A reproducible embedding-based analysis of Arday (2015) and Zwozdiak-Myers (2009)
Abstract
Following press coverage of plagiarism allegations concerning a Cambridge professor, I ran a sentence-level semantic similarity analysis on two openly deposited UK doctoral theses: Jason Arday’s 2015 PhD (Liverpool John Moores University) and Paula Zwozdiak-Myers’ 2009 PhD (Brunel University). Both are freely downloadable from their institutional repositories.
The headline aggregate similarity is unremarkable. Median cosine similarity across all 11.09 million cross-document sentence pairs is 0.280 - exactly what two theses in the same subfield should look like. Anyone reporting a single document-level similarity score here would be reporting noise.
The signal is in the tail, and it survives controls. Against two independent education doctorates matched on discipline and partially on topic, the focal pair shows:
- 9 near-identical sentence pairs (cosine ≥ 0.999) in 11.09M comparisons, against 1 in 34.29M control comparisons - and that single control match is the standard thesis declaration (“This work has not previously been presented for an award at this, or any other, university”).
- 179 sentence pairs sharing 12 or more consecutive identical words (107 spatially independent blocks), against an expected 0.32 under the null - an exact count over all 11.09M pairs, no embedding model involved. Longest shared run: 63 words.
- Conditional on high semantic similarity, cross-document pairs share a median run of 11.5 identical consecutive words, versus 4.0 and 7.5 for sentences within each thesis - that is, among semantically matched sentences, the two documents phrase shared ideas alike more often than either thesis does when restating itself.
Under the most conservative assumptions available, the probability of observing this pattern under independent composition is 5.7 × 10⁻⁴; on the central estimate of the null rate, 8 × 10⁻¹¹.
Twenty-eight of the matched pairs are Zwozdiak-Myers writing about her own study - chapter structure, research findings, her stated conceptual definition. A shared third source cannot produce sentences like “This thesis is divided into six chapters.” Chronology fixes direction: 2009 precedes 2015.
Estimated extent: roughly 7,000–11,000 words showing clear derivation, depending on where the paraphrase threshold is set, concentrated almost entirely in the introduction and literature review, where local density reaches 21–26% of sentences. The methodology, data and findings chapters are essentially clean (1.1–4.9% across encoders).
What this establishes is textual derivation. It does not establish intent, and it is not a finding of misconduct - that determination involves citation conventions, supervision, and institutional process, none of which is recoverable from text. Full code is included for replication.
Disclosure: the content of this article was generated by Claude Opus 5.
1. Why this analysis
On 24 July 2026 the Telegraph published a piece headlined “Cambridge’s diversity poster boy in plagiarism row.” The underlying allegations have circulated for some time on PubPeer and in outlets including Varsity. I have not reproduced or assessed the claims made in that coverage; this article is an independent measurement exercise on two public documents, conducted from the primary sources.
The motivating question was narrow and technical: can standard sentence embeddings distinguish genuine textual derivation from the ordinary similarity of two theses in the same field?
That question matters beyond this case. Embedding similarity is increasingly reached for as a plagiarism heuristic, and it is close to useless when applied naively - two documents about the same thing score high whether or not a word moved between them. Getting a defensible answer requires controls, and most published applications don’t use them.
2. Data
| Document | Institution | Year | Words | Sentences (post-clean) |
|---|---|---|---|---|
| Arday, J. - PhD thesis | Liverpool John Moores | 2015 | 146,201 | 4,259 |
| Zwozdiak-Myers, P. - PhD thesis | Brunel | 2009 | 134,983 | 2,605 |
| Control 1: Kushkiev, P. - EdD | Sheffield | 2022 | 79,455 | 1,837 |
| Control 2: Alhumaidan, A. - PhD | York | 2025 | 85,674 | 2,492 |
Both focal theses concern reflective practice among student teachers in initial teacher education and draw on an overlapping literature (Dewey, Schön, Habermas, Kolb, Zeichner, Hatton & Smith).
