#KindBridge & CL^k — Cross-context Mapping of Kinds

C.3.3 · Cluster C.I - Core CALs / LOGs / CHRs · Stable · Part C - Kernel Extension Specifications

#About this pattern

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#How to use this pattern

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One-line summary. Defines KindBridge as the direct cross-context relation between one exact source local kind and one exact target local kind under pinned reference-scheme editions and a declared mapping predicate. A separate C.2.1 bridge-assertion episteme states direction, paired KindSignature editions, order preservation or collapse, CL^k, loss notes, definedness, evidence, and admitted use. Target classification is always a fresh four-input C.3.2 judgment; a source result or bridge assertion never creates target truth. CL^k affects only the receiving reliance value R, while F and Claim scope G remain with their own owners.

Status. Normative in Part C. Identifier C.3.3. Audience. Engineering managers, architects, assurance leads, editors.

Depends on.

• C.3.1 — U.Kind & SubkindOf (Core): kinds are context-local U.Kind values; U.SubkindOf is an obtaining direct relation under an exact effective reference scheme; kinds carry no Scope.
• C.3.2 — Kind intent, judgment, and extension: KindSignature is a declaration episteme; J(candidate, kind, signatureEdition, slice) returns true, false, or unknown; an optional pinned-edition KindExtension is only a representation of true candidates.
• A.2.6 — USM (Context slices & Scopes): Claim scope (G) and Work scope live on claims/capabilities; scope bridging and CL penalties are defined there.
• C.2.2 — F–G–R: weakest‑link; penalties land in R, not F/G.
• C.2.3 — U.Formality (F): signature rigor.

Non‑goals. — No repository/notation mandates; conceptual only. — No Scope mapping here (that’s USM); KindBridge maps kinds, not scopes. — No new arithmetic on CL^k; it reuses the ordinal anchor semantics of CL (Part B) but applies to kinds.

Cross‑context reuse fails in two orthogonal ways:

#Keywords

• KindBridge direct relation
• bridge assertion episteme
• target judgment
• CL^k
• loss
• R penalty.

#Relations

#Content

#Purpose & Audience

Cross‑context reuse fails in two orthogonal ways:

1. Applicability (G): where the claim holds (handled by USM Scope Bridge).
2. entityOfConcern (Kind): what the claim quantifies over (handled by KindBridge).

C.3.3 gives managers an explicit, auditable channel for (2), so a team can say, with evidence: “Vehicle in Lab maps to TransportUnit in Plant with CL^k=2; the EV subkind collapses; here’s what we lost.” Guards stay deterministic; assurance math stays clean (penalties in R only).

#Context

Contexts use different classifications: ontology classes vs shape Standards, regulatory cohorts vs app types, etc. Informal “same‑name” reuse silently mutates entityOfConcern. USM already made scope moves explicit. KindBridge does the same for kinds: declare the mapping, rate its congruence, and capture known losses.

#Problem

1. Semantic drift. Moving a claim into a target‑context with a different taxonomy changes “what counts” without anyone noticing.
2. Hidden order breaks. Subkind relationships invert or vanish; downstream proofs/tests are misapplied.
3. Entangled channels. Teams conflate “scope mapping” with “kind mapping,” making it impossible to assign penalties coherently.
4. Incomputable guards. “We map it somehow” yields non‑deterministic classification at guard time.

#Forces

#Solution — Direct relation and bridge assertion

A KindBridge occurrence is an obtaining direct relation between one exact source local U.Kind and one exact target local U.Kind. The kinds remain independently identified in their source and target reference schemes. The bridge does not move, clone, or construct either kind. Its obtaining predicate states the exact mapping direction, source and target scheme editions, definedness, and the direct kind-intent correspondence required for that pair. Preservation, collapse, inversion, or non-preservation of a source U.SubkindOf fact is instead a separate assertion over the relevant pair of obtaining KindBridge relations and the exact source and target order facts. The paired KindSignature editions are declaration epistemes used to evaluate the correspondence predicate; they are not relation participants or occurrence-identity discriminators.

KindBridge is the direct relation kind governed here under the common U.Relation occurrence discipline of A.6.REL. This spelling does not by itself admit a durable dependent U-kind named U.KindBridge. An F.9 Bridge, Bridge Card, mapping row, or publication can serve as a bridge assertion or representation only when its exact content and EntityOfConcern support that use; its existence does not make a KindBridge relation obtain or identify an occurrence by record identity.

