Library / First Principles Framework (FPF) - Core Conceptual Specification
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Source changed 2026-10-03 08:25:59 UTC · snapshot created 2026-10-03 08:26:43 UTC · last check 2026-10-03 10:15:17 UTC

C.30:4.8 - Architecture mathematical-lens boundary

Architecture descriptions may use C.29 lenses, but the lens does not become architecture ontology.

ArchitectureMathLensUseBoundary:
  noMLUNeeded?: yes | no
  lensOneLine?:
    lensRef,
    structureClaimRef,
    preservedStructure,
    lostStructure,
    lensRelationKind,
    stopCondition,
    claimPatternRefs?

Use the one-line boundary only when it is enough to keep the lens from being overread. Use a C.29 Mini or Full card when the lens choice, preserved structure, lost structure, relation class or admissible-use value, or stop condition changes the architecture move.

Lens use by architecture problem:

Architecture problemCandidate mathematical lensPreserved structureTypical loss or stop
Hidden dependency or modularity.Typed graph, DSM, or hypergraph.Dependency, coupling, or clustering.Semantics, interface law, evidence, and work remain outside unless bridged.
Flow bottleneck.Mathematical expression for the selected transformation-flow structure; network flow; or queueing.Path, crossing, valuation, and capacity.Purpose, proof, causality, and safety remain non-architecture claims.
Control-rate mismatch.Mathematical expression for the LCA control structure; hybrid systems; assumption-guarantee relations; or control relations.Feedback participant meanings and scale or rate relations.Stability proof and safety proof remain outside the lens.
Cross-scope residual.Coarse-graining or renormalization-group-style lens.Preserved and lost structure across scale.Utility, causal-use claims, and selector authority remain outside unless separately grounded.
Extracted structure from traces.Epiplexity or MDL-style bounded-observer lens.Learnable structural regularity.Task relevance, assurance, and causal proof remain non-architecture claims.
Physical separation or spatial arrangement.Topology, geometry, or spatial graph lens.Adjacency, containment, separation, reachability, energy-transfer relation, or material-transfer relation.Safety proof, accessibility, regulatory acceptance, and causal-use claims remain outside unless separately grounded.
Composition relation.Category, open-systems, or compositional lens.Interface, composition, and coherence.Domain semantics remain outside unless bridged.

This table is not a C.29 replacement and does not make mathematics mandatory. It helps the practitioner see when a lens may add a useful architecture move; C.29 still carries lens-use result, preserved structure, lost structure, relation class or admissible-use value, and stop condition when those description or view uses are being made.

Epiplexity-like use remains a C.29 bounded-observer structural-information lens. It may help recover learnable structure from traces, but it is not an architecture quality, task relevance proof, causal proof, assurance, or selector authority.