Editorial Philosophy

The editorial standard is clarity with accountability. A page should help a serious reader understand the question, identify the mathematical objects, reconstruct the reasoning, check assumptions and limits, and find the sources that support the treatment.

Trust is not conferred by tone, length, notation, or a metadata label. It is earned when claims are specific, evidence is appropriate, derivations are auditable, conventions are declared, uncertainty is visible, and correction is routine.

Core Principles

Prefer clarity over cleverness

Use the simplest language that preserves the real structure. Compact notation is valuable when it reduces repetition; it is harmful when it conceals an assumption or changes the type of an object without explanation.

Quantum mechanics does not need mystery-first framing. Begin with the physical question, mathematical object, operational prediction, or experimental fact. Metaphor may orient a reader, but it must not replace the model.

Avoid words such as “obvious,” “just,” and “clearly” when a step depends on a theorem, approximation, convention, or nontrivial calculation.

Separate kinds of claims

A definition, convention, postulate, theorem, derivation, approximation, experimental result, interpretation, and open problem make different demands on evidence.

• A definition fixes language.
• A convention chooses among equivalent representations.
• A postulate states part of a theoretical framework.
• A theorem requires explicit hypotheses and a valid argument.
• A derivation requires a declared setup and checkable steps.
• An approximation requires a control parameter or validity regime.
• An experimental result requires a measured quantity, uncertainty, and source.
• An interpretation must not be presented as an empirical consequence when alternatives fit the same data.
• An open problem must not be written in the past tense of a solution.

Use Evidence Labels when the claim type could otherwise be mistaken.

State assumptions

Assumptions belong near the result they control. Typical assumptions include:

• finite versus infinite-dimensional Hilbert space;
• bounded versus unbounded operators;
• operator domains and boundary conditions;
• pure versus mixed states;
• closed versus open dynamics;
• weak coupling, adiabaticity, Markovianity, or scale separation;
• nonrelativistic versus relativistic kinematics;
• fixed versus variable particle number;
• finite volume versus thermodynamic limit;
• idealized versus measured apparatus.

A result without its domain of validity is not a more elegant result. It is an incomplete one.

Use stable notation

Follow the canonical Conventions unless a local alternative is necessary. When alternatives are common, state the chosen one and explain how to translate.

Notation should expose object type:

• distinguish scalars, vectors, operators, states, functions, distributions, and measures;
• distinguish wave number from momentum and frequency from energy;
• label tensor factors when order matters;
• declare bases before displaying matrices;
• keep units and dimensions visible when they carry physical information.

Changing notation during a derivation is acceptable only when the change is declared and its purpose is clear.

Cite authoritative sources

Use the source that fits the claim.

1. Original papers support historical priority and first results.
2. Standard textbooks support settled pedagogy and conventional derivations.
3. Monographs and review articles support advanced or research-facing synthesis.
4. Current primary papers support specific frontier claims.
5. Official documentation supports software, standards, and tooling.
6. High-quality lecture notes may supplement, but should not carry the full weight of a disputed or high-stakes claim.
7. Popular accounts provide context, not technical authority.

A long bibliography does not compensate for an unsupported sentence. Every reference should support a claim, preserve history, document a method, or offer a useful next step. See Citation and Source Standards.

Maintain one canonical home

Each topic has one page that owns its full definition, derivation, theorem, experiment, or reference entry. Other pages may summarize what they need and link to that home.

The canonical-home rule prevents:

• slightly different derivations from drifting apart;
• sign or normalization fixes from reaching only one copy;
• search results from competing without a clear authority;
• long pages from re-teaching every dependency;
• maintenance work from scaling with duplication.

A bridge or roadmap may show the role of a result without reproducing its canonical derivation. A worked exercise may use the result, but should link to the page that owns the general method.

Cross-link rather than duplicate

Cross-links should explain why the destination matters. A sentence such as “Use the spectral-theorem page to justify the continuous resolution used here” is more useful than an unexplained list of related links.

Links are not a substitute for local coherence. A page should contain enough orientation to state its question and use its dependencies, but it should not silently become a second canonical home.

Keep revision visible

Scientific writing improves through correction. Material changes to conventions, canonical ownership, scope, or major conclusions should be recorded through the Changelog and review metadata.

