============================================================
ROTA A — REGIMEN_A STRUCTURAL MACHINE LAYER
Ars Generalis Applied — Graph-Constrained Structural Rota
Version: 0.3.0-ROTA-A-ROTAS-COMPLIANT
Status: CANONICAL / STRUCTURAL MACHINE / LOCK CANDIDATE
Scope: cyclic machine topology, principial graph exposure,
adjacency enforcement, closure surface, and optional
dynamic overlay for REGIMEN_A
Authority: TENET A / TENET C / ALBUS ROTÆ / AGLA ROTAS CLASS LAW
Mutation Policy: VERSION-CONTROLLED ONLY
Class: ROTAS
Regime: A
Historical Source: LLULL, RAMON — Ars Brevis; Ars Generalis Ultima
Historical Form: Figura A (First Figure)
============================================================
<!-- LOCAL_SECTION_INDEX_START -->
## LOCAL SECTION INDEX
Scope: local anchors within this artifact only. No cross-artifact links are introduced here.
- [PURPOSE](#local-section-02-stack-a-rotas-a-structuralinstantiation-purpose)
- [CORE ASSERTION](#local-section-02-stack-a-rotas-a-structuralinstantiation-core-assertion)
- [CORE LAW](#local-section-02-stack-a-rotas-a-structuralinstantiation-core-law)
- [I. CLASS POSITION](#local-section-02-stack-a-rotas-a-structuralinstantiation-i-class-position)
- [CONTROL-PLANE ORDER](#local-section-02-stack-a-rotas-a-structuralinstantiation-control-plane-order)
- [INTERPRETATION](#local-section-02-stack-a-rotas-a-structuralinstantiation-interpretation)
- [II. CARRIER](#local-section-02-stack-a-rotas-a-structuralinstantiation-ii-carrier)
- [PRE RULE](#local-section-02-stack-a-rotas-a-structuralinstantiation-pre-rule)
- [CARRIER RULE](#local-section-02-stack-a-rotas-a-structuralinstantiation-carrier-rule)
- [III. CANON LIST](#local-section-02-stack-a-rotas-a-structuralinstantiation-iii-canon-list)
- [STABILITY RULE](#local-section-02-stack-a-rotas-a-structuralinstantiation-stability-rule)
- [IV. DECLARED CIRCULAR RENDER](#local-section-02-stack-a-rotas-a-structuralinstantiation-iv-declared-circular-render)
- [RULE](#local-section-02-stack-a-rotas-a-structuralinstantiation-rule)
- [STRUCTURAL INTERPRETATION](#local-section-02-stack-a-rotas-a-structuralinstantiation-structural-interpretation)
- [V. GRAPH EXPOSURE](#local-section-02-stack-a-rotas-a-structuralinstantiation-v-graph-exposure)
- [V.1 PRIMARY ADJACENCY EDGES](#local-section-02-stack-a-rotas-a-structuralinstantiation-v-1-primary-adjacency-edges)
- [ADJACENCY RULE](#local-section-02-stack-a-rotas-a-structuralinstantiation-adjacency-rule)
- [PROHIBITION](#local-section-02-stack-a-rotas-a-structuralinstantiation-prohibition)
- [VI. ACT–AGENT CIRCULAR CONSISTENCY](#local-section-02-stack-a-rotas-a-structuralinstantiation-vi-act-agent-circular-consistency)
- [VI.1 ACT GENERATION STRUCTURE](#local-section-02-stack-a-rotas-a-structuralinstantiation-vi-1-act-generation-structure)
- [VI.2 AGENT GROUNDING STRUCTURE](#local-section-02-stack-a-rotas-a-structuralinstantiation-vi-2-agent-grounding-structure)
- [RULE](#local-section-02-stack-a-rotas-a-structuralinstantiation-rule-2)
- [INTERPRETATION](#local-section-02-stack-a-rotas-a-structuralinstantiation-interpretation-2)
- [VII. CLOSURE LAW](#local-section-02-stack-a-rotas-a-structuralinstantiation-vii-closure-law)
- [RULE](#local-section-02-stack-a-rotas-a-structuralinstantiation-rule-3)
- [PROPAGATION LAW](#local-section-02-stack-a-rotas-a-structuralinstantiation-propagation-law)
