Log — Mathematics Wiki

Append-only history. Entries start with ## [YYYY-MM-DD] <op> | <title>.

[2026-08-02] split | mathematics-wiki created from _inbox (3 sources)

Scaffolded from ../CLAUDE.template.md when mcmullen-probability-theory arrived over Telegram and completed a cluster the hub _inbox had already predicted. The two parked records did the analytical work before this spoke existed: fourier-analysis-for-beginners (2026-07-28) argued that Fourier analysis is infrastructure beneath four spokes and the subject of none, and set the trigger at three; vector-calculus-corral (2026-07-29) made the same argument for calculus, tallied two, and listed the shapes a third could take — with probability/statistics among them. The trigger source was the second item on that list.

Migrated sources. Three, under three different _inbox tags (mathematics, signal-processing, and the arriving course):

The Thibos PDF was git mv'd out of _inbox/ (it arrived over Telegram with no URL, so the held copy is the only one). Corral was re-fetched from mecmath.net, which returns HTTP 406 to curl's default user-agent and serves the file to a browser one — noted on the source page so a future refetch failure isn't read as a dead link. Both _inbox records deleted.

Pages. Three source summaries, four concepts (mathematics, probability-theory, vector-calculus, fourier-analysis), and six entities: curtis-mcmullen, michael-corral, larry-thibos, harvard-university, indiana-university, schoolcraft-college. entity-index matched none of them (the university-of-cambridge hits on Harvard and Indiana are the fuzzy matcher catching the word "University"). Two entity nodes per ingested source, well inside budget.

The naming question is open and recorded. The parked record flagged the fork — mathematics (the subject) versus quantitative methods (the use) — before the split. Called mathematics on the two-out-of-three: Corral and McMullen are unambiguously teaching the subject, and Thibos would sit in either. synthesis carries it as open question 1 so the next few sources settle it rather than the name deciding for them.

A deliberate non-move. ../machine-learning-wiki received information-theory-inference-learning-algorithms (MacKay) hours before this spoke existed, and roughly half of it is compression and coding theory that no spoke claimed at the time. The routing stands — it was correct on dominant substance and re-filing it now would be churn — but information and coding theory as a subject belongs here, and the CLAUDE.md scope boundary says the next such source lands here rather than dragging the first one over.

Founding weaknesses, recorded rather than discovered later. Every page rests on exactly one source; nothing is corroborated. There is no linear algebra and no analysis, which are the two largest holes under all three founding subjects. And the corpus's provenance ranking runs opposite to its usefulness ranking — the T1 Harvard notes are the least self-sufficient of the three, the community-college text the most complete. synthesis makes both the founding tension.

avoid-ai-writing run over the founding prose. Site rebuilt + verified at the clean rung, as the hub requires for a split.

[2026-08-02] ingest | Elementary Calculus: An Infinitesimal Approach (Keisler, 1976/1986)

Arrived over Telegram the same afternoon the spoke was created, routed here by the hub. T1 — commercially published twice (Prindle, Weber & Schmidt 1976 and 1986; Dover third edition 2012), free online under CC BY-NC-SA since 2002, by a research mathematician. Held at raw/keisler-elementary-calculus.pdf (28.8 MB).

Reading it took work worth recording. The file is a 992-page scan with no text layer — pypdf returns empty strings for every page except the copyright notice. The first download truncated at 24.6 MB against a stated 28.8 MB and produced a corrupt PDF; a resumed fetch (curl -C -) fixed it. pdftoppm is unavailable on this device and there is no root to install poppler, so the front matter was read by extracting the embedded CCITT-G4 page images with pypdf, converting them to PNG with Pillow, and reading those visually. The author's own calc.html supplied the edition and licence history. Method noted so the next scanned book doesn't get parked as unreadable.

Pages. Source summary keisler-elementary-calculus plus one concept, infinitesimal-calculus. Updated vector-calculus (it now has two accounts), mathematics (four texts, and the analysis hole is partly filled), index and synthesis. Entities h-jerome-keisler and university-of-wisconsin-madison created; entity-index matched neither. Abraham Robinson and Sister Kathleen Sullivan are subjects of the book rather than agents around it, so they stay prose mentions per ../ENTITIES.md.

This is the ingest that gave the spoke something to argue about. Keisler's chapters 10–13 cover corral-vector-calculus's entire book — gradients, line integrals, Green's, Stokes, Gauss — so the corpus has its first corroboration. It also has its first disagreement, and the two are the same event: Corral assumes the limit-based Calculus I/II sequence as prerequisite, Keisler rebuilds it on hyperreals and defers limits to chapter 5. Recorded in synthesis as a foundational fork, stated carefully — the theorems agree, the pedagogy does not, and this is not a contradiction about mathematics.

Two more things the source changed. It breaks the spoke's founding rigour-spectrum thesis: the other three sit at different points on one axis, and Keisler moves off the axis entirely by changing the foundation and claiming accessibility and rigour together. And it is the only source here with evidence for its pedagogy — a 1972–74 controlled experiment across five schools, in a Wisconsin PhD thesis and the American Mathematical Monthly — cited second-hand by the author in his own preface, which is weighed rather than taken at face value.

Open question 1 moved. The mathematics-versus-quantitative-methods naming call is now three of four; an argument about a subject's foundations is not a quantitative method. Left open for one more source rather than closed.

Content-only, no page moves — verify deferred per the hub's standing policy. avoid-ai-writing run over the new prose.

[2026-08-04] ingest | Hefferon, Linear Algebra (4th ed. 2020) — via research pass

Closes the spoke's largest hole (synthesis open question 4 / growth edge 1): linear algebra sat under every text in the corpus and was the subject of none. Hunted against the hub's ## Most wanted entry "mathematics-wiki · linear algebra + analysis". T1.

Six pages, three of them new subject nodes: hefferon-linear-algebra (source, T1), jim-hefferon (Person), university-of-vermont (CollegeOrUniversity), and the linear-algebra concept page the index's DefinedTerm group wanted.

The tier is argued on the page rather than asserted, because this corpus has already had one fight about grading. Free licence, free price and a LaTeX-on-Linux production stack are exactly what corral-vector-calculus has and they are not what earns the T1 — the MAA Solow Award (2020) does, being peer judgement in the sense the ladder means. That separation is the useful result: it makes licence and provenance independent axes, where the founding four had them confounded.

Hefferon also lands a third position on the rigour axis this spoke tracks. He proves everything and asks only one semester of calculus, paying for it in length rather than in omitted proofs — which is an argument that the rigour-versus-reach trade-off the corpus recorded is partly an artefact of page count. Noted in linear-algebra and folded into the provenance-versus-usefulness tension, which is weakened rather than withdrawn: this is the first source here where tier and reader value point the same way.

[2026-08-04] ingest | Trench, Introduction to Real Analysis (free ed. 2013) — via research pass

The second half of the same edge, and the spoke's second T1. Four pages: trench-real-analysis (source), william-trench (Person), trinity-university (CollegeOrUniversity), real-analysis (concept).

T1 on different grounds from Hefferon's — the book was a Pearson Education title before Trench reissued it free under CC BY-NC-SA once the rights reverted, so it carries a commercial publisher's review that the corpus's self-published texts do not. Two T1s earned two ways in one day is why the grading reasoning now sits on each page.

The interesting result is negative, and it goes to the foundational fork. Analysis is the course where the ε-δ choice stops being implicit — chapter 1 builds the reals from completeness and everything follows — so it is where an argument for the standard foundation would live if anyone were making one. Trench does not mention infinitesimals. That is a second text assuming the standard side and still nothing arguing it, which is a data point for Keisler's inertia thesis and none for the merit reading. Promoted to growth edge 3: the spoke now wants a text that considered non-standard analysis and declined it in print. Closing two edges made the third one worse, which is worth recording as such.