The Versioning and Review Policy defines review intervals. A recent date is evidence that a review was claimed, not proof that every statement is correct. Readers should still be able to inspect sources and report problems.

What a Mature Page Must Do

Page structure depends on topic type, but maturity has common requirements.

Concept pages

A mature concept page normally provides:

• a direct definition or purpose;
• motivation tied to a physical or mathematical question;
• prerequisites and conventions;
• mathematical formulation;
• physical interpretation;
• at least one worked example or limiting case;
• common mistakes;
• references;
• cross-links;
• exercises when they improve understanding.

Derivation pages

A derivation should name:

1. the goal;
2. assumptions;
3. setup and notation;
4. each nontrivial step;
5. the result;
6. dimensional, algebraic, symmetry, normalization, or limiting checks;
7. the physical interpretation;
8. failure modes or alternative methods.

Skipping algebra that is routine for the declared audience is reasonable. Skipping the step where an approximation, boundary condition, or theorem is introduced is not.

Theorem pages

A theorem page should distinguish:

• formal statement;
• definitions;
• hypotheses;
• proof or proof sketch;
• examples satisfying the hypotheses;
• counterexamples or failure modes when hypotheses are removed;
• physical use;
• original and pedagogical references.

The theorem’s name is not a substitute for its statement.

Experiment pages

An experiment page should separate:

• the question asked;
• historical context;
• apparatus and preparation;
• measured quantity;
• classical or competing expectation;
• quantum prediction;
• result and uncertainty;
• later refinements;
• modern interpretation;
• limitations on what the experiment establishes.

Historical chronology and modern textbook reconstruction should not be blended into one timeless narrative.

Frontier pages

A frontier page should state:

• review date;
• what is established;
• what is active;
• what is conjectural or speculative;
• where terminology is unsettled;
• which calculations or experiments bear on the question;
• entry reviews and key primary sources.

Frontier material ages faster than core formalism. A page that cannot be kept current should be narrowed, marked for update, or replaced by a stable crosswalk.

Reference pages

Reference pages may be compact, but they must still declare conventions, assumptions, symbol definitions, and the canonical teaching pages behind the formulas. A formula sheet that encourages convention mixing is not a reliable reference.

Derivations Should Be Auditable

An auditable derivation lets a reader answer:

• What space do the objects live in?
• Which equality is exact?
• Which step invokes a theorem?
• Where is an approximation introduced?
• What is the expansion parameter?
• Which boundary or initial condition selects the solution?
• Are domains, measures, and normalization controlled?
• Does the result have the correct dimensions?
• Does it respect the expected symmetry or conservation law?
• Does it reduce correctly in a known limit?

Long calculations may be factored into canonical sub-derivations. The local page should preserve the logical chain and link to the owned details.

Approximations Need Control

Every approximation should identify at least one of:

• a small dimensionless parameter;
• a large separation of energy, length, or time scales;
• a spectral gap;
• a semiclassical action scale;
• weak coupling;
• a truncation with a convergence test;
• a statistical or thermodynamic limit;
• an empirical calibration regime.

State the leading neglected effect when possible. “Higher-order terms are small” is incomplete unless the reader can tell small compared with what and where.

Numerical work should report discretization, truncation, tolerance, convergence, and reproducibility information. Agreement with an expected plot is not by itself validation.

Physical Interpretation Without Overclaiming

Interpretation should follow, not replace, the mathematical and experimental statement.

• Do not infer a unique interpretation from a result compatible with several.
• Do not describe a basis-dependent component as an invariant physical object.
• Do not treat a calculational representation as ontology.
• Do not say entanglement transmits controllable information faster than light.
• Do not call a mixed state an imperfect pure state.
• Do not present decoherence as a complete solution to every measurement question.
• Do not turn the classical limit into the claim that $\hbar$ literally vanishes.

Where interpretations disagree, describe the shared formal predictions first, then state the additional commitments of each view.

Historical Accountability

Historical pages should distinguish:

• what an original author or experiment actually claimed;
• what later theory clarified;
• what modern textbooks reconstruct for pedagogy;
• how terminology changed;
• which priority claim is disputed or source dependent.

