Articulation Hygiene

Purpose

This document fixes the operator-factorization protocol for all "self-X" / "auto-X" / "само-X" constructions in the UHM corpus. The protocol is not a stylistic preference but a structural invariant, established by theorem NO-19 (Articulation Hygiene) in Noesis (diakrisis.gst.st/11-noesis/07-theorems). The protocol is mandatory for every articulation passing the Noesis core pipeline (SMT → Axi → AFN-T → Hygiene).

Principle

Any "self-X" construction in an articulation is underdetermined without an explicit operator-factorization. It does not specify:

• which operator $\Phi$ performs the recursive/reflexive action,
• which trajectory $\Phi^\kappa$ (ordinal $\kappa$) generates the construction,
• which terminal/fixed object $t$ closes it.

Hygiene requirement: for each surface-level "self-X" in an articulation, an explicit triple $(\Phi, \Phi^\kappa, t)$ must be defined. Without such a triple, the articulation is rejected at the Hygiene stage of the pipeline.

Philosophical context

The protocol formalises an observation by E. Churilov (anticomplexity.org) within the metastemological programme: "self-"-constructions are syntactically suspicious because they conflate the describing and described positions in a single sign. The resolution is to separate these positions explicitly via operator + trajectory + terminal.

Within the Diakrisis / Актика framework, this discipline is already built into the canonical primitive (accessible endofunctors $\mathsf{M}$ and $\mathsf{A}$, ordinal $\nu/\varepsilon$-stratification, $\mathrm{Fix}$-sets). NO-19 elevates it from an implicit formal property to an explicit invariant of the Noesis core pipeline.

Canonical factorisation table

For each recurring "self-X" construction in UHM:

Surface form	Operator $\Phi$	Trajectory $\Phi^\kappa$	Terminal $t$	Source theorem
self-model / самомодель	$\varphi: \mathrm{D}(\mathbb{C}^7) \to \mathrm{D}(\mathbb{C}^7)$	$\varphi^\kappa$ on states	$\rho^* = \varphi(\Gamma)$	T-96
self-modelling / самомоделирование	$\varphi$ — categorical map (functor)	iteration in Lindblad dynamics	$\rho^* \in \mathrm{eq}(\mathrm{id}, \varphi)$	T-96 + T-39a
autopoiesis / автопоэзис	$\mathsf{A}^\mathrm{act}$ (activation) on AC-side	$\mathsf{A}^{\omega^2}$-iteration	$\varepsilon \in \mathrm{Fix}(\mathsf{A}^{\omega^2})$	113.T (Diakrisis)
self-observation / самонаблюдение	terminal coalgebra $\Gamma \to F(\Gamma)$ for $F = \varphi$ + reflection-measure $R$	unfolding of the coalgebra	$\nu F$ — terminal coalgebra; $R \geq 1/3$	T-126 + T-96
self-reference / самореференция	Lawvere fixed-point $f: X \to X^X$	stratified Yanofsky diagonal	fixed point $p \in X$, bounded by T-2a*	87.T (Lawvere), 105.T
self-consistency / самосогласованность	equivalence operator $\varphi \simeq \mathrm{id}$	— (point-level)	equaliser $\rho^* = \varphi(\Gamma)$	T-96
self-awareness / самосознание	reflexive measure $R = 1/(7P)$ + Φ-integration	(P, R, Φ, D)-threshold	consciousness predicate $P > 2/7 \wedge R \geq 1/3 \wedge \Phi \geq 1 \wedge D \geq 2$	T-96 + T-126 + T-129 + T-151
self-closure / самозамыкание	$\mathsf{M}^\kappa$-iteration on the articulation side	trajectory $\alpha \mapsto \mathsf{M}(\alpha) \mapsto \mathsf{M}^2(\alpha) \mapsto \ldots$	$\alpha \in \mathrm{Fix}(\mathsf{M})$	04.T1, Axi-7
self-amplification / самоусиление	positive feedback $\Psi$	$\Psi^k$-iteration	threshold activation value	Diakrisis §kinetic (context)

What is not subject to replacement (standard technical terms)

• self-adjoint — fixed mathematical term denoting a Hermitian operator, not a reflexive turn of phrase.
• self-attention (the Transformer mechanism) — an ML term, preserved as is.
• self-assembly (in chemistry / nanotechnology) — a physical term, preserved as is.
• self-similarity (fractal) — a mathematical term, preserved as is.

