#MM-CHR — Measurement & Metrics Characterization

Pattern C.16 · Stable Part C - Kernel Extension Specifications

Name. Measurement & Metrics Characterization (MM‑CHR). This is a user‑oriented name: in user‑facing narrative we may say metrics; in Tech register we speak Characteristic / Scale / Level / Coordinate / Value / Score / Unit / ScoringMethod; in Formal register we use U.DHCMethod(Ref) / U.Measure / U.Unit / U.EvidenceStub. Intent. Provide a transdisciplinary substrate for measurement that any FPF pattern can rely on: a small, stable set of intensional constructs and relations—U.DHCMethodRef, U.Measure, U.Unit, U.EvidenceStub—disciplined by CSLC (Characteristic / Scale / Level / Coordinate) so that every recorded value is interpretable, and any claim of “comparability” is auditable (physics lab time‑of‑flight, figure‑skating judging, architectural modularity, etc.). C.16 does not re‑define Characteristic (A.17) nor the CSLC kernel Standard (A.18); instead, it exports the measurement substrate that binds an FPF pattern’s measurable notions to one Characteristic and one Scale and frames a conceptual link to evidence. This characterization is notation‑neutral, tool‑agnostic, and open‑ended (no “lifecycle” narrative; evolution proceeds via RSG moves with checklists).

#Keywords

• measurement
• measurement template
• U.DHCMethod(Ref)
• U.Measure
• U.Unit
• U.EvidenceStub
• polarity
• direct comparability (same-template)
• scoring method (𝒢) disclosure
• CSLC.

#Relations

#Content

#Intent (Normative)

Name. Measurement & Metrics Characterization (MM‑CHR). This is a user‑oriented name: in user‑facing narrative we may say metrics; in Tech register we speak Characteristic / Scale / Level / Coordinate / Value / Score / Unit / ScoringMethod; in Formal register we use U.DHCMethod(Ref) / U.Measure / U.Unit / U.EvidenceStub. Intent. Provide a transdisciplinary substrate for measurement that any FPF pattern can rely on: a small, stable set of intensional constructs and relations—U.DHCMethodRef, U.Measure, U.Unit, U.EvidenceStub—disciplined by CSLC (Characteristic / Scale / Level / Coordinate) so that every recorded value is interpretable, and any claim of “comparability” is auditable (physics lab time‑of‑flight, figure‑skating judging, architectural modularity, etc.). C.16 does not re‑define Characteristic (A.17) nor the CSLC kernel Standard (A.18); instead, it exports the measurement substrate that binds an FPF pattern’s measurable notions to one Characteristic and one Scale and frames a conceptual link to evidence. This characterization is notation‑neutral, tool‑agnostic, and open‑ended (no “lifecycle” narrative; evolution proceeds via RSG moves with checklists).

One‑minute mental model (didactic; non‑normative).

• Template (U.DHCMethod) says what a value means: the Characteristic, Scale (and Unit when applicable), plus polarity and applicability.
• Reading (U.Measure) says what was claimed about a subject: a value on that Scale, with a time stance and (when required) an EvidenceStub.
• Direct comparability is conservative: same template; everything else requires a named, cited transformation or equivalence owner.

Non‑ownership boundary (single‑writer). C.16 is not the semantic owner for (i) characterization mechanisms (e.g., normalization / indicatorization / scoring / comparison / selection), (ii) any normalization/equivalence notions (method tokens, “invariant value” notions, equivalence relations), (iii) contract routing policies (comparability modes, legality gates), or (iv) suite protocol obligations. Those belong to their single owners (e.g., the CN/CG contract surfaces and the CHR mechanism owner patterns). C.16 may cite such owners when motivating evidence or interpretability, but MUST NOT introduce or restate their terminology or laws.

Outcomes. (1) A uniform way for FPF patterns to declare what is measured and read what has been measured; (2) explicit Characteristic anchoring and Scale typing per CSLC; (3) principled comparability and polarity (declared at the template level); (4) traceability via conceptual evidence stubs; (5) seamless alignment with cross‑domain quantity notions (ISO 80000, ISO/IEC 25024, QUDT, SOSA/SSN, Verspoor) through Unification rows (Part F).

#Scope & Status (Normative)

Scope. C.16 specifies the measurement substrate for FPF patterns: the roles of U.DHCMethodRef, U.Measure, U.Unit, U.EvidenceStub; their CSLC discipline (by reference to A.17/A.18); and evidence linkage semantics at the level of conceptual conditions. It defines direct interpretability and direct comparability (same template), and it equips other patterns to state—and audit—stronger comparability claims by citing their single owners. It exports these constructs for all FPF patterns (KD‑CAL, Arch‑CAL, etc.) without prescribing domain formulae, procedures, or any CHR mechanism semantics.