Original papers are indispensable for historical claims but may be poor teaching sources. Pair them with modern scholarship or technical treatments when needed.

Avoid narratives in which one experiment instantly established the entire modern formalism. Scientific change is usually distributed across evidence, models, interpretation, and later synthesis.

Figures and Computational Evidence

A figure should answer a question that prose or equations answer less well. It should:

• label axes, states, regions, and parameters;
• define units and normalization;
• distinguish data from theory and guides to the eye;
• avoid decorative complexity;
• include alt text and an explanatory caption;
• link to source data or generation code when applicable;
• preserve a source file for maintained diagrams.

Numerical and notebook results should report:

• software and dependency versions;
• input parameters;
• algorithms and tolerances;
• truncation or discretization;
• convergence checks;
• random seeds when relevant;
• enough source material to reproduce the result.

Agreement with a familiar picture is not validation if the numerical method does not preserve the relevant norm, symmetry, positivity, or boundary condition.

Exercises as Editorial Tests

Exercises reveal whether a page has taught usable structure. A balanced set may include conceptual distinctions, derivations, calculations, limiting cases, error diagnosis, method selection, and numerical verification.

Solutions should explain reasoning and checks, not only state a final answer. Problems should be original rather than lightly modified copies from a source.

Correction Is Part of Reliability

Errors in signs, factors, units, domains, links, figures, references, or historical claims should be corrected promptly. A correction is evidence that the maintenance process works.

Use Report Errors with:

• page and section;
• the exact claim or formula;
• why it appears wrong or unclear;
• a source or reproducible calculation when available;
• the expected correction.

High-priority issues include broken mathematics, physically incorrect claims, misstated theorem hypotheses, invalid internal links, and stale frontier conclusions.

Editorial Decision Cases

Case 1: Two Fourier formulas disagree

Two textbooks place different signs and factors of $2\pi$ in a Fourier transform. Should a page choose one as physically correct?

Solution

No. First classify the difference as convention. Choose the canonical Fourier Transform Conventions, state it, and translate the alternative as a complete transform pair. Compare a convention-invariant result such as normalization or an expectation value.

One formula is erroneous only if it is internally inconsistent, dimensionally invalid, or combined with operator and inverse-transform rules from another convention.

Case 2: A promising frontier claim

A recent preprint reports evidence for a new phase in one numerical method, but independent confirmation and a thermodynamic extrapolation are absent. How should it be described?

Solution

Describe the reported calculation specifically, including system sizes, method, observable, and limitations. Label the topic or claim active rather than settled. Cite the primary preprint and, when available, a review or independent analysis. Do not write “the phase exists” when the evidence supports only “this calculation reports behavior consistent with the proposed phase.”

Set a short review interval because the evidence may change quickly.

Case 3: A useful repeated derivation

A scattering page and a Green-function page both need the Lippmann–Schwinger equation. Should both derive it in full?

Solution

Choose one canonical derivation, ordinarily in the scattering-theory chapter. The Green-function page should state the equation in the notation needed locally, explain why the resolvent matters there, and link to the canonical derivation.

If the second page derives a genuinely different result, such as a new boundary-condition representation, it should make that distinct purpose explicit rather than duplicating the original derivation.

What Metadata Can and Cannot Say

Page status describes editorial maturity. Knowledge status describes the epistemic character of the topic. Topic type describes the page’s function. Evidence labels describe individual claims. These are separate axes.

A reviewed page can discuss active research. A draft page can explain a settled theorem. A canonical convention page records a choice rather than a law of nature.

Metadata is a routing and maintenance aid. It does not replace reading the page, checking references, or evaluating an argument. The canonical meanings are defined in Page Status Labels.

References

• Committee on Publication Ethics, Core Practices, for general publication-integrity principles.
• National Academies of Sciences, Engineering, and Medicine, Reproducibility and Replicability in Science, National Academies Press, 2019.
• A. Peres, Quantum Theory: Concepts and Methods, Kluwer, 1995.
• L. E. Ballentine, Quantum Mechanics: A Modern Development, World Scientific, 1998.
• B. C. Hall, Quantum Theory for Mathematicians, Springer, 2013.
• R. K. Merton, The Sociology of Science: Theoretical and Empirical Investigations, University of Chicago Press, 1973.