Abstract
The corpus’s “form” looks as though it were one style, fixed from the start. This paper shows that there are several habits, each adopted at its own time—and the adoption curves can be measured. No new theorem or law is claimed.
First, there are $\mathbf{498}$ numbered papers and $\mathbf{3078}$ directed internal citations—forming a single component of diameter $5$ and mean shortest path $\mathbf{2.7265}$ (Section 2).
Second, $\mathbf{344}$ papers contain the word “separator”, $\mathbf{1462}$ times in all, and $\mathbf{280}$ carry it in a section heading (Section 3).
Third, this is the core of the paper. Its adoption runs $\mathbf{5.05}\to41.00\to99.00\to100.00\to\mathbf{100.00}$ per cent by band, strictly monotone, with no band falling (Section 3).
Fourth, the disclaimer traces a different curve—$4$ papers in $1$--$100$, $99$ in $401$--$499$, and $\mathbf{75.30}$ per cent overall (Section 4).
Fifth, $\mathbf{186}$ papers cite Paper 300, but $\mathbf{401}$ contain the phrase “distinct root”—the phrase spread first (Section 4).
Sixth, the separator is whether the form is one style or several overlapping habits (Section 5).
Keywords: corpus census, adoption of practices, separator, scope note, bibliometrics.
Scope (what is not claimed)
No new theorem or law is claimed—this is a census, and what is measured is the corpus itself. No stylistics—whether the habits are good, or how they compare with other ways of writing, is not the subject; only when each was adopted. Counting is by string match—papers are counted by whether they contain the word “separator”, so papers doing the same work under another name are not counted. The adoption rates are lower bounds. Revisions cannot be traced—only the versions now on disk are examined, so a separator added in revision is not distinguished from one present from the start. The English texts were not counted—only the Japanese bodies were scanned. Relation to earlier papers: Paper 300 showed that a shared root can be decided—this paper measures how far that criterion spread. Paper 481 counted that a refutation can be blamed on any assumption, and that $k-1$ separators make the blame unique—this paper counts how many the corpus actually wrote. Papers 100, 200 and 400 are censuses of the same type—this is the fifth. Paper 94 showed that “dimension” is not one thing—the same shape is applied here to the corpus’s own form. What is added is giving the adoption of the separator across five bands, confirming it strictly monotone and saturating in the third, showing that the disclaimer traces a different curve, showing that “distinct root” is more widely distributed than citations of Paper 300, and re-measuring the citation graph at $498$ papers.
1. Notation and the Question
Setting: Numbered folders are matched by $\hat{}(\backslash d\{1,3\})\_$ and their Japanese bodies scanned. The scanner was self-tested on words whose counts are known before being run. “Golden ratio” gives $3$ papers and “contact angle” $2$, both matching. “Dimensional analysis” stood at $29$ papers when $478$ existed and stands at $30$ now, the one addition falling inside this batch.
Observation 1.1 The corpus’s “form” looks as though it were one style, fixed from the start. Abstract, scope note, separator, census—one template, runs the picture.
Observation 1.2 But that is an impression taken from the recent papers. The early ones lack some of these habits—and when each entered can be counted.
Question: Is the form one habit or several, and when was each adopted.
2. The Size of the Corpus
Computation 2.1: Measure the citation graph over $498$ papers.
| Quantity | Value |
|---|---|
| Nodes (numbered papers) | $\mathbf{498}$ |
| Directed internal citations | $\mathbf{3078}$ |
| Mean degree | $12.2048$ |
| Connected components | $1$ ($100.00$ per cent) |
| Diameter | $5$ |
| Mean shortest path | $\mathbf{2.7265}$ |
| Clustering coefficient | $0.327570$ ($13.34$ times random at the same density) |
Observation 2.2 Not one paper is isolated. One component at $100.00$ per cent—any paper reaches any other in $2.7265$ steps on average.
Observation 2.3 Only two papers cite nothing. Papers 1 and 2—the foundation; every other paper cites some other.