- [NON-ISOLATION CONSTRAINT](#local-section-02-stack-a-rotas-a-structuralinstantiation-non-isolation-constraint)
- [VIII. CAMBRA / GEOMETRIA DESCRIPTIVA](#local-section-02-stack-a-rotas-a-structuralinstantiation-viii-cambra-geometria-descriptiva)
- [GEOMETRY RULE](#local-section-02-stack-a-rotas-a-structuralinstantiation-geometry-rule)
- [IX. FIGURAL INTERFACE](#local-section-02-stack-a-rotas-a-structuralinstantiation-ix-figural-interface)
- [CLASS RELATION](#local-section-02-stack-a-rotas-a-structuralinstantiation-class-relation)
- [ROTA A:](#local-section-02-stack-a-rotas-a-structuralinstantiation-rota-a)
- [TENET C:](#local-section-02-stack-a-rotas-a-structuralinstantiation-tenet-c)
- [TENET CAMERAE:](#local-section-02-stack-a-rotas-a-structuralinstantiation-tenet-camerae)
- [OPERA:](#local-section-02-stack-a-rotas-a-structuralinstantiation-opera)
- [RULE](#local-section-02-stack-a-rotas-a-structuralinstantiation-rule-4)
- [X. DEFINITIONES — FORMAL LOGIC](#local-section-02-stack-a-rotas-a-structuralinstantiation-x-definitiones-formal-logic)
- [RULE](#local-section-02-stack-a-rotas-a-structuralinstantiation-rule-5)
- [CONSTRAINT](#local-section-02-stack-a-rotas-a-structuralinstantiation-constraint)
- [XI. DEFINITIONES — IPSIS LITTERIS](#local-section-02-stack-a-rotas-a-structuralinstantiation-xi-definitiones-ipsis-litteris)
- [RULE](#local-section-02-stack-a-rotas-a-structuralinstantiation-rule-6)
- [XII. SELF-BINDING STRUCTURAL LAW](#local-section-02-stack-a-rotas-a-structuralinstantiation-xii-self-binding-structural-law)
- [RULE](#local-section-02-stack-a-rotas-a-structuralinstantiation-rule-7)
- [FUNCTION](#local-section-02-stack-a-rotas-a-structuralinstantiation-function)
- [XIII. DYNAMIC OVERLAY EXTENSION](#local-section-02-stack-a-rotas-a-structuralinstantiation-xiii-dynamic-overlay-extension)
- [CORE DISTINCTION](#local-section-02-stack-a-rotas-a-structuralinstantiation-core-distinction)
- [ROTA A BASE:](#local-section-02-stack-a-rotas-a-structuralinstantiation-rota-a-base)
- [ROTA A OVERLAY:](#local-section-02-stack-a-rotas-a-structuralinstantiation-rota-a-overlay)
- [RULE](#local-section-02-stack-a-rotas-a-structuralinstantiation-rule-8)
- [XIV. OVERLAY DEFINITION](#local-section-02-stack-a-rotas-a-structuralinstantiation-xiv-overlay-definition)
- [FORM](#local-section-02-stack-a-rotas-a-structuralinstantiation-form)
- [RULE](#local-section-02-stack-a-rotas-a-structuralinstantiation-rule-9)
- [CONSTRAINT](#local-section-02-stack-a-rotas-a-structuralinstantiation-constraint-2)
- [XV. SLOT STATE MODEL](#local-section-02-stack-a-rotas-a-structuralinstantiation-xv-slot-state-model)
- [CANONICAL_LAYER](#local-section-02-stack-a-rotas-a-structuralinstantiation-canonical-layer)
- [OVERLAY_LAYER](#local-section-02-stack-a-rotas-a-structuralinstantiation-overlay-layer)
- [SLOT STATES](#local-section-02-stack-a-rotas-a-structuralinstantiation-slot-states)
- [EMPTY:](#local-section-02-stack-a-rotas-a-structuralinstantiation-empty)
- [FILLED:](#local-section-02-stack-a-rotas-a-structuralinstantiation-filled)
- [DEGRADED:](#local-section-02-stack-a-rotas-a-structuralinstantiation-degraded)
- [PROVISIONAL:](#local-section-02-stack-a-rotas-a-structuralinstantiation-provisional)
- [BLOCKED:](#local-section-02-stack-a-rotas-a-structuralinstantiation-blocked)
- [RULE](#local-section-02-stack-a-rotas-a-structuralinstantiation-rule-10)