Control 1 was chosen as a near control: a doctorate on reflective practice and teacher identity, sharing the core theoretical literature. Control 2 is a far control: an education doctorate on a different subject. The pair gives a range of topical proximity, which matters because topical proximity is the confound the whole analysis has to defeat.
All four are openly deposited. Links in §7.
3. Methodology
3.1 Extraction and segmentation
Text extracted with pdftotext (poppler 25.07; Xpdf-based pdftotext builds recover a materially different corpus and will not reproduce these counts). Cleaning removed tables of contents (dot-leader lines), bibliographies (last-occurring references heading in the final 45% of the document), page-number-only lines, and de-hyphenated across line breaks before reflowing paragraphs. Sentences were segmented with an abbreviation-aware splitter, then filtered to 10–120 words with an alphabetic-character ratio above 0.80, and deduplicated within each document.
Removing bibliographies matters: leaving them in produces large spurious overlap, because both theses cite the same literature.
3.2 Embedding
sentence-transformers/all-MiniLM-L6-v2 - 384 dimensions, L2-normalised, cosine similarity by dot product. A widely used general-purpose sentence encoder, deliberately chosen as a standard rather than optimal instrument. All findings were replicated with five further encoders - all-mpnet-base-v2, bge-large-en-v1.5, e5-large-v2, gte-large and Qwen3-Embedding-0.6B - with similarity thresholds re-derived per model from the control corpus; replication code in §7.
3.3 The control design
This is the part that carries the argument.
A raw count of similar sentence pairs is uninterpretable without knowing what two unrelated documents in the same field produce. I used two baselines:
Within-document baseline. Similarity between sentences in the same thesis, separated by at least 200 sentences. This is the ceiling for independent prose on one topic in one voice, and it is deliberately conservative - authors restate themselves across chapters, so this baseline is inflated relative to a true independent-composition null.
Cross-document control baseline. All pairings among the four documents that exclude the focal pair: A×C1, A×C2, Z×C1, Z×C2, C1×C2 - 34.29M sentence pairs of known-independent authorship.
3.4 Statistics
Three, chosen for increasing immunity to topical confounding:
- Cosine distribution - heavily topic-confounded, reported for completeness.
- Near-identity count (cosine ≥ 0.999) - a different mechanism from topical similarity.
- Longest shared run of identical consecutive words, conditional on high cosine - nearly immune to topic, and the statistic that does the work.
Significance via Poisson tests against the pooled control rate. Because matched sentences can cluster within copied passages, I additionally collapsed matches into spatially independent blocks (matches within 3 sentence positions of each other in both documents treated as one event) and re-ran the tests on block counts.
4. Findings
4.1 The aggregate says nothing
| mean | p99 | p99.9 | p99.99 | max | |
|---|---|---|---|---|---|
| Within Arday | 0.311 | 0.712 | 0.797 | 0.856 | 0.986 |
| Within Zwozdiak-Myers | 0.312 | 0.686 | 0.805 | 0.898 | 0.990 |
| Cross-document | 0.280 | 0.619 | 0.742 | 0.825 | 1.000 |
Mean cross-document similarity is lower than either within-document baseline. At a threshold of 0.95 the cross-document rate of high-similarity pairs is 0.9× the within-document rate - no enrichment whatsoever.
If you stopped here you would conclude there is nothing to see. The maximum column is the tell: within-document maxima top out at 0.986 and 0.990. The cross-document maximum is exactly 1.000.