Keep the direct relation separate from the C.2.1 bridge-assertion episteme used to communicate or rely on it. That episteme designates the exact bridge occurrence when occurrence identity is needed and carries the mapping rule, order-preservation status, CL^k, loss notes, definedness area, evidence, and admitted receiving use. An assertion, bridge card, table row, or mapping expression neither makes the bridge relation obtain nor creates a target KindSignature. If a target declaration is needed, author and identify that separate C.3.2 declaration episteme first.

For every classified candidate, the target context performs its own exact judgment:

J(candidate, targetKind, targetSignatureEdition, TargetSlice) ∈ {true, false, unknown}

A source-context judgment may support the bridge or reliance assertion but is never reused as target truth. Missing target-side evidence, an unavailable target-declaration dependency, or a candidate outside the target evaluation domain yields unknown for the target C.3.2 judgment. An unavailable mapping dependency or a bridge use outside declared definedness instead leaves the required bridge reliance unsettled or inadmissible; a receiving guard declines that cross-context use without rewriting an independently evaluated target judgment.

When a receiving claim relies on an obtaining bridge and the target judgment, the bridge-assertion episteme supplies the assessed CL^k and loss basis. Apply the monotone Ψ(CL^k) consequence to R only. Do not change declaration formality F or Claim scope G.

#Norms & Invariants (normative)

The following formalize the KB‑01…KB‑12 rules announced in C.3.

#Direct relation subject and scope

KB-01 (Participants and obtaining). A KindBridge relation occurrence has exactly two direct participants: one source local kind and one target local kind. It obtains only under the named source and target reference-scheme editions when the directional correspondence predicate holds for the paired kind interpretations within declared definedness. Order preservation or collapse is not an obtaining condition for one pair relation; it is asserted separately over the relevant KindBridge and U.SubkindOf occurrences. The KindSignature epistemes used to evaluate the correspondence, their formality values, mapping expression, bridge assertion, evidence, CL^k, and loss notes are not relation participants.

KB-02 (No Scope). A KindBridge MUST NOT map Claim or Work scope G. Scope translation uses the USM Bridge + CL channel (A.2.6, Part B). U.ContextSlice values appear in bridge applicability and target judgments, not as scope stored on either kind.

No blended score. Congruence for Scope (CL) and for Kind (CL^k) MUST NOT be aggregated into a single interoperability score in guards; each channel is assessed and penalized separately. See Annex C.3.A §5 (E-06).

#Settlement, assertion, and identity

KB-03 (Direct settlement). The C.3.3 direct relation settlement SHALL make recoverable:

1. the exact source-kind and target-kind participants, direction, and source/target reference-scheme editions;
2. the directional mapping obtaining predicate and its definedness area, with no implicit latest; and
3. the occurrence-identity rule: when explicit identity is needed, source kind, target kind, direction, and both reference-scheme editions distinguish the occurrence.

A separate C.2.1 bridge-assertion episteme SHALL name the paired source and target KindSignature editions used to evaluate the predicate and, for the receiving use, state the mapping-rule expression, the status of each selected obtaining U.SubkindOf relation as preserved, collapsed, not preserved, or unknown, plus any current CL^k, loss notes, evidence, admitted use, and assertion polarity. Another assertion, mapping expression, card, row, signature edition, or publication edition does not create another relation occurrence. A changed assertion, signature, or mapping-rule edition prompts reevaluation of obtaining; it does not reidentify a continuing relation when the participants, direction, and scheme editions remain fixed and the same relation still obtains. A changed participant, direction, or scheme edition is another proposed occurrence and must establish obtaining independently.

KB-04 (Determinism and local evaluation). With fixed scheme versions and mapping-rule edition, the asserted bridge use MUST be reproducible. Independently, with fixed candidate, target KindSignature edition, TargetSlice, and target-declaration dependencies, evaluate reproducible J(candidate, targetKind, targetSignatureEdition, TargetSlice) in the target context. A source judgment or bridge assertion may support reliance but MUST NOT be copied into the target result. Preserve unknown only for a target judgment whose own declared evaluation cannot settle; an unsettled or inadmissible bridge use and the guard's refusal remain separate receiving predicates.