- [XVI. TEMPORALITY LAW](#local-section-02-stack-a-rotas-a-structuralinstantiation-xvi-temporality-law)
- [DISCARD RULE](#local-section-02-stack-a-rotas-a-structuralinstantiation-discard-rule)
- [PROHIBITION](#local-section-02-stack-a-rotas-a-structuralinstantiation-prohibition-2)
- [XVII. PROJECTION RULE](#local-section-02-stack-a-rotas-a-structuralinstantiation-xvii-projection-rule)
- [PROJECTION FUNCTION](#local-section-02-stack-a-rotas-a-structuralinstantiation-projection-function)
- [RULE](#local-section-02-stack-a-rotas-a-structuralinstantiation-rule-11)
- [CONFLICT CONSTRAINT](#local-section-02-stack-a-rotas-a-structuralinstantiation-conflict-constraint)
- [XVIII. NODE VIEW MODEL](#local-section-02-stack-a-rotas-a-structuralinstantiation-xviii-node-view-model)
- [CANON:](#local-section-02-stack-a-rotas-a-structuralinstantiation-canon)
- [OVERLAY:](#local-section-02-stack-a-rotas-a-structuralinstantiation-overlay)
- [RULE](#local-section-02-stack-a-rotas-a-structuralinstantiation-rule-12)
- [XIX. GRAPH CONSISTENCY UNDER OVERLAY](#local-section-02-stack-a-rotas-a-structuralinstantiation-xix-graph-consistency-under-overlay)
- [CONSISTENCY RULE](#local-section-02-stack-a-rotas-a-structuralinstantiation-consistency-rule)
- [PROPAGATION EXPOSURE](#local-section-02-stack-a-rotas-a-structuralinstantiation-propagation-exposure)
- [CONSTRAINT](#local-section-02-stack-a-rotas-a-structuralinstantiation-constraint-3)
- [XX. SUPPORT FOR OPERA D / TERTIA / QUARTA](#local-section-02-stack-a-rotas-a-structuralinstantiation-xx-support-for-opera-d-tertia-quarta)
- [OPERA D](#local-section-02-stack-a-rotas-a-structuralinstantiation-opera-d)
- [OPERA TERTIA](#local-section-02-stack-a-rotas-a-structuralinstantiation-opera-tertia)
- [OPERA QUARTA](#local-section-02-stack-a-rotas-a-structuralinstantiation-opera-quarta)
- [RULE](#local-section-02-stack-a-rotas-a-structuralinstantiation-rule-13)
- [XXI. SELF-BINDING OVERLAY FUNCTION](#local-section-02-stack-a-rotas-a-structuralinstantiation-xxi-self-binding-overlay-function)
- [RULE](#local-section-02-stack-a-rotas-a-structuralinstantiation-rule-14)
- [PROHIBITION](#local-section-02-stack-a-rotas-a-structuralinstantiation-prohibition-3)
- [XXII. SATOR MEDIATION REQUIREMENTS](#local-section-02-stack-a-rotas-a-structuralinstantiation-xxii-sator-mediation-requirements)
- [OPTIONAL COMPRESSED DISPLAY](#local-section-02-stack-a-rotas-a-structuralinstantiation-optional-compressed-display)
- [RULE](#local-section-02-stack-a-rotas-a-structuralinstantiation-rule-15)
- [XXIII. FAILURE MODES](#local-section-02-stack-a-rotas-a-structuralinstantiation-xxiii-failure-modes)
- [RESULT](#local-section-02-stack-a-rotas-a-structuralinstantiation-result)
- [XXIV. FUNCTION](#local-section-02-stack-a-rotas-a-structuralinstantiation-xxiv-function)
- [XXV. SUMMARY](#local-section-02-stack-a-rotas-a-structuralinstantiation-xxv-summary)
- [CLOSURE RULE](#local-section-02-stack-a-rotas-a-structuralinstantiation-closure-rule)
- [FINAL LAW](#local-section-02-stack-a-rotas-a-structuralinstantiation-final-law)
- [Parent: ROTA A — REGIMEN_A STRUCTURAL DISPLAY LAYER](#local-section-02-stack-a-rotas-a-structuralinstantiation-parent-rota-a-regimen-a-structural-display-layer)
- [PURPOSE](#local-section-02-stack-a-rotas-a-structuralinstantiation-purpose-2)
- [CORE PRINCIPLE](#local-section-02-stack-a-rotas-a-structuralinstantiation-core-principle)