Chapters 5–7 also give the corpus multivariable calculus a third time (corral-vector-calculus, Keisler ch. 10–13, Trench ch. 5–7), all three agreeing on results.

[2026-08-04] ingest | Larsen & Marx, An Introduction to Mathematical Statistics and Its Applications (5th ed.)

Routed here by the hub (runner-up: none). T1 — Prentice Hall / Pearson, fifth edition across 31 years (1981, 1986, 2001, 2006, 2012), two university professors, LC record QA276.L314 2012. Same grounds as trench-real-analysis and stronger, since this is a current commercial edition rather than a reverted one.

Closes growth edge 4 — statistics and inference, open since the split. Six pages: larsen-marx-mathematical-statistics (source), mathematical-statistics (concept), richard-larsen and morris-marx (Person), vanderbilt-university and university-of-west-florida (CollegeOrUniversity). The subject list in CLAUDE.md and the wikis.md registry were both refreshed — they still advertised linear algebra, analysis and statistics as wanted, three days after two of them closed and hours before the third did.

Fetch note. The PDF is 11 MB and exceeded the fetcher's limit, so it was downloaded and its text extracted locally rather than skipped or stubbed. Title, authors, both institutions, publisher, edition history, copyright and the full fourteen-chapter table of contents are read from the file itself, not inferred from the filename.

What makes it worth more than a syllabus. Every chapter closes with "Taking a Second Look at Statistics" — short essays on how the machinery just taught misleads: statistical versus "practical" significance, how not to interpret a sample correlation coefficient, why samples are never "valid," outliers, Type II error. A text that spends a section per chapter undercutting itself is doing something no other source in this corpus does, and it is the natural counterpart to ../quant-trading-wiki's backtest-overfitting material.

It breaks the corpus's licence pattern, and that is recorded rather than smoothed. The other five texts are free by licence — GFDL, CC, or an author's own university web space. This one is © 2012 Pearson, all rights reserved, read from a PDF on an Emory course page. It is the first text here that is accessible without being freely licensed, two properties the corpus had been treating as one because they had always arrived together. New growth edge 5: a freely-licensed statistics text.

Two open questions moved. The origin-predicts-quality thread gains its sharpest case — a regional public university and a private research university co-authored one text, indistinguishably — and the institution and the publisher finally come apart, having been the same fact for five texts. And the research-methods fork, flagged in CLAUDE.md before the split and dormant since, is now live: this book contains ANOVA and randomized block designs, which is experimental design. Read as strengthening the mathematics side (it derives its distributions and proves its theorems, where a research-methods text would give protocols), but the next statistics source decides it.

[2026-08-06] ingest | Understanding Statistics and Experimental Design (hub-routed, Telegram, T1, open access)

Herzog, Francis & Clarke, Springer Learning Materials in Biosciences, 2019, 142pp, CC BY-NC 4.0. Arrived as a Springer PDF link; the direct PDF and the book page both 303'd to an auth endpoint, so the metadata came via firecrawl and the full text from a direct curl of the open-access PDF (146 pages).

Created herzog-understanding-statistics (Book, url-only, T1) plus four entity nodes: michael-herzog, gregory-francis, epfl, purdue-university — 4 of the 8 budget; Aaron Clarke (Bilkent) kept as a plain mention. Entity-index caution recorded on two pages: the index returned MATCH for "Michael Herzog"→michael-corral and "Purdue University"→university-of-cambridge, both false positives on name shape. New nodes created; the Herzog/Corral collision is noted on the page itself so a later pass does not "fix" it by merging.

Closed growth edge #5 (a freely-licensed statistics text) with the qualification kept: CC BY-NC is free to read and share but carries a non-commercial restriction that hefferon-linear-algebra and trench-real-analysis do not, so the edge is closed by the weaker kind of open.

mathematical-statistics refreshed in place rather than duplicated — it now names two accounts at two altitudes (Larsen & Marx derives the machinery; this teaches its use) and gained a section on the Test for Excess Success: sum the power across a set of studies and compare with the number of significant results. Precognition, ten experiments: 6.27 expected vs 9 reported, p = 0.058. Bystander effect, nineteen studies: 10.77 expected vs 10 reported, p = 0.76 — the test separates rather than condemns. Consequence recorded for the concept page: at moderate power, power becomes a parameter for reading someone else's result, not only for planning your own, and the authors state that replication cannot be the final arbiter unless power is very high.

Open question 5 (the research-methods fork) answered against the easy reading. That question said the next statistics source would decide the fork. This one has no derivations and spends a third of its length on research practice — by the question's own test it votes for the fork. Routed here anyway under the spoke's first-principles boundary rule, with the reasoning written into the synthesis rather than hidden, and a stated trigger: a second source of this shape should split the spoke, not generate another routing note.

Cross-spoke context noted on the source page, not fragmented: chapters 10–12 are the psychology replication crisis (Open Science Collaboration 36% of 97 studies; Amgen 47 of 53 cancer papers), which is ../psychology-wiki's standing caveat and the runner-up destination; the TES generalizes to any literature reporting many significant results, touching ../agentic-tooling-wiki and ../quant-trading-wiki.

[2026-08-06] ingest | Measurement Across the Sciences (Mari, Wilson & Maul — hub-routed, Telegram, URL-only, T1)

Springer, 2nd ed. 2023, 307pp, open access CC BY 4.0 — the corpus's first unrestricted open licence (Herzog is CC BY-NC; Keisler and Trench are NC-SA). Created source summary mari-measurement-across-sciences (Book, url-only, T1 — peer-reviewed monograph in the Springer Series in Measurement Science and Technology) and a new subject page measurement-theory, plus six entity nodes: luca-mari / mark-wilson / andrew-maul and liuc / uc-berkeley / uc-santa-barbara (first non-US institution and first engineering school in the corpus; two of the three authors sit in schools of education, not mathematics departments).

Substance. Four necessary conditions for a process to be a measurement (empirical · designed on purpose · input is a property of an object · output is values of that property), then several hundred pages hunting sufficient ones. Model-dependent realism as the position (ch. 4), taking parts of naive realism, operationalism and representationalism while rejecting their strong forms; two consequences worth recording because they contradict the usual account — measurement is not quantification, and a result is not a preexisting true value being transmitted. Ontology of properties and scale types (chs. 5–6), a general process model with the new Hexagon Framework for measurand identification (ch. 7), and a semiotic close (ch. 8). Temperature and reading-comprehension ability run as paired examples throughout, chosen to be as far apart as possible.

The most useful piece for this corpus is ch. 3's split: the physical sciences answer imperfect measurement with uncertainty (a set of compatible values, made portable by traceability to units), the human sciences with validity (does the procedure measure the intended construct). One question, two literatures, little contact. Folded into mathematical-statistics as a new "What happens before the data" section — inference begins once numbers exist, and nothing in Larsen & Marx or herzog-understanding-statistics asks whether the measurand was well defined.

Routing is arguable and recorded as such. This is the first source here that is not mathematics: it is measurement science and philosophy of measurement, with no theorem the spoke would otherwise hold. Carried on three grounds — no hub spoke owns measurement as a subject, at least three borrow it, and the spoke's boundary rule files a first-principles theory text here. ../psychology-wiki was runner-up (psychometrics/validity), ../philosophy-wiki declined (it owns philosophers and their systems, not philosophy of science). Opened open question 7 in synthesis.md, which reads this as evidence for the quantitative methods answer to open question 1 rather than as the research-methods fork of question 5 — the book sits under both. Condition to watch: a second measurement-science source makes a cluster the hub could spin out instead of a stretch this spoke absorbs.

