Before the arrow: can the parts make a whole?
The most productive result of H10 is a static composition question: what makes locally distinct contacts, sections or observations compatible with one extended object? It connects the user’s cone/arrow suggestion to the repository’s cut-state work without first selecting an equation of motion.
Searches began with specific remembered arguments: Vasubandhu’s six contacts, Nagarjuna’s three descriptions of traversal, the Mohist re-created shadow, Liu Hui’s dissected solids, and Ibn Sina’s millstone. Verification elevated the contact arguments and solid dissection above the more familiar arrow. The millstone remains a precisely targeted retrieval lead.
1. The strongest pair: contacts before motion
Vasubandhu’s Vimsatika verse 12 asks how one partless atom joins six neighbours. Distinct directional junctions give it parts; placing the six in one location leaves an aggregate only atom-sized. Verse 13 then challenges the reply that aggregates join although atoms do not. The surrounding text argues about external perceptual objects within vijñaptimātra.
Ibn Sina’s Physics III.4, in the translated passage indexed from McGinnis pp. 75–76, tests the analogous alternatives of differentiated contact and interpenetration. Here the middle member of a three-body chain must distinguish its two contacts. This is a powerful structural parallel: adding neighbours asks more of a constituent than merely naming it.
The Indian companion and Avicennian companion preserve passages, contexts and the different access levels. The similarity is in the argument; the present batch establishes no route of transmission.
For our model design, separate three premises: a constituent has no internal parts; its contacts occupy distinguishable places; the composite has greater extension. A modern model can put relations in an ambient space or in explicit interface variables. The interesting research question is which of those resources the physical premises permit. This is the static counterpart of asking what information must cross a time cut in R03–R04.
2. China supplies both solid dissection and actual statics
Liu Hui’s received commentary in Nine Chapters, juan 5, explains a 2:1 solid-volume ratio through dissection and increasingly fine remainders. It is closer to the cone problem than a generic story about infinitesimals: the disputed passage from pieces to whole is already spatial. Its precise finite construction deserves comparison with Newton’s accumulated area error. The solid companion records the unproofread facsimile transcription and the next scan check.
The Mohists offer two complementary distinctions. B17 treats a shadow as re-cast rather than transported. B25a/b examine rigidity and the changed effectiveness of a weight when its configuration changes. These passages give object/effect and body/apparatus distinctions useful to the measurement branch. The new source edition and selected pages are saved locally; the ancient text and modern editors’ restorations are tracked separately.
The older Zhuangzi 33 witness preserves the flying shadow, arrow and endlessly halved stick among the debaters’ theses. Preserve that collective attribution rather than assign every listed paradox to Hui Shi personally.
3. The arrow becomes a question about the description
Nagarjuna’s Mulamadhyamakakarika II.1–3 tests locating traversal in the traversed, untraversed and being-traversed. The reply in II.3 makes the dependency explicit: being-traversed already presupposes traversal. The argument prompts us to ask what relational structure a supposedly self-contained instantaneous description has borrowed from a whole path.
The existing al-Shahrastani report on al-Nazzam adds a different response to traversing divisible intervals: the leap. The Arabic/Persianate route therefore contains competing responses to the continuum problem, not a single regional doctrine.
The user’s ziggurat image is a useful search prompt for stepped solids. A cuneiform problem about their section or volume would be the evidential starting point. Architecture alone supplies the image, not the argument.
4. One useful map, four different problems
| Source construction | Operation to specify in our model | Decisive question |
|---|---|---|
| Vasubandhu / Ibn Sina contacts | Compose constituents and interfaces | Where is directional information stored? |
| Liu Hui’s residual dissection | Refine a static partition | What controls the total remainder? |
| Mohist shadow and statics | Choose a body–apparatus relation | Which quantity survives a change of arrangement? |
| Nagarjuna’s traversal exchange | Assign a local motion description | What path relations does that description presuppose? |
These are historically attested arguments feeding modern research questions. They neither establish an action unit nor document what Newton read or privately suspected. Historical transmission, modern implication and physical scale selection retain separate evidence requirements.
5. A static entrance to the quantum question
The user’s measurement observation suggests beginning with kinematics: which states, observables and measurement arrangements are jointly compatible at one time? Mechanical statics concerns equilibrium; fixed-time quantum compatibility is broader. Dynamics subsequently specifies how an apparatus establishes its record.
I007 turns this into a bounded test: specify local measurement descriptions, their common restrictions, and the proposed rule for combining them into one global state. Compare explicit classical models before introducing a quantum observable algebra. Then trace where an action-valued calibration enters. A compatibility obstruction and a positive dimensional constant are distinct deliverables.
R12 has now compared constituent and whole-body information scales, finding an exact cost for discarding constituent records. R13 remains next on the main track. Supporting task K01 will test this static compatibility route; H11 strengthens the Chinese and Arabic witnesses. This source visit adds a way to ask for the missing premise, rather than another fitted value for it.