Abstract
Paper 300 counted the corpus’s judgements of “shared root” and “different roots”, and recorded as a warning to itself that in the latest band more papers answered “shared root” while papers stating a criterion did not increase. It wrote that whether judgements resting on numerical agreement alone had crept in ought to be checked. This paper carries out that check on the $299$ papers since ($301$--$599$). No new theorem or law is claimed.
First, citing Paper 300 became almost a fixed custom——it is cited by $88.00$ per cent of papers in $301$--$400$, $99.00$ per cent in $401$--$500$ and $97.98$ per cent in $501$--$599$ (Section 2).
Second, answers of “shared root” rose sharply in the last band——papers answering “shared root” in a sentence citing Paper 300 number $6$, $5$ and $39$ in the three bands; those answering “different roots” $76$, $97$ and $59$ (Section 3).
Third, divided by the batches in which the papers were written, the rise comes in steps——papers answering “shared root” number $1$ in $501$--$520$, $6$ in $521$--$546$, $11$ in $547$--$570$, $14$ in $571$--$590$ and $7$ in $591$--$599$; in $571$--$590$ they exceed the $5$ answering “different roots” (Section 3).
Fourth, and this is the core. Reading the $39$ papers in $501$--$599$ that answered “shared root”, $30$ of them ($\mathbf{0.769231}$) called two consequences of one formula “sharing a root”——written as “A and B come from the same formula and share a root”, first in $554$ and last in $595$, and before that only once, in $349$. In this use it is obvious by construction that the two come from the same formula, and the judgement can never come out “different roots” (Section 4).
Fifth, the form Paper 300 feared did not come——as far as reading shows, no paper answered “shared root” on numerical agreement alone. The remaining $9$ judged that two things met in separate places have one source, and all $6$ of $521$--$541$ name their criterion (Section 4).
Sixth, the separator is whether two things were met in separate places or divided within one formula——“sharing a root” in the first case is a judgement that can fail; in the second, a restatement (Section 5).
Keywords: corpus census, common root and distinct root, audit of judgements, consequences of one formula, structural interpretation.
Scope (what is not claimed)
No new theorem or law is claimed——this paper only counts and reads the corpus’s text. The moment is fixed——the Japanese texts of papers $1$--$599$ are measured ($598$ papers without the vacant $47$, references excluded); this paper itself is not counted. One counting rule is used——sentences (divided at the Japanese full stop) containing “Paper 300” were taken; those containing “shared root” were counted as “shared root”, those containing “different roots” or phrases such as “not a shared root” or “not evidence of a shared root” as “different roots”; the question form “shared root or different roots” was not counted. No comparison with Paper 300’s counts is made——the same rule applied to $1$--$299$ gives $57$ papers with “are different roots” and $8$ with “share a root”, not the $43$ and $23$ that Paper 300 counted by reading; $1$--$299$ have since been revised, and Paper 300 counted by reading. Only bands under the same rule are compared. The sorting was done by reading——the sentences answering “shared root” were read one by one and sorted, not by keyword; the result was written into the verification script as sets and checked to coincide exactly with the papers picked up by the counting rule. No published paper is changed——“two consequences of one formula share a root” is not false; it is only said that it is not a judgement. Relation to earlier papers: Paper 300 gathered five criteria for sharing a root, took the rise of “shared root” in the latest band as a warning to itself, and recorded in Observation 5.6 that whether judgements of numerical agreement alone had crept in ought to be checked——this paper carries out that check. Paper 500 showed that the corpus’s method is not one habit, each part adopted at its own time——this paper shows that the use of the word “shared root” changed from a certain time. Paper 405 showed that a numerical coincidence becomes evidence of a common root only when there is a bijection——the use found here does not even use numerical agreement; it is closed within one formula. What is added is giving, band by band, the share of papers citing Paper 300 and the numbers answering “shared root” and “different roots”, dividing the last band by the batches of writing, reading every sentence answering “shared root” and sorting it into “two appearances”, “one formula” or “caution”, and placing the separator on met in separate places versus divided within one formula.
1. Notation and the Question
Setting: from the Japanese texts of papers $1$--$599$, sentences containing “Paper 300” are taken, divided at the full stop. A sentence containing “shared root” counts as “shared root”; one containing “different roots” or phrases such as “not a shared root” or “not evidence of a shared root” counts as “different roots”; the question form “shared root or different roots” is not counted. Bands are $100$ papers each, the last being $501$--$599$.
Observation 1.1 Paper 300 wrote a warning to itself. In the latest band ($251$--$299$) the ratio reversed to $7$ “shared root” against $3$ “different roots”, and only $1$ paper in that band stated a criterion. Connections were increasing while statements of criteria were not——it could not be said that judgements of numerical agreement alone had not crept in; they had not been checked one by one, and it recorded that they ought to be.
Question: how was “shared root” used in the $299$ papers since, and did the feared judgements of numerical agreement alone creep in?