Also refreshed mathematics, whose corpus table had been stale since 2026-08-04 (listed four texts and called linear algebra the largest hole after Hefferon closed it) — now eight texts across seven subjects, with the missing-subjects paragraph rewritten and a short "odd one out" note for measurement theory.

[2026-08-06] ingest | Elementary Probability, 2nd ed. (Stirzaker — hub-routed, Telegram, URL-only, T1)

Cambridge University Press, 2003, 538pp, © CUP — read from a PDF on ctanujit.org, a third-party teaching site whose right to host it is not established. Created source summary stirzaker-elementary-probability (Book, url-only, T1) plus david-stirzaker (Person) and university-of-oxford (CollegeOrUniversity). The shared URL carried an fbclid Facebook tracker, stripped before recording — the same shape as the mcmullen-probability-theory link, so both probability sources here arrived through a social share.

Second account of probability-theory, and a different kind of second account. The vector-calculus pair disagrees about foundations; this pair agrees about the mathematics and differs in how much the reader must supply — 98 terse pages with Feller assumed, against a self-contained course with worked examples, clustered exercises, end-of-chapter problems and solutions. Coverage overlaps heavily for six chapters, then Stirzaker continues into the material McMullen never reaches: martingales and optional stopping, Markov chains, the Poisson process, and the Wiener process and diffusions. Added a "Where the subject continues: stochastic processes" section to probability-theory for that layer, and widened the ../quant-trading-wiki cross-note — the second edition added Brownian motion because it underpins Black–Scholes, which is the first time this spoke's corpus reaches option-pricing mathematics from the theory side.

Pedagogy thread. Stirzaker defends the formal definition of probability "not because of high principles, but merely because the alternative intuitive approach seems to lead more students into errors" — Keisler's kind of argument, about student outcomes, reaching the opposite conclusion in a different subject and with no data behind it. Folded into the rigour-spectrum section of synthesis.md: both authors who argue their foundation choice argue it on pedagogy, not principle. Also noted that his chapter 0 opens on determinism and "what is probability really", then explicitly refuses to let the answer matter — McMullen's notes open the same way. Both probability texts here start with philosophy and then wall it off.

Licensing. Second in-copyright text in the corpus after larsen-marx-mathematical-statistics, and both exceptions to the free-by-licence pattern are commercially published probability/statistics books. Recorded on the page rather than smoothed over.

Spine updates: probability-theory (two new sections, header rewritten), mathematics (corpus table, nine texts), index.md (stale header note fixed — it still said only vector-calculus was doubled), synthesis.md (single-sourcing paragraph, rigour spectrum, open question 1).

[2026-08-08] ingest | Algebra 1: Groups, Rings, Fields and Arithmetic (Ramji Lal, Springer 2017)

Routed from the hub (Telegram). T1 — Springer academic textbook, Infosys Science Foundation Series (Mathematical Sciences), DOI 10.1007/978-981-10-4253-9, 11 chapters / ~433pp, volume one of three.

New pages: lal-algebra-1 (source summary), abstract-algebra (subject), plus entities ramji-lal, harish-chandra-research-institute, springer and infosys-science-foundation-series.

Closes growth edge 7 — abstract algebra and number theory, the last untouched subject on the list and the structural layer under linear-algebra. Partially: the edge asked for an open textbook and this one is commercial ($49.99 eBook / $89.99 hardcover), so the licence half is refiled as its own edge (8), together with the parts of algebra this volume does not reach — Galois theory, modules, representation theory, all in Lal's later volumes.

Provenance, stated on the page. The link that arrived was a scanned PDF on a file-sharing service. I documented the book from the publisher's own page — description, chapter list, pagination, series, price — and did not read the body. Every claim on the page is about the book's scope and position, none about the mathematics inside.

Folded into synthesis as "Paid first, free second." Statistics arrived paid (larsen-marx-mathematical-statistics) with an open text following two days later (herzog-understanding-statistics); algebra has now arrived paid. The point is about this wiki's own collection policy — a corpus that accepted only open licences would have neither subject today — and springer makes it from the publisher side, issuing both the paywalled algebra text and the open-access statistics one.

Structural note worth keeping: Lal puts two chapters of logic and set theory before any algebra. The spoke's foundations argument so far has been about which foundation to stand on (Keisler's infinitesimals, Stirzaker's formal definitions); this is a text that simply teaches the foundation first. A table of contents cannot say whether that works.

Entities: 4 created, 0 linked. entity-index matched "Springer" to behringer (music-tech) — a substring false positive, not a duplicate; the memory note about that failure mode holds.

[2026-08-08] ingest | Abstract Algebra: Theory and Applications (Thomas Judson) — research pull

Curator asked for depth on algebra beyond what lal-algebra-1's publisher page could support. The honest way to get it was a text I can actually read, so I pulled judson-abstract-algebra (GNU FDL, maintained since 1997, 23 chapters) — T1, read from the 2012 PDF mirrored on a Colorado State course page since abstract.ups.edu was unreachable from this host.

Closes growth edge 8 the same day it opened. Edge 8 (an open-licensed algebra text) was created hours earlier when lal-algebra-1 closed the subject and left the licence half unmet. Judson also carries Galois theory to the fundamental theorem, which Lal defers to a later volume. What remains open in algebra: modules and representation theory, in neither book.

New pages: judson-abstract-algebra, group-theory, plus entities thomas-judson and stephen-f-austin-state-university. abstract-algebra rewritten to rest on read definitions — the group axioms, and the ring → commutative ring → integral domain → division ring → field hierarchy with the separating examples (ℤ a domain but not a field, ℤ₁₂'s zero divisors 3·4 ≡ 0, 2×2 matrices as a noncommutative ring, the quaternions as a noncommutative division ring).

lal-algebra-1 enriched with its eleven public chapter abstracts — Springer's own metadata, not the chapters. They fix the scope precisely: Zermelo–Fraenkel with choice over Gödel–Bernays, number systems from Peano's axioms, Lagrange and the isomorphism theorems, permutation and matrix groups as "the two main sources of groups", Sylow, Schreier/Jordan–Hölder, Remak–Krull–Schmidt, quadratic reciprocity.

Synthesis records what the pair buys: the corpus's first subject to arrive with two treatments that disagree about what a first course is for — foundations-first and classification-heavy (Lal) against applications-forward and Galois-complete (Judson), with Judson stating the reason in his preface (applications motivate students meeting rigorous proof for the first time). That is this corpus's recurring unmeasured pedagogical argument, now about content selection rather than rigour.

Standing asymmetry, recorded on every page that compares them: Judson's body was read, Lal's was not. Comparisons are of stated scope, not of exposition.

Entities: 2 created.

[2026-08-10] ingest | A Course in Game Theory (Osborne & Rubinstein, 1994)

Routed from the hub — a 372-page Internet Archive scan of the MIT Press graduate text, sent by the curator over Telegram. T1, held in raw/ and read directly (preface, Chapter 1, the Chapter 2 and 3 definitions, and the full table of contents; the OCR mangles symbols, so the source page quotes prose and paraphrases formulas).

A new subject, and a text that denies it belongs here. game-theory is the corpus's twelfth text and its tenth body of theory. The routing is straightforward under the boundary rule — a text teaching a body of theory from first principles, examples from economics — but the rule had to override the authors themselves for the first time. Osborne and Rubinstein state that they treat game theory "not as a branch of mathematics but as a social science," and that in principle the same book could be written "devoid of mathematics." They then give precise definitions and full proofs for 373 pages. Recorded in synthesis rather than argued away.

New pages: osborne-rubinstein-course-in-game-theory, game-theory, plus entities martin-j-osborne, ariel-rubinstein, mit-press, mcmaster-university, tel-aviv-university. mathematics table corrected — it had also fallen behind on abstract-algebra, which had a page but no row.

