocation occurs.
\end{definition}

\begin{proposition}[Matter-side counterpart]
A bound material system is the registered availability of a timeless lawful structure: the structure is in force at the region of spacetime supporting the bound state, and detector invocations yield registrations consistent with the structure's content. There is no traveler-substance, no granule, and no component process maintaining the state between invocations.
\end{proposition}

\begin{proof}
Standard quantum mechanics describes the bound system through a time-independent stationary state. The state's structural content does not evolve in time. Reading this time-independence as the spacetime-side appearance of a timeless lawful structure adds no new equations and modifies no predictive content; it states the ontological consequence the formalism already permits.

A detector interaction with the bound system invokes the lawful structure at the spacetime region where the detector and the system overlap. The invocation produces a registration whose statistics are governed by the state's structure: the probability density, the matrix elements, the energy spectrum. Between detector interactions, no further registration occurs, because no further invocation occurs. The bound system is not idle in the sense of waiting for something to happen; the lawful structure is in force, and would register if invoked.

The substance-reading---according to which some primitive material is sitting at the atomic location, persisting through time---is an interpretive addition to the formalism. The formalism does not require such material. The bound state is computed without it. The detector registrations are predicted without it. The substance-reading is an ontological gloss, not a formal requirement. The published matter-side no-go on traveler ontology~\cite{Timebound} has already established that timebound systems do not license bead-path ontology by way of quantum admissibility; the present reading is the affirmative structural account consistent with that no-go.

Therefore the bound material system is best read as the registered availability of a timeless lawful structure, with detector invocations producing registrations and no traveler-substance underlying them.
\end{proof}

\begin{remark}
This is the matter-side instance of general timelessness. The photon case exhibits it in single-event form: lawful structure is timeless because null structure leaves no interior. The bound atom exhibits it in continuous in-force availability: lawful structure is timeless because standard quantum mechanics describes its structural content as time-independent. The two cases differ in regime---photon as single-event registration, atom as continuous in-force availability---but share the same architectural inversion: timelessness is the general condition; spacetime registration is the special case.
\end{remark}

\section{Why the Electron Is Not Orbiting}

The clearest case of the timeless reading is the canonical bound state of hydrogen. The electron in the ground state of hydrogen is not orbiting the proton. This is not a novel claim; it has been the standard quantum-mechanical understanding for a century. The Bohr orbit picture was retired with the introduction of wave mechanics in 1926. The ground state of hydrogen is described by a wavefunction whose magnitude is spherically symmetric and time-independent. The electron has no trajectory, no path, no motion in the classical sense. Its expectation values for position, momentum, and angular momentum are determined by the state's structure, not by a sequence of intermediate positions through which it moves.

Standard physics already says: the electron is not orbiting. The present paper draws the ontological consequence: the electron is not doing anything at all, in the sense of internal kinetic process, because the state's structural content is time-independent. The lawful structure governing the bound state is in force at the region of the atom. Detector interactions with the atom---spectroscopic measurements, ionization events, scattering---invoke the structure and yield registrations. Between such interactions, no internal process occurs. The atom is not running; it is available.

\begin{proposition}[Hydrogen ground state]
The ground state of hydrogen is a stationary state. Its structural content is time-independent. The electron's spatial distribution is determined by the state's structure, not by intermediate positions through which it moves. The atom does not require an internal kinetic process to persist.
\end{proposition}

\begin{proof}
The ground state of hydrogen is an eigenstate of the time-independent Coulomb Hamiltonian \(\hat{H} = \hat{p}^2/2m - e^2/r\) (in Gaussian units), with ground-state energy \(E_1 = -13.6\) eV (negative, since the state is bound). The eigenstate wavefunction \(\psi_{100}(\mathbf{r}) = (1/\sqrt{\pi a_0^3})\, e^{-r/a_0}\) is independent of \(t\) in its structural content. Time evolution introduces only the phase \(e^{-iE_1 t/\hbar}\), which contributes to no observable. The electron's expectation values are determined by integrals over \(|\psi_{100}|^2\), which are time-independent. No internal kinetic process is invoked in the calculation; the state is solved by separation of variables in the time-independent Schr\"odinger equation. Therefore the ground state's structural content is time-independent, and the standard formalism does not invoke an internal kinetic process to maintain it.
\end{proof}

\begin{remark}
The kinetic energy operator has a nonzero expectation value in the ground state: \(\langle \hat{T} \rangle = |E_1| > 0\). This is sometimes read as evidence that the electron is ``moving'' inside the atom. The reading is not required. The expectation value is a feature of the state's structure, not evidence of a sequence of motions in time. The virial relation \(2\langle\hat{T}\rangle = -\langle\hat{V}\rangle\) is a structural identity of the stationary state, not a time-average of a dynamical process; it holds because of the form of the Coulomb potential, not because anything is being averaged over time. The state is stationary; its kinetic energy expectation value is a constant of the state, not a record of dynamical activity.
\end{remark}

