C.18.1:4 - Solution — binding lens for generator/selector profiles (normative)

C.18.1:4.1 - Types (aliases; ΔKernel = 0).

SLL.Profile is an annotation on a MethodFamily/Generator or a Selector profile; no durable U-kinds are minted (LEX discipline).

C.18.1:4.2 - Fields (conceptual descriptors).

S — Scale Variables. Minimal set of monotone knobs for the Context: compute (steps/tokens/FLOPs/time/energy), data (size/quality), model capacity (params/branches), iteration budget, freedom‑of‑action (FoA)/environment richness, etc. Declare units under C.16 and bind S to a ScaleWindow. Keep planned budget values with A.15.2; bind dated resource-use accounts to A.15.1, B.1.6, and A.10. Where training/inference trade, name the phase the claim concerns.
ScaleWindow. Declared range of S values for which behaviour claims hold (editioned). This is distinct from FreshnessWindow used by parity.
Scale‑Probe. At least two (preferably ≥ 3) parity‑respecting points in S within the ScaleWindow, recorded with replicates/seeds and CI/error bars to support elasticity classification. Pick points via a small factorial or Latin‑hypercube when multiple knobs vary.
ElasticityClass χ ∈ {rising, knee, flat, declining} — a qualitative class supported by the probe over the declared ScaleWindow. Leave χ unassigned when the observations and their uncertainty do not support a class, and state what remains unresolved. Numeric exponents/fits live in domain annexes, not Core.
ParityNotes. iso‑scale parity? flag and loss notes if not achieved, plus applicable Bridge, Φ, and Ψ IDs for actual crossings under G.9; penalties affect R only.

C.18.1:4.3 - Norms (SLL).

SLL‑1 (Declaration). Any profile claiming scale behaviour SHALL declare S and a ScaleWindow for the Context.
SLL‑2 (Probe). Early investigation SHALL include a scale‑probe (≥ 2 points in S, with replicates/CI) and record the supported χ, or the unresolved classification. Multi‑knob probes SHALL hold unspecified knobs fixed or pinned, and disclose invariants.
SLL‑3 (Parity). Where S is declared, comparisons SHALL ensure iso‑scale parity and lawful UNM/NormalizationMethod‑based mapping across heterogeneous knobs (e.g., FLOPs↔tokens) before comparing outcomes; FreshnessWindows/editions must be equal/pinned per G.9. Record seeds/replicates, ComparatorSet, and policy‑ids in telemetry/SCR.
SLL‑4 (Selection lens). Within the same Context and ScaleWindow, if other heads (N/U/C) are tied, selectors MAY use illumination as a tie‑breaker, but it SHALL NOT change default dominance; illumination remains report‑only telemetry unless a CAL policy promotes it.
SLL‑5 (Knee test). A knee is claimed only where a monotone rise is followed by a statistically significant slope drop across adjacent probe points within the ScaleWindow; thresholds (e.g., Δslope & CI level) are policy‑defined (E/E‑LOG) and must be cited. Failure to establish a knee leaves that claim unsupported. Report rising, flat or declining only when the probe supports that class; otherwise leave χ unassigned. Absence of a confirmed knee is not evidence of rising performance.
SLL‑6 (Telemetry invariants). Probes SHALL export seeds/replicates, edition pins, policy‑ids, and resource-account units governed by C.16 and B.1.6, with dated-work and provenance links under A.15.1 and A.10, to G.11.

C.18.1:4.4 - Method — minimal SoTA probe recipe (notation‑agnostic; informative).

Choose knobs S that are plausibly monotone in the Context (compute/data/capacity/FoA).
Pick 3–5 probe points per active knob (edge/mid/edge) under iso‑scale parity; use a fractional factorial if >2 knobs.
Run replicates (≥ 3 preferred) and bootstrap 95% CI on the primary objective(s); log seeds.
Estimate local slopes on a log‑log grid only where the declared Scale operations are admissible under A.18 and the logged values are positive; apply piecewise/segmented regression or a knee detector (e.g., L‑curve/Kneedle) to support χ.
Record invariants (pinned knobs, safety envelope) and publish SLL.Card@Context.
If χ changes across the window, split the ScaleWindow and re‑classify per segment.