Observation 2.4 $52$ papers have never been cited. $10.4$ per cent of the whole—a tenth are leaves, and these are mostly the recent ones.
Observation 2.5 The spine is Paper 300. $\mathbf{186}$ citations—against $74$ for Paper 100 in second place and $73$ for Paper 95 in third: the first stands well clear.
Observation 2.6 The citation distribution departs from a power law. Slope $-0.9414$, $R^{2}=0.875851$—the fit predicts $490.7$ at rank $1$ against a measured $186$, an over-prediction by a factor of $2.6$.
Observation 2.7 A balanced bisection cuts $134$ edges. $4.41$ per cent of the $3039$ undirected edges, splitting $328$ against $170$—with $\lambda_{2}=0.564549$: not hard to cut.
3. The Census of Separators
Computation 3.1: Count the word “separator”.
| Counting | Value |
|---|---|
| Papers containing it | $\mathbf{344}$ |
| Total occurrences | $\mathbf{1462}$ |
| Papers with it in a section heading | $\mathbf{280}$ |
Computation 3.2: Give the adoption rate by number band.
| Band | Papers writing a separator | Share |
|---|---|---|
| $1$--$100$ | $5$ of $99$ | $\mathbf{5.05}$ per cent |
| $101$--$200$ | $41$ of $100$ | $41.00$ per cent |
| $201$--$300$ | $99$ of $100$ | $99.00$ per cent |
| $301$--$400$ | $100$ of $100$ | $100.00$ per cent |
| $401$--$499$ | $99$ of $99$ | $\mathbf{100.00}$ per cent |
Observation 3.3 No band falls. $5.05\to41.00\to99.00\to100.00\to100.00$—strictly monotone.
Observation 3.4 The first two bands differ by $8.1180$. From $5.05$ to $41.00$—not a gradual diffusion but a sharp adoption.
Observation 3.5 It saturates in the third band. $99.00$ per cent—by $201$--$300$, nearly every paper was writing one.
Observation 3.6 Fewer carry it in a heading than contain it. $280$ against $344$—$64$ papers write a separator in the body without giving it a section.
4. The Disclaimer Traces a Different Curve
Computation 4.1: Count phrasings of “no new theorem or law is claimed”.
| Counting | Value |
|---|---|
| Short form | $150$ |
| Long form (mathematical theorem, physical law) | $42$ |
| Either | $\mathbf{375}$ ($\mathbf{75.30}$ per cent) |
| In $1$--$100$ | $\mathbf{4}$ |
| In $401$--$499$ | $\mathbf{99}$ |
Observation 4.2 The curve differs from the separator’s. $4$ in $1$--$100$, $99$ in $401$--$499$—both denser later, but neither the rise nor the saturation matches.
Observation 4.3 It is not universal. $123$ papers lack it—the impression of a single settled form comes from looking only at the later half.
Computation 4.4: Count the spread of Paper 300’s criterion two ways.
| Counting | Value |
|---|---|
| Papers citing Paper 300 | $\mathbf{186}$ |
| Papers containing “distinct root” | $\mathbf{401}$ |
Observation 4.5 The phrase is more than twice as widespread. $401$ against $186$—it has spread ahead of the citation.
Observation 4.6 So “Paper 300 created the method” cannot be asserted. The phrase may have come first—what was counted is a distribution, not an origin.
Observation 4.7 All $21$ papers of this batch ($479$--$499$) write a separator. $18$ cite Paper 481 and $20$ cite Paper 300—all $21$ also carry “to be honest”, which stands at $150$ papers, or $30.12$ per cent, across the whole corpus. Paper 499, immediately preceding, is one of them: having shown that four classical measurements do not respond to a one-way anisotropy, it writes that four cases returning zero is no proof that there is no fifth.
5. The Separator
The separator: is the form one style, or several overlapping habits.
Observation 5.1 One style, and adoption should have one date. A single switch somewhere—but the separator and the disclaimer trace different curves.