Two growth edges opened (12 and 13). The book assumes von Neumann–Morgenstern utility and Savage probability and explicitly declines to defend them, so game-theory rests on decision-theoretic foundations no page here states. And the authors name their own gaps: experimental game theory, and learning and evolution, two chapters they say they would add if writing now. Mechanism design is present only as Chapter 10's pure implementation theory.

Cross-spoke tension recorded, not resolved. The rationality assumptions are, in the authors' words, "under perpetual attack by experimental psychologists" — that attack is the heuristics-and-biases material in ../psychology-wiki, and nothing in this corpus can adjudicate between them.

Entities: 5 created.

[2026-08-10] ingest | Carroll, Geometric Function Theory — the corpus's first second course

Routed from the hub; a PDF, not a URL — sent to Telegram as a document, downloaded, extracted with pypdf locally per the standing rule, and the file placed in raw/carroll-geometric-function-theory.pdf. Springer 2024, SUMS, 358pp, ISBN 978-3-031-73726-8. T1, read in the original for structure, preface and scope rather than worked through — the page says so.

New pages: carroll-geometric-function-theory (source), complex-analysis (field), tom-carroll (author), university-college-cork (institution), springer-undergraduate-mathematics-series (series). springer updated in place — third title, and it lands in the middle of that node's access axis rather than at either end.

The finding, and it is about curricula rather than mathematics. Every text here so far teaches a first course, and the whole rigour-spectrum argument in synthesis is authors disagreeing about how to teach a syllabus none of them chose. Carroll's preface names why that was possible: there is "general agreement" on the first-course list, and "this consensus evaporates when it comes to a second course." Settledness is a property of a subject's first year, and it ends.

What he does about it: §1.4, "What Is Not in This Book" — an explicit non-goals section naming the omissions (curvature, conformal invariants past the hyperbolic metric, Riemann surfaces beyond the sphere, Denjoy–Wolff) and where each is treated properly. No other text in this corpus has one. The nearest comparison, coding-interview-university in ../engineering-education-wiki, announces exclusions too — but an exam dictates those and nothing dictates these.

A pedagogy result the corpus had been misattributing. 54 pages of complete worked solutions, and no computational tool assumed (no Sage, no Matlab). Both come from the SUMS series specification, so this is the first case here of a publisher setting pedagogy where the spoke had been reading such choices as authorial.

Two new growth edges (15, 16), and an admission with them: complex analysis was never on the edge list at all. The shelf ran calculus → analysis → algebra and skipped the complex plane through eight revisions of that list — which says something about the method, since edge-listing catches subjects the existing sources gesture at and misses the ones they never mention.

[2026-08-12] ingest | Illowsky & Dean, Introductory Statistics 2e (OpenStax)

Arrived via Telegram as a PDF link (assets.openstax.org); the URL carried Google-Analytics linker params (_gl=…), stripped before recording. Routed here by the hub: probability, statistical inference and the pedagogy around them are this spoke's domain. PDF held in raw/ as illowsky-introductory-statistics.pdf (23 MB, 847pp) and read locally with pypdf — front matter, full contents, and the preface in full.

Source: illowsky-introductory-statistics — OpenStax / Rice University, ©2026, CC BY-NC-SA 4.0, built 2026-04-20. Senior contributing authors Barbara Illowsky and Susan Dean of De Anza College; grown out of their earlier Collaborative Statistics. T1, whole text read.

New pages: 5. The source plus openstax, barbara-illowsky, susan-dean and de-anza-college. Updated: mathematical-statistics, synthesis, index.md.

What it gives the corpus. A rigour floor stated as policy rather than reached by omission: "focuses on statistics application over theory," for "students majoring in fields other than math or engineering," assuming intermediate algebra. It reaches confidence intervals, two-sample testing, chi-square, regression and one-way ANOVA with no calculus and no proofs. Against larsen-marx-mathematical-statistics on the same tests, that is the spoke's cleanest pairing yet on what a derivation is actually for — recorded on mathematical-statistics as two subjects sharing a vocabulary rather than as better and worse books.

The assumed-tool observation paid off. CLAUDE.md asks for the computational tool alongside the tier. Three data points now: carroll-geometric-function-theory assumes none and proves everything, judson-abstract-algebra assumes Sage and proves everything, this assumes a TI-83/84 and proves nothing. The calculator supplies the numbers a derivation would have justified.

A new publisher shape. Every prior open text here was author-released; openstax is institutional publishing with the licence applied at the end. The tell is in the preface: revisions keep problem numbering stable so online homework providers can move editions with minimal impact. No other source here reports downstream-integration pressure on a textbook. Also recorded: the licence is CC BY-NC-SA, so "free textbook" does not mean unrestricted reuse.

2e changes, stated: "currency, relevance, accuracy, and belonging" — several hundred edits on gender, race, ethnicity, age, academic status and societal issues; data and references refreshed; the mathematics unchanged.

Entities: 4 created, all new to the hub (no OpenStax, Illowsky, Dean or De Anza page existed anywhere before today).

[2026-08-13] ingest | Baggett — Analysis of Functions of a Single Variable

Routed here by the hub from a Telegram URL (spot.colorado.edu/~baggett/book.pdf, arriving with a Facebook tracking parameter, stripped before recording). PDF downloaded and read locally with pypdf — 233 pages, 229 numbered, dated 29 October 2006. Held in raw/ as baggett-analysis-single-variable.pdf. T1, no runner-up spoke: a mathematics textbook teaching a body of theory from first principles is this spoke's centre, not its boundary.

New pages: 3. baggett-analysis-single-variable, lawrence-baggett, university-of-colorado-boulder. Updated: complex-analysis, real-analysis, synthesis, index.md.

What it closes. Most of growth edge 15, the first course in complex analysis, opened three days ago by carroll-geometric-function-theory and described then as the largest hole any subject page here had. Chapter VII carries Cauchy's Theorem and Integral Formula, Taylor and Laurent, Liouville, the Fundamental Theorem of Algebra, Maximum Modulus, Open Mapping and the Residue Theorem. What is left of the edge is narrow and now stated precisely: the Argument Principle and Rouché's Theorem from Carroll's own list, plus conformal mapping, which nothing here holds.

The structural finding. The book refuses the real/complex split — "separating these two subjects does not at all jive with their development historically" — and cuts on dimension instead, staying with one variable throughout. That is perpendicular to how this spoke had organised the shelf, and it doubles two subject pages at once. Green's Theorem is proved in Chapter VI over plane regions specifically so Cauchy's Theorem can be deduced from it in Chapter VII, which is the join the design buys.

The pedagogy finding. Seven named truths in the preface, six of them proved over the book, and the definitional order arranged to make that possible: π defined as the smallest positive zero of sine, sine defined by a power series so arc length is not needed first, area defined only for regions between graphs of continuous functions so measure theory can be skipped. The cost shows: e^(iπ) = −1 cannot be had in Chapter III where the series already give exp(iz) = cos z + i sin z, and he says so. A third kind of pedagogical argument for the corpus — Keisler argues foundation, Corral and Illowsky argue rigour, Baggett argues the order of definitions.

Integrability, narrowed on purpose. Integrable = uniform limit of step functions, stated outright as a smaller class than the Riemann-integrable functions, taken to make uniform convergence carry more of the book.

Growth edge 3 got worse. The word infinitesimal appears nowhere in 229 pages, in the one text here that constructs ℝ from Dedekind cuts and proves the complete ordered field unique. Recorded on real-analysis and in synthesis → the foundational fork.

Licence, recorded honestly. The faculty-page PDF carries no licence notice. The same book was published through OpenStax CNX (col11249) under CC BY 3.0, and that is where the open licence comes from — see university-of-colorado-boulder for why the hosting arrangement is the corpus's least durable.

