Unit 4 — Citation, Provenance, and the Source Notebook

1 Learning outcomes

This unit has the stable identifier O017-U04. After completing it, you will be able to:

1. distinguish the functions of citation, evidence provenance, and computational provenance without substituting one for another;
2. record works, versions, copies, and internal locations as distinct but connected objects;
3. connect a normalized claim to a locator precise enough for another reader to find the wording that was actually examined;
4. retain the grounds for accepting, rejecting, or qualifying a mathematical claim, rather than merely retaining its bibliography;
5. record corrections as relationships between versions without overwriting or deleting the historical state of an earlier source;
6. record uncertainty in a structured way and refuse to fill missing metadata with guesses;
7. design a source notebook that can be updated, reviewed, and exported without losing the decision trail; and
8. assemble a claim dossier that brings together citation, provenance, mathematical audit, and the limits of the conclusions.

2 A bibliography is not yet an evidence trail

A bibliography entry usually answers questions such as “Which work is being referenced?” and “How can the reader identify it?” For a mathematical audit, that is not enough.

Consider the sentence:

This result follows from Source A.

At least seven questions remain open.

1. Which edition or version of Source A?
2. Did the reader examine the full text or only its metadata?
3. On which page, or in which section, theorem, equation, or paragraph, does the result appear?
4. Is its wording the same as the claim being used?
5. Do all its hypotheses match?
6. Was there a correction after that version?
7. Does “follows from” mean cited, proved, tested with examples, or merely considered plausible?

A good source record does not turn a citation into a long story. It adds structure that allows each question above to be answered, or honestly marked not yet known.

3 Three records with three different jobs

The following three terms often appear within one project, but answer different questions.

These can overlap. A code package can be cited; one of its outputs can serve as empirical evidence; its execution record can retain computational provenance. But one DOI does not replace an execution record, and one execution record does not replace a theorem’s proof.

[normalized claim] -> [locator] -> [version examined] -> [work]
         |
         +-> [proof / counterexample / data / reference]
         |
         +-> [decision + reason + uncertainty]

4 Four levels of source identity

The notebook must distinguish the following four levels.

1. Work. An intellectual identity that may have many editions or versions.
2. Version. The state of a work at a particular date, release, edition, revision, or commit.
3. Copy. The bytes or physical object actually examined: a local file, printout, archive, or capture that may be incomplete.
4. Location. A part within a version or copy: a page, theorem, equation, paragraph, line, or stable anchor.

A page number without an edition may point to different text. A version without a location makes readers search the entire document again. A copy’s checksum without the work’s identity preserves the bytes but does not explain their intellectual content. All four levels are needed when the risk of miscitation is sufficiently high.

5 A two-layer source notebook

A notebook that withstands change has two layers.

6 A protocol from claim to notebook

Use this sequence for every claim important enough to cite.

1. Freeze the working statement. Write the claim with explicit quantifiers, domain, and hypotheses; assign a claim_id.
2. Identify the source objects. Separate the work, version, and copy actually examined. Record missing fields.
3. Create a locator. Choose a location that remains meaningful for that version. Record its start and end if a claim spans several paragraphs.
4. Record factual relationships. Record VERSION-02 as correcting VERSION-01; then locate CLAIM-01 at LOC-01. Do not insert mathematical conclusions into bibliographical relationships.
5. Audit the mathematics. Link a proof, reconstruction, counterexample, or computational result as separate evidence.
6. Decide the status. Use accepted, rejected, qualified, or not yet established, then state the reason and scope.
7. Choose the citation. Choose the work or version according to the purpose of the sentence to be written; record the reason for the choice.
8. Retain uncertainty and events. Add what remains unknown and any changes in decisions; do not clean away the history after a correction.

The protocol ends when another reader can follow the chain without guessing the version, location, meaning of an arrow, or reason for a status.

7 Worked case: an integral claim with a missing rate

The following case is entirely synthetic and embedded in this unit. Its IDs are classroom IDs, not DOIs or public identifiers. The aim is not to find a source outside this unit, but to build a correct notebook from a limited excerpt packet that is complete for this case. The packet does not represent the full contents of a book.

C01 --appearsAt--> LOC01 --locatesIn--> V01 --isPropositionExcerptOf--> W01
                       |
                       +--partOf--> CP01
  |
  +--refutedBy--> EV01 (counterexample and exact integral)

K01 --appearsAt--> LOC02 --partOf--> CP01
K01 --corrects--> V01
K01 --motivates--> V02 --isPropositionExcerptOf--> W01

C02 --appearsAt--> LOC03 --locatesIn--> V02
                       |
                       +--partOf--> CP01
  |
  +--provedBy--> EV02 (comparison proof)

8 Corrections do not erase earlier versions

When a correction is found, take five actions.