Status. Normative C.16 depends on A.17 (canonical Characteristic) and A.18 (minimal CSLC in Kernel). Where C.16 cites external CG‑frames, the stance is through Part F rows and Bridges (with CL and loss notes), not by vocabulary import.

Out of scope. No computational recipes, no workflow prescriptions, no governance/process guidance. No definitions of normalization/indicatorization/scoring/comparison/selection mechanisms, no comparability routing policies, and no legality gate specifications. C.16 concerns objects of thought (intensions) and their validity conditions for measurement claims, not records or tooling. (Implementation guidance, if any, belongs outside Part C.)

#Problem & Context (Informative)

#The problem C.16 solves

Across FPF patterns, people say “score”, “metric”, “rating”, “property”. Without a shared substrate, numbers drift: 42 of what? on which scale? comparable to whom? C.16 eliminates drift by requiring every metric notion to bind to one Characteristic and one Scale, and by separating intensional anchors from descriptions and ScoringMethods. The result is portable meaning: a measure is always readable as a Coordinate on a declared Scale of a named Characteristic, with a principled path to evidence.

#Context and prior art

• Kernel canon. A.17 makes Characteristic the sole canonical anchor for measurability; A.18 fixes CSLC as the minimal sufficiency for interpretability. C.16 relies on both.
• Cross‑domain alignment. The MM‑CHR family already maps FPF U.Types to ISO 80000‑1 (Quantity), ISO/IEC 25024 (Data‑quality Characteristic), QUDT (QuantityKind/QuantityValue), W3C SOSA/SSN (Observable/Observed/Result), and domain “feature/metric” usage (Verspoor, TF Metrics). C.16 uses these rows as Bridges (Part F), preserving local senses and documenting losses.
• Open‑ended evolution. FPF replaces “lifecycle” with Role‑State Graph (RSG) style state checklists (A.2.5): movement is along certified states with checklists; re‑entry is allowed when distinctions change. C.16 uses this device only to frame readiness and revision of metric notions conceptually (no processes implied).

#Forces (Informative)

F1 — Interpretability first. A value detached from its Characteristic/Scale is meaningless; CSLC supplies minimum context. F2 — Transdisciplinarity. Physics, architecture, curation, sport judging—one substrate must cover all while respecting scale types and polarity. F3 — Intension vs description. Confusing the Characteristic (intensional object) with its rubric or exemplar text (descriptions) corrupts claims; C.16 keeps them distinct. F4 — Comparability without coercion. Ordinal ≠ interval; ratio admits unit change, ordinal does not; polarity matters for “better/worse”. C.16 encodes these as conceptual constraints, not formulas. F5 — Evidence sufficiency. A measure should be checkable in principle; evidence is a conceptual link (not storage advice). F6 — Lexical discipline. One canon in normative register; narrative labels are didactic only (Part E). C.16 reuses E.10’s register mapping.

#Solution Outline (Normative)

S1 — Exported objects. C.16 exports four intensional constructs to be used by any FPF pattern:

1. U.DHCMethod — a measurement template (a Definition) that binds one U.Characteristic to one Scale form, with declared polarity and (optionally) a citation point to the semantic owner of any non‑trivial equivalence/comparability claim that is relied upon elsewhere (e.g., a Bridge or a declared transformation owner). References to this template use U.DHCMethodRef. It is an intensional specification, not a record layout.
2. U.Measure — an assertion that a subject occupies a Coordinate (or Level, if discrete) on that Scale; the measure references its template and carries a conceptual pointer to evidence (U.EvidenceStub).
3. U.Unit — the unit kind associated with the Scale where applicable (physical quantities, normalized “points”, “stars”, “%”); unit coherence is part of comparability conditions.
4. U.EvidenceStub — a conceptual locator of grounds for the asserted value (type, identifier, brief summary, optional integrity notion); sufficiency criteria are conceptual (see §9, later).

S2 — Comparability stance (boundary‑aware). C.16 states only the direct comparability condition for measurement claims: same template (hence, same Characteristic + Scale + Unit semantics by reference to A.17/A.18). Any comparability claim that relies on transformations (normalization, scoring, aggregation, cross‑context transport, bridge losses, legality gating) MUST cite its single semantic owner (CN/CG surfaces and/or the relevant mechanism cards). C.16 does not define those transformations or their laws. (Details: §7–§8 in later parts.)

S3 — Evidence stance. A measure that, by its template, requires evidence, is inadmissible without a meaningful U.EvidenceStub. C.16 defines what it means conceptually for evidence to “connect” the subject, the Characteristic, and its symbolic description; mechanisms are out of scope. (Details: §9 in later parts.)