2. Papers Citing Paper 300
Computation 2.1: papers containing “Paper 300” in the text or listing Paper 300 in the references (bands before Paper 300 give $0$).
| band | papers | citing Paper 300 |
|---|---|---|
| $301$--$400$ | $100$ | $88$ ($88.00$ per cent) |
| $401$--$500$ | $100$ | $99$ ($99.00$ per cent) |
| $501$--$599$ | $99$ | $97$ ($97.98$ per cent) |
Observation 2.2 citing Paper 300 became almost a fixed custom. From $401$ on, nearly every paper cites it——citing is not judging; the next section looks at what the citing sentences answer.
3. Shared Root and Different Roots
Computation 3.1: sentences and papers answering “shared root” or “different roots” in sentences containing Paper 300. A sentence containing both counts as “both”, and its paper is counted on each side.
| band | “shared” sentences | “different” sentences | “both” sentences | papers “shared” | papers “different” |
|---|---|---|---|---|---|
| $301$--$400$ | $9$ | $173$ | $0$ | $6$ | $76$ |
| $401$--$500$ | $7$ | $352$ | $7$ | $5$ | $97$ |
| $501$--$599$ | $89$ | $145$ | $4$ | $39$ | $59$ |
Dividing the last band by the batches in which it was written ($501$--$520$ on 9 September, $521$--$546$ on the 10th, and $547$--$599$ in three batches on the 11th),
| papers | answering “shared” | answering “different” |
|---|---|---|
| $501$--$520$ ($20$ papers) | $1$ | $20$ |
| $521$--$546$ ($26$ papers) | $6$ | $18$ |
| $547$--$570$ ($24$ papers) | $11$ | $13$ |
| $571$--$590$ ($20$ papers) | $14$ | $5$ |
| $591$--$599$ ($9$ papers) | $7$ | $3$ |
Observation 3.2 answers of “shared root” rose sharply in the last band, and in steps. From $1$ “shared” against $20$ “different” in $501$--$520$ to $14$ against $5$ in $571$--$590$——the reversal Paper 300 saw in $251$--$299$ came back, larger.
Observation 3.3 these numbers cannot be compared with Paper 300’s. The same rule applied to $1$--$299$ gives $57$ papers with “are different roots” and $8$ with “share a root”, not Paper 300’s $43$ and $23$——$1$--$299$ have since been revised, and Paper 300 counted by reading, not by words. Only bands under the same rule can be compared.
4. Sorting by Reading
Computation 4.1: the sentences of the $50$ papers in $301$--$599$ that answered “shared root” in a sentence citing Paper 300 were all read and sorted three ways. “Two appearances”: judging that two things met in separate places have one source. “One formula”: calling two consequences (or two variables) of one formula or model “sharing a root”. “Caution”: stating method rather than judging. The result was written into the verification script as sets and checked to coincide exactly with the $50$ papers picked up by the counting rule.
| papers | two appearances | one formula | caution |
|---|---|---|---|
| $301$--$400$ | $3$ | $1$ | $2$ |
| $401$--$500$ | $4$ | $0$ | $1$ |
| $501$--$520$ | $1$ | $0$ | $0$ |
| $521$--$546$ | $6$ | $0$ | $0$ |
| $547$--$570$ | $0$ | $11$ | $0$ |
| $571$--$590$ | $0$ | $14$ | $0$ |
| $591$--$599$ | $2$ | $5$ | $0$ |
Observation 4.2 this is the core. Of the $39$ papers in $501$--$599$ answering “shared root”, $30$ ($\mathbf{0.769231}$) were “one formula”, first in $554$ and last in $595$, and before that only once, in $349$——for example, $554$ called “the median is twice the mean” and “the chance of ringing by the mean is $1-1/e$” sharing a root because both come from the same geometric distribution; $584$ called “inside $\sqrt2$ damping reduces the shaking” and “outside it increases it” sharing a root because both come from one transmissibility formula. That two things come from the same formula is obvious by construction, and such a judgement can never come out “different roots”.
Observation 4.3 the form Paper 300 feared did not come. As far as reading shows, no paper answered “shared root” on numerical agreement alone——what came was a different looseness: a “shared root” that does not even use numerical agreement, closed within one formula.
Observation 4.4 “two appearances” is the use Paper 300 originally asked about. $501$ judged that the waiting time for a bus and the number of citations of a paper’s neighbours in the citation graph, two different objects, have one source; $596$, that the two $2e$ in the moon’s libration and in the gap between sundial and clock do; $598$, that the total reflection of sound in air and of light in a stone do. All $6$ of $521$--$541$ name their criterion (the second criterion, identity-preserving correspondence, or path)——these are judgements that can fail.
Observation 4.5 keywords alone could not do this sorting. Of the $93$ sentences answering “shared root” in $501$--$599$ ($89$ “shared” and $4$ “both”), $15$ carry a keyword for “one formula” and $3$ a keyword for “two appearances”; the other $75$ carry neither——the sorting could only be done by reading each sentence.