Observation 5.2 Several habits, and each is separately measurable. The separator saturates in the third band; the disclaimer stops at $75.30$ per cent—and they were indeed measured separately.
Observation 5.3 The two are distinct roots by the criterion of Paper 300. Both are called “the corpus’s form”—one a habit of writing what separates, the other of writing what is not claimed: different functions.
Observation 5.4 Returning to the count of Paper 481, the separator is the tool that narrows blame. $2^{k}-1$ candidates for $k$ assumptions, unique after $k-1$—the corpus has written at least the first of them in $344$ papers.
Observation 5.5 The disclaimer narrows nothing. It only states what is not claimed—armour, not a separator.
Observation 5.6 So “the form is settled” conflates two things. They were adopted at different times—applying to the corpus’s own form the shape with which Paper 94 split “dimension”.
Observation 5.7 To be honest—the counting is by string match. Whether the word “separator” appears—papers doing the same work under another name are not counted, so the rates are lower bounds. And only the versions now on disk are examined, so a separator added in revision is not distinguished from one present from the start; the early figure of $5.05$ per cent can move in either sense.
6. Roll Call and Closing
- $498$ papers, $3078$ directed citations (Computation 2.1): one component, diameter $5$.
- Mean shortest path $2.7265$ (Observation 2.2): no isolated paper.
- The spine is Paper 300 at $186$ (Observation 2.5): well clear of $74$.
- $344$ papers contain a separator (Computation 3.1): $1462$ occurrences.
- Adoption $5.05\to41.00\to99.00\to100.00\to100.00$ (Computation 3.2): the core.
- No band falls (Observation 3.3): strictly monotone.
- Saturating in the third band (Observation 3.5): nearly all by $201$--$300$.
- The disclaimer at $75.30$ per cent (Computation 4.1): a different curve.
- “Distinct root” $401$ against $186$ (Observation 4.5): the phrase is wider.
- Counted by string match (Observation 5.7): the rates are lower bounds.
Closing: The corpus’s “form” looks as though it were one style, fixed from the start—abstract, scope note, separator, census: one template. But that is an impression taken from the recent papers; the early ones lack some of these habits, and when each entered can be counted. The size of the corpus—there are $\mathbf{498}$ numbered papers and $\mathbf{3078}$ directed internal citations, at a mean degree of $12.2048$. They form a single component at $100.00$ per cent, of diameter $5$ and mean shortest path $\mathbf{2.7265}$, with not one paper isolated. Only Papers 1 and 2 cite nothing; every other cites some other. $52$ papers have never been cited, $10.4$ per cent of the whole, and these are mostly the recent ones. The spine is Paper 300 with $\mathbf{186}$ citations, against $74$ for Paper 100 and $73$ for Paper 95. The distribution departs from a power law: slope $-0.9414$, $R^{2}=0.875851$, with rank $1$ predicted at $490.7$ against a measured $186$. A balanced bisection cuts $134$ of the $3039$ undirected edges, $4.41$ per cent, splitting $328$ against $170$, with $\lambda_{2}=0.564549$. The census of separators—$\mathbf{344}$ papers contain the word, $\mathbf{1462}$ times in all, and $\mathbf{280}$ carry it in a section heading. Adoption by band runs $\mathbf{5.05}$, $41.00$, $99.00$, $100.00$ and $\mathbf{100.00}$ per cent, with no band falling: strictly monotone. The first two bands differ by $8.1180$, so this is not a gradual diffusion but a sharp adoption. It saturates at $99.00$ per cent in the third band, meaning that by $201$--$300$ nearly every paper was writing one. Fewer carry it in a heading, $280$ against $344$, so $64$ papers write one in the body without giving it a section. The disclaimer traces a different curve—$\mathbf{375}$ papers carry a form of “no new theorem