# Primary texts and the gallery — epoch 013

Selected passages read on 22 September 2026 before revising the narration.
This is a targeted source trace, not a systematic review or independent proof
audit. Public text was retrieved over verified HTTPS. The source PDFs remain
research intake; the website publishes references and a claim ledger.

| Encounter | Primary material actually inspected | What it supports | Reading limit |
|---|---|---|---|
| Newton | *Principia* (1687), Latin text in Project Gutenberg eBook 28233: **Leges motus, Lex I–III; Book III, Proposition VII, Theorem VII** | Laws of motion, mutual reaction, gravitation proportional to quantity of matter and inverse square of distance in the proposition's discussion | Modern transcription; corrected typography and notation are declared by the transcriber. No original scan comparison. |
| Euler | Euler Archive **E327 catalogue**, *De motu rectilineo trium corporum se mutuo attrahentium*, written 1763, published 1767, pp. 144–151 | Title, dates, publication context and the historical straight-line problem | Full original and translation were inaccessible; this is catalogue evidence. E327 is not used as a verified derivation of our rotating symmetric reference. |
| Lagrange | *Essai sur le Problème des trois Corps* (1772), **Avertissement**, in *Œuvres*, tome VI, pp. **229–230**, within the article pp. **229–331**; Wikisource revision **13975608** | Lagrange describes a method built around the three mutual distances: the triangle at each instant. He introduces the straight-line and equilateral constant-ratio cases. | Community transcription of the collected edition, not an inspection of every formula against the original printing. |
| Poincaré | **Introduction**, *Acta Mathematica* 13 (1890), pp. **5–7**, PDF, DOI **10.1007/BF02392506**; acknowledgment on p. 5 | Poincaré calls the work a revision of his prize memoir and thanks **Edvard Phragmén**, whose attention to a delicate point helped him discover and rectify an important error. | Three-page introduction only. Neither the full memoir nor a general nonintegrability theorem was audited. Our phase comparison is a separate modern teaching example. |
| Sundman | *Mémoire sur le problème des trois corps*, *Acta Mathematica* 36, pp. **105–179**, Project Euclid PDF; **p. 105 imprint and §34, pp. 178–179** | The opening leaf says **“Imprimé le 8 juillet 1912.”** The final theorem uses nonzero constants of areas (nonzero angular momentum), a changed independent variable, and its stated collision-continuation convention for a convergent infinite representation across real time. | Selected passages and PDF text layer read, not every proof or equation verified. OCR/text-layer mathematical symbols are imperfect. Our local Taylor construction remains separate. |

## Source links

- Newton: [Latin primary-text transcription](https://www.gutenberg.org/cache/epub/28233/pg28233.txt); [edition/credits](https://www.gutenberg.org/ebooks/28233). The inspected text credits Jonathan Ingram, Keith Edkins and the Online Distributed Proofreading Team. The catalogue's automated summary was not used as primary evidence.
- Euler: [E327 catalogue](https://scholarlycommons.pacific.edu/euler-works/327/). Its linked original PDF and translation returned HTTP 403. MAA paths returned 404; Dartmouth alternatives failed TLS negotiation. No weakened TLS or HTTP downgrade was used.
- Lagrange: [fixed transcription revision](https://fr.wikisource.org/w/index.php?oldid=13975608). The Avertissement begins “Elle consiste à n’employer … d’autres éléments que les distances entre les trois Corps,” followed by the triangle formed at each instant. The site uses an English paraphrase, not an invented quotation or historical plate.
- Poincaré: [primary Introduction PDF](https://link.springer.com/content/pdf/10.1007/BF02392506.pdf); [DOI record](https://doi.org/10.1007/BF02392506). Attribution and correction are established by the author's own acknowledgment, not solely by a later biography.
- Sundman: [primary article PDF](https://projecteuclid.org/journals/acta-mathematica/volume-36/issue-none/M%C3%A9moire-sur-le-probl%C3%A8me-des-trois-corps/10.1007/BF02422379.pdf); [publisher catalogue](https://doi.org/10.1007/BF02422379).

## A correction made possible by the trace

Epoch 012 preferred the publisher's 1913 year and described 1912 as a
biographical convention. The original article now supplies direct evidence:
its opening leaf was printed on 8 July 1912; another sheet, printed p. 177,
carries 15 August 1912. The publisher catalogues the volume/article as 1913.
The current labels therefore preserve **printed 1912 / catalogued 1913**.
A catalogue date does not invalidate the date printed on the work. Earlier
receipts remain historical; they are not silently rewritten.

## From evidence to presentation

Lagrange's own emphasis on relationships guides *A shared shape*, a new
portrait-and-triangle companion. Poincaré's acknowledgment guides *Looking
again*, a portrait with returning paths. Both were generated with
`image_gen.imagegen` under Ergentics art direction. These are contemporary
interpretations, not authenticated likenesses, historical artworks or exact
mathematical diagrams. Captions, source labels and checked reference diagrams
remain separate and readable. No museum artwork was reproduced.

The saved PNGs are the original generated bytes. The site uses local assets,
declared dimensions and lazy loading. It makes no new third-party image request.
The frames add material and tonal depth without animating the portraits or
changing scientific coordinates. Browser checks qualify rendering states, not
historical fidelity, appreciation, educational benefit or depth perception.

## Intake identity

The research packet’s SOURCES.json binds successful retrieval URLs, timestamps, byte
counts and SHA-256 identities. The trace includes four primary texts, one
remaining catalogue-only encounter, and contextual sources retained from epoch
012. Successful HTTP status alone was insufficient: a Springer Sundman URL
returned an HTML landing page, and unrelated Crossref search hits were excluded.
No protected Oracle payload was read and no protected exam was performed.