4.2 The controls
Per million sentence pairs:
| pair | mean cos | max | ≥.95 | ≥.98 | ≥.999 | median run | max run | run≥12 |
|---|---|---|---|---|---|---|---|---|
| Arday × Zwozdiak-Myers | 0.280 | 1.000 | 5.50 | 2.25 | 0.811 | 11.5 | 63 | 6.04 |
| Arday × Kushkiev | 0.243 | 0.858 | 0 | 0 | 0 | - | 0 | 0 |
| Arday × Alhumaidan | 0.152 | 0.914 | 0 | 0 | 0 | 6.0 | 6 | 0 |
| Zwozdiak-Myers × Kushkiev | 0.255 | 0.879 | 0 | 0 | 0 | - | 0 | 0 |
| Zwozdiak-Myers × Alhumaidan | 0.174 | 0.881 | 0 | 0 | 0 | - | 0 | 0 |
| Kushkiev × Alhumaidan | 0.161 | 1.000 | 0.22 | 0.22 | 0.218 | 16.0 | 16 | 0.22 |
The decisive comparison is topical proximity against tail behaviour. The focal pair sits at mean cosine 0.280; the near-controls at 0.243 and 0.255 - roughly 10% less proximate. The tail statistics differ by two orders of magnitude. Topic cannot carry that gap.
The null validates itself. The single near-identical pair anywhere in 34.29M control comparisons is:
“This work has not previously been presented for an award at this, or any other, university.”
That is what incidental sentence identity between unrelated theses actually looks like.
4.3 Lexical structure
Taking only pairs at cosine ≥ 0.90 and asking how they are worded:
| n | median Jaccard | median identical run | % run ≥ 12 | |
|---|---|---|---|---|
| Within Arday | 122 | 0.292 | 4.0 words | 16.4% |
| Within Zwozdiak-Myers | 280 | 0.471 | 7.5 words | 32.1% |
| Cross-document | 134 | 0.631 | 11.5 words | 50.0% |
Half of all high-similarity cross-document pairs share a run of twelve or more identical consecutive words.
These run statistics are conditioned on an embedding gate (cosine ≥ 0.90). Removing the encoder entirely and counting over all 11.09M cross-document pairs: 179 pairs share a run of 12 or more identical consecutive words - 16.1 per million, forming 107 spatially independent blocks - against one such pair in 34.29M control comparisons. Without the gate the within-document picture also changes: Zwozdiak-Myers repeats her own 12-word runs at 82.6 per million pairs, five times the cross-document rate, so the table above is a statement about how matched ideas are phrased, not about overall rates of verbatim reuse.
4.4 The paraphrase signature
Of 185 deduplicated pairs above cosine 0.85: 32 near-verbatim (Jaccard ≥ 0.80), 114 semantically near-identical but lexically altered, 39 topical only.
The middle band shows consistent single-word substitution inside preserved syntactic frames:
| Zwozdiak-Myers (2009) | Arday (2015) |
|---|---|
| “sought to add to” | “attempted to contribute to” |
| “One major challenge” | “A significant challenge” |
| “explicitly links … to his theory of” | “explicitly associates … to his conception and theoretical paradigm of” |
| “generate or develop” | “stimulate or cultivate” |
| “In a similar vein” | “Similarly” |
4.5 Provenance
The most important test. If both authors paraphrased a common third source, overlap arises without derivation between them. Classifying the 185 matched pairs by what the Zwozdiak-Myers sentence is:
| category | n | % |
|---|---|---|
| Her own study, framework or findings | 28 | 15.1% |
| Third-party literature discussion (cited) | 54 | 29.2% |
| Generic methodological boilerplate | 2 | 1.1% |
| Uncited prose, no own-study marker | 101 | 54.6% |
The 29% carrying third-party citations are common-source explicable. The 15% are not:
| Zwozdiak-Myers (2009) | Arday (2015) | cos |
|---|---|---|
| “The present chapter provides an overview of the rationale and professional landscape that have guided the direction and purpose of this study.” | “The present chapter provides an overview for the rationale and professional landscape that has guided the direction and purpose of this study.” | 0.997 |
| “The main research findings of this study are drawn together in a summary, which concludes the chapter.” | “The main research findings of this study are drawn together in a brief summary, which concludes the chapter.” | 0.979 |
| “1.4 Structure of the thesis This thesis is divided into six chapters.” | “1.6 Structure of the thesis The thesis is divided into seven chapters.” | 0.944 |
| “In this study, reflective practice has been defined as: a disposition to enquiry incorporating the process through which student teachers’ structure or restructure actions, knowledge, theories or beliefs…” | “Reflective practice, within the confines of this study, has been defined as a disposition to enquiry incorporating the process through which student teachers’ structure, or restructure actions informed by…” | 0.935 |
Self-referential statements about one’s own chapter structure and findings cannot be inherited from shared literature. The fourth is the conceptual definition Zwozdiak-Myers’ abstract describes as a new framework - her stated original contribution.