S4 — RSG framing (open‑endedness). Readiness, calibration, and revision of metric notions are expressed as RSG node moves with checklists (e.g., “characteristic anchored”, “Scale typed”, “Unit coherent”, “ScoringMethod declared”), allowing re‑entry when distinctions change; there is no terminal “lifecycle”. (Details: §10, later.)

#Lexical Discipline & Registers (Normative)

L1 — Canon. Use Characteristic / Scale / Level / Coordinate / Value / Score / Unit / ScoringMethod in Tech register; their U.* counterparts in Formal. Narrative labels (e.g., axis, points, stars) are didactic only, and are mapped at first mention to the Tech canon (E.10). L1‑bis — “metric”. The noun metric is not a Tech‑register canonical token for measurables; use Characteristic / Scale / Coordinate / Score / ScoringMethod. It may appear in the pattern title and in the Formal names U.DHCMethodRef / U.Measure. Do not use metric as a synonym for Characteristic or Score in normative prose. L2 — Intension vs Description. Keep intensional objects (U.DHCMethodRef, U.Characteristic) distinct from descriptions (rubrics, exemplars) and from claims (U.Measure). No collapsing of names across these layers. L3 — No synonym sprawl. In normative clauses do not substitute dimension/axis/property/feature for Characteristic; A.17 governs canonicalization. (C.16 inherits A.17’s rename policy.) L4 — Bridge‑only unification. Cross‑vocabulary sameness appears only via F.9 Bridges with CL and loss notes; C.16’s lexicon is the source side for measurement rows. L5 — Plain‑register shorthand. In Plain register metric MAY be used as shorthand for “template + readings”, but on first use it MUST be mapped to U.DHCMethod (template) and U.Measure (reading), and to the Tech canon terms that matter for meaning. L6 — No CHR‑mechanism terminology ownership. Tokens and laws owned by characterization mechanisms (e.g., normalization method tokens, invariant‑value notions, indicatorization policy terms) MUST be introduced only by their owner patterns. C.16 may mention them only as cited external terms, never as locally defined canon.

#Relations (pointers; details later)

To A.17 / A.18. C.16 uses A.17’s canonical Characteristic and A.18’s CSLC sufficiency; it neither re‑states nor weakens them. To Part F. C.16 is the exporting pattern behind measurement rows in UTS/Bridges (e.g., result‑value ↔ SOSA Result, ISO QuantityValue). To Arch‑CAL. Architectural qualities (Coupling, Cohesion, Evolvability) become Characteristics measured via C.16 templates; architectural dynamics read as trajectories in CharacteristicSpace (A.17 context).

#Normative Core Model (types & Standards)

Position. MM‑CHR does not redefine kernel terms; it binds them to an FPF‑level Standard that every metric must satisfy. Canonical vocabulary and CSLC duties are inherited from A.17/A.18 and referenced here without duplication.

Source of Truth A.17/A.18 are the sole sources of truth for Canon and CSLC; C.16 adopts by reference and forbids restatements of their definitions. C.16 only exports U.* constructs, comparability stance, evidence semantics, and RSG touch‑points.

CHR boundary reminder. Any notion that belongs to characterization mechanisms (normalization, indicatorization, scoring, aggregation, comparison, selection) appears in C.16 only as a pointer to its semantic owner. C.16 MUST NOT become a shadow owner for any such terminology or laws.

#U.DHCMethod — the measurement template (normative)

Role. An intensional Standard that fixes what is measured and how values must be read—without producing any values itself. It is a Definition, not a Measure. References to this template use U.DHCMethodRef. (Didactic: think “the meaning contract for a reading”.)

R‑MT‑1 (CSLC anchor). A DHCMethod SHALL bind to exactly one U.Characteristic and exactly one Scale‑form admissible for that Characteristic (cf. A.18). Level is optional (used when the scale is enumerated); otherwise values are given directly as Coordinates.

R‑MT‑2 (Unit). If the scale carries units (interval/ratio), the template SHALL designate a Unit of presentation. For ordinal/nominal scales, unit may be absent or a nominal label (e.g., “stars”). (Old MM‑CHR Annex A already listed these structural elements; here we fix the conceptual obligation. )

R‑MT‑3 (Polarity). For any ordered scale, the template SHALL declare polarity (higher‑is‑better / lower‑is‑better / target‑is‑best), as a semantic reading aid and as an input to consuming patterns. If polarity is target‑is‑best, the template SHALL name the target value (or target set) and MAY cite (by reference) the semantic owner of any tolerance/fall‑off convention used by downstream mechanisms or methods. C.16 does not standardize tolerance/fall‑off semantics; those belong to the semantic owner of the relevant scoring/normalization/selection mechanism or method description.

R‑MT‑4 (Applicability). A template SHALL state the applicability frame (what kinds of subjects it meaningfully applies to) in conceptual terms; this is a property of the definition, not of any measure.

