Unit 2 — Tracing the Literature and Assessing Source Authority

Identifying the exact version, following citation chains, and testing claims

A practical unit on turning mathematical claims into bounded searches, distinguishing a work’s record from a particular version, and keeping an auditable record of the basis for source assessment.

1 Learning outcomes

This unit has the stable identifier O017-U02. After completing it, you will be able to:

turn a mathematical claim into a bounded, repeatable search question;
distinguish discovery tools, metadata records, full texts, particular editions or versions, and correction notices;
assess source authority with respect to a particular question, rather than relying only on a famous name or search-result ranking;
distinguish persistent identifiers for a work in general from identifiers for a particular version;
draw citation chains as directed graphs with typed relationships;
separate evidence that “this source states the claim” from a proof that the claim is true; and
record uncertainty without filling missing data with guesses.

Prerequisites and how to use this unit

This unit assumes that you can read definitions, theorems, and proofs as in Unit 1, and that you know the basics of series of functions. All core assessment can be completed using the synthetic source packets embedded in this page. Searching online databases is an extension, not a requirement for completing the unit.

2 From a network of claims to a network of sources

In Unit 1, we separated an argument into definitions, assumptions, claims, justifications, and open tasks. Now add source questions to each important claim:

who or which organisation states it;
in which work the claim appears;
which edition or version was actually read;
on which page, in which section, or under which result number the statement appears;
whether there is a newer version, correction, or erratum;
which sources the work cites; and
what mathematical support can be checked independently.

A network of sources is not a substitute for a network of claims. A publisher’s record may be a good authority for a title and publication year, but it does not by itself prove a theorem. Conversely, a valid proof can establish a claim’s truth even if the copy containing it has poor metadata.

Principle: authority depends on the question

A source is not “the most authoritative” for every purpose. First state the question: bibliographic identity, the content of a particular version, the history of changes, historical priority, or mathematical truth. Only then assess the source with respect to that question.

3 Writing a search card

A search that starts with general words can easily expand without limit. Before opening a catalogue or search engine, write a search card.

Field	What to record
Object	the mathematical object under discussion
Claim	explicit hypotheses, conclusion, and quantifiers
Variants	possible synonyms, translations, notation, and spellings of names
Question	the identity, version, proof, correction, or priority being sought
Boundary	the routes to be checked and the stopping conditions
Initial uncertainty	what is not yet known and must not be guessed

For example, the phrase “the square of a convergent series still converges” is not yet a good card. The word converges might mean ordinary convergence or absolute convergence; “square” might mean $\sum a_n^2$ or the square of the sum. A good card records these two possibilities as questions instead of silently choosing one.

3.1 A three-pass procedure

Use the following bounded procedure.

Terminology pass. Search for distinctive phrases, notation, objects, and term variants. The results are candidate sources, not evidence.
Backward pass. From one relevant candidate, follow one or two references that actually support the claim under examination.
Comparison pass. Find one independent source that states or proves the same result, or one correction notice that changes it.

Each pass produces a short note: the query or starting point, date, candidate examined, reason for accepting or rejecting that candidate, and next step. A “not found” note is still informative when the search boundary is clear.

3.2 Stopping conditions

The search may stop when:

the exact text of the claim and a locator for it have been found;
its edition or version has been established as far as the evidence allows;
at least one backward relationship or one independent comparison has been checked; and
contradictions or remaining missing data are recorded openly.

These conditions do not guarantee that all the literature has been found. They ensure that others can see and test the boundaries of the work.

4 Five evidence surfaces that must not be conflated

Surface	Appropriate function	What it does not yet establish
Search result or index	finding candidates and term variants	the full content or the version cited
Catalogue/publisher record	the work’s identity, publisher, year, edition	the truth of claims within the work
Work/concept record	grouping versions of the same work	the bytes or wording of the version used
A particular version’s artifact	showing what is written in that version	the mathematical truth of its statements
Proof or counterexample	testing the mathematical status of a claim	the bibliographic identity of the original source

One page may contain more than one surface, but their evidentiary roles must still be kept separate. A screenshot of search results, for example, may help explain how a candidate was discovered. It is not a substitute for the complete file and a page locator.

4.1 A source-assessment matrix

Instead of assigning a single “trustworthy” score, record the following dimensions.

Dimension	Audit question
Proximity	Does the source contain the statement/proof, or only a paraphrase?
Version traceability	Can the edition or version be identified and retrieved again?
Provenance	Are the creator, publisher/repository, date, and change history clear?
Locator	Can another reader reach the same page, section, or result number?
Support	Is there a proof, counterexample, or independent source?

A secondary source may provide a clearer introduction than the first source. The first source may provide the best evidence of historical priority. The two answer different questions.