4.6 Attribution
Re-derived from raw text rather than normalised text, because Arday’s thesis uses single quotation marks that Unicode normalisation collapses into apostrophes - an error I made on the first pass:
- Near-verbatim band: 24 of 32 Arday sentences carry neither quotation marks nor any citation.
- Paraphrase band: 88 of 114.
- Across all 185 pairs, 7 cite Zwozdiak-Myers. She is named 14 times in the thesis overall.
4.7 Significance
Pooled control rate: 0.029 near-identical pairs per million (95% CI 0.0007–0.16). Expected in the focal corpus: 0.324 events (CI 0.008–1.803). Observed: 9, forming 8 spatially independent blocks.
| test | P(observed | independent composition) | ≈ σ (one-sided) |
|---|---|---|
| Near-identity, point estimate of null rate | 8.0 × 10⁻¹¹ | 6.4σ |
| Near-identity, upper 95% CI on null rate | 1.1 × 10⁻⁴ | 3.7σ |
| Near-identity, upper CI and block-corrected | 5.7 × 10⁻⁴ | 3.2σ |
| Shared runs ≥ 12 words, embedding-gated (67 vs 0.32 expected) | ~10⁻⁷⁹ | ~19σ |
| Shared runs ≥ 12 words, encoder-free, upper CI and block-corrected (179 vs 0.32) | 3.3 × 10⁻¹⁴⁶ | ~26σ |
For calibration: in the one-sided Gaussian convention used in particle physics, the 5σ discovery standard corresponds to p ≈ 2.9 × 10⁻⁷. The fully conservative near-identity test does not reach that bar on its own; the point-estimate and shared-run figures clear it by a wide margin.
Converting to a posterior requires a prior. At the conservative likelihood ratio of 1,760: 0.95 at a 1% prior, 0.99 at 5%, 0.995 at 10%. On the point estimate (LR ≈ 1.25 × 10¹⁰) any prior above 10⁻⁸ exceeds 99%.
The gap between the conservative and central figures comes entirely from having observed one incidental event in 34M control pairs. More control documents would collapse it. That is the single highest-value extension of this work.
4.8 Extent
Best-match per Arday sentence against Zwozdiak-Myers, measured as excess over the control baseline, against the 127,607-word cleaned body text:
| threshold | sentences (excess) | words | % of thesis |
|---|---|---|---|
| ≥ 0.99 | 15 | 370 | 0.29% |
| ≥ 0.95 | 60 | 1,898 | 1.49% |
| ≥ 0.90 | 109 | 3,677 | 2.88% |
| ≥ 0.85 | 196 | 6,722 | 5.27% |
| ≥ 0.80 | 322 | 11,045 | 8.66% |
| ≥ 0.75 | 485 | 16,465 | 12.90% |
The thesis-wide figure badly understates the concentration:
| section | sentences with a counterpart (≥0.80) | words |
|---|---|---|
| Deciles 1–2 - introduction, literature review | 177 / 852 - 20.8% | 6,351 |
| Deciles 9–10 - discussion, conclusion | 60 / 851 - 7.1% | 2,029 |
| Deciles 3–8 - methodology, data, findings | 29 / 2,556 - 1.1% | 917 |
Decile 2 alone runs at 25.8%. The empirical core of the thesis is clean - 1.1–4.9% depending on encoder, with front-to-middle concentration of 6–19× under all six. Whatever happened, happened in the framing chapters.
