C.29:4.4.6 - Subject-pattern boundary table
Use this table when the mathematical result contributes to a separately governed question. Name that question and the first receiving action; cite the existing result when it already supplies the needed basis.
CandidateMathObject names the mathematical object used in the representation. State its correspondence and preserved and lost structure in the accompanying account.
For a relation claim with clear participants and meaning, apply the current direct relation pattern’s rule and use its result. If the rule needs an unavailable case fact, identify that fact and leave the claim unresolved pending it. Use A.6.P when the relation or participant meaning remains unclear; use A.6.RCD only after recovery when no current direct predicate can state the needed claim. Explicitly identify an obtaining relation occurrence under its direct identity rule only when a receiving claim or operation must distinguish that occurrence.
Use A.6.0’s FormalSubstrate profile when a separate declaration of vocabulary, laws, imports and applicability is needed. Apply A.6.1 for mechanism import or realization of that declaration, and E.18.1 when accepted problem-side material needs the declaration carried into later work. The same mathematical object may be designated in several epistemes or uses; select the subject pattern for the actual object and claim.
| Object or claim being made | Governing FPF pattern | C.29 contribution |
|---|---|---|
| mathematical-lens use | C.29 | Names the C.29 discipline: candidate mathematical object, lens mapping mode, preserved structure and lost structure, invariant or distinction, LensUseBoundaryValue, declared lens use, any justified blocked overread, and stop or return condition. |
| durable reusable names beyond pattern-local fields | F.18 | Cite when MathLensUse names become durable beyond C.29-local use. |
| broad wording and epistemic precision restoration | F.19, E.10, C.2.P | Use F.19 for ordinary precise-plain-language repair, E.10 for cues and unresolved wording, and C.2.P for unresolved epistemic meaning. |
| relation precision, arity, polarity, needed-claim derivation, and slot structure | The direct relation pattern; A.6.P for unresolved relation or participant meaning; A.6.RCD for a needed claim with no suitable current predicate; A.6.5 for reusable typed participant declarations | C.29 applies only if a mathematical object represents the settled claim or derivation and changes the stated lens use. |
| object, description, and carrier distinction | A.7 | Do not identify the phenomenon directly with the mathematical object. |
| dynamics state space and transition law; temporal aspect | A.3.3; C.27.TA for the temporal aspect | Supply the imported or contested representation and its losses to the stated dynamics/temporal question. |
CharacteristicSpace, slots, topology, order, and metric-space distance overlays | A.19 | C.29 applies only when an overlay becomes a domain-transferring or publication-bearing lens. |
| local choice among available options | C.11 | Supply the bounded mathematical result or rival-lens note to the option comparison; use C.11 for the ChoiceResult or local choice record. |
selected method, method-family selection, U.WorkPlan, performed U.Work, work-result record, or work-relevant appearance-based reliance repair | A.15, A.15.1, A.15.2, A.15.4 | Can contribute method-relevant lens use; method, plan, performed Work, and any result record stay with their direct patterns, while A.15.4 only repairs reliance on a misleading appearance. |
| evidence relation, source currentness, provenance, evidence carrier, or model card or datasheet used as evidence | A.10 | States LensUseBoundaryValue only; evidence relations and provenance remain A.10 matters. |
| assurance, readiness, reliability, release confidence, safety, trust, or engineering justification | A.15.5 for work-entry readiness; A.10 for evidence reliance; B.3 only for an actual named assurance claim; the direct domain pattern for other readiness, reliability, release, safety, trust, or engineering-justification claims, plus relevant G patterns when their claims are made | Treats declared lens use as possible input only; mathematical elegance does not raise assurance. |
| measurement construction, scale, unit, or comparability, or evidence-stub adequacy | C.16 | States measurement-dependent LensUseBoundaryValue only; measurement construction, scale, unit, or polarity, direct comparability, and evidence-stub adequacy stay with C.16. |
| explanation-facing rendering or generated explanation use | E.17.EFP | States mathematical-lens use for the mathematical explanation used inside the rendering; explanation-use discipline stays with E.17.EFP. |
| bounded comparative review unit | E.17.ID.CR | States declared lens use for a mathematical comparison construction or rival lens when that construction affects the comparative review use. |
| same-EntityOfConcern representation-scheme transition | A.6.3.RT | C.29 applies only if the representation shift imports a contested or use-affecting mathematical lens. |
| coarsened rendering with narrower declared lens use and source-bearing reopen | A.6.3.CSC | C.29 applies only if the coarsening depends on mathematical abstraction, quotienting, or coarse-graining. |
| cross-context meaning, bridge kind, direction, CL, loss, and substitution | F.9 | Reference the Bridge and its separate bounded-use claim; keep Bridge semantics in F.9. |
| causal-use question or verdict | C.28 | Block causal overread or cite a C.28 application or CausalUseSupportResultRef. |
| forecast, rate, trajectory, rhythm, recovery, convergence, stabilization, temporal window, or rate-change used as sufficient for a use | C.27 | Can state a prediction-relevant or distinction-relevant mathematical-lens use; temporal-claim adequacy stays with C.27. |
| scale-law and Bitter-Lesson preference claims | C.18.1, C.19.1, C.31.ASAP | Cite scale-window, scale-law, BLP, or architecture scale-preference evidence when scale behavior, general method scale preference, or architecture scale preference is being claimed. |
| quantum-like modeling | C.26 | Treat C.26 as C.29-compatible specialization, not as full-card inheritance for every QL-lite note. |
| selected-set result declaration, parity or benchmark result use, source harvesting and synthesis, Part-G shipping, or publication | G.5, G.9, G.2, G.10, E.17, and E.24.PUB | Use G.5 for selected-set result declaration, G.9 for parity or benchmark result use, G.2 for source harvesting and synthesis, G.10 for shipping Part-G outputs, E.17 for a source-backed publication face and return to source, and E.24.PUB for an actual publication occurrence and availability. Supply the bounded mathematical result or rival-lens note with its declared use as input. |