Entities: 2 created, both new to the hub — no Baggett or CU Boulder page existed in any spoke.

[2026-08-15] ingest | Information and coding theory — the half of MacKay's ITILA no spoke had written

A subject arrives without a book. At the curator's instruction ("build out the coding theory half in mathematics-wiki"), the coding and information half of information-theory-inference-learning-algorithms is now paged here. The book itself did not move: it stays in ../machine-learning-wiki, where the hub router sent it on 2026-08-02 on the machine-learning half of its substance, with the PDF in that spoke's raw/. Text extracted locally with pypdf (640 pages) and read for parts I, II, III and VI plus chapters 1, 11 and 13.

Eight pages written, all citing the source across the spoke boundary and all saying so in their second paragraph:

• information-theory — the field page. Slug shared with ../machine-learning-wiki, which is the documented dual-lens pattern and not a duplicate: the subject here, the learning lens there. Both pages now carry a "Which lens this is" note naming the sibling, and site/src/lib/valid-slugs.mjs gains ['information-theory', 'mathematics-wiki'] so a bare link from a third spoke resolves to the subject page.
• coding-theory — the constructive half: the very good / good / bad / practical taxonomy, why linearity is not the obstacle and decoding is (NP-complete), and MacKay's argument that the minimum-distance obsession costs exactly half the tolerable noise level (f_bd = f*/2).
• entropy — why the logarithm is forced by additivity rather than chosen, mutual information, and typicality as the law of large numbers applied to log 1/P(x).
• source-coding-theorem — the floor at NH bits; Kraft, Huffman's one-bit slack, arithmetic coding, and MacKay's verdict that Lempel–Ziv's universality theorem is asymptotically true and practically beside the point.
• noisy-channel-coding-theorem — capacity, the three parts, and the babies-on-a-weighing-machine proof that establishes existence and withholds construction.
• error-correcting-code — repetition and Hamming (7,4) as the baselines, concatenation, and the Voyager/Galileo state of the art the sparse-graph codes overtook.
• low-density-parity-check-code — invented 1962, ignored 33 years, rediscovered 1995; thresholds ((3,6) at f = 0.084 against a rate-½ Shannon limit of 0.11).
• fountain-code — rateless erasure coding; any K′ ≈ 1.05K drops, no feedback, no rate fixed in advance.

One entity: claude-shannon (Person), paged for his method as much as his results. No entity-index match — david-mackay already exists in the destination spoke of the book and was not duplicated here.

Tier. The source is T1 and was tiered so on the original ingest; nothing here re-tiers it. What is new is a structural weakness worth naming: this is the spoke's only subject whose depth depends on another spoke keeping its holdings. Recorded in synthesis as a dated section, and growth edge 6 is left open — the edge asked for a text landing here and none did.

Spine: mathematics gains an information-theory row explicitly marked as sourced elsewhere; index gains eight concepts, one person, and a header note that the Book section does not cover this subject; synthesis gains the dated section, an answer-in-part to open question 3, and the rewritten edge 6.

[2026-08-16] ingest | Stochastic processes — the subject opens (3 sources, research pass)

Curator-directed research arriving via Telegram: "research stochastic processes - basically the main field of mathematical finance." Routed here by the hub rather than to ../quant-trading-wiki on the standing boundary rule — the maths is the subject here, the market claim is the subject there.

Sources (3, all T1):

• lawler-stochastic-calculus — Gregory Lawler, Stochastic Calculus: An Introduction with Applications, © 2014, last revised 15 Feb 2023, 260pp, free from his university-of-chicago page. Body read (PDF extracted locally with pypdf; grep needs -a, the extraction carries NUL bytes and grep otherwise reports nothing on a file that does contain the string).
• gamarnik-advanced-stochastic-processes — MIT 15.070J, Fall 2013, CC BY-NC-SA. Read as a syllabus, not as notes: description + full lecture list.
• wu-introduction-stochastic-processes — MIT 18.445, Spring 2015, CC BY-NC-SA. Same, and the page says so.

New concept pages (5): stochastic-processes (subject home), markov-chain, martingale, brownian-motion, stochastic-calculus.

Entities (5): gregory-lawler, university-of-chicago, david-gamarnik, hao-wu, mit-opencourseware. massachusetts-institute-of-technology already exists in ../quant-trading-wiki and was linked, not duplicated — dedup halts the branch.

Spine: probability-theory now hands its "where the subject continues" section to the new pages; mathematics gains a corpus row and a sharper measure-theory note; index gains five concepts, three sources and five entities; synthesis gains the dated section Three entrances, one summit and a new ranked growth edge (17, measure theory).

The finding. Three sources, three incompatible entrances to one subject — finite Markov chains, discrete martingales, large deviations — and one agreed destination in Itô calculus. It is the second instance in this corpus of carroll-geometric-function-theory's complaint that consensus holds for the core of a subject and evaporates over the route in.

Two corrections made during the ingest, both against my own drafts: a claim that ../machine-learning-wiki's monte-carlo-methods rests on Markov chains, and one that ../quant-trading-wiki's market-regime-analysis assumes a Markov state. Neither page says any such thing — grep, not memory, settled it, and markov-chain now records the absence of the MCMC bridge at both ends as the honest version.

[2026-08-17] refresh | Understanding Statistics and Experimental Design (re-sent as direct PDF)

The curator sent the Springer PDF link; the book was already ingested on 2026-08-06 from the landing page. Re-seen-source rule applied — herzog-understanding-statistics refreshed in place, no second page. Downloaded and re-read with pypdf (146 pages incl. front matter). The pdf: URL is now recorded in frontmatter beside the canonical landing page.

The first pass took the TES worked examples and stopped at them. Chapter 11 answers the question they raise — a few bad papers, or a literature? — and that is what the refresh adds:

• The Science audit. 133 psychology/education research articles published 2005–2012; the 18 with four or more experiments and enough reported detail were TES-tested, and 15 of 18 (83%) come out too good to be true (success probability < 0.1), in a journal with a ~7% acceptance rate. Individual values run 0.002 to 0.957.
• The Stapel row. Disordered Contexts Promote Stereotyping was fabricated in a spreadsheet and fails TES like the rest. The authors' inference is the sharp one: a forger models fake data on the published literature, and the published literature carries the same signature — so the fraud is indistinguishable from the real thing because the real thing already looks wrong.
• Two computation-free diagnostics, which make the book's argument portable to any literature: effect size should not correlate with sample size (valid set r = 0.25 against r = −0.86 / −0.83, and −0.89 for the precognition studies — optional stopping stated backwards, since a sample can only get large when the effect came out small), and valid experiments produce very small p-values rather than a shelf of them between 0.02 and 0.05.
• The exercise that lands it. Three experiment sets; pooled effect sizes g* = 0.82 / 0.89 / 0.70 separate nothing, TES gives 0.042 / 0.45 / 0.052, and the valid one is the set with the middling replication record. Experienced scientists reportedly cannot pick it — so under publication bias and optional stopping, researchers often cannot tell no effect from a very large one.

synthesis.md open question 5 (the maths-vs-research-methods fork) updated: chapter 11 is a research-methods instrument rather than a theorem, so the book's centre of gravity moves further from the mathematics reading again. Routing still stands on the first-principles rule; recorded, not hidden. No new pages, no contradictions.

[2026-08-17] ingest | Grinberg — An introduction to graph theory (arXiv 2308.04512v3)

Routed here by the hub from Telegram (runner-up: none — no spoke owns graph theory, and this is a textbook teaching a body of theory from first principles, which is this spoke's own rule). PDF fetched from arXiv into raw/grinberg-graph-theory.pdf and read with pypdf — 454 pages. file reports it as 10 pages; that is wrong, and worth remembering next time a linearized PDF looks empty.