\section{What \texorpdfstring{\(c\)}{c} Does in the Matter Case}

The information speed limit \(c\) plays a structural role in the corpus: it bounds the propagation of lawful invocation between spacelike-separated spacetime points~\cite{cBound}. In the photon case, \(c\) bounds the spacetime relation between emission and absorption events. In the matter case, \(c\) bounds the propagation of detector invocation across the relevant separation.

\begin{proposition}[\(c\)-bound on matter-side invocation]
The propagation of lawful invocation between a detector at spacetime point \(B\) and a bound system at spacetime region \(A\) is bounded by \(c\). The registration at \(B\) consistent with invocation of the bound system at \(A\) is therefore \(c\)-bounded from \(A\).
\end{proposition}

\begin{proof}
The bound system at region \(A\) is described by a stationary state whose structural content is in force at \(A\). A detector at point \(B\) interacts with the bound system through the relevant gauge interaction (electromagnetic, for the cases most directly at issue). The interaction is mediated by the relevant gauge field, whose propagation in spacetime is bounded by \(c\). Therefore the registration at \(B\) consistent with invocation of the bound system at \(A\) is bounded by \(c\) along the relevant null or timelike interval from \(A\) to \(B\). The \(c\)-bound applies to the propagation of invocation, not to any hidden internal process of the bound system.
\end{proof}

\begin{remark}
This is consistent with the registration-bound reading of \(c\)~\cite{cBound}. The bound system itself is not bounded by \(c\) in any internal process, because no internal process occurs. The bound system is in force; invocation from elsewhere is \(c\)-bounded in its propagation. The matter-side application of the \(c\)-bound is symmetric with the photon-side application: in both cases, \(c\) bounds invocation propagation in spacetime, not internal traveler-process.
\end{remark}

\section{Persistence}

Persistence in the present reading is the non-lapse of the lawful structure across timelike ordering. A bound system persists not because some primitive material remains in place across time, but because the lawful structure that licenses the bound state remains in force across the relevant region of spacetime.

\begin{definition}[Persistence]
A bound material system persists across a timelike interval if the lawful structure governing its stationary state remains in force across the interval. Persistence is the non-lapse of the lawful structure, not the continued existence of an underlying material.
\end{definition}

\begin{proposition}[Operational consequence of persistence]
For a bound system, persistence is the operational mark of the lawful structure remaining in force: detector interactions across the relevant timelike interval continue to register consistently with the same stationary state.
\end{proposition}

\begin{proof}
A bound system whose lawful structure remains in force across a timelike interval is invokable at any spacetime point within that interval. Detector interactions at different points produce registrations whose statistics are governed by the same stationary state. The detector at \(t_1\) and the detector at \(t_2\) both register consistently with the same structural content. Therefore persistence---the consistency of registrations across the timelike interval---is the operational mark of the lawful structure remaining in force.
\end{proof}

\begin{remark}
Persistence in this reading is not a process. The bound system is not doing something repeatedly across time. The lawful structure is in force; detector interactions register consistently because the structure is the same one across the interval. If at some point the lawful structure no longer applies---if the bound state is broken by ionization, by absorption of sufficient energy, by chemical reaction---the system does not persist beyond that point. Persistence is the in-force condition of the lawful structure, not the continued existence of an underlying substance.
\end{remark}

\section{What This Does Not Change}

\begin{proposition}[No formal revision]
The present proposal does not modify the equations of special relativity, general relativity, quantum mechanics, or quantum field theory.
\end{proposition}

\begin{proof}
The proposal introduces no new equations, no new postulates, and no modifications to the Schr\"odinger equation, the Dirac equation, the standard treatment of stationary states, the role of \(c\), the metric structure of spacetime, or any predictive relation in standard physics. It concerns only the ontological reading attached to bound states, persistence, and matter. Therefore it introduces no formal revision.
\end{proof}

\begin{proposition}[No empirical claim]
The present proposal makes no new empirical prediction.
\end{proposition}