5 Editions, versions, and persistent identifiers

Working definition: work PIDs and version PIDs

A persistent identifier, or PID, is designed to keep an object’s identity referable even when its access location changes. PIDs do not always refer to the same level.

A work or concept PID refers to the work as a whole and may take the reader to the latest version.
A version PID refers to one particular state of the work. Use this when others need to inspect the same wording or files.

Some repositories implement this distinction as a concept DOI and a version DOI (The Turing Way Community 2025). Do not infer that every DOI behaves in the same way: check the documentation and metadata of the issuing repository.

A test for choosing an identifier

Ask: does the next reader need the same state of the work, or the work in general in its latest state? Reproducing quotations, auditing proofs, and reporting corrections usually require the exact version. When recommending a living book in general, a concept record may be more appropriate.

An auditable citation records at least the creator, title, year or date, publisher or repository, edition/version where applicable, access information or PID, and a locator within the work. This practice adapts the research-object citation elements described in The Turing Way (The Turing Way Community 2025).

5.1 Relationships must be typed

Relationship metadata makes it possible to connect two objects using the appropriate verb. Examples relevant to mathematical readers include:

cites: work A cites work B;
references: A mentions B without asserting a version relationship;
isVersionOf: V1 is a version of work K;
isNewVersionOf: V2 is a successor to V1;
corrects: a new statement or version corrects the old one;
quotes: A copies locatable wording from B.

The donor metadata illustrates the first four relationship labels. The local pedagogical labels corrects and quotes do not claim that every repository provides those relationship types.

These relationships are directed. “V2 is a new version of V1” is not the same as “V1 is a new version of V2”. Nor does a cites relationship prove that A is derived from B, that A agrees with B, or that B’s claim is true.

6 Worked case: two versions of a claim about series

All personal names, titles, dates, and identifiers in this case were created specifically for learning. The form PID-KELAS-... is a local simulation identifier, not a DOI; it is not registered with a public service and must not be used as a real-world citation. These synthetic identifiers and the claim codes K1/K2 are retained unchanged across the Indonesian and English editions.

6.1 Candidate source packet

ID	Candidate	Available content	Initial role
`O017-U02-SRC-S0`	class index snippet	a title and one truncated sentence	discovery tool
`O017-U02-SRC-S1`	Series Seminar Summary, 20 March	quotes the claim and cites the concept record	secondary source
`O017-U02-SRC-S2`	Squares of Convergent Series, version 1, 10 March	statement K1 and an abridged proof	version artifact
`O017-U02-SRC-S3`	the same work, version 2, 8 April	statement K2, a new proof, a change note	version/correction artifact
`O017-U02-SRC-S4`	Real Analysis: Classroom Edition, edition 3	the alternating series test, harmonic series, comparison	synthetic comparator

The concept record has the simulation identifier PID-KELAS-O017-DERET-KONSEP. Version 1 and version 2 have PID-KELAS-O017-DERET-V1 and PID-KELAS-O017-DERET-V2, respectively. The class record states the following relationships:

Source	Relationship	Target
Seminar summary	`cites`	Concept record
Concept record	`hasVersion`	Version 1
Concept record	`hasVersion`	Version 2
Version 2	`isNewVersionOf`	Version 1
Claim K2	`corrects`	Claim K1
Version 2	`cites`	Real Analysis, edition 3

The seminar summary appeared after version 1 but before version 2. Its wording matches K1, but its citation points only to the concept record. After 8 April, the concept record takes readers to version 2. The concept record is therefore insufficient to retrieve the wording that the seminar author may have seen. The matching wording and date sequence support an inference that version 1 was used, but this inference is not metadata recorded by the source.

6.2 Auditing the version 1 claim

Theorem 1 For every real sequence $(a_n)$ , if the series $\sum_{n=1}^{\infty}a_n$ converges, then the series $\sum_{n=1}^{\infty}a_n^2$ converges.

Counterexample to K1

K1 is false. Take

$a_n=\frac{(-1)^{n+1}}{\sqrt n}.$

The sequence $1/\sqrt n$ decreases to zero, so the alternating series test shows that $\sum a_n$ converges. However,

$\sum_{n=1}^{\infty}a_n^2 =\sum_{n=1}^{\infty}\frac1n$

is the harmonic series and diverges. This counterexample tests the mathematical truth of K1; the version 1 artifact establishes that K1 is indeed written there. These are two different jobs.

6.3 Auditing the version 2 correction

Theorem 2 For every real sequence $(a_n)$ , if $\sum_{n=1}^{\infty}|a_n|$ converges, then $\sum_{n=1}^{\infty}a_n^2$ converges.