R‑MT‑5 (Intension vs description). The template is an intensional object. Any rubric, checklist, or prose that explains it is a Description; they are related but not identical (E.10 discipline).

R‑MT‑6 (Cardinality hint). A Template MAY declare its intended cardinality semantics for a subject within a time stance (e.g., latest‑only, at‑most‑one‑per‑day, time series). Where declared, claims outside that semantics are inadmissible conceptually (they must be reframed or versioned). Purpose: prevent silent duplicates and mixed regimes without imposing storage logic.

R‑MT‑7 (MAY). UncertaintyPolicy — optional conceptual guidance on how uncertainty is expressed/read (e.g., band/CI/quantile), without prescribing methods/tools. (Informative examples: calibrated probability with a confidence band; a prediction interval; a set‑valued reading such as a prediction set.)

#U.DHCMethod — the measurement template (normative)

Role. An intensional Standard that fixes what is measured and how values must be read—without producing any values itself. It is a Definition, not a Measure. References to this template use U.DHCMethodRef. (Didactic: think “the meaning contract for a reading”.)

R‑MT‑1 (CSLC anchor). A DHCMethod SHALL bind to exactly one U.Characteristic and exactly one Scale‑form admissible for that Characteristic (cf. A.18). Level is optional (used when the scale is enumerated); otherwise values are given directly as Coordinates.

R‑MT‑2 (Unit). If the scale carries units (interval/ratio), the template SHALL designate a Unit of presentation. For ordinal/nominal scales, unit may be absent or a nominal label (e.g., “stars”). (Old MM‑CHR Annex A already listed these structural elements; here we fix the conceptual obligation. )

R‑MT‑3 (Polarity). For any ordered scale, the template SHALL declare polarity (higher‑is‑better / lower‑is‑better / target‑is‑best), as a semantic reading aid and as an input to consuming patterns. If polarity is target‑is‑best, the template SHALL name the target value (or target set) and MAY cite (by reference) the semantic owner of any tolerance/fall‑off convention used by downstream mechanisms or methods. C.16 does not standardize tolerance/fall‑off semantics; those belong to the semantic owner of the relevant scoring/normalization/selection mechanism or method description.

R‑MT‑4 (Applicability). A template SHALL state the applicability frame (what kinds of subjects it meaningfully applies to) in conceptual terms; this is a property of the definition, not of any measure.

R‑MT‑5 (Intension vs description). The template is an intensional object. Any rubric, checklist, or prose that explains it is a Description; they are related but not identical (E.10 discipline).

R‑MT‑6 (Cardinality hint). A Template MAY declare its intended cardinality semantics for a subject within a time stance (e.g., latest‑only, at‑most‑one‑per‑day, time series). Where declared, claims outside that semantics are inadmissible conceptually (they must be reframed or versioned). Purpose: prevent silent duplicates and mixed regimes without imposing storage logic.

R‑MT‑7 (MAY). UncertaintyPolicy — optional conceptual guidance on how uncertainty is expressed/read (e.g., band/CI/quantile), without prescribing methods/tools. (Informative examples: calibrated probability with a confidence band; a prediction interval; a set‑valued reading such as a prediction set.)

#U.Measure — the recorded reading (normative)

Role. A claim that a subject occupies a Coordinate (or named Level) on the template’s scale, backed by a minimal pointer to its grounds.

R‑ME‑1 (Template binding). Every Measure SHALL reference exactly one DHCMethodRef; its Value/Coordinate must be valid for that template’s scale (type, range, category).

R‑ME‑2 (Subject). A Measure SHALL identify its subject‑of‑measurement (the bearer) unambiguously in the same Context of meaning as the template’s applicability frame.

R‑ME‑3 (Evidence stub). Where the template requires it, a Measure SHALL include an EvidenceStub—a conceptual pointer sufficient to support independent reasoning about the claim’s origin. (The old spec framed this as “traceability/provenance”; we keep only the conceptual role here. )

R‑ME‑4 (Time stance). A Measure SHALL carry a time stance (e.g., “as‑observed at T”, or “as‑aggregated over W”), expressed conceptually; it disambiguates the reading’s intended window without prescribing formats.

R‑ME‑5 (Entity vs relation). If the Characteristic is relational, the subject is a tuple (pair, k‑tuple); the wording of the claim reflects that arity and the template’s relation topology (cf. A.17).

R‑ME‑6 (MAY). UncertaintyStub — optional conceptual pointer to the adopted uncertainty estimation for this Measure, if required by the template.

Informative anchor. The old Annex B example “Article Completeness” illustrates the split template/measure/evidence; C.16 keeps the split but forbids storage‑level talk.