The overlap is also scattered rather than block-copied: at cosine ≥ 0.85 the matches form 103 separate runs, only 16 of length ≥ 2, longest 3 consecutive sentences. That pattern is consistent with sentence-by-sentence reworking of a source rather than lifted sections.
My estimate: roughly 7,000–11,000 words showing clear derivation. Six encoders, each held to a matched false-positive rate of one error against the controls, land in a 7,400–9,800 band. I would not defend the ≥ 0.75 row - below roughly 0.80, measurements shade into ordinary shared-field phrasing. The threshold dependence is not a technicality: where the paraphrase line falls moves the answer by a factor of five, and that line is a judgement about scholarly norms, not something embeddings can settle.
5. What this establishes, and what it doesn’t
Establishes: the two documents are not independently composed. The overlap includes material originating with Zwozdiak-Myers that a common source cannot explain, and chronology fixes the direction.
Does not establish: intent. Nothing here distinguishes deliberate appropriation from note-taking that lost its provenance, or from reliance on intermediate materials. Nor does it constitute a finding of academic misconduct - that determination rests on citation conventions in the discipline, supervisory practice, institutional definitions and due process, none of which is recoverable from text.
Two further routes are worth naming. Zwozdiak-Myers published The Teacher’s Reflective Practice Handbook (Routledge, 2012), which consolidates her doctoral work; material reaching the 2015 thesis via the book rather than the thesis would still originate with her, though some matches - the chapter-structure sentence, for instance - are specific to the thesis artifact. And where matched passages carry third-party citations, the shared-source explanation remains live.
Neither Arday nor Zwozdiak-Myers was contacted before publication, and neither has commented on this analysis.
6. Limitations
- Two controls is thin. The conservative confidence interval is wide because a single incidental event underpins the null rate. Three or four more matched theses would tighten it substantially.
- Controls are imperfectly matched - shorter (79k and 86k words) and less topically proximate to each other than the focal pair. The topical gap is small relative to the effect, but a control matched precisely on subfield would be better.
- Quotation detection is the weakest measurement. It depends on quote glyphs surviving PDF extraction. Block quotes indented without quote marks read as unattributed.
- One source only. Material Arday may have drawn from elsewhere is invisible here, so extent figures are a lower bound on any global claim.
- Percentages are of cleaned body text, excluding bibliography and front matter.
7. Sources and code
Primary documents
- Arday, J. (2015). PhD thesis, Liverpool John Moores University.
researchonline.ljmu.ac.uk/id/eprint/4552/- local mirror - Zwozdiak-Myers, P. (2009). An analysis of the concept reflective practice and an investigation into the development of student teachers’ reflective practice within the context of action research. PhD thesis, Brunel University.
bura.brunel.ac.uk/handle/2438/4316- local mirror
Controls
- Kushkiev, P. (2022). EdD thesis, University of Sheffield.
etheses.whiterose.ac.uk/id/eprint/31670/- local mirror - Alhumaidan, A. (2025). PhD thesis, University of York.
etheses.whiterose.ac.uk/id/eprint/38362/- local mirror
Press
- The Telegraph, 24 July 2026: “Cambridge’s diversity poster boy in plagiarism row.”
telegraph.co.uk/news/2026/07/24/cambridges-diversity-poster-boy-in-plagiarism-row/
Code
Full pipeline attached - extraction, segmentation, embedding, control construction, Poisson testing, provenance classification and extent estimation. It downloads all four documents from their repositories and reproduces every figure in this article from scratch. Runs on CPU in about twenty minutes.
Download overlap_analysis.pyFull list of 185 matched pairs (appendix)
The six-encoder replication - per-model statistic suites, the encoder-free run analysis, and the cross-model consensus - is attached as a bundle: Download analysis_v2.zip
If you replicate this and get different numbers, I want to hear about it.