T1. darij-grinberg's own course text for Math 530 at drexel-university, Spring 2022; v1 August 2023, v3 of 7 June 2025, with a named errata channel and four people credited for corrections. Deposit on arXiv is not review and the arxiv page says so — the grade rests on authorship and revision history.

New pages: grinberg-graph-theory (source), graph-theory (field), matrix-tree-theorem (concept), darij-grinberg, drexel-university, arxiv (entities). Six pages, no dedup hits — a grep across all 36 spokes found "graph theory" only in a ../research-wiki page about proof counts and in this spoke's own McMullen notes.

What the ingest turned on:

• The prerequisite list decides the syllabus. "No analysis (or even calculus) is required anywhere in this text," and therefore no planarity and no four-colour theorem — both mentioned and both forwarded to another book, because proving K₅ non-planar "must use some analysis or topology." Recorded in synthesis.md as a third kind of pedagogical decision beside Keisler's (rigour) and Judson's (content selection), and the only one of the three that can be checked from inside the text.
• The corpus's first source off its own spine. Every other subject here descends from calculus or probability. This one imports one thing, determinants, and spends 65 pages cashing it in — matrix-tree-theorem, Cayley's n^(n−2) (Borchardt 1860, per Grinberg), BEST, de Bruijn sequences. Same move as markov-chain: a finite object handled as a matrix.
• First CC0 source, and the licence floor. A public-domain dedication, more permissive than mari-measurement-across-sciences (CC BY 4.0) and everything else free here. Both ends of the access axis are now occupied, nine days apart.
• No consensus at the first course either. ~25 rival textbooks named, and past the basics they "often cover different ground" — extending carroll-geometric-function-theory's finding from the second course to the first, in a subject most of whose material postdates 1950. §6.8 prints a 1971 conjecture proved in 2019 with the general form still open, and cites MathOverflow.

Growth edge 10 half closed. Graphs: covered past what a first course needs. Counting and recurrences: untouched, and the source keeps forwarding the reader elsewhere for them. Edge rewritten to name the residue (enumerative combinatorics; within graphs, planarity and random/extremal/spectral) rather than ticked off.

No contradictions with existing pages.

[2026-08-18] ingest | Klazar, Elementary Real Analysis (arXiv 2508.19405v14)

Routed by the hub from Telegram. 400pp PDF, CC BY 4.0, T1, freshness: volatile.

New pages: klazar-elementary-real-analysis (source), martin-klazar, jiri-matousek (Person), charles-university (CollegeOrUniversity). Updated: synthesis (growth edge 3), index. Downloaded and extracted locally with pypdf — 704 KB of text, searchable, which is what made the foundations check below possible.

Two things worth the ingest.

1. Four chapters are title pages. Newton, Riemann and Henstock–Kurzweil integrals plus applications — chapters 11 to 14 — are one page each, heading and page number. A four-hundred-page book called Elementary Real Analysis with no integration in it. Not concealed: the contents carry a per-section completeness marker, "(c … means a relatively complete section)", which no other text in this spoke offers. So it does not displace trench-real-analysis; it goes further down and has not come back up.

2. It is the fifth ε-δ assumer and the least excusable one. Growth edge 3 wants a text that argues for the standard foundation rather than adopting it. Klazar rebuilds ℕ₀, ℤ, ℚ, ℝ and ℝ* from ZFC with a characterization theorem each, derives induction as a theorem, calls his ℝ* result "completely new", writes an appendix section titled "How do we know that a theorem is true?", and opens by naming sixteen texts he means to beat. Full-text search: no Keisler, no Robinson, no hyperreals, no "non-standard analysis". Infinitesimal appears three times — twice defining what an Archimedean field excludes, once calling Cauchy's 1821 Cours d'analyse a textbook of infinitesimal calculus. The edge's note is updated to say the obvious thing: after this, inattention stops being a plausible explanation.

Also recorded. A combinatorialist's analysis book — Fekete's lemma, set series, Pólya generalized, Sierpiński, asymptotics of ordered partitions — and one passage that quotes Theorem I of §2.3 of Cauchy's Cours d'analyse and gives counterexamples to it. Structure is chapter → section → passage, with at least one exercise per passage and 37 pages of solutions. Dedicated to jiri-matousek, who was preparing the same course in 2014/15 when illness stopped him.

Licence: CC BY 4.0 — attribution only, more open than Trench (CC BY-NC-SA) and Herzog (CC BY-NC), short of grinberg-graph-theory's CC0. Second arXiv source here.

Entity note: entity-index returned Harvard, McMaster and Cornell as MATCH for "Charles University" — a fuzzy hit on the shared word. Checked by hand (ls */wiki/charles-university.md) before creating the node; the same false-match class as the vercel case recorded in the hub log.

[2026-08-22] ingest | Bergman, An Invitation to General Algebra and Universal Constructions (hub-routed, Telegram, T1)

george-bergman's Math 245 notes, uc-berkeley, version dated 2015-04-02, 551pp, © springer. PDF held in raw/bergman-invitation-general-algebra.pdf. URL arrived with a Facebook fbclid parameter — stripped before recording, so re-seen-source dedup will work.

Created bergman-invitation-general-algebra (Book, T1 — a published graduate text read from the author's own copy, body read for structure, front matter read in full).

Two new subject pages. universal-algebra — the rung above abstract-algebra: prove it about varieties, get groups/rings/lattices at once. category-theory — paged from ~180pp inside this book, with its limits stated on the page (no dedicated text here; monoidal categories, topoi and the homotopy side absent). Both link back into abstract-algebra, which now names the rung above it.

Entity: george-bergman created (Person). uc-berkeley and springer already existed and were linked, not duplicated.

What made it worth the space. A fourth kind of pedagogical argument for the spoke's pedagogy thread — not rigour (keisler-elementary-calculus), not content selection (judson-abstract-algebra), not prerequisites (grinberg-graph-theory), but what class time is for (the photocopying-machine passage, and the "question a day" mechanism that enforces the reading). Also: a text that names its own field's naming dispute; a stated prerequisite that is a test rather than a course list; a published difficulty map; and an author warning about the failure mode his own handwaving might cause. 629 exercises, no solutions, indexed by telegraphic description. 44 years of revision — the spoke's oldest continuously maintained text.

Boundary flagged, not decided. The spoke header lists seven subjects and names neither abstract algebra (paged 2026-08-08) nor general algebra / category theory (today). That is the second time the header has fallen behind; the 2026-08-04 widening set the precedent. Whether to widen it again is a curator call — raised with the curator, header left alone.

[2026-08-22] ingest | Bright, Edelman & Johnson, Matrix Calculus (for Machine Learning and Beyond) (hub-routed, Telegram, T1)

arxiv:2501.14787v1, 7 Jan 2025, 101pp, CC BY-NC-SA 4.0, PDF held in raw/edelman-johnson-matrix-calculus.pdf. Write-up of MIT 18.S096 / 18.063, the 16-hour IAP short course taught by alan-edelman and steven-g-johnson in January 2023, notes by paige-bright.

Created edelman-johnson-matrix-calculus (Book, T1) and the subject page matrix-calculus. Linked upward from vector-calculus and linear-algebra, which each gained a short section.

Entities: alan-edelman, steven-g-johnson, paige-bright created (thin). massachusetts-institute-of-technology linked cross-wiki to ../quant-trading-wiki — entity-index returned it at 1.00, so no duplicate was made. mit-opencourseware and arxiv already existed here. Julia recorded as prose, not a node: ENTITIES.md puts ProgrammingLanguage out of scope.