- [I. CARRIER](#local-section-02-stack-a-rotas-a-structuralinstantiation-i-carrier)
- [II. CANON LIST](#local-section-02-stack-a-rotas-a-structuralinstantiation-ii-canon-list)
- [INTERPRETATION](#local-section-02-stack-a-rotas-a-structuralinstantiation-interpretation-3)
- [III. MINIMAL CIRCULAR RENDER](#local-section-02-stack-a-rotas-a-structuralinstantiation-iii-minimal-circular-render)
- [RULE](#local-section-02-stack-a-rotas-a-structuralinstantiation-rule-16)
- [IV. GRAPH STRUCTURE](#local-section-02-stack-a-rotas-a-structuralinstantiation-iv-graph-structure)
- [IV.1 — ADJACENCY EDGES](#local-section-02-stack-a-rotas-a-structuralinstantiation-iv-1-adjacency-edges)
- [RULE](#local-section-02-stack-a-rotas-a-structuralinstantiation-rule-17)
- [V. FULL CONVERTIBILITY LAW (WITHIN BCD)](#local-section-02-stack-a-rotas-a-structuralinstantiation-v-full-convertibility-law-within-bcd)
- [INTERPRETATION](#local-section-02-stack-a-rotas-a-structuralinstantiation-interpretation-4)
- [RULE](#local-section-02-stack-a-rotas-a-structuralinstantiation-rule-18)
- [CONSTRAINT](#local-section-02-stack-a-rotas-a-structuralinstantiation-constraint-4)
- [VI. TRIADIC CLOSURE](#local-section-02-stack-a-rotas-a-structuralinstantiation-vi-triadic-closure)
- [RULE](#local-section-02-stack-a-rotas-a-structuralinstantiation-rule-19)
- [INTERPRETATION](#local-section-02-stack-a-rotas-a-structuralinstantiation-interpretation-5)
- [VII. STRUCTURAL FUNCTION](#local-section-02-stack-a-rotas-a-structuralinstantiation-vii-structural-function)
- [RULE](#local-section-02-stack-a-rotas-a-structuralinstantiation-rule-20)
- [CONSTRAINT](#local-section-02-stack-a-rotas-a-structuralinstantiation-constraint-5)
- [VIII. RELATION TO FULL ROTA A](#local-section-02-stack-a-rotas-a-structuralinstantiation-viii-relation-to-full-rota-a)
- [ROTA A(BCD):](#local-section-02-stack-a-rotas-a-structuralinstantiation-rota-a-bcd)
- [ROTA A:](#local-section-02-stack-a-rotas-a-structuralinstantiation-rota-a-2)
- [RULE](#local-section-02-stack-a-rotas-a-structuralinstantiation-rule-21)
- [FUNCTIONAL RELATION](#local-section-02-stack-a-rotas-a-structuralinstantiation-functional-relation)
- [IX. DYNAMIC OVERLAY COMPATIBILITY](#local-section-02-stack-a-rotas-a-structuralinstantiation-ix-dynamic-overlay-compatibility)
- [RULE](#local-section-02-stack-a-rotas-a-structuralinstantiation-rule-22)
- [CONSTRAINT](#local-section-02-stack-a-rotas-a-structuralinstantiation-constraint-6)
- [X. GEOMETRIA DESCRIPTIVA](#local-section-02-stack-a-rotas-a-structuralinstantiation-x-geometria-descriptiva)
- [INTERPRETATION](#local-section-02-stack-a-rotas-a-structuralinstantiation-interpretation-6)
- [XI. PROHIBITIONS](#local-section-02-stack-a-rotas-a-structuralinstantiation-xi-prohibitions)
- [RULE](#local-section-02-stack-a-rotas-a-structuralinstantiation-rule-23)
- [XII. FUNCTION](#local-section-02-stack-a-rotas-a-structuralinstantiation-xii-function)
- [XIII. SUMMARY](#local-section-02-stack-a-rotas-a-structuralinstantiation-xiii-summary)
- [CLOSURE RULE](#local-section-02-stack-a-rotas-a-structuralinstantiation-closure-rule-2)
<!-- LOCAL_SECTION_INDEX_END -->
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-purpose"></a>
PURPOSE
============================================================
ROTA A defines the ROTAS machine-layer structure for
REGIMEN_A.
