By John Joseph O'Connor and Edmund Frederick Robertson, credited as J J O'Connor and E F Robertson. Hosted by the University of St Andrews in the MacTutor History of Mathematics Archive. Last Update: July 1999; this is an online revision date, not a publication date.

Online biography: mathshistory.st-andrews.ac.uk/Biographies/Al-Khwarizmi/

Cited passages: Quick Info, approximate life dates about 780 and about 850; six standard forms and verbal algebra; geometric completion with squares and rectangles; footer byline and Last Update.

By Lynn Marecek and Andrea Honeycutt Mathis, whole-book authors. OpenStax publishes and hosts the book. Published 6 May 2020; the later website footer copyright year is not the publication date.

Official book: openstax.org/details/books/intermediate-algebra-2e

By John Joseph O'Connor and Edmund Frederick Robertson, credited as J J O'Connor and E F Robertson. Their full names are established by their own MacTutor profile headings.

Hosted by the University of St Andrews in the MacTutor History of Mathematics Archive. Last Update: March 2024; this is an online revision date, not a publication date.

Online biography: mathshistory.st-andrews.ac.uk/Biographies/Robertson_Edmund/

Cited passages: Quick Info: born 1 June 1943; Mathematical training/group theory research, MacTutor archive co-originator; Footer byline and Last Update March 2024.

By John Joseph O'Connor and Edmund Frederick Robertson, credited as J J O'Connor and E F Robertson. Their full names are established by their own MacTutor profile headings.

Hosted by the University of St Andrews in the MacTutor History of Mathematics Archive. Last Update: March 2024; this is an online revision date, not a publication date.

Online biography: mathshistory.st-andrews.ac.uk/Biographies/OConnor/

Cited passages: Quick Info: born 31 July 1945; Summary: mathematician and MacTutor creator; Footer byline and Last Update March 2024.

By John Joseph O'Connor and Edmund Frederick Robertson, credited as J J O'Connor and E F Robertson. Their full names are established by their own MacTutor profile headings.

Hosted by the University of St Andrews in the MacTutor History of Mathematics Archive. Last Update: January 2000; this is an online revision date, not a publication date.

Online biography: mathshistory.st-andrews.ac.uk/Biographies/Viete/

Cited passages: Byline: Written by J J O'Connor and E F Robertson; Last Update January 2000; Quick Info: born 1540 died 13 December 1603; Paragraphs describing the 1591 In artem analyticam isagoge notation, known/unknown symbols, dimensional homogeneity and connection of positive roots to coefficients.

University of California, Berkeley course, Fall 2023. The course homepage identifies James Demmel as instructor and labels the course Matrix Computations / Numerical Linear Algebra. The instructor role does not establish authorship of each resource.

Course homepage: people.eecs.berkeley.edu/~demmel/ma221_Fall23/

Senior contributing authors: Gilbert Strang and Edwin “Jed” Herman. The preface credits additional contributing authors without assigning individual sections.

Publisher and web host: OpenStax, part of Rice University.

Official text: openstax.org/books/calculus-volume-2/pages/1-introduction

Whole-book publication: 30 March 2016, as stated in the citation information. The website copyright notice is separate.^[ref]

By Mark Krein and David Milman. Studia Mathematica, volume 9 (1940), pp. 133–138.

DOI: doi.org/10.4064/sm-9-1-133-138

Publisher volume index: www.impan.pl/pl/wydawnictwa/czasopisma-i-serie-wydawnicze/studia-mathematica/all/9/1

EuDML record: eudml.org/doc/219061

Main supplied this exact indexed metadata. David Milman (1912–1982) by Israel Gohberg and others, printed p. 4, refers to the original paper as citation 3; the hosted memoir excerpt does not contain the full reference list. The original scan was not read; no theorem statement is attributed here to inspection of it. Batch131’s historical citation uses the memoir instead.

By Israel Gohberg, Moshe Livšic and Ilya Piatetski-Shapiro; the credited names are I. Gohberg, M. S. Livšic and I. Piatetski-Shapiro. Integral Equations and Operator Theory, volume 9, pp. ii–7, January 1986. The years 1912–1982 in the title are David Milman’s life years.

University-hosted memoir: www.math.tau.ac.il/images/stories/documents/david_milman.pdf

Publisher metadata: link.springer.com/article/10.1007/BF01257057

DOI: doi.org/10.1007/BF01257057

Tel Aviv University hosts this copy; the journal is the publication venue. Main inspected the first journal page and running headers; the publisher independently confirms the title, credits, pagination and issue date.

Cited historical passage: printed p. 4, the 1940 publication with M. G. Krein, citing the original paper as reference 3. This hosted excerpt contains a cover and printed pp. 1–7, but no full reference list. This memoir is used for publication history; its stated theorem hypotheses are not treated as the most general modern formulation.

The front page is titled Convex geometry and identifies course BMETE94AM22, 2025/26 spring, updated 2 June 2026. BME’s geometry website hosts these course notes. No individual author byline is present on the inspected front page, and no instructor is assigned authorship from the URL.

Course notes: geometria.math.bme.hu/sites/geometria.math.bme.hu/files/users/vranap/convex/convex-notes.pdf

Cited passages: §6, Definitions 6.2 and 6.6 and Proposition 6.7, printed pp. 36–37 (PDF page indices 35–36). No source illustration or Example 6.8 is reused; the batch’s examples, proofs and figures are original.

