UPS Protocol: An Operational Formalization of Dialectic

This paper presents dialectic not as semantics but as an operational discipline. We couple a control plane **U–P–S (Universal–Particular–Singular)** with a data plane **B–T–Π (Values–Transitions–Propositions)** to form a coherent pipeline that preserves contradiction as an engine (**B**) and authorizes conclusions only by **commit (=)**. Equality is not a global property but a **one-shot license event** scoped to a window **W** (**Non-Transport**, **No-Promotion**). The process operator **σ** is restricted to **one-shot**. **Observation‑equivalence (≈_obs)** has priority and any global **π** (a "God’s‑eye" perspective) is forbidden. Semantically, we adopt the Belnap/FDE four values **{T, F, B, N}** with **{T, B}** designated. Only passage through the ``` Gate(W) := stage = s ∧ δ_abs ∧ (σ_trace ≍) ∧ Guards(Exh/Det/Coh/No3‑Lock/Arrow) ``` triggers a commit. **Explosion** (EFQ: *p, ¬p ⊢ q*) is underivable, and the **=‑free** fragment obtained by deleting `'='`, `σ`, and the gate rules is **conservative** over FDE/LP. An external logic **L** is embedded via an adapter into **{T, F, B, N} × margin** and connected through **π_W**; the **judgement form (J‑Form)**, by the **No‑Compute** constraint, does not interfere with value computation. Philosophically, identity is interpreted not as an invariance (**δ_abs**) but as an **event (=)**; truth is the **state of the commit log**. Lacan’s **extimité** is rendered as the scope structure **D/D′/W**, while Hegelian negativity is engine‑ized as the preservation and unfolding of **B**. A topological reading (gate = boundary; crossing index = **a_eff**) converges to the indexation of the operational log. The separation of **observation / ontology / event** and a **trace‑compatibility** decision procedure make implementation and audit feasible. Applications include (i) conflict‑preserving commits in knowledge graphs / data integration, (ii) model governance and compliance with tracked **promotion / issuance / TTL / contention**, and (iii) reproducibility gates that require commits to precede experiments / claims. In short, the system is non‑trivially coherent and formalizes dialectic not as mere description but as an **executable protocol**. UPS redefines equality as a window‑local one‑shot event. By combining the gate (**Abs= · trace‑compat · stage · guards · ¬mark**) with an **append‑only** ledger, it guarantees **non‑explosion** together with **concurrency‑safe uniqueness**, and the **=‑free** fragment remains a conservative isomorph of FDE. **Keywords:** paraconsistent logic, dialectic, operational semantics, commit event, σ‑lag (one‑shot), observation‑equivalence, conservativity, Belnap/FDE, extimité, gate discipline, UPS Protocol. Translation of: "UPS 프로토콜: 변증법의 운영적 형식화". PhilArchive ID: CDAOEC. Commentary: "UPS Protocol Commentary: “= Is an Event” — σ One-Shot and Gate Discipline" PhilArchive ID: CUPCWW