Where is that claim written down?

The same result can have a different history

A modern program may reproduce the value found in a manuscript while using a method the historical author never wrote. Each calculator therefore states whether it presents a source-attested procedure, a modern equivalent, a teaching reconstruction, or a comparative extension.

National Diet Library: “Mathematics in the Edo Period”

The National Diet Library’s digital exhibition provides accessible introductions to Chinese influence, tengenjutsu, Seki, circles, numerical calculation, and sangaku. It is a reliable orientation, not a substitute for reading a specific manuscript or critical edition when a claim depends on the exact wording.

Manuscripts, holdings, and critical scholarship

When this site discusses the exact layout of a table, an unusual character, a sequence of operations, or whether a name appears in a source, the ideal evidence is the relevant page image. Catalog records establish that an item exists; they do not by themselves establish every claim about its contents.

Modern studies by historians and mathematicians are cited for transcriptions, interpretations, and comparisons. A later reconstruction remains attributable to that researcher even when the computation is reproduced here.

Compare a procedure with the history claimed for it

A formula can be checked algebraically or numerically. A historical attribution asks a different question: who wrote it, in what form, in which document, and when? Passing the first test does not pass the second.

• VERIFIED: proved or exhaustively checked in the present research.
• ATTRIBUTED: tied to a primary source or identified scholarly publication.
• UNRESOLVED: competing interpretations remain open.
• UNVERIFIED: a source has been identified but not yet inspected closely enough here.

Small differences are evidence

Two arrangements may agree through order four and diverge at order five. Two dates may differ because one source gives an era date and another a Gregorian conversion—or because scholarship genuinely disagrees. Variant readings, characters, signs, and representative choices are not discarded merely to make a diagram look tidy.

Use exact and approximate results differently

An exact rational value can be checked by substitution. A decimal approximation needs a stated error model. Some tools provide certified rational intervals; others provide floating-point estimates and residuals. The number of displayed digits is not, by itself, a guarantee of accuracy.

Clear language, careful qualifications

Plain English should make distinctions easier to see, not erase them. Dates with competing sources, uncertain name readings, direct and indirect lineages, and historical versus modern methods are therefore explained at the point where a reader needs them.

Sources for integers, counting, and numerical tables

Several topics in the calculator collection have different historical statuses. These links are starting points for the source trail; a modern research paper is not treated as the same level of evidence as the original historical document.

• Sanpō Tenzan Shinanroku commentary — stacked sums such as square and cubic stacks.
• Kyoto University repository research — jiyaku and the study of prime numbers.
• Mathematical Society of Japan public lecture material — Kurushima Yoshihiro and number theory.
• National Diet Library: trigonometric tables and logarithm tables.
• Yamagata University: Sanpō Chikusakujutsu — exhaustive enumeration.
• Dou, Hwang & Li (2022) — a peer-reviewed modern study of Matsunaga, Arima, Genjikō combinatorics, and the sequence now called the Bell numbers.

Each calculator separately identifies what is source-attested, what comes from later scholarship, and what is a modern reconstruction or comparison.