#U.Unit — semantics of quantities (normative)

Role. A conceptual marker of quantity kind and admissible conversions within that kind; not every scale requires it.

R‑UN‑1 (Quantity kind). Where units apply, the template SHALL indicate the quantity kind (e.g., Time, Length, Dimensionless‑Score). Units are meaningful only within one kind.

R‑UN‑2 (Convertibility). Comparisons across different units are permitted iff they are convertible by kind‑preserving transformation (ratio/interval scales); for ordinal/nominal scales, no numeric conversions exist. (Old Annex A listed conversion hints; here we assert the conceptual boundary. )

R‑UN‑3 (Canonical labels). % denotes “fraction×100”; “points” denotes dimensionless magnitudes used for scores; “stars” denotes discrete ordinal marks. These are labels of representation, not new characteristics.

R‑UN‑4 (Quantity‑kind bridge). A Template on an interval/ratio Scale SHOULD name the underlying quantity kind (e.g., ISO 80000/QUDT category) to enable safe external bridges. This does not import external vocabularies; it declares an alignment point.

#U.EvidenceStub — pointer to grounds (normative)

Role. A compact tie from a Measure to the grounds sufficient for reasoned audit (not a repository prescription).

R‑EV‑1 (Minimal sufficiency). An EvidenceStub SHALL carry, at minimum, a type‑of‑ground and an identifier sufficient to retrieve or reconstruct the grounds in the appropriate Context of meaning.

R‑EV‑2 (Compositionality). Multiple grounds may be composed as a finite set; composition is commutative/associative/idempotent at the level of stubs, enabling conceptual merge of corroborations.

R‑EV‑3 (Soundness axiom). A Measure is MM‑CHR‑admissible only if at least one auditable chain of grounds can be stated from the bearer to the Characteristic via an appropriate Description (Object–Concept–Symbol triangle in the episteme). (Note: mechanism‑level admissibility gates (e.g., legality/evidence thresholds in CG‑frames or CHR mechanisms) are owned elsewhere; C.16 defines only the conceptual “has grounds” link.) R‑EV‑3 (Soundness axiom). A Measure is MM‑CHR‑admissible only if at least one auditable chain of grounds can be stated that connects: bearer (subject) → grounds → Characteristic → Coordinate/Level on the declared Scale, in the appropriate Context of meaning. (Informative: this is the object–concept–symbol triangle.)
(Boundary note: mechanism‑level admissibility gates (e.g., legality/evidence thresholds in CG‑frames or CHR mechanisms) are owned elsewhere; C.16 defines only the conceptual “has grounds” link.)

#Polarity, Comparability, and ScoringMethods (normative)

Notation. To avoid clashes with the kernel’s global aggregation symbol, this FPF pattern denotes a ScoringMethod (score‑level mapping) by 𝒢 (calligraphic 𝒢).

R‑POL‑1 (Declared polarity). Every ordered scale SHALL declare polarity at the template. Any disclosed scoring method 𝒢 that issues a Score for that template SHALL be order‑compatible with the declared polarity semantics (monotone for ↑/↓ polarity; target‑aware only when the target semantics is explicitly declared and cited where it depends on external conventions).

R‑CMP‑1 (Direct comparability). Two readings are directly comparable only when they reference the same U.DHCMethodRef (hence share Characteristic + Scale + Unit semantics by reference to A.17/A.18). “Same‑template” is the only comparability relation defined by C.16. (Clarification: sharing a name, unit label, or scale type across distinct templates is not sufficient for comparability in MM‑CHR; cross‑template comparability must be established via R‑CMP‑2.)*

R‑CMP‑2 (Transformed comparability is cited, not defined). If a comparison relies on any transformation or routing step (e.g., normalization, indicatorization, scoring, aggregation, cross‑context transport, bridge conversions, legality gates), that step SHALL be named and cited via its single semantic owner. C.16 does not define such transformations, their law sets, or their admissibility conditions.

R‑G𝒢‑1 (ScoringMethod disclosure). If a pattern issues a Score (a value on a score scale), its scoring method 𝒢 : Coordinate → Score SHALL be identified by reference to its semantic owner (e.g., a method description card), and SHALL disclose: (i) a bounded codomain / score range, and
(ii) an explicit order‑compatibility statement (e.g., monotonicity) consistent with the template’s declared polarity.
When reproducibility matters, the reference SHOULD be edition‑pinned (per the owner’s authoring discipline).
C.16 does not define scoring methods; it only requires that a score be interpretable as a reading on a declared scale.

R‑G𝒢‑2 (Ordinal respect). For ordinal inputs, any cited scoring method must be order‑preserving; interval assumptions MUST NOT be smuggled in. (Normative source for scale legality remains A.18; C.16 only enforces “no silent semantics upgrade”.)

