Architecture / a clause-linked instrument

The Timber Is the Ancestor

Li Jie’s Yingzao Fashi says building begins with eight timber grades: each cai is 15 material fen wide and 10 thick, while a 72-fen bracket arm branches by puzuo count. Choose a grade, then set the manual’s chi bays against those fen. The arithmetic closes seven of eight Siku witness notes, and exposes the grade 7 slip and the overlap the clauses do not resolve.

The manual begins with a rule that is almost a world view: 凡構屋之制皆以材為祖. In the building standard, timber is not a detail added after the plan. It is the ancestor from which the rest of the measure is inherited.

Engine headline, frozen default baseline

Seven of eight Siku grade notes agree with their printed widths and thicknesses; in the manual’s 15-chi by 10-chi example, the 92-fen 慢栱 overlaps adjacent chi-laid sets at grades 1 and 2.

This sentence summarizes the default Siku and double-bracket example. The controls below report the current state without rewriting the shareable baseline.

I / choose the cai

The operable base

A timber grade is a ruler

Choose one of the eight grades. The bars below are a schematic elevation of the printed gong lengths. Their positions are an interpolation for seeing the lengths together, not a claim about a surviving bracket.

Cai grade Grade 1 The selected row is parsed from its source characters, then converted to cun and material fen.

Witness used for the note The Siku scan remains the default. The other readings are visible alternatives, not silent repairs.

Printed lengths are scaled to the selected material section. Where the source does not place a dou or describe a curve, the drawing interpolates.

Width as written: 廣九寸
Thickness as written: 厚六寸
Width in ordinary cun: loading
Thickness in ordinary cun: loading
Printed unit note: loading
Unit note check: loading
Selected huagong branch: loading
Selected huagong in cun: loading
栔 width, in cun: loading
Source image: scan image n117

Grade 1 is loading.

Live choices are loading.

The text checks itself

The source prints a note beside every grade. It says how many ordinary fen make one material fen. That note is one division per grade, not an independent measurement. The engine parses the width and thickness separately, divides by 15 and 10, and then compares both answers with the note.

Seven of eight unit notes agree under the Siku scan.

各以其材之廣分為十五分以十分為其厚 juan 4, 材, scan images n119 to n120. The source distinguishes ordinary 分 from material 材分.

The check

Recomputed from the frozen transcription: the table below runs the same parser on all eight grade rows. It does not copy the expected answer into the result. Grade 7 is deliberately left as the Siku witness prints it.

Grade	Width	Thickness	Printed note	Width and thickness	Image

Grade 7: the Siku note is loading.

Active comparison witness: Siku scan as written. Its grade 7 note is 以二分五釐為一分, read at scan image n119.

What closes

The engine is checking all notes.

What remains

The Siku scan has a grade 7 slip. The 1929 witness prints a different note and closes all eight. The page shows both.

Free choices

The witness choice changes the displayed note and the agreement count. It is not a historical fact that the two witnesses are interchangeable.

Primary record: 欽定四庫全書 scan, images n117 through n140. The scan image files are not copied into this page.

The bracket has named lengths

The source gives each named gong a length in material fen, and often gives the number and length of its carved瓣. The table is a transcription of those load-bearing lengths. The browser converts them to the selected grade only after reading the source value.

Gong	Length, material fen	瓣	Each瓣, material fen	Selected grade, cun	Source clause	Image

The engine also carries the small 栱頭 row, but the five named rows above are the first compact reading of the bracket family.

II / where the module stops closing

The flagship depth layer

When fen meets chi

The bracket clauses speak in material fen. The bay example leaves that unit and speaks in ordinary chi: a central bay of 15 chi, a side bay of 10 chi, and evenly distributed supplement sets. Put those clauses into one instrument and see whether the same scale survives the seam.

Building term Only terms present in the frozen eligibility clauses are offered.

Bay count Counts inside a frozen range are accepted, including named even bays such as 4, 6 and 10. Counts outside every range are refused.

殿身 and 殿 Strict keeps the source categories separate. Merged makes the interpretive choice visible.

Building role The step-down clause names 副階, 殿挾屋 and 廊屋.

Step-down clause Changing this moves the eligible output grade, not just the label.

Bracket configuration 重栱 exposes 慢栱. 單栱 exposes 令栱.

鋪作 count four to eight This controls the conditional reading of the 72-fen rule.

72-fen reading The source says each 4-fen cut applies to the inner and outer jump. Three readings remain exposed.

鋪作多 threshold The source does not define how many is 多.

六鋪作以下不減 This is a reading choice where the clause leaves the threshold implicit.

一尺 tolerance Compare spacing, or compare the bay widths. The page keeps both readings live.

Bay unit Chi as printed. Chen Mingda’s fen-based lead is prior art only.

Central bay width, chi

Central intercolumnar sets

Side bay width, chi

Side intercolumnar sets

Line lengths scale from the current chi bay widths, and bracket bars scale from the current wall-line gong against each computed material-fen spacing. Placement of each set on the line is an interpolation so the unit seam can be seen.

Eligible output grades: loading
Wall-line gong: loading
Central spacing, chi: loading
Side spacing, chi: loading
Central spacing, material fen: loading
Side spacing, material fen: loading
Wall-line gong, material fen: loading
Minimum clear spacing, chi: loading
Selected-grade central collision: loading
Selected-grade side collision: loading
One-chi test: loading
Spacing or bay spread: loading

The bay calculation is loading.