#Order & Monotonicity

KB-05 (Monotone order). If a bridge assertion states that source order fact SubkindOfObtains(k1, k2; sourceRS) is preserved, it SHALL designate exact target kinds k1' and k2', the respective obtaining KindBridge relations from k1 to k1' and from k2 to k2', and the basis on which SubkindOfObtains(k1', k2'; targetRS) holds. Identify a target R_sub : U.SubkindOf occurrence only when a receiving use needs occurrence identity. KB-06 (No inversions). A bridge assertion MUST NOT state preservation when the mapped target order is inverted. If SubkindOfObtains(k2', k1'; targetRS) holds for distinct mapped kinds, state non-preservation and the exact loss. If the required target order cannot be settled, state unknown; do not turn non-settlement into either preservation or inversion. KB-07 (Collapse semantics). A bridge assertion may classify selected source subkind distinctions as collapsed when several source kinds correspond to one target kind. The assertion SHALL designate the affected obtaining U.SubkindOf relations and state the lost properties; the direct bridge relation does not alter either local order.

#Congruence & Assurance

KB-08 (Anchor reuse and AT neutrality). CL^k reuses the ordinal anchor semantics of CL but assesses the declared bridge use over kind intent and order. The bridge-assertion episteme labels it kind-congruence. Neither the obtaining KindBridge relation nor its assertion computes or alters KindAT; AT is editorial and independent of CL^k. KB-09 (Effect on R only). When a receiving claim relies on an obtaining KindBridge relation and on J(candidate, targetKind, targetSignatureEdition, TargetSlice), apply the bridge-assertion episteme's monotone Ψ(CL^k) consequence to R alongside any independent scope-bridge penalty. Do not alter F or G. An unknown target judgment remains unknown even when the guard declines use. KB‑10 (Chaining). For a chain of bridges, effective CL^k = min of the links (weakest‑link).

#Loss Notes & Definedness

KB-11 (Loss notes). The bridge-assertion episteme SHALL state which KindSignature invariants are not preserved, which obtaining source U.SubkindOf relations are collapsed or not preserved, and any higher-equality caveats. These claims do not rewrite the source or target kinds. KB-12 (Definedness and guard use). The bridge obtaining predicate and assertion SHALL state the definedness area. Outside it, a receiving guard declines that cross-context bridge use. The independently evaluated target classification retains its own true, false, or unknown value; bridge inapplicability neither rewrites it nor denies that another bridge could obtain.

#Interactions (informative)

#With USM Scope bridges (two channels)

When using a claim across Contexts, expect two concurrent bridges:

• Scope Bridge (USM): the exact scope-bridge occurrence supports translation of G; its separate assessment supplies CL and the Φ(CL) consequence to R.
• KindBridge (this pattern): the obtaining direct relation connects exact source and target kinds; its separate bridge assertion supplies CL^k, loss, and the Ψ(CL^k) consequence to R.

Discipline: compute both; do not collapse them into one “interoperability score.”

See Annex C.3.A §5 (E‑01) for the normative evaluation order in guards.

#With target classification (C.3.2)

After an obtaining KindBridge relates source kind k to independently identified target kind k', evaluate the exact target judgment J(candidate, k', targetSignatureEdition, TargetSlice). If a mapping rule motivates another target KindSignature, a system authors and identifies that declaration episteme separately; the bridge relation and its assertion do not construct it. A source judgment may be evidence for the receiving reliance claim but never substitutes for the target judgment.

#With Role masks (C.3.4)

A cross-context masked use requires an obtaining KindBridge relation between exact source and target kinds, the separate bridge assertion, a target RoleMask declaration episteme, and a MaskAdapter declaration episteme when constraints or bindings differ. The target context evaluates its exact J_mask; source masked results are not target truth. Any justified bridge penalties affect R only, and a stable target refinement requires an independently identified local kind and obtaining U.SubkindOf relation.

#With guards (Annex C.3.A)

Use the Guard_XContext_Typed macro (Annex C.3.A), which requires both bridges and applies both penalties to R:

• find Scope bridge (CL≥threshold), translate G, check coverage;
• establish the exact KindBridge relation and its bridge assertion, recover the independently identified target kind and signature edition, and evaluate the exact target judgment;
• apply Φ(CL) and Ψ(CL^k) to R; keep F/G untouched.