Proof 1. Absolute convergence implies $a_n\to0$ . Therefore, there is an $N$ such that $|a_n|\leq1$ for every $n\geq N$ . For those indices,

$0\leq a_n^2=|a_n|^2\leq |a_n|.$

The comparison test shows that the tail $\sum_{n=N}^{\infty}a_n^2$ converges. Adding the finite sum $\sum_{n=1}^{N-1}a_n^2$ does not change convergence. Thus the entire series $\sum a_n^2$ converges.

The final audit note must say three things, not one: version 1 contains K1; K1 is false because of the counterexample above; version 2 replaces the hypothesis with absolute convergence, and K2 is valid by the comparison proof.

6.4 Choosing citations for different questions

To quote the wording of K1 or explain the error, use the identity of version 1 and the locator for K1.
To cite the corrected result, use the identity of version 2 and the locator for K2.
To recommend the synthetic work in general, the concept record may be used, with a note that it leads to the latest version.
To state that the seminar summary used version 1, write “most likely” and give the basis for the inference; do not turn an inference into a fact.

7 A minimal search ledger

This unit does not yet teach a complete provenance ledger; that is the focus of Unit 4. For now, use one row per decision:

Time	Question/query	Candidate	Decision	Basis	Uncertainty
10 April, 10:00	phrase K1 + “series of squares”	S1	follow the citation	contains the full wording	version not specified
10 April, 10:08	concept record	S2, S3	inspect both	two linked versions	the file seen by S1 is still uncertain

Do not add times, queries, or results that were not actually observed. A complete ledger means that every important decision can be traced, not that every click must be recorded.

8 Exercises

O017-U02-X01. Claim card. Turn the phrase “the square of a convergent series still converges” into a search card containing the object, two possible hypotheses, conclusion, term variants, question, and stopping conditions.
O017-U02-X02. Candidate source roles. For S0–S4, write one question that each candidate can answer and one conclusion that may not yet be drawn from it.
O017-U02-X03. Identity without guessing. Suppose the copy of S4 shows only the title, “edition 3”, page 141, and the year 2024, but does not show the publisher’s name. Create a provisional citation record and mark every unknown field.
O017-U02-X04. Choosing a PID level. Choose the concept record or a particular version for: (a) reproducing the K1 audit,
1. recommending a continually updated work, (c) reporting the correction to K1, and (d) quoting a sentence from version 2. Explain each choice.
O017-U02-X05. A directed chain. Redraw the S1–S4 chain. Give each edge a type and direction, then mark the relationship “the seminar summary used version 1” as a metadata fact or an inference.
O017-U02-X06. Mathematical and source audit. Write a memo of at most 500 words that separates: what version 1 says, the counterexample to it, what version 2 changes, the proof of K2, and the uncertainty about the seminar summary’s source.

9 Hints and answer guidance

O017-U02-H01. Separate “converges” from “converges absolutely”, and distinguish $\sum a_n^2$ from $(\sum a_n)^2$ . The stopping conditions must mention a version, a locator, and a check of one comparator.
O017-U02-H02. S0 discovers candidates; S1 shows the wording of a secondary source; S2 and S3 establish version content; S4 supplies mathematical tools for comparison. No conclusion becomes true merely because its source appeared earlier or was published as a book.
O017-U02-H03. Record the visible title, edition, year, and page. Enter the publisher as “unknown in the copy examined”, rather than guessing from another source without a note.
O017-U02-H04. Use particular versions for (a), (c), and (d), because the same wording must be retrievable. A concept record suits (b) if the explicit aim is the latest version.
O017-U02-H05. Every arrow needs a verb and a direction. S1’s citation of the concept is a fact; its use of version 1 is an inference based on wording and dates.
O017-U02-H06. A good memo uses version artifacts to establish content, the example $(-1)^{n+1}/\sqrt n$ to reject K1, and the comparison $a_n^2\leq|a_n|$ on the tail to prove K2.

10 Unit completion task

Prepare a source-tracing dossier from the second synthetic packet. All IDs below are again nonpublic classroom IDs, not DOIs.

PID-KELAS-O017-FUNGSI-KONSEP: the work record for Limits of Continuous Functions.
PID-KELAS-O017-FUNGSI-V1: version 1 states that a pointwise limit of continuous functions on $[0,1]$ is always continuous.
PID-KELAS-O017-FUNGSI-V2: version 2 replaces “pointwise” with “uniform” and records that change.
A set of lecture notes cites the concept record without a version number.
A synthetic textbook, edition 2, §6.4, contains the uniform limit theorem.