The eligibility clauses are loading.

Conditional huagong: raw loading material fen, reduction loading, second-tier reading loading. The branch is loading.
Printed caps: each jump loading material fen at the centre, total projection loading material fen.

The collision reading is loading.

Current bay computation is loading.

The overlap is not inside the bracket

Inside the bracket clauses, changing grade redraws the same material pattern at a new scale. The deeper result appears only when the text changes unit. With the manual’s own bay example and a 重栱 wall line, the selected grade can make neighbouring 慢栱 lengths overlap. That collision is not a proof that a historical building was impossible. It is a precise statement about what these clauses do together.

Printed example: 15/3 chi = 10/2 chi, so it closes exactly. This is a fixed source annotation, not a readout of the edited bay inputs.

What the corner clause offers

The source names 連栱交隱, and it names 從上減一跳 near a corner. It also names the 鴛鴦交手栱 joint.

Those are clauses for the corner condition. They are not silently applied to a collision between two mid-bay sets.

What the text does not say

For a mid-bay collision, the instrument prints UNSPECIFIED BY THE TEXT. It does not invent a repair, move a set, or turn an interpolation into a rule.

Changing the bay unit to Chen’s reported 375-fen reading would be a different model. That lead is named in the research file, not smuggled into this one.

The depth check

Every choice is live: witness, huagong reduction, the meaning of 鋪作多, the six-or-fewer reading, hall vocabulary, step-down context, bracket configuration, and the one-chi comparison. Change them and an output moves. The bay unit is the one declared inert choice because Chen’s 375-fen reading was not independently sourced here.

Material calculation

Two cai and two 栔 at grade 1 read as loading when 栔 uses its printed material width.

Secondary anchor

The same engine gives loading for the cited 62-fen 瓜子栱 conversion and loading for the cited 36-fen corner 栌斗 conversion.

Clean closure

The manual’s central and side spacing close exactly in its example. This does not close the separate grade 7 witness slip.

Published secondary summary values are shown as published, not adopted as the anchor: the Chinese Wikipedia page prints 37.2 cun and 21.6 cun for the two examples, and 19.2 cun and 17.6 cun for the ordinary-fen reading of the two cai plus two 栔 illustration. The live material-fen reading is separate.

Where the instrument refuses

Counts named by the frozen clause ranges are accepted, including four bays. Counts outside every range remain refused.

A four-bay request is accepted because the frozen 3-to-5 clause range names it; a thirteen-bay request will be refused because no frozen range names it.

A non-comparability panel

Do not turn a mismatch into a proof

Xu’s 2025 OSF preprint reports a fitted ruler of 314.5 mm and a basic module of 2 chi for the East Hall of Foguang Temple. The same paper says the hall did not use the cai-fen system.

The paper says the East Hall did not use the cai-fen system.

No residual against the Yingzao Fashi is computed here.

This is not a validation panel. It is a refusal to compare two different modular systems as though one were a test of the other. Source: Xu, OSF Preprints, version 1.

Witnesses, prior art, and the limits of the reading

Witnesses. The primary input is a hand transcription from the Siku Quanshu scan in Internet Archive item 06051718.cn, with image numbers carried beside every datum. The same-edition Wikisource route is a second transcription of the Siku text. The 1929 National Central Library colour-printed edition is a second witness for the load-bearing grades and the grade 7 note. The page keeps the discrepancies instead of choosing one as invisible truth.

Visible route discrepancies. The same-edition route reads 材分 where the scan has 村分 in a grade 1 reduction note, 到 where the scan has 至 in the grade 3 eligibility wording, 相交 where the scan has 相六, and 底四面 where the scan has 底四百. It also uses 裏 where the scan reads 裹. These are comparison readings, not silent substitutions in the live rows.

Prior art. Andrew I-kang Li’s 2001 shape grammar and his 2025 Computing Chinese Architecture; the 2020 parametric modelling paper in ISPRS IJGI 9(3), article 167; Hui Li’s 2013 analysis in AIJ 78(687), pages 1171 to 1177; Liang Sicheng’s commentary; Chen Mingda’s 1981 大木作研究; Pan Guxi and He Jianzhong’s 營造法式解讀; and the Tao Xiang and Kan Duo witness collations. We searched Google web results, J-STAGE, SpringerLink, MDPI, ResearchGate and institutional publication records on 2026-09-14 and did not find a public browser instrument that combines the juan 4 clauses, exact rational arithmetic, conditional branch provenance and an ordinary-fen versus material-fen audit trail in one page.

Scope. This is a juan 4 reading of material units, selected gong lengths, eligibility clauses and bay spacing. Columns, beams, rafters, eaves and corner-column rise belong to juan 5 and are not modelled. No metric conversion is offered for the Song system. The page does not reconstruct, date, certify or calculate the strength of a surviving building.

Uncertainty. The English glosses for 材分, ordinary 分, 鋪作, 裏跳 and the building categories are glosses, not replacements for the Chinese source. The drawing places named lengths in a schematic stack and therefore interpolates geometry where the source is silent. The 1929 edition is cited as the Commons record names it, without assigning it a recension the evidence does not establish.