\begin{proof}
Reading the bound state as the registered availability of a timeless lawful structure does not predict new experimental outcomes. The expectation values, spectra, transition probabilities, and other observables computed from stationary-state quantum mechanics remain unchanged. The proposal is interpretive only.
\end{proof}

\begin{proposition}[No denial of matter]
The proposal does not deny matter.
\end{proposition}

\begin{proof}
Matter remains the ordinary regime of bound systems registered by detectors. Atoms, molecules, condensed matter, and other bound systems retain their standard physical roles: they have energies, spectra, response functions, and interaction structures. The proposal denies only that these features require a primitive substance underlying the registrations. The registrations are real; the lawful structure that licenses them is real; the substance underneath is not required.
\end{proof}

\section{Scope and Limitations}

The present paper is restricted to bound matter: atoms, molecules, bound condensed-matter systems, and other systems describable by stationary states. The treatment of free particles, scattering states, wave packets, and unbound matter raises additional issues---propagation, dispersion, wave-packet structure, scattering amplitudes---that the bound-state case avoids. The unbound case is left to a separate treatment.

The paper is also restricted to non-relativistic bound-state quantum mechanics and to the canonical relativistic generalizations (Dirac equation, bound states in QED). The treatment of strongly relativistic bound states, of bound states in curved spacetime under general relativity, and of bound states in quantum field theory generally is consistent with the present reading but is not developed here.

The present paper does not address the question of how lawful structures come to be in force at particular regions of spacetime, why some regions support bound states and others do not, or how the conditions for the in-force status are themselves established. These questions belong to a more general account of admissibility structure and are not taken up here.

\section{Discussion}

This paper supplies the matter-side instance of general timelessness on standard-physics territory. The architectural inversion result was already established in the corpus~\cite{Inversion}: timelessness is the general condition of lawful structure, and spacetime registration is the special case in which the structure is invoked. The photon case exhibits this inversion in single-event form; the present paper places the matter-side instance under the same umbrella on territory standard quantum mechanics has already claimed for a century.

The general timelessness claim reaches bound matter through different formal terrain than it reaches the photon. The photon case is forced by null proper time, no rest frame, and no rest-frame spatial predicates: there is no temporal interior in which a photon-traveler biography could occur. The bound-matter case is supported by the time-independence of stationary-state structural content: standard physics already describes the bound state as time-independent in its structural content, and the lawful structure underlying that content is read as timeless in the same structural sense as the photon's. The matter-side no-go on traveler ontology~\cite{Timebound} is the negative complement to the present affirmative reading: that paper closes the bead-path inference; this paper supplies the structural account of what is in force instead.

Two grounds, one architecture. The photon's lawful structure is timeless because null structure leaves no interior for it. The bound state's lawful structure is timeless because standard quantum mechanics describes its structural content as time-independent. In both cases, the lawful structure is in force; registrations occur in spacetime when the structure is invoked; no traveler-substance occupies the interval between invocations.

The formal ingredients are standard. The ontological reading is not. Standard quantum mechanics supplies lawful bound-state structure; the present paper reads matter as the registered availability of that structure rather than as primitive substance beneath registration. The bound system is real; the lawful structure is real; the registrations are real. What is not required, and not supplied by the formalism, is a substrate sitting beneath the registrations as their hidden material.

The affirmative form of the claim is direct. The atom is the lawful availability of a stationary structure. The structure is in force at the region of spacetime supporting the bound state. Detector interactions register according to the structure. Between detector interactions, no internal process occurs. The atom is not running, vibrating at a hidden rate, or maintaining itself by an internal process. It is available. When called on, it registers.

This reading clarifies several features that the substance-reading complicates. The electron is not orbiting because the state is stationary; standard physics already says so. The bound state does not require maintenance by an internal process because its structural content is time-independent; the formalism does not invoke such a process. The \(c\)-bound applies to detector invocations propagating between spacelike-separated points, not to an internal traveler in the atom. The atom persists because the lawful structure remains in force, not because some primitive material remains in place.

\section{Conclusion}

This paper has supplied the matter-side instance of general timelessness on standard-physics territory. Standard quantum mechanics describes bound systems through stationary states whose structural content is time-independent. The present paper draws the ontological consequence: the lawful structure underlying the bound state is timeless. The bound state is in force at the region of spacetime supporting it. Detector invocations register according to the structure. Persistence is the non-lapse of the structure across timelike ordering.