or law is claimed”, $\mathbf{75.30}$ per cent, with $4$ in $1$--$100$ and $99$ in $401$--$499$. Both habits are denser later, but neither the rise nor the saturation matches the separator’s. $123$ papers lack it, so the impression of a single settled form comes from looking only at the later half. $\mathbf{186}$ papers cite Paper 300 while $\mathbf{401}$ contain “distinct root”: the phrase is more than twice as widespread and has spread ahead of the citation. So “Paper 300 created the method” cannot be asserted—the phrase may have come first, and what was counted is a distribution, not an origin. All $21$ papers of this batch write a separator, $18$ cite Paper 481 and $20$ cite Paper 300, and all $21$ carry “to be honest”, which across the whole corpus stands at $150$ papers or $30.12$ per cent. One thing separates them—is the form one style, or several overlapping habits. One style, and adoption should have one date, a single switch somewhere—but the two curves differ. Several habits, and each is separately measurable: the separator saturates in the third band while the disclaimer stops at $75.30$ per cent. The two are distinct roots by the criterion of Paper 300: both are called “the corpus’s form”, but one is a habit of writing what separates and the other of writing what is not claimed. Returning to the count of Paper 481, the separator narrows blame—$2^{k}-1$ candidates, unique after $k-1$—and the corpus has written at least the first of them in $344$ papers. The disclaimer narrows nothing, stating only what is not claimed: armour, not a separator. So “the form is settled” conflates two things adopted at different times, applying to the corpus’s own form the shape with which Paper 94 split “dimension”. To be honest—the counting is by string match, on whether the word “separator” appears, so papers doing the same work under another name are not counted and the rates are lower bounds. Only the versions now on disk are examined, so a separator added in revision is not distinguished from one present from the start, and the early figure of $5.05$ per cent can move in either sense.
References
- Newman, M. E. J. (2010). Networks: An Introduction. Oxford University Press.
- Blondel, V. D., Guillaume, J.-L., Lambiotte, R., & Lefebvre, E. (2008). Fast Unfolding of Communities in Large Networks. Journal of Statistical Mechanics.
- Clauset, A., Shalizi, C. R., & Newman, M. E. J. (2009). Power-Law Distributions in Empirical Data. SIAM Review.
- Yamagishi, Y. (2026). “Dimension” Is Not One Thing [Paper 94]. Zenodo. 10.5281/zenodo.21758581
- Yamagishi, Y. (2026). Convention and Fact: Poincaré’s Conventionalism and the Corpus’s “Scaffolding” (the Defined Value of $c$, Unit Conventions) [Paper 95]. Zenodo. 10.5281/zenodo.21758621
- Yamagishi, Y. (2026). The Crossing of Royal Roads: A Census of Structural Interpretation (Papers 63--99), and the One Discipline of “One Word, Distinct Roots” [Paper 100]. Zenodo. 10.5281/zenodo.21758864
- Yamagishi, Y. (2026). The Three Hundredth Census: Whether Two Things Share a Root Is Decidable [Paper 300]. Zenodo. 10.5281/zenodo.22171914
- Yamagishi, Y. (2026). A Broken Law Can Be Blamed on Any of the Assumptions [Paper 481]. Zenodo. 10.5281/zenodo.22733927
- Yamagishi, Y. (2026). Not One of the Four Classical Measurements of the Speed of Light Measures One Way [Paper 499]. Zenodo. 10.5281/zenodo.22760231
Reference
Yamagishi, Y. (2026). The Five Hundredth Census: The Corpus’s Method Is Not One Habit, and Each Was Adopted at Its Own Time [Paper 500]. YOI: https://www.yamagishiyuuki.com/yoi/500
DOI: 10.5281/zenodo.22760262
ORCID: 0009-0006-8587-3450
PDF (English) · PDF (Japanese) · Date proof of the English PDF (OpenTimestamps .ots) · SHA256SUMS
The record page for this paper (in Japanese, with the PDFs in each language and the date proof): YOI 500. This paper is a preprint and has not been peer reviewed.