C.13:9 - Rationale (informative)
Why exactly three forms?
sum, set, and slice keep three recurring practitioner questions apart:
sumasks how exact constituents and constructive relations assemble an integrated whole;setasks which entities belong to a collection under that collection’s identity and belongs-to rule;sliceasks which exact aspect is distinguished from one bearer under a governed facet.
The forms are intentionally small, but their inputs do not determine ontology by themselves. An assembly is more than a set of part names; a collection is not automatically a holon or agent; and a facet label is not an aspect occurrence. The direct patterns provide relation obtaining and occurrence identity, while the candidate’s direct pattern decides whether the existing whole continues or a new whole must be identified.
Why traces remain epistemic. A construction can obtain before anyone writes its account. A materialized trace is claim-bearing content used to inspect, communicate, or support that account. Evidence and assurance may warrant the claim, G.11 may govern the selected edition’s currentness, and the account may be relied on in receiving work or declined for that use. None of those epistemic results changes the world-side assembly by itself.
Why order, time, selected structure, and transformation composition are outside. Method order and temporal extent answer different questions from parthood. A selected U.Structure is an organization of relations for a use, not automatically another holon. Entity construction also supplies no law by which several actual changes compose into one transformation. Keeping these stops explicit prevents an economical notation from becoming an ungoverned ontology.