#Entity vs Relation bindings (normative clarifications)

R‑ER‑1 (Arity preservation). If the Characteristic is U.EntityCharacteristic, the subject is one bearer; if U.RelationCharacteristic, the subject is a k‑tuple (k ≥ 2). The Measure’s claim text SHALL reflect this arity.

R‑ER‑2 (Relation scale). Relation‑valued scales SHALL fix their symmetry/antisymmetry and directionality (e.g., distance symmetric; influence directional), at the template level.

R‑ER‑3 (Bridge to CG‑frames). In architectural CG‑frames, Coupling/Cohesion are Characteristics over modules (structure) or roles (function). Their measures are relational (Coupling) or unary (Cohesion within an element), but both live in the same MM‑CHR substrate. (Alignment hinted in the old mapping rows across contexts. )

#Acceptance (conceptual, RSG‑aware)

Acceptance here is thought‑level. It uses the Role‑State Graph (A.2.5) pattern to organise mental checks—no “lifecycle” narratives.

SCR‑C16‑A (Template sufficiency). You can check—without invoking tooling—that the template has: (i) a fixed Characteristic (A.17),
(ii) a typed Scale form (A.18), and
(iii) coherent Unit semantics where applicable (plus declared polarity for ordered scales).

SCR‑C16‑B (Reading sufficiency). For a given subject, you can check that the reading: (i) cites the template,
(ii) states a value valid for the Scale (Coordinate/Level),
(iii) states a time stance,
(iv) names 𝒢 when a Score is issued, and
(v) provides EvidenceStub(s) where the template requires them.

SCR‑C16‑C (Comparability). When two readings are placed side‑by‑side, you can state in one breath whether they are comparable as‑is or only after 𝒢, and why.

SCR‑C16‑D (Evidence adequacy). For any required EvidenceStub, you can sketch at least one auditable chain of grounds from the subject to the Characteristic via a Description in the right Context.

#C.16:5.7 Cross‑references & anchors

• A.17 (CHR‑NORM). Canonical Characteristic and Entity/Relation split; lexical rules and alias sunset.
• A.18 (CSLC‑KERNEL). One Characteristic + one Scale per template; Level optional; operation guard by scale type.
• Annex C (old MM‑CHR). Cross‑domain alignment hints for Characteristics/Observations/Quantities across ISO 80000, ISO/IEC 25024, QUDT, SOSA/SSN (used here only as conceptual witnesses).

#Scale‑type legality quick reference (Informative)

Didactic note. This table is a memory aid for engineers and managers. It does not introduce new legality rules. Normative legality of operations by scale type is owned by A.18 (CSLC) (and, where mechanized in CG‑frames, by the relevant legality profiles). If any row below conflicts with A.18, treat it as an illustrative example and follow A.18.

Reminders (informative; see A.18 for normative rules). G‑1 (Order). On ordinal, transforms should be monotone. G‑2 (Differences). On interval/ratio, Δ is meaningful; on ordinal/nominal, it is undefined. G‑3 (Ratios). Only ratio Scales admit x/y semantics; interval/ordinal/nominal do not. G‑4 (Unit coherence). Interval/ratio arithmetic presumes compatible units (or a declared conversion). G‑5 (Target polarity). If polarity is targeted, comparisons use distance‑from‑target semantics as declared by the relevant owner (template + cited method/mechanism).

(These rules line up with the MM‑CHR exposition of CSLC and term discipline; A.17 fixes the lexical side.)

#Evidence Semantics (Normative)

#What an Evidence Stub is (and is not)

Definition. U.EvidenceStub is a conceptual pointer that ties a measure to the grounds sufficient for independent checking (observations, arguments, lawful transformations). It is not the run log, not the carrier, and not the intensional characteristic itself. This keeps intension–description–specification distinct per E.10.D2 and the Clarity Lattice.

Rule Σ‑1. Whether evidence is required is a property of the metric template; if required, each U.Measure SHALL include an U.EvidenceStub. Rule Σ‑2. Evidence composition is commutative, associative, idempotent at the concept level (sets/multisets of grounds); combining grounds can never reduce what is knowable about the measure’s warrant. Rule Σ‑3. Soundness minimum: there exists a conceptual chain linking bearer → Characteristic → Scale/Unit → admissible method/episteme. (No “free‑floating numbers”.) Rule Σ‑4. Any declared agreement construct used as evidence (e.g., dual readings, panels) SHALL respect the template’s scale type (per A.18) (e.g., order‑based concordance for ordinal; tolerance‑based agreement for interval/ratio). Note (boundary). CG‑frame evidence thresholds (e.g., “minimal evidence” gates used by selection/scoring/comparison mechanisms) are owned elsewhere. C.16 defines only the EvidenceStub semantics that such gates may cite. Anchors: MM‑CHR units/evidence notion; Strict Distinction and the separation of objects from their descriptions/specs.