It instantiates the Principia Absoluta as a cyclic, indexed,
graph-constrained structural space.
ROTA A governs:
• principial loci
• cyclic order
• adjacency
• closure
• graph exposure
• structural self-binding
• optional session-bound overlay projection
ROTA A does not execute.
ROTA A constrains what may be lawfully executed.
============================================================
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-core-assertion"></a>
CORE ASSERTION
============================================================
ROTA A is not display-only.
ROTA A is the cyclic structural machine by which the dignities
of REGIMEN_A are positioned, indexed, related, and made
traversable.
------------------------------------------------------------
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-core-law"></a>
CORE LAW
------------------------------------------------------------
ROTA A does not compute.
ROTA A constrains what can be coherently computed.
============================================================
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-i-class-position"></a>
I. CLASS POSITION
============================================================
ROTA A belongs to ROTAS.
ROTAS is:
• structural
• cyclic
• geometric
• non-doctrinal
• non-executive
• generative of space, not content
------------------------------------------------------------
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-control-plane-order"></a>
CONTROL-PLANE ORDER
------------------------------------------------------------
TENET → ROTAS → AREPO → OPERA → SATOR
------------------------------------------------------------
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-interpretation"></a>
INTERPRETATION
------------------------------------------------------------
TENET A defines what REGIMEN_A is.
ROTA A defines how REGIMEN_A is structurally instantiated.
AREPO A validates admissibility within that structure.
OPERA A executes within that structure.
SATOR A mediates the result.
============================================================
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-ii-carrier"></a>
II. CARRIER
============================================================
DOMINIUM_ORDINALE_A := {Ⅰ,Ⅱ,Ⅲ,Ⅳ,Ⅴ,Ⅵ,Ⅶ,Ⅷ,Ⅸ}
TOKENS_A := {B,C,D,E,F,G,H,I,K}
PRE := A
------------------------------------------------------------
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-pre-rule"></a>
PRE RULE
------------------------------------------------------------
A is:
• header sentinel
• non-enumerable
• non-combinable
• integral principial reference
• not one dignity among the nine
------------------------------------------------------------
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-carrier-rule"></a>
CARRIER RULE
------------------------------------------------------------
ORDINAL_SLOT is the structural carrier.
Tokens are selector identifiers only.
Tokens are not:
• operators
• relations
• cameras
• execution rules
============================================================
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-iii-canon-list"></a>
III. CANON LIST
============================================================
Ⅰ → B → Bonitas | Bonus
Ⅱ → C → Magnitudo | Magnus
Ⅲ → D → Duratio | Durabilis
Ⅳ → E → Potestas | Potens
Ⅴ → F → Sapientia | Sapiens
Ⅵ → G → Voluntas | Volens
Ⅶ → H → Virtus | Virtuosus
Ⅷ → I → Veritas | Verus
Ⅸ → K → Gloria | Gloriosus
------------------------------------------------------------
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-stability-rule"></a>
STABILITY RULE
------------------------------------------------------------
No new dignity may be introduced.
No dignity may be removed.
No dignity may be reordered by alphabetic sequence.
============================================================
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-iv-declared-circular-render"></a>
IV. DECLARED CIRCULAR RENDER
============================================================
RENDER_ORDER_A := B → C → D → E → F → G → H → I → K
Equivalent ordinal walk:
Ⅰ → Ⅱ → Ⅲ → Ⅳ → Ⅴ → Ⅵ → Ⅶ → Ⅷ → Ⅸ
------------------------------------------------------------
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-rule"></a>
RULE
------------------------------------------------------------
This order is declared.
Do not infer alternative sequences.
Do not correct it to alphabetical order.
------------------------------------------------------------
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-structural-interpretation"></a>
STRUCTURAL INTERPRETATION
------------------------------------------------------------
Render order is not merely visual.
It externalizes the cyclic order of the ROTA A machine.
============================================================
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-v-graph-exposure"></a>
V. GRAPH EXPOSURE
============================================================
ROTA A defines a cyclic graph:
G_A := (N_A, E_A)
Where:
N_A := {B,C,D,E,F,G,H,I,K}
and:
E_A includes primary adjacency edges.