5. The Separator
Observation 5.1 the separator is whether two things were met in separate places or divided within one formula. Whether two things met in separate places have one source cannot be known without looking, and may come out “different roots”. Two things divided within one formula have the same formula from the start——“sharing a root” is a judgement in the first case and a restatement in the second.
Observation 5.2 carrying out Paper 300’s check. Paper 300 warned that “shared root” was increasing and recorded that judgements of numerical agreement alone ought to be checked for——this paper’s answer: none of those had crept in, but $30$ papers’ worth of “shared root” that are not judgements had.
Observation 5.3 the shape of Paper 500. Paper 500 showed that the corpus’s method is not one habit, each part adopted at its own time——the use of “shared root” also changed from a certain time ($554$). Papers $547$--$599$ were written on the same day, 11 September 2026.
Observation 5.4 beside Paper 405. It showed that a numerical coincidence becomes evidence of a common root only when there is a bijection——a “shared root” closed within one formula has no two independent appearances, so there is nowhere to ask for a bijection.
Observation 5.5 the corpus has already begun to return. $596$ and $598$ use “shared root” only in the sense of two appearances, and $597$ and $599$ do not answer “shared root”——this paper adds one question to ask before writing “shared root”: were these two met in separate places?.
Observation 5.6 what is not said. No published paper is changed, and “two consequences of one formula share a root” is not false——it is only said that it is not a judgement. The numbers were counted by one rule and the sorting decided by reading; there was one reader, and the agreement between several readers that content analysis asks for (Krippendorff 2018) was not measured. Both are fixed at $599$.
6. Roll Call and Closing
- papers citing Paper 300: $88.00$, $99.00$, $97.98$ per cent (Computation 2.1): almost a fixed custom.
- papers answering “shared root”: $6$, $5$, $39$ (Computation 3.1): a sharp rise in the last band.
- $571$--$590$: $14$ “shared” against $5$ “different” (Observation 3.2): the reversal came back larger.
- $1$--$299$ give $57$ and $8$, not Paper 300’s $43$ and $23$ (Observation 3.3): compare only bands under one rule.
- $30$ of $39$ ($\mathbf{0.769231}$) are “one formula” (Observation 4.2): the core.
- “one formula” runs from $554$ to $595$ (Observation 4.2): before that, once, in $349$.
- no “shared root” on numerical agreement alone (Observation 4.3): the feared form did not come.
- $9$ papers of “two appearances” (Observation 4.4): all of $521$--$541$ name a criterion.
- keywords sorted only $18$ of $93$ sentences (Observation 4.5): reading was the only way.
- the separator is met in separate places versus divided within one formula (Observation 5.1): judgement or restatement.
Closing: Paper 300 recorded, as a warning to itself, that papers answering “shared root” were increasing while those stating a criterion were not, and left word that judgements of numerical agreement alone ought to be checked for. This paper made that check on the $299$ papers since——from $401$ on nearly every paper cites Paper 300 ($99.00$ and $97.98$ per cent), and papers answering “shared root” in a sentence citing it number $6$, $5$ and $39$ in the three bands, rising sharply in the last. Divided by the batches of writing the rise comes in steps, and in $571$--$590$ it is $14$ “shared” against $5$ “different”. The warning came true, but not in the form it feared——reading the $39$ papers of $501$--$599$ that answered “shared root”, none rested on numerical agreement alone, and $30$ ($\mathbf{0.769231}$) called two consequences of one formula “sharing a root”. This use began at $554$ and ran to $595$; since it is obvious by construction that the two come from one formula, the judgement can never come out “different roots”. The other $9$ judged that two things met in separate places have one source, the use Paper 300 originally asked about. The separator is whether two things were met in separate places or divided within one formula——“sharing a root” is a judgement that can fail in the first case and a restatement in the second. The corpus has begun to return to the first from $596$, and this paper adds a question to ask before writing “shared root”: were these two met in separate places?. Placed among the earlier papers——this carries out the check Paper 300 recorded in Observation 5.6 and, like Paper 500, shows in numbers the time at which a practice changed ($554$). The bijection Paper 405 asked for has nowhere even to be asked of a “shared root” closed within one formula. To be honest——the numbers were counted by one rule and the sorting decided by reading, so misreadings are possible, and Paper 300’s counts cannot be compared. No published paper is changed, and “two consequences of one formula share a root” is not called false. And the hand that wrote $547$--$599$ is the same hand that wrote this census.
References
- Krippendorff, K. (2018). Content Analysis: An Introduction to Its Methodology (4th ed.). SAGE Publications.
- 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 Numerical Coincidence Becomes Evidence of a Common Root Only When There Is a Bijection [Paper 405]. Zenodo. 10.5281/zenodo.22699433
- 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]. Zenodo. 10.5281/zenodo.22760262
Reference
Yamagishi, Y. (2026). The Six Hundredth Census: The Warning of the Three Hundredth Came True, but Not in the Form It Feared [Paper 600]. YOI: https://www.yamagishiyuuki.com/yoi/600
DOI: 10.5281/zenodo.22805283
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 600. This paper is a preprint and has not been peer reviewed.