#Integration with RSG & Dynamics (Normative/Clarifying)

#RSG (Role‑State Graph) touch‑points

MM‑CHR supplies recognisers used in State Checklists. A checklist criterion may refer to a measure (e.g., “Cohesion ≥ T on ordinal ladder”), but the state itself remains intensional; the checklist is its description, and a StateAssertion is an evidence‑backed verdict over a Window. No lifecycle language is implied; RSGs are open‑ended graphs with re‑entry edges.

Rule RSG‑M1. When a checklist cites a measure, it SHALL do so by Characteristic + Scale semantics (and unit if applicable), not by colloquial aliases; Tech/Formal registers apply. Rule RSG‑M2. Thresholds in checklists MUST respect the scale type (no ratio talk on interval scales; no arithmetic on ordinal ladders).

#Dynamics & CharacteristicSpace

U.Dynamics.stateSpace is a CharacteristicSpace—a named set of Characteristics with units/topology. MM‑CHR provides the measurement side of that space; patterns specify the transition law. Architectural or epistemic dynamics are then trajectories in the declared CharacteristicSpace. No procedural or storage commitments are implied.

#Conformance Checklist (Normative)

Thought‑level acceptance conditions for authors and reviewers; they constrain meaning, not tooling.

CC‑MCHR‑1 - CSLC anchoring. Each U.DHCMethodRef binds exactly one U.Characteristic and exactly one scale; each U.Measure carries a value valid for that scale (cf. A.18). CC‑MCHR‑2 - Polarity declared. Every ordered scale in a template declares polarity; any Score via 𝒢 is monotone w.r.t. that polarity. CC‑MCHR‑3 - Unit coherence. Claims that compare or combine values are grounded in unit coherence (or declared conversions for interval/ratio). CC‑MCHR‑4 - Comparability honesty. Ordered comparisons are asserted only when R‑CMP‑1 holds (same‑template direct comparability) or when a named, cited transformation owner is provided per R‑CMP‑2; otherwise authors use qualitative/set‑level language. CC‑MCHR‑5 - Evidence sufficiency. Where evidence is required by the template, the measure’s grounds are conceptually sufficient to retrace the claim; composition respects Σ‑1…Σ‑4. CC‑MCHR‑6 - RSG alignment. If a measure gates a state in an RSG, the checklist criteria respect scale semantics and the intensional vs description split. No lifecycle phrasing; use RSG open‑ended moves. CC‑MCHR‑7 - Dynamics awareness. Where discussions involve change, the CharacteristicSpace is named (characteristics, units, topology) and separated from the transition law. CC‑MCHR‑8 - Lexical guard‑rails. Tech identifiers and headings use Characteristic/Scale/Level/Value/Score/Unit/ScoringMethod; aliases (axis/dimension/points/stars) appear only in explanatory Plain register with a first‑mention mapping to the Tech canon.

#Invariants & Anti‑Patterns (Normative unless marked “Informative”)

#Invariants (N‑rules)

N‑1 — One Characteristic + one Scale per template. Every U.DHCMethodRef binds exactly one Characteristic and exactly one Scale (its type + admissible range or level‑set). This is the CSLC sufficiency condition for interpretability.

N‑2 — Value validity. A U.Measure holds a Value that is admissible for the template’s Scale (numeric range, categorical level); when a Level is used, it is among the named rungs declared for that Scale.

N‑3 — Polarity is declared at the template. For ordered Scales, the template states the comparison direction (↑ better / ↓ better / target‑is‑best). Any ScoringMethod mapping to Score preserves that monotonic ordering. (Note: we use “ScoringMethod mapping” instead of the Greek letter used elsewhere in FPF to avoid symbol conflicts.) For ordered Scales, the template states the comparison direction (↑ better / ↓ better / target‑is‑best). Any scoring method 𝒢 that issues a Score is order‑compatible with that declared polarity semantics.

N‑4 — Unit coherence. Within one template there is one primary Unit of expression (or an explicit level‑set for non‑numeric Scales). Conversions are conceptually allowed only where the Scale supports meaningful arithmetic (interval/ratio); nominal/ordinal Scales are not subject to numeric conversions.

N‑5 — Comparability guard. Two Measures are comparable iff they share the same template (hence, the same Characteristic + Scale + Unit) or stand in an explicit comparability relation whose single semantic owner is cited (e.g., an F‑cluster Bridge, or a cited characterization mechanism’s declared equivalence). Otherwise, comparability is not presumed.