1. Freeze the earlier version’s identity and the location of the affected claim.
2. Record the correction as a separate object with a locator and directional relationships.
3. Create a new claim if the hypotheses or conclusion change.
4. Update the decision about current use, but retain earlier decisions in the event log.
5. Check all derivative writing that cites the earlier claim; do not assume that replacing one bibliography entry repairs its argument.

A new version is not automatically more correct. It is merely a new candidate to audit. Conversely, finding an error in one proposition does not justify declaring the entire work useless.

9 Guided practice: one traceable line

Start from the sentence “version 2 repairs the condition in version 1.” Break it into six records:

1. V01 and V02 as two proposition-excerpt versions of W01;
2. LOC01 and LOC03 as two locators;
3. C01 and C02 as two normalized claims;
4. K01 as a correction object that corrects V01;
5. EV01 and EV02 as different mathematical grounds; and
6. D01 and D02 as decisions with stated scopes.

Now try removing EV01. The trail still shows that a correction was stated, but no longer independently shows that C01 is false. Remove LOC01: the counterexample still refutes C01, but the reader can no longer check whether C01 really is V1’s wording. This deletion test shows why source provenance and evidence must connect without being conflated.

10 Exercises

1. O017-U04-E01. Classify each of the following records as citation, evidence provenance, computational provenance, or a combination: (a) a work DOI; (b) “Theorem 3.7, page 82, second edition”;

   3. a code file, runtime version, parameters, and output checksum; (d) a counterexample linked to C01; (e) an author’s name and title; (f) a rejected decision with EV01 as its reason. For each item, explain one question that it still leaves unanswered.

2. O017-U04-E02. A note says only “Lemma 5 in the blue book proves this result.” Turn it into an auditable record scheme: work, version, copy, location, normalized claim, lemma contract, and fields that remain unknown. Do not invent an author, year, or page number.

3. O017-U04-E03. Using the semantic relationship table as the authoritative list, separate arrows that record source observations from arrows that record mathematical conclusions. Do K01 corrects V01, K01 motivates V02, and C02 provedBy EV02 derive their support from the same object? Explain.

4. O017-U04-E04. For $0<\beta\leq1$, take $f_\beta(x)=x^\beta$. Determine whether the function satisfies C01 and C02, calculate $\int_0^1 f_\beta(x)/x\,dx$, then explain why this successful family of examples does not rescue the universal claim C01.

5. O017-U04-E05. Suppose the packet adds a Proposition 4.1 excerpt labelled V03 with the same mathematical wording as V02, but a different layout and page numbering. State which objects remain, which are new, which relationships must be added, and why the citation “p. 9” without an excerpt version is insufficient. Distinguish a content change from a locator change.

6. O017-U04-E06. Design a record for a numerical experiment that evaluates the truncated integral at five values of $\varepsilon$. Do not write code. Specify the inputs, artifacts, environment, parameters, invocation command or procedure, outputs, rerun status, and a claim-scope sentence that prevents five samples from being treated as a proof of the limit.

11 Hints and answer guidance

1. O017-U04-H01. (a) and (e) are primarily citation;

   2. is a discovery element that becomes part of evidence provenance when linked to a claim and version; (c) is computational provenance; (d) and
   3. are evidence provenance. No one item alone establishes source identity, the claim’s truth, and the ability to rerun a computation all at once.

2. O017-U04-H02. Create local IDs for the work, version, copy, location, claim, and lemma. Enter only “blue-covered book” as an observed characteristic of the copy. Author, official title, edition, year, and page number remain unknown until evidence is available. The lemma contract must compare all its hypotheses with the claim’s context.

3. O017-U04-H03. K01 corrects V01 and K01 motivates V02 are two source relationships both supported by text K01. Neither proves C02. The relationship C02 provedBy EV02 is grounded in proof EV02 and records a mathematical conclusion. Source relationships and grounds for truth must not be conflated.

4. O017-U04-H04. Take $C=1$ and $\alpha=\beta$; then C02 applies and the integral is $1/\beta$. These examples also satisfy C01, but one counterexample suffices to refute a universal claim, whereas many positive examples do not prove it.

