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14 changes: 7 additions & 7 deletions FPF-Spec.md
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Expand Up @@ -28326,13 +28326,13 @@ This approach is inspired by contemporary practices in both ontology engineering

## C.2 - Epistemic holon composition (KD-CAL)

**Scope & exports.** A substrate‑neutral calculus for composing **epistemic holons** (`U.Episteme`) and reasoning about their motion and equivalence. Exports: (i) three **point‑characteristics**—**Formality F**, **ClaimScope G**, **Reliability R**—that locate a single episteme; (ii) a **pairwise ladder** of **Congruence Levels (CL 0…3)**; (iii) four **Δ‑moves** (*Formalise, Generalise/Specialise, Calibrate/Validate, Congrue*); (iv) **composition rules** (Γ_epist) for aggregates; (v) propagation laws for CL through mappings and notation bridges. KD‑CAL sits on the `U.Episteme` *semantic triangle* (Symbol–Concept–Object) and never confuses **notation** with **carrier**. All F–G–R computations are **context‑local**; Cross‑context traversals **require** an explicit **Bridge** with **CL** and apply the **B.3** congruence penalty **Φ(CL)** to **R**. // Contexts ≡ U.BoundedContext; substitution is plane‑preserving only.
**Scope & exports.** A substrate‑neutral calculus for composing **epistemic holons** (`U.Episteme`) and reasoning about their motion and equivalence. Exports: (i) two **characteristics**—**Formality F** and **Reliability R**—plus one **scope object**—**ClaimScope G**—that together describe a single episteme; (ii) a **pairwise ladder** of **Congruence Levels (CL 0…3)**; (iii) four **Δ‑moves** (*Formalise, Generalise/Specialise, Calibrate/Validate, Congrue*); (iv) **composition rules** (Γ_epist) for aggregates; (v) propagation laws for CL through mappings and notation bridges. KD‑CAL sits on the `U.Episteme` *semantic triangle* (Symbol–Concept–Object) and never confuses **notation** with **carrier**. All F–G–R computations are **context‑local**; Cross‑context traversals **require** an explicit **Bridge** with **CL** and apply the **B.3** congruence penalty **Φ(CL)** to **R**. // Contexts ≡ U.BoundedContext; substitution is plane‑preserving only.

**Formality F** is the rigor characteristic defined **normatively in C.2.3**. All KD‑CAL computations and guards **SHALL** use `U.Formality` (F0…F9) as specified there; **no parallel “mode” ladders** are allowed.

### C.2:1 - Problem Frame

FPF fixes two archetypal sub‑holons: **`U.System`** (physical/operational) and **`U.Episteme`** (knowledge holon). KD‑CAL is the **home pattern** of `U.Episteme`, giving engineers a compact, testable way to say (a) how strictly an episteme is written (**F**), (b) how much structure it manages (**G**), (c) how well it is warranted by evidence or severe tests (**R**), and (d) how closely **two** epistemes coincide (**CL**). KD‑CAL is built atop **C.2.1 U.Episteme — Semantic Triangle via Components**, which reifies every episteme as **Concept** (claim‑graph), **Object** (describedEntity & evaluation rules), and **Symbol** (notation)—*not the file itself*; **carriers** and **work/executions** remain outside and are linked via `isCarriedBy` / `producedBy(U.Work)`.
FPF fixes two archetypal sub‑holons: **`U.System`** (physical/operational) and **`U.Episteme`** (knowledge holon). KD‑CAL is the **home pattern** of `U.Episteme`, giving engineers a compact, testable way to say (a) how strictly an episteme is written (**F**), (b) where its claim is asserted to apply (**G**), (c) how well it is warranted by evidence or severe tests (**R**), and (d) how closely **two** epistemes coincide (**CL**). KD‑CAL is built atop **C.2.1 U.Episteme — Semantic Triangle via Components**, which reifies every episteme as **Concept** (claim‑graph), **Object** (describedEntity & evaluation rules), and **Symbol** (notation)—*not the file itself*; **carriers** and **work/executions** remain outside and are linked via `isCarriedBy` / `producedBy(U.Work)`.

### C.2:2 - Problem

Expand All @@ -28349,9 +28349,9 @@ Teams routinely entangle **programs, specifications, proofs, and datasets**; a

### C.2:4 - Solution

#### C.2:4.1 - Coordinates and the triangle
#### C.2:4.1 - Assurance components and the triangle

**KD‑CAL characteristics (single‑episteme, point‑values).**
**KD‑CAL assurance components for a single episteme.**

* **Formality F.** From free prose to **machine‑checkable proof/specification**. Litmus: *would a machine reject it if wrong?*
* **Claim scope (G), a set‑valued applicability over `U.ContextSlice`, with ∩/SpanUnion/translate algebra; CL penalties apply to R, not to F/G.** Litmus: *how wide is the declared scope, and under what minimal assumptions does the claim hold?*
Expand Down Expand Up @@ -31141,9 +31141,9 @@ A facet (not a Characteristic) that helps plan **ΔF/ΔR** and forecast bridge s
**C.3‑D7 — Guard shapes are standardized and fail‑closed.**
Typed compatibility first (same‑Context **`⊑`** or **KindBridge**), then **Scope coverage** (USM), then **R** penalties and freshness. *(See C.3.A.)*

> **Manager’s picture — Two characteristics (keep them separate).**
> – **characteristic 1 (USM, G):** *Where* the claim holds → set of **Context slices**; composed by ∈ (membership) / ∩ (intersection) / **SpanUnion** (union across independent lines) / translate (scope mapping).
> – **characteristic 2 (Kind extent):** *Which instances* in a **given slice** belong to the kind → `MemberOf(e, k, slice)`.
> **Manager’s picture — Scope vs kind extent (keep them separate).**
> – **scope object 1 (USM, G):** *Where* the claim holds → set of **Context slices**; composed by ∈ (membership) / ∩ (intersection) / **SpanUnion** (union across independent lines) / translate (scope mapping).
> – **kind extent:** *Which instances* in a **given slice** belong to the kind → `MemberOf(e, k, slice)`.
> **Never “widen G” by abstract wording; widen only by ΔG with support.**


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