Why it earns its space. Three findings for standing threads. (1) The canon-edge thread gets its first source that treats the edge as a defect to fix rather than a fact to report — "it seems as though this sequence of material is being cut off arbitrarily", with Scalar → Vector → Matrices → Higher-Order Arrays named as the missing term and a syllabus attached. (2) The ε-δ vs infinitesimals tension gets its first text that uses differential notation and explicitly disclaims the infinitesimal reading — Remark 6, "δx is not an infinitesimal but rather a small number". Five texts here assume ε-δ silently; this one chooses it out loud. (3) The computational tool axis: Julia assumed, but with JAX equivalents given in Chapter 14, so the assumption is portable rather than silent.

Cross-spoke context, not split. The AD/backpropagation chapters are the seam to ../machine-learning-wiki; the source itself claims "modern automatic differentiation is more computer science than calculus." Recorded inside the source page and matrix-calculus rather than fragmented across spokes. arXiv agrees from outside: primary math.HO, cross-listed cs.LG / math.NA / stat.ML.

Also names its own omissions in a closing chapter (custom Jvp/vJp, Wirtinger calculus, the factorization literature) — the second text here to do that after carroll-geometric-function-theory.

[2026-08-30] ingest | Harju — Lecture Notes on Graph Theory

Routed here by the hub router from Telegram (runner-up: none — this is the boundary rule's clean case, a text teaching a body of theory from first principles). Model: claude-opus-5 · effort: high. The URL arrived with a Facebook fbclid tracking parameter; it was stripped before recording.

harju-graph-theory (T1, PDF downloaded and held in raw/harju-graph-theory.pdf, extracted locally with pypdf). Tero Harju's 98-page course notes from the University of Turku, title page "1994 – 2012", PDF produced 2014-04-24 by dvips/Ghostscript. No published: recorded — an eighteen-year span and a typesetting timestamp are not a publication date.

Why this is the ingest the graph-theory page was waiting for. That page ended with a warning that grinberg-graph-theory is "one route through the subject rather than its map," and named the missing corner: planarity and the four-colour theorem, dropped by Grinberg because their proofs need analysis or topology he keeps out of his prerequisites. Harju's Chapter 5, Graphs on Surfaces, is that corner — planar graphs, Kuratowski, Euler's formula, four- and five-colour, and genus — plus Ramsey theory (§4.2) and network flows (§6.2).

And it tests the claim rather than merely filling the hole. Harju agrees the topology is needed and answers it differently: "The geometry of the plane will be treated intuitively." He builds region and continuous curve by hand from open sets, then proceeds, omitting the genus form of Euler's formula and citing Mohar & Thomassen. So the mathematical claim is confirmed by the book that keeps the chapter — stronger evidence than the book that dropped it saying so — while the implication that the syllabus had to shrink is not. Two honest exits: protect rigour, or protect coverage.

Pedagogy contrast, recorded because this spoke's domain names exercise design. Grinberg: 116 numbered exercises, no solutions. Harju: no exercise sets at all — the word appears ten times in 98 pages, always inline ("Proof. Exercise."), with a few proofs omitted and cited instead (Cayley's formula, stable matchings, the genus formula).

Licence: none stated. Searched in full — no copyright notice, no licence. A PDF on a university web server. That is a third position on the access axis, distinct from both "paid, terms stated" and "free, terms stated," and it is the practical condition of most lecture notes.

New pages: harju-graph-theory, tero-harju (homepage as identifier — no Wikipedia or Wikidata entry found), university-of-turku (same-as Wikipedia + Wikidata Q501841 + utu.fi, all checked). Updated: graph-theory (new section "The second route"; still-missing list restated for two texts), index.md, synthesis.md (the 2026-08-17 syllabus-cut section gains a control; the access axis gains its third condition).

Note on tooling: entity-index again returned confident false matches — university-of-vermont at 0.71 for "University of Turku" — before correctly concluding "create new". The ranking is not usable as an identity judgment on its own.

[2026-09-05] route | Dynkin & Yushkevich, Markov Processes: Theorems and Problems (1969) → mathematics-wiki

Telegram arrival, from the sources directory of the Harvard course page that supplied mcmullen-probability-theory. Tracking parameters stripped from the URL before recording it.

The PDF is a 2020 tiff2pdf scan with no text layer — pypdf extracted nothing, which is a fact about the scan and not about the document. Read page by page as rendered images instead. Held at raw/dynkin-yushkevich-markov-processes.pdf; new page dynkin-yushkevich-markov-processes (T1).

Dedup: rg found no Dynkin page, no optimal-stopping page and no Dirichlet-problem page in any spoke; the only prior mention of the Dirichlet problem is one line on brownian-motion.

Why it is more than a fourth textbook. The spoke's stochastic cluster is three courses that disagree about the order and converge on Itô calculus (synthesis.md, Three entrances, one summit). This is not a course — it is organised by problem area, out of Dynkin's 1962–63 Moscow lectures — and it goes the opposite way. Chapter II proves the Dirichlet problem for the Laplace equation has a solution by probabilistic argument; Chapter IV derives boundary conditions for differential equations from the paths of a birth-and-death process. No finance in 245 pages. The section title in synthesis.md was a claim about three teaching sources, not about the field, and it is now marked as such.

Two positions the book states about other people, both kept because they date the ideas. Feller is "the pioneer in the application of the probabilistic approach to boundary problems" and is faulted for introducing his constructions "in purely analytical form" — which matters here because mcmullen-probability-theory is explicitly a companion to Feller, so the spoke holds both sides. And Doob (1954) derived the Dirichlet solution from Wiener paths "in a direction converse to our own." Two directions between the same two subjects, named in print by the people running them.

Growth edge 17 (measure theory) gains its fourth data point and stays open. The other three sources avoid measure theory by indenting it, teaching it in passing, or excluding it from the prerequisites; this one writes the avoidance into the foreword as a decision — "We have consciously avoided references in the main text to measure theory and measurability." Four sources, four avoidances, zero constructions.

Cross-spoke: Chapter III's optimal stopping runs from the secretary problem to optimal strategies for a Markov chain and the Wiener process. ../optimization-algorithms-wiki owns optimisation method; the probabilistic theory of stopping rules stays here with the process theory, noted on the page.

Updated: stochastic-processes, markov-chain, synthesis.md (the three-entrances section and edge 17), index.md.

[2026-09-09] ingest | Essential Math for AI (Hala Nelson, O'Reilly 2023)

Arrived via Telegram as an Amazon product link (tracking params lv/channelId/plpRedirect dropped; recorded url is the clean /dp/B0BRNYDGQR). Amazon's detail DOM is obfuscated, so bibliographic facts were confirmed against OpenLibrary: O'Reilly Media, 2023, ISBN-13 978-1-098-10763-5. Body not read — the page rests on the publisher description and chapter topics, and says so.

Source: nelson-essential-math-for-ai, T2 — a professionally published survey by a working mathematician, but explicitly a bridge "rather than dense academic theory," and unread here. Not T1 (not a first-principles development, body unseen); not T3 (specific, authored, real textbook). published: 2023-01 (year known, not the day).

Routing turned on the spoke's own boundary rule. Title and framing look like ../machine-learning-wiki — it is "math for AI," motivated end to end by CV/NLP/generative/RL/operations-research. But the rule is the maths is the subject here, the application is the subject there, and the book teaches the mathematics (regression, neural nets/convolution, optimization, probability, graphs/random walks, Markov processes, ODEs) rather than making a claim about a model. Same shape as thibos-fourier-analysis. Runner-up ML-wiki logged; the MacKay note applies (a maths text with an AI spine lands here, does not pull ITILA over).

Why it earned a synthesis section. It is the corpus's first text organized by application rather than by mathematical subject — chapters are "the math for convolution," not "a chapter of analysis." That is a new point on the organization axis, and the second source (with edelman-johnson-matrix-calculus) saying AI is pulling on the shape of the mathematics. It also extends the rigour floor: wider than illowsky-introductory-statistics or corral-vector-calculus and necessarily thinner.