#Authoring, Review & Rating Guidance (informative)

#Authoring a KindBridge assertion

• Start narrow & honest. Declare only the kinds and ⊑ links you actually preserve; mark the rest unknown.
• Prefer independently identified target kinds. If the target already has a suitable kind and declaration edition, relate that kind directly. If a new target declaration is required, author it separately before asserting bridge obtaining; list what the mapping predicate preserves, relaxes, or drops.
• Write loss notes in plain language. Example: “EV vs ICE subkinds collapsed; battery‑health invariants dropped.”
• Fix the definedness area. Bind to target Standards/versions and any environment selectors essential to classification.
• Assign CL^k from exemplars. Calibrate on concrete counter‑examples and preserved properties; resist optimistic ratings.

#Review playbook (10 minutes)

1. Two bridges present? Scope Bridge and KindBridge?
2. Order claims honest? Any ⊑ inversions? Collapses disclosed?
3. CL^k plausible? Based on preserved properties, not name similarity?
4. Loss notes present? Will they force narrowing of Scope or extra tests?
5. Definedness area clear? Guard will fail closed outside it?
6. Penalties wired to R? No hidden tweaks to F/G?

#Rating CL^k (rules of thumb)

• High CL^k: signature equivalence or up‑to‑iso; ⊑ fragment preserved; only cosmetic losses.
• Medium CL^k: some invariants relaxed or lost; selected subkinds collapsed; order preserved on critical path.
• Low CL^k: name‑only correspondences; properties diverge; order not preserved. Expect significant R penalty and/or adapters.

#Worked Examples (informative)

#Vehicle → TransportUnit (manufacturing)

Source kinds Vehicle and PassengerCar, target kinds TransportUnit and PassengerTransportUnit, and their exact declaration editions are independently identified. One KindBridge relation obtains from Vehicle to TransportUnit and another from PassengerCar to PassengerTransportUnit under the pinned scheme editions. The bridge assertion states that source fact SubkindOfObtains(PassengerCar, Vehicle; sourceRS) is preserved by target fact SubkindOfObtains(PassengerTransportUnit, TransportUnit; targetRS), while the EV distinction is collapsed; it records CL^k=2, the lost battery-health invariants, and definedness limited to registryAPI v1.4 in the selected time window. A candidate is classified only by J(candidate, TransportUnit, transportUnitEdition, TargetSlice) or the more specific target judgment when that receiving use is current. The independent scope-bridge and kind-bridge reliance penalties reduce R; F and G are unchanged.

#AuthenticatedRequest across services (software)

Source and target AuthenticatedRequest kinds and their exact declaration editions are independently identified. The bridge mapping predicate states the authHeader to x-auth correspondence and preservation of the signature-validity invariant; the bridge assertion gives CL^k=3 and its definedness under AuthStandard v2.3. It does not construct the target declaration. The frontend evaluates each exact request with its target signature edition and slice; unavailable target dependencies yield unknown.

#AdultPatient across jurisdictions (clinical)

The obtaining bridge relates source kind AdultPatient to independently identified target kind AdultPerson_Y. Its assertion gives CL^k=1, states the 18-versus-21 boundary loss, and limits definedness to the declared jurisdictional editions. The target classification uses its own signature edition. Missing DOB support yields unknown; a mask adapter or narrower Scope may support a later use, while the guard's refusal and R penalty remain separate from target truth.

#Anti‑patterns & Remedies (informative)

#Conformance Checklist (normative)

Integration requirements with Part B (bridges):

• B-P1. Part B (Bridges) SHALL distinguish the kind channel—reliance on an obtaining C.3.3 KindBridge direct relation plus its separate bridge assertion—from USM scope and F.9 sense-Bridge channels. A Bridge Card or bridge-class row does not become the KindBridge occurrence.
• B‑P2. Part B SHALL state that CL^k penalties route to R via a monotone Ψ, never to F/G.
• B‑P3. Part B SHALL define chaining = min for both CL and CL^k (weakest‑link).
• Templates. ESG/Method templates should expose references to the exact relied-on Scope-Bridge and KindBridge relation/assertion pairs. CL, CL^k, loss notes, and definedness remain assertion or assessment content; template fields neither create nor identify the world-side relation by record identity.

#C.3.3:End

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Last Updated: 2026-08-04 — upstream FPF commit 67092138 (github.com/ailev/FPF)