Criterion: if "self-" expresses a property of a map or object definable independently of the reflexive interpretation, the term is preserved unchanged.

Application to UHM

Tier 1: conceptual files (prose rewrite)

Files where "self-X" appears in a descriptive sense are fully subject to replacement per the table above. High-priority targets:

• /consciousness/foundations/self-observation.md — canonical document, refactored first (see §"Applied factorisation" below).
• /proofs/categorical/formalization-phi.md — formalisation of $\varphi$, already operator-oriented, requires only language synchronisation.
• /core/foundations/consequences.md, axiom-septicity.md — base consequences, surface layer.
• /consciousness/hierarchy/interiority-hierarchy.md, depth-tower.md — hierarchical structures.
• /proofs/consciousness/interiority-hierarchy.md, conscious-window.md — proofs.
• /applied/coherence-cybernetics/theorems.md, definitions.md — applications.

Tier 2: status registry and summary theorems

/reference/status-registry.md, /reference/specification.md — theorem descriptions. "Self-" occurrences in theorem titles are rewritten per the protocol; theorem numbers are preserved.

Tier 3: formal proof files

In proofs (/proofs/*) formal definitions are already operator-based ($\varphi$, $\mathcal{L}_\Omega$, CPTP, T-96). Replacement is needed only in transitional commentary and motivation paragraphs.

Applied factorisation: canonical example

Demonstration of the protocol on the key concept.

Before (rhetorical):

UHM establishes self-modelling through the operator $\varphi$. Self-observation is the system's ability to describe its own state. Autopoiesis is the system's self-reproduction through self-modelling.

After (operator-based):

UHM establishes a categorical map $\varphi: \mathrm{D}(\mathbb{C}^7) \to \mathrm{D}(\mathbb{C}^7)$ with a fixed point $\rho^* = \varphi(\Gamma)$ (T-96). Reflection of the system relative to its own state is formalised as a terminal coalgebra structure on the $\Gamma$-dynamics, characterised by the measure $R = 1/(7P)$ (T-126). Closure under the $\varphi$-trajectory (on the dual AC-side, an $\mathsf{A}$-fixed point at level $\omega^2$ per 113.T Diakrisis) — trajectory reproduction without external maintenance.

The operator-based content is identical to the rhetorical version. But:

1. Every element is explicitly typed ($\varphi$ is an operator, $\rho^*$ a state, $R$ a measure, iteration a trajectory).
2. The describing and described positions are separated ($\Gamma$ and $\varphi(\Gamma)$ are distinct points in $\mathrm{D}(\mathbb{C}^7)$, connected by the fixed-point equation but structurally distinct).
3. The protocol is compatible with Noesis hygiene verification (NO-19): the factorisation is explicit.

Relation to other documents

• diakrisis.gst.st/11-noesis/07-theorems §NO-19 — structural source of the protocol; theorem NO-19.
• diakrisis.gst.st/12-actic/07-beyond-metastemology — historical context (Churilov's metastemological programme).
• diakrisis.gst.st/06-limits/10-maximality-theorems §105.T — universal paradox-immunity via T-2f*, the formal basis of the hygiene invariant at Level 5+.
• UHM /proofs/categorical/formalization-phi — source-level formalisation of the $\varphi$-operator.

Refactoring plan

1. Phase A (this document + self-observation.md refactor) — protocol established, canonical example given.
2. Phase B — sweep over Tier-1 files (from the Tier-1 list above), applying the table.
3. Phase C — Tier-2 (status registry and summary) and Tier-3 (proof files).

Each phase is a separate commit with an audit (count of replaced "self-X", verification that theorem statements are not touched, build check).

Note

The protocol does not revoke existing UHM theorems — all T-1..T-223+ remain formally correct. The refactor is interface-level, affecting only the prose layer. The formal core ($\varphi$, $\mathcal{L}_\Omega$, T-96, T-190, T-223) already operates in operator language; hygiene synchronises the surface with the core.