Entities: hala-nelson paged thin (author; no identity URL verified at ingest, so no same-as claimed). oreilly-media created as the spoke's first trade publisher (same-as Wikipedia + Wikidata Q1065097, both checked), distinct from the academic springer/mit-press nodes.

Recorded as unverified: an Amazon "1045 pages" field is not trusted and left off; per-subject depth and whether the book derives or states are for a later reading of the body.

[2026-09-10] ingest | Algebra, Topology, Differential Calculus, and Optimization Theory (Gallier & Quaintance)

Arrived via Telegram as Gallier's "Books in Progress" landing page (cis.upenn.edu/~jean/gbooks/geomath.html). The page carries almost nothing — a title, two authors, a terms-and-conditions block and one link — so the PDF was downloaded and read: 24.6 MB, held in raw/gallier-quaintance-math-deep.pdf, table of contents and cover extracted with pypdf.

Source: gallier-quaintance-math-deep, T1 — a Penn full professor of computer science and mathematics developing the subject from first principles with complete proofs, published first-party. Not peer-reviewed as a book and openly unfinished; the tier grades what the source is.

Facts the landing page got wrong. It says "approx. 2192 pages (2023)" and is signed 2017-04-15. The PDF cover says April 14, 2025, the file's Last-Modified is 2025-04-15, and it is 2,204 pages counted. published: 2025-04-14 from the manuscript itself; the page count is counted, not quoted.

Pages: source summary; topology (new subject); entities jean-gallier (same-as Wikipedia + Wikidata Q29034984 + faculty page, all checked), jocelyn-quaintance (thin — cover page is the only evidence, no identity URL claimed, Wikidata search returns nothing), university-of-pennsylvania (same-as Wikipedia + Q49117 + upenn.edu). Updated linear-algebra (second account, at a second altitude), abstract-algebra (first modules and tensor algebra in the corpus), graph-theory (spectral side, reached from linear algebra), mathematics (map).

Synthesis: new section — the book is the direct counter-example to nelson-essential-math-for-ai, routed the day before. Same audience, opposite organization: subject order and proofs first, machine learning as the last chapters of the optimization part. Also breaks the one-book-one-subject pattern the spoke's map assumes, and adds a fourth access position (free to read, mirroring forbidden).

Boundary noted, not resolved. Roughly 700 pages are convex and nonlinear optimization — ../optimization-algorithms-wiki territory by keyword, and it holds convex-optimization and linear-programming pages already. Routed here on the spoke's own rule (theory from first principles is the subject here) and on dominant substance; runner-up logged at the hub. A second optimization-heavy text should be re-argued rather than filed by this precedent.

[2026-09-14] ingest | Bishop's review of Keisler (Bull. AMS 1977) — via research pass

Hunted against growth edge 3 (a text that argues for ε-δ). Source: bishop-review-keisler, T1, published: 1977-03; the review is paywalled at Project Euclid and was read in the passages quoted by the secondary literature — stated on the page. Edge 3 closed, successor 3a written (a modern text that argues the standard route). Synthesis section The foundation finally has a defender. keisler-elementary-calculus and real-analysis link to it. Halmos, Davis and Sullivan are named once and not paged.

[2026-09-17] ingest | An introduction to graph theory (Grinberg) — re-seen

Telegram (msg 2143) re-sent arXiv 2308.04512. Already held as grinberg-graph-theory (T1, ingested 2026-08-17 from the PDF). Refresh in place: listing re-read, still v3; date note added (arXiv 8 Jun vs PDF 7 Jun 2025). No new pages.

[2026-09-27] ingest | What does it mean to 'control' for variables? (Ramos, The Conversation)

Arrived pre-routed by the hub (runner-up ../machine-learning-wiki, logged there for the GLP-1/ health-records analysis pattern; kept here on the boundary rule — the piece teaches the general statistical distinction from first principles, the drug-trial material is illustration, not subject).

Source: ramos-controlling-variables, T2 — mark-louie-ramos (Penn State) in the-conversation, published: 2026-09-25. Editorially reviewed but not peer-reviewed, no citation trail of its own; usable for the statistical distinction it explains, not as evidence about GLP-1 drugs.

New page: confounding — the corpus's first page on study design and causal inference rather than inference machinery: experimental vs statistical control, stratification (renamed from larsen-marx-mathematical-statistics's randomized block designs, ch. 13, with a clinical-trial motivation), and the collider failure mode (new to the spoke — more controls can make an estimate worse).

Entities: mark-louie-ramos (thin; same-as his Conversation profile and Penn State faculty page, both checked, matching on title + department), pennsylvania-state-university (same-as Wikipedia + Wikidata Q49116, both checked), the-conversation (same-as Wikipedia + Wikidata Q17185145, both checked) — the spoke's first news-media publisher node.

Updated: mathematical-statistics (new section on confounding as the layer before inference), synthesis.md (growth-edge question 5, the research-methods fork — a third candidate, from a third genre, kept by the same rule), index.md.

[2026-10-03] ingest | Introduction to Vectors and Tensors, Vol. 2 (Bowen & Wang)

Arrived by Telegram as a local PDF, pre-routed by the hub (runner-ups ../physics-wiki, for possible applied use, and ../engineering-education-wiki; both declined on the boundary rule: the text is theory throughout, with no physical claim and no pedagogy about teaching). Held in raw/bowen-wang-vectors-tensors-vol-2.pdf; no URL.

Source: bowen-wang-vectors-tensors-vol-2, T2. 246pp, ISBN 0-306-37509-5 (v. 2). No year on the title page, so no published:; web search places it at Plenum 1976 with a 2009 Dover second edition. Pitched at a student past a first linear-algebra course; theorem and proof throughout. Equations garble in text extraction, so it was read from section openings, theorem statements and the index.

New pages: tensor-analysis, euclidean-manifold, differential-forms (dedup: rg over every spoke found no existing page on any of them). Entities: ray-bowen (same-as Wikipedia + Wikidata Q26236282, checked), c-c-wang (thin; no identifier checked), texas-am-university and rice-university (same-as Wikipedia + Wikidata, checked).

Updated: vector-calculus (a second "course after this one" section), linear-algebra, topology, mathematics (corpus table), synthesis.md (new section: the multivariable course gets a coordinate-free ending), index.md.

Gap-relevance: no open question closed. It opens a third direction off the calculus edge and leaves a prerequisite (Volume 1) unheld.

[2026-10-04] ingest | Algebra & Number Theory (Baker, Glasgow)

Arrived by Telegram as a URL, pre-routed by the hub (runner-up ../cryptography-wiki, noted as context only and not ingested there: the notes teach the number theory cryptography uses and never mention cryptography). Held in raw/baker-algebra-number-theory.pdf; URL recorded without the Facebook tracking parameter.

Source: baker-algebra-number-theory, T1 (author's own course notes), third-year level, 73pp, © 2009. Title page also carries "09/01/2018," ambiguous between two readings, so no published:. Read from headings, theorem statements and proofs; equations garble in extraction.

New pages: number-theory, cardinality-and-countability (dedup: rg over every spoke found no existing page on either; number theory previously appeared only inside abstract-algebra). Entities: andrew-baker (homepage checked, no Wikipedia entry, so no same-as), university-of-glasgow (same-as Wikipedia + Wikidata Q192775, checked).

Updated: group-theory (third route in: arithmetic first, group actions, Burnside), abstract-algebra, mathematics (corpus table), synthesis.md (new section: arithmetic before rings), index.md.

Gap-relevance: no ranked edge closes. Supplies number theory as a standalone subject and a third ordering of arithmetic and algebra.