By Stuart H. Hurlbert. Ecological Monographs, volume 54, issue 2, pp. 187–211, June 1984; published by the Ecological Society of America. The article separately records receipt on 25 February 1983, revision on 21 June 1983 and acceptance on 25 June 1983.

DOI: doi.org/10.2307/1942661

Institutionally hosted scan: sciences.ucf.edu/biology/pascencio/wp-content/uploads/sites/24/2016/11/Hurlbert1984.pdf

Inspected OCR mirror: paperzz.com/doc/7415879/hulbert_ecmonograph1984.pdf

Paperzz hosts the OCR mirror; it is not the author or original publisher. The UCF scan is a corroborating copy; the OCR can interleave columns.

Cited passages: printed p. 190; pp. 194–195, combined or hybrid allocation and the account of the Hurlbert–Mulla pond experiment; p. 201, Multiple samples per experimental unit; p. 210, reference to the 1981 paper.

Institutional guidance issued and hosted by NC3Rs through its Experimental Design Assistant. No personal author byline is established. First published 16 December 2014; last updated 31 October 2023.

Online text: eda.nc3rs.org.uk/experimental-design-unit

Cited passages: Why is the experimental unit important?; Know your experimental unit; A breeding female and litter; The cage of animals; Experiments with more than one experimental unit.

By Constantin Carathéodory. Rendiconti del Circolo Matematico di Palermo, volume 32, pp. 193–217 (1911).

Publisher metadata: link.springer.com/article/10.1007/BF03014795

English translation: nchlswllms.github.io/translations/cc1911.pdf

The translation is titled On the Domain of Variability of Fourier Coefficients of Positive Harmonic Functions and credits Nicholas J. Williams as translator. It records the original announcement on 26 March 1911 and printing on 16 August 1911; neither dates the translation. The original German scan was not accessible.

Cited passages: Introduction §4, original printed p. 195; §I opening.

Online text: math.ucla.edu/~sharifi/notes/algebra.html

By Romyar Sharifi, credited on the introduction and chapter pages. UCLA hosts these lecture notes; no publication or revision date is established.

Online text: jmilne.org/math/CourseNotes/FT.pdf

By James S. Milne, credited as J.S. Milne on the cover and James S. Milne in the author-supplied BibTeX. Version 5.10, September 2022; this is a version date. The version history separately dates the first web version to 21 August 1996.

Cited passages: Chapter 1, Review of polynomial rings, printed p. 10, §1.6, unique polynomial division with zero remainder or strict polynomial degree bound; §1.7, division by a linear factor and evaluation. No separate chapter byline is supplied.

Historical research article by Claude Brezinski, published in Revue d’histoire des mathématiques 11 (2005), pp. 205–238. Numdam hosts the original journal article. The printed received date, 4 November 2004, and revised date, 11 May 2005, are distinct from publication.

Original article: www.numdam.org/item/RHM_2005__11_2_205_0.pdf

Section 4 reproduces a primary manuscript authored by André-Louis Cholesky and dated Vincennes, 2 December 1910. Cholesky is the author of that manuscript; Brezinski is the author of the surrounding 2005 article. The manuscript date does not establish an exact invention date or a broad priority claim.

Cited passages: pp. 210–211: constrained geodetic corrections and the matrix $M{M}^T$; p. 217: manuscript title, 2 December 1910 date and uncertainty about the exact invention date; §4, p. 229: the primary manuscript’s reported 56-equation altitude adjustment for Algerian triangulation and closing date. The primary manuscript transcription was inspected as text; no inspection of handwriting images is claimed.

Official versioned routine documentation from the LAPACK project, hosted by Netlib. The Author section credits University of Tennessee, University of California Berkeley, University of Colorado Denver and NAG Ltd.; no individual author is inferred.

Online text: netlib.org/lapack/explore-html/d2/d09/group__potrf_gae6842f47b241caed33a19ace77f482a4.html

Version: LAPACK 3.12.1. The footer date 20 January 2025 is a Doxygen generation timestamp, not a verified code publication date.

Cited passages: Purpose: complex Hermitian positive-definite factorization and conjugate transpose; Author section: institutional credits.

Official versioned routine documentation from the LAPACK project, hosted by Netlib. The Author section credits University of Tennessee, University of California Berkeley, University of Colorado Denver and NAG Ltd.; no individual author is inferred.

Online text: www.netlib.org/lapack/explore-html/d2/d09/group__potrf_ga84e90859b02139934b166e579dd211d4.html

Version: LAPACK 3.12.1. The footer date 20 January 2025 is a Doxygen generation timestamp, not a verified code publication date.

Cited passages: Purpose: real symmetric positive-definite factorization; UPLO and INFO arguments; Author section: institutional credits.

Standalone expository note by Paul Garrett, verified from the full-name byline on p. 1. Hosted on his University of Minnesota faculty website; the host is not the author.

Online text: www-users.cse.umn.edu/~garrett/m/algebra/cantor_schroeder_bernstein.pdf

The document header is dated 19 February 2005; this does not establish a first publication date.

Cited passages: p. 1, theorem for two injections between arbitrary sets and introductory no-choice statement; pp. 1–2, chain types and forward or reversed pairings. The article independently proves its alternative complement pairing.

Course issued by Massachusetts Institute of Technology and hosted by MIT OpenCourseWare. Fall 2010 is the course term, not an independently verified publication or revision date of each resource. No course-wide author byline is assigned.