Two grounds, one architecture: the photon's lawful structure is timeless because null structure leaves no interior for it; the bound state's lawful structure is timeless because standard quantum mechanics describes its structural content as time-independent. In both cases, timelessness is the general condition; spacetime registration is the special case; no traveler-substance occupies the interval between registrations.

The atom is the lawful availability of a stationary structure, registered when called on.

\section*{TLM Summary}

The Timeless Light Model (TLM) is a minimal interpretive framework. It treats the photon as a lawful charge-state relation registered in spacetime at paired endpoint events, not as a particle in transit. The present paper places the matter-side instance of the same timelessness claim within the architectural inversion: stationary-state time-independence is the atom's route to timeless lawful structure, as null proper time is the photon's. Stationary states have time-independent structural content. The lawful structure underlying a bound state is timeless: it is not a spacetime object, has no temporal interior, and is in force at the region of spacetime supporting the bound state. Detector interactions invoke the structure and yield registrations. Persistence is the non-lapse of the structure across timelike ordering. The \(c\)-bound applies to the propagation of detector invocation between spacelike-separated points. The atom does not orbit, vibrate at a hidden rate, or maintain itself by an internal process. The atom is the lawful availability of a stationary structure, registered when called on.

\section*{Glossary}

\begin{description}
    \item[In force] A lawful structure is in force at a region of spacetime if the admissibility conditions for its application are met at that region. Being in force is not itself a spacetime event.

    \item[Lawful admissibility] The physical constraint structure under which an outcome, interaction, registration, or appearance is realizable, including conservation principles, coupling structure, boundary conditions, and other relevant constraints.

    \item[Matter] The registered availability of a timeless lawful structure governing a bound system. The structure is in force at the region of spacetime supporting the bound state; detector invocations yield registrations consistent with the structure's content.

    \item[Persistence] The non-lapse of a lawful structure across timelike ordering. A bound system persists across an interval if its governing lawful structure remains in force across the interval.

    \item[Registered when called on] The condition under which a lawful structure in force at a region produces a registration in spacetime: when the structure is invoked by lawful coupling with an admissible interactant (a detector, a probe, another bound system, or other physically eligible system), a registration occurs. Between invocations, the structure remains in force; no registration is produced because no invocation occurs.

    \item[Registration] A spacetime-side event in which a lawful state change is recorded as a definite physical occurrence.

    \item[Stationary state] A quantum state whose structural content is time-independent. For an energy eigenstate, time evolution acts only as an overall phase that contributes to no observable.

    \item[Timeless lawful structure] A lawful structure that is not a spacetime object: it has no worldline, no proper time, no rest frame, and no location in spacetime. It is the rule under which spacetime registrations admissible to it can occur.
\end{description}

\begin{thebibliography}{9}
\bibitem[McKinley(2026a)]{Bedrock}
J.~C.~W.~McKinley.
\newblock \emph{A Minimal Structural Statement of the Timeless Light Model}.
\newblock Zenodo (2026).
\newblock \doi{10.5281/zenodo.19167403}.

\bibitem[McKinley(2026b)]{cBound}
J.~C.~W.~McKinley.
\newblock \emph{c Is a Registration Bound, Not a Traveler's Speed: A Registration-Based Interpretation of the Information Speed Limit}.
\newblock Zenodo (2026).
\newblock \doi{10.5281/zenodo.20114176}.

\bibitem[McKinley(2026c)]{Inversion}
J.~C.~W.~McKinley.
\newblock \emph{Timelessness Is the General Condition: Spacetime Is the Special Case}.
\newblock Zenodo (2026).
\newblock \doi{10.5281/zenodo.19771925}.

\bibitem[McKinley(2026d)]{Timebound}
J.~C.~W.~McKinley.
\newblock \emph{Timebound Does Not Mean Traveler: A No-Go on Deriving Bead-Path Ontology from Quantum Admissibility}.
\newblock Zenodo (2026).
\newblock \doi{10.5281/zenodo.20114078}.

\bibitem[Sakurai and Napolitano(2017)]{Sakurai}
J.~J.~Sakurai and J.~Napolitano.
\newblock \emph{Modern Quantum Mechanics}.
\newblock Cambridge University Press, 2nd edition (2017).

\bibitem[Griffiths and Schroeter(2018)]{Griffiths}
D.~J.~Griffiths and D.~F.~Schroeter.
\newblock \emph{Introduction to Quantum Mechanics}.
\newblock Cambridge University Press, 3rd edition (2018).

\end{thebibliography}

\end{document}