The dossier must contain:

separate claim cards for version 1 and version 2;
a bounded search log with the reason for stopping;
a table of each candidate source’s role and authority;
exact version/edition identities and locators, without inventing unavailable fields;
a citation-chain graph with at least five vertices and six typed edges;
the counterexample $f_n(x)=x^n$ on $[0,1]$ : determine the pointwise limit and show that the limit function is not continuous at $x=1$ ;
an $\varepsilon/3$ proof that a uniform limit of continuous functions is continuous;
one version citation for the audit and one concept citation for a recommendation, with reasons for the choices; and
an uncertainty paragraph: what can and cannot be concluded about the version used by the lecture notes.

For step 7, fix $x_0$ and $\varepsilon>0$ . Choose $N$ so that $|f-f_N|<\varepsilon/3$ uniformly. Use continuity of $f_N$ at $x_0$ for the middle term, then apply the triangle inequality to

$|f(x)-f(x_0)| \leq |f(x)-f_N(x)| +|f_N(x)-f_N(x_0)| +|f_N(x_0)-f(x_0)|.$

10.1 Rubric

Each criterion is scored 0, 1, or 2.

Criterion	0	1	2
Search	unbounded or untraceable	some steps recorded	complete questions, passes, decisions, and stopping conditions
Source identity	versions/editions confused	some fields/locators correct	concepts, versions, editions, locators, and missing data distinguished correctly
Citation chain	direction/type cannot be checked	graph partly correct	all vertices and edges directed and typed, with facts/inferences separated
Mathematical audit	example or proof incorrect	correct idea but gaps remain	complete pointwise limit, counterexample, and proof of the uniform limit theorem
Exposition	conclusions exceed the evidence	some uncertainty visible	every conclusion linked to a source or argument, with its limits stated

The passing score is at least 8 out of 10, with a score of 2 for Source identity and Mathematical audit. Fabricated bibliographic data, a concept PID used as though it referred to a fixed version, or reputation treated as proof requires revision even if the total score is sufficient.

11 Boundaries with B80 and other units

This unit does not teach Python syntax, catalogue/DOI APIs, web scraping, Git, release creation, software environments, or how to compute hashes. If a checksum is available, we only interpret its function as a witness to exact bytes. Those computational skills are B80 prerequisites, not material to be retaught in O017.

The search ledger here is deliberately minimal. Designing a full source and provenance ledger is the subject of Unit 4; computational reproducibility is the subject of Unit 6; writing an erratum is the subject of Unit 7. Unit 2 teaches only the citation information and version relationships needed to assess source authority.

12 Provenance, component rights, and changes

The Indonesian connective text translated here, both synthetic source packets, the mathematical examples, proofs, exercises, answer guidance, and rubric in this unit are original O017 material by O017 contributors, 2026, licensed under CC BY-SA 4.0.

The distinction between version DOIs and concept DOIs, version management, typed relationship metadata, and research-object citation elements are adapted 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;
book/website/communication/citable/citable-metadata.md; and
book/website/communication/citable/citable-otherscite.md.

That donor material is licensed under CC BY 4.0. It has been translated, abridged, reorganised, and contextualised for mathematical literature searches; the examples, proofs, exercises, and source packets were not copied from the donor.

The distinction between artifact identities through DOIs and researcher identities through ORCID was reviewed with the help of the provenance section of 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 local selected copy is:

selected-slice/provenance-selected.Rmd

This source’s prose is licensed under CC BY 4.0. This unit does not copy its code, images, or exercises.

Changes have been made to all adapted material. The Turing Way Community, the six authors of Research Software Engineering with Python, and their publishers or affiliations do not endorse, approve, or sponsor this O017 adaptation. Each frozen source remains subject to its own licence; the CC BY-SA 4.0 licence for original O017 material is not intended to replace donor source licences.

References

Irving, Damien, Kate Hertweck, Luke Johnston, Joel Ostblom, Charlotte Wickham, and Greg Wilson. 2021. Research Software Engineering with Python: Building Software That Makes Research Possible. Chapman & Hall/CRC Press. https://third-bit.com/py-rse/.

Irving, Damien, Kate Hertweck, Luke Johnston, Joel Ostblom, Charlotte Wickham, and Greg Wilson. n.d. Research Software Engineering with Python: Frozen Source Witness. https://github.com/merely-useful/py-rse/tree/62217e6606842ab9752fcf8e73954d1eb4a3cf07.

The Turing Way Community. 2025. The Turing Way Handbook for Reproducible, Ethical and Collaborative Research. Version 1.2.3. https://doi.org/10.5281/zenodo.3233853.

The Turing Way Community. 2026. The Turing Way Handbook for Reproducible, Ethical and Collaborative Research: Frozen Source Witness. https://github.com/the-turing-way/the-turing-way/tree/c98a0e6ca47450456cca7c5eedda2d5ee131d1ce.