C.13:4 - Solution

C.13:4.1 - Solution sketch

Use the coarsest of three construction narratives that fits the named whole, collection, or aspect. In each case, write the shorthand only after the required facts are recoverable.

The familiar argument lists are readable shorthand, not complete ontological signatures. A complete use names the whole, collection, or aspect and states the direct facts beside the shorthand. Input order does not matter to the list of designated inputs, but assembly relations, rules, facets, and identity conditions do matter. The same input set under a different assembly can yield another whole.

A construction may obtain in the world even when no trace episteme has been written. When another piece of work needs an inspectable trace, materialize a C.2.1 episteme whose claim content names the whole, collection, or aspect; its constituents, entities that belong, or bearer; the relation occurrences that obtain; the construction rule; and the identity conditions. Creating, editing, publishing, or losing that episteme changes the account or its availability, not the past or present construction facts.

Do not add a fourth constructor merely to carry time, execution order, parallelism, representation, evidence, or a domain label. Keep those claims with their direct patterns beside the construction account.

C.13:4.2 - Normative Standard (high‑level)

• C13-N1 — Direct facts first. A C.13 trace is conformant only when every named constituent or collection entity and every named part, collection-belonging, or aspect occurrence is independently identified under its direct pattern.
• C13-N2 — Whole identity stays direct. The candidate whole follows its direct identity and reidentification rule. Equality of an input list or trace does not decide whether the existing whole continues or a new whole must be identified; a permitted constituent replacement can preserve one whole, while the same constituents under another assembly can form another whole.
• C13-N3 — Construction form. sum, set, and slice are the only C.13 forms. Reordering or duplicate designation does not change the listed inputs; it does not merge distinct entities or relation occurrences and does not erase assembly or facet differences.
• C13-N4 — Mereological discipline. Direct part patterns and A.14 govern acyclicity, antisymmetry, transitivity where applicable, recurrence, and occurrence identity. C.13 does not strengthen a direct relation by calculus convention.
• C13-N5 — Trace separation. A materialized trace is a C.2.1 episteme. It creates none of the following: the whole, collection, or aspect it describes; the inputs; the relation occurrences; the construction rule; the identity conditions; or holonhood.
• C13-N6 — A collection account is not component assembly. set supports a collection account; it does not imply integrated assembly, ComponentOf, system agency, or A.1 recognition. Use sum only when constructive part relations and assembly are independently grounded.
• C13-N7 — Elected assurance grounding stays with B.3.5. A direct structural Working-Model edge may be published without a C.13 trace. When that publication elects B.3.5 or a named current requirement demands the profile, follow B.3.5 for the required tv:groundedBy link and declared validationMode; C.13 supplies the reconstructible trace content. Evidence, warrant, currentness, and reliance remain separate, and neither the link nor the mode replaces the direct construction or identity facts.
• C13-N8 — Subject owners remain authoritative. Method, work, and discipline construction may use C.13 only after their direct patterns identify actual parts and whole-forming relations. A selected dependent U.Structure does not become a whole, collection, aspect, or holon by selection or name.
• C13-N9 — Transformation composition stays fail-closed. A C.13 entity-construction trace, method decomposition, work decomposition, common changed referent, or temporal subdivision establishes neither transformation parthood nor a composite transformation. Without a direct transformation-composition governor, retain the independently identified changes and the exact blocker; infer neither composition nor atomism.

C.13:4.3 - Scope, applicability, terms & notation

Use Compose-CAL when the current claim concerns the construction of one exact system, episteme, method, work occurrence, discipline, collection, or aspect and its direct part patterns already supply the required participants and obtaining relations. Do not apply it merely because a sentence contains part, a diagram groups nodes, or a selected structure organizes relations.

• Γ_m — the three-form notation for a C.13 construction narrative.
• construction trace — claim content that names the whole, collection, or aspect; its inputs; the direct relations that obtain; its construction rule; and its identity conditions; when materialized, it is a C.2.1 episteme.
• constructive part relation — an exact world-side relation occurrence governed by its direct pattern; it is designated by the trace but not created by it.
• assembly rule or method — the rule by which the named constituents assemble the whole, the members form the collection, or the bearer and facet distinguish the aspect; a rule-description episteme is not the assembly, collection, or aspect itself.
• identity or reidentification rule — the direct rule that identifies the whole, collection, or aspect and says which changes preserve or end it.

Alias readiness. These are common readable projections only when their direct relation meanings match the case:

• ComponentOf may accompany a sum construction;
• an ordinary belongs-to sentence may accompany a set construction; the collection’s own pattern supplies its meaning, occurrence history, and any recurrence rule;
• AspectOf may accompany a slice construction;
• PortionOf needs the direct portion relation and metrical semantics in A.14, not a facet spelling alone;
• ConstituentOf needs the direct logical or content-part relation; material mixtures use their exact portion or component owner.

The readable label and the trace answer different questions. The label states which direct relation obtains; the trace explains how the exact relation set supports this construction. Neither one is evidence merely by being present.

C.13:4.4 - Structural CT2R Typing-Grounding Use

When a target kind or logical representation must reuse both a Γ_m construction account and an independently grounded Working-Model relation, use StructuralCT2RTypingGroundingUnfoldingStructureBlock from B.3.5. C.13 contributes the account of the subject-side relations that actually obtain and states which mereological structure the target preserves or loses inside that B.3.5-governed local A.22.CGUS structure specialization. C.13 does not create separate unfolding-structure authority and does not by itself supply a bridge, kind intent, proof, empirical evidence, or admissible reuse. Apply A.7.1, rather than this structural CT2R block, when an inadequate working account must be diagnosed against the subject construction.

Use this split especially when a readable relation label such as ComponentOf, a collection’s belongs-to predicate, AspectOf, ConstituentOf, or RepresentationOf is being reused beyond what its sentence warrants. The label does not by itself prove constructive grounding or a wider structural projection. Name the construction trace and Working-Model relation, the target kind or logical representation, any bridge used, the structure preserved and collapsed, and the proof or evidence relation required by the stronger claim. If the evidence instead diagnoses a mismatch that requires revision of the working ontology, apply A.7.1.