N‑6 — Evidence as conceptual anchoring. If a template requires it, each Measure includes an EvidenceStub that conceptually links the Value to its grounds; absence where required makes the Measure inadmissible for use. (This is a conceptual obligation; no process mechanics are implied.)

N‑7 — Arity clarity. If the Characteristic is relational (applies to a pair/tuple), the subject of measurement is the relation itself; the reading must not be re‑described as a unary property of either participant.

N‑8 — Open‑ended evolution; graph, not lifecycle. When MM‑CHR is used in change reasoning, movement happens in a CharacteristicSpace and along a Role‑State Graph (RSG). There is no lifecycle terminal; revisions may re‑enter earlier framing nodes as per A.17. (Conceptual control structure only.)

#Anti‑Patterns (A‑rules) — with cures

A‑1 — Scale drift under the same template. Smell: the Scale meaning (bounds, categories) shifts while the template ID remains. Cure: version the template; declare the relation in the Unification suite.

A‑2 — Arithmetic on ordinal. Smell: averaging “stars” or ranking labels as if they were intervals. Cure: either keep order‑respecting operations only, or introduce a ScoringMethod that defines a proper Score range.

A‑3 — Unit soup. Smell: mixing milliseconds and seconds for the same template, or “%” and “points” for one Scale. Cure: one primary Unit per template; conversions (when meaningful) are declared conceptually, not ad‑hoc.

A‑4 — Alias leakage. Smell: “axis/dimension/point/ladder” in normative identifiers or headings. Cure: use only canonical tokens in normative prose; narrative labels are allowed solely in Plain register with first‑mention mapping (A.17).

A‑5 — Multi‑Characteristic stuffing. Smell: one template tries to carry a vector of Values for several Characteristics. Cure: separate templates (one Characteristic each) and compose coordinates explicitly when needed.

A‑6 — Evidence afterthought. Smell: Measures required to have grounds are introduced without an intelligible EvidenceStub. Cure: treat the EvidenceStub as part of the measurement claim itself, not an accessory.

A‑7 — Template mutation after Measures exist. Smell: retro‑editing Characteristic/Scale/Unit of an active template. Cure: immutability of that triad post‑use; publish a successor template if the concept changes.

A‑8 — Score‑of‑everything. Smell: collapsing heterogeneous Values into a single “points” Score without declared ScoringMethod and SCP. Cure: retain the Value on its Scale; add an explicit scoring method (by reference to its owner) and an explicit legality profile (owned elsewhere) only when there is a justified need for a Score.

#Cross‑Domain Vignettes (Informative, transdisciplinary)

Each vignette shows an CSLC‑conformant template → measure, without duplicating the A.17/A.18 glossaries.

V‑A (Architecture — relational property). Characteristic: Coupling (relational) between modules; Scale: ordinal {Low, Med, High}; Unit: level‑labels; Polarity: ↓ better. Reading: subsystem pair ⟨M₁, M₂⟩ gets Med; ScoringMethod (optional) maps levels monotonically to a bounded Score for comparative dashboards.

V‑B (Physics — interval/ratio). Characteristic: ResponseTime; Scale: ratio with non‑negative reals; Unit: seconds; Polarity: ↓ better. Reading: subject S has 0.237 s; direct comparability holds with readings on the same template; cross‑template comparability requires an explicitly cited equivalence/Bridge/transformation owner.

V‑C (Performing arts — ordinal). Characteristic: EdgeControlQuality; Scale: ordinal levels 1…5; Unit: level‑labels; Polarity: ↑ better. Reading: performance P gets 4; any aggregation remains order‑respecting. If a numeric dashboard score is needed, cite a scoring method 𝒢 that maps levels monotonically to a bounded Score.

V‑D (AI ethics — ratio). Characteristic: ParityGap (difference of positive rates); Scale: interval with symmetric bounds; Unit: percentage points; Polarity: ↓ better (0 is target). Reading: model M on cohort C shows 3.2 pp; evidence points conceptually to the derivation rationale (inputs, reference cohorts).

#Relations & Placement (Informative)

Kernel. MM‑CHR imports the canonical Characteristic vocabulary and the CSLC discipline fixed by A.17 and A.18; it does not redefine them. CharacteristicSpace reasoning (for change) lives in the patterns that consume MM‑CHR readings.

Using patterns. KD‑CAL, Arch‑CAL and others instantiate templates and produce measures; MM‑CHR remains a neutral measurement substrate. Trade‑off analyses and architectural trajectories operate over coordinates that MM‑CHR makes available, not inside MM‑CHR.

Unification (F‑cluster). External standards (e.g., ISO 80000 quantity types; W3C SOSA/SSN observable properties; QUDT units/quantity kinds) are related via Concept‑Set rows and Bridges; MM‑CHR treats those alignments as context supplied by F‑patterns, not as local re‑definitions.

#C.16:End