5. O017-U04-H05. W01 remains, and V03 is a new proposition-excerpt version.

   isPropositionExcerptOf links V03 to W01.

   hasSamePropositionTextAs links V03 to V02 only when evidence supports it.

   LOC03 still points to V02, while V03 needs a new locator because its pagination has changed. Do not use corrects if the mathematical content has not changed.

6. O017-U04-H06. The record must identify one execution, not “the program in general,” and must retain the command or sequence of procedures actually used. An appropriate scope statement is, for example: “the five outputs show increasing values on the selected inputs and serve as a diagnostic; divergence is established by the exact limit calculation EV01.” Rerun status must not be succeeded before a second execution has actually taken place.

12 Unit completion task

Assemble a citation and provenance dossier for the following synthetic packet. All IDs are nonpublic classroom IDs.

The dossier must contain:

1. separate records for the work, V1, correction, V2, one partial copy/packet, all three locators, and all directional relationships; explicitly state that the packet is incomplete and link each locator to both its copy and its version;
2. two normalized claims with quantifiers, domain, and unambiguous norm notation;
3. a counterexample to V1 using $A=\begin{pmatrix}0&1\\0&0\end{pmatrix}$: prove $A^2=0$ and $\lVert A\rVert_2=1$, rather than merely stating software output;
4. a proof of V2 directly from the operator-norm definition, showing $\lVert A^2x\rVert_2\leq\lVert A\rVert_2\lVert Ax\rVert_2$ and then taking the appropriate supremum;
5. evidence objects, decisions with explicit scopes, and a claim–locator–copy–version–work graph for both claims;
6. one citation for discussing the history of the error and one for using the valid result, with reasons for the choices;
7. a list of metadata that is available, unknown, and not applicable, without inventing a DOI, author, date, or checksum;
8. a proposed computational provenance record for checking candidate matrices, labelled not yet executed unless there is evidence of an actual execution; and
9. a statement of limits: explain why the example matrix refutes the universal equality but does not show that the equality fails for every matrix.

13 Boundaries with B80 and other units

This unit does not teach Python, SageMath, SymPy, or NumPy/SciPy syntax, reference-manager APIs, particular database schemas, Git commands, checksum generation, environment management, or test writing. Those implementation skills all belong to B80. This unit specifies only what information must be preserved and how to limit conclusions drawn from computational results.

Unit 4 also does not repeat Unit 2’s search strategies and authority matrix, Unit 3’s gap reconstruction, Unit 5’s full exposition writing, Unit 6’s reproducibility package, or Unit 7’s erratum format. The notebook created here will supply inputs to those units: it preserves identities and decisions, while later units teach the products that use them.

14 Sources, provenance, changes, and rights

The original Indonesian prose, claim–locator–version chain model, two-layer notebook, decision tables, integral and matrix-norm packets, counterexamples, proofs, exercises, answer guidance, completion task, and rubric in this unit are original O017 material by the O017 contributors, 2026, licensed under CC BY-SA 4.0. This English translation retains that attribution and license.

General concepts of citation metadata, work and version identifiers, and version relationships were reviewed and adapted in a bounded way from The Turing Way (The Turing Way Community 2025, 2026), The Turing Way Community, at the fixed commit:

c98a0e6…131d1ce, specifically:

• book/website/communication/citable/citable-versioning.md; and
• book/website/communication/citable/citable-metadata.md.

That donor material is licensed under CC BY 4.0. The concepts used have been summarized, bounded, reorganized, and contextualized; no donor sentences, images, or exercises were copied.

The distinction between elements of computational provenance and per-result documentation was reviewed from Research Software Engineering with Python (Irving et al. 2021, n.d.) by Damien Irving, Kate Hertweck, Luke Johnston, Joel Ostblom, Charlotte Wickham, and Greg Wilson, at the fixed commit 62217e66…a3cf07, specifically chapters/provenance.Rmd. The selected local copy is:

selected-slice/provenance-selected.Rmd

The donor prose is licensed under CC BY 4.0. This unit copies no code, images, quotations, or external activities from the donor.

All adaptations have been newly contextualized for mathematical source auditing and changed substantively. The Turing Way Community, the six authors of Research Software Engineering with Python, their publishers, and their affiliations do not endorse, approve, or sponsor O017.

The calculus facts about the integral of $x^{\alpha-1}$ and the submultiplicativity of the operator norm are standard mathematical results. O017 does not claim to have discovered them; the proofs’ wording and pedagogical roles are original to this unit. Frozen sources remain subject to their own rights. The CC BY-SA 4.0 license for original O017 material does not replace or relicense donor components.