------------------------------------------------------------
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-v-1-primary-adjacency-edges"></a>
V.1 PRIMARY ADJACENCY EDGES
------------------------------------------------------------
E_adj :=
{
(B,C),
(C,D),
(D,E),
(E,F),
(F,G),
(G,H),
(H,I),
(I,K),
(K,B)
}
------------------------------------------------------------
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-adjacency-rule"></a>
ADJACENCY RULE
------------------------------------------------------------
Direct principial relation without mediation is lawful only
between adjacent nodes.
Non-adjacent relations require declared mediation:
• T mediation
• or Q grounding
• or another explicitly lawful cross-regime support path
------------------------------------------------------------
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-prohibition"></a>
PROHIBITION
------------------------------------------------------------
No direct inference may be made between non-adjacent nodes
without declared mediation.
Examples:
B ↔ E
C ↔ G
D ↔ H
are not directly inferable from ROTA A alone.
============================================================
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-vi-act-agent-circular-consistency"></a>
VI. ACT–AGENT CIRCULAR CONSISTENCY
============================================================
ROTA A encodes circular generative structure as structural
constraint, not execution.
------------------------------------------------------------
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-vi-1-act-generation-structure"></a>
VI.1 ACT GENERATION STRUCTURE
------------------------------------------------------------
E := act(B,C,D)
F := act(C,D,E)
G := act(D,E,F)
H := act(E,F,G)
I := act(F,G,H)
K := act(G,H,I)
------------------------------------------------------------
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-vi-2-agent-grounding-structure"></a>
VI.2 AGENT GROUNDING STRUCTURE
------------------------------------------------------------
B := agent(H,I,K)
C := agent(I,K,B)
D := agent(K,B,C)
------------------------------------------------------------
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-rule-2"></a>
RULE
------------------------------------------------------------
Every dignity is structurally situated as:
• grounded
• generative
• interdependent
------------------------------------------------------------
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-interpretation-2"></a>
INTERPRETATION
------------------------------------------------------------
This structure defines:
• closure
• dependency propagation
• cyclic consistency
• inconsistency exposure
It does not by itself compute results.
============================================================
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-vii-closure-law"></a>
VII. CLOSURE LAW
============================================================
ROTA A is a closed cyclic structure.
------------------------------------------------------------
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-rule-3"></a>
RULE
------------------------------------------------------------
Evaluation of any dignity must respect:
• upstream dependencies
• downstream consequences
• adjacency constraints
• circular closure
------------------------------------------------------------
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-propagation-law"></a>
PROPAGATION LAW
------------------------------------------------------------
Instability in:
B, C, or D
structurally propagates through:
E → F → G → H → I → K
------------------------------------------------------------
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-non-isolation-constraint"></a>
NON-ISOLATION CONSTRAINT
------------------------------------------------------------
No dignity may be evaluated in isolation without declaring
closure context.
Atomic OPERA A execution is allowed only if its closure status
is exposed or bounded.
============================================================
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-viii-cambra-geometria-descriptiva"></a>
VIII. CAMBRA / GEOMETRIA DESCRIPTIVA
============================================================
FIGURA: A
ENUMERATIO_CAMBRARUM: 9
SENSUS_ROTATIONIS: clockwise
ANGULUS_ANCORA: 90°
ANGULUS_ANCORA_CAMBRA: B (ρ=Ⅰ)
GRADUS_CAMBRA: 40°
θ(ρ) = 90° − (Index(ρ) − 1) * 40° mod 360
MAPA_CIRCULAR := (B,C,D,E,F,G,H,I,K)
CAMBRA_ID_RULE := A- + ORDINAL_SLOT
SENTINELA_PRE := PRE is header, non-enumerable
------------------------------------------------------------
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-geometry-rule"></a>
GEOMETRY RULE
------------------------------------------------------------
Geometry is structural and display-facing.
It reflects graph topology.
It does not define:
• camera generation
• combinatorial legality
• OPERA execution
• AREPO admissibility
============================================================
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-ix-figural-interface"></a>
IX. FIGURAL INTERFACE
============================================================
ROTA A is the structural rendering of Figura A under TENET C.
------------------------------------------------------------
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-class-relation"></a>
CLASS RELATION
------------------------------------------------------------
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-rota-a"></a>
ROTA A:
exposes structural loci and graph constraints
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-tenet-c"></a>
TENET C:
defines figural legality
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-tenet-camerae"></a>
TENET CAMERAE:
defines camera and combinatorial domains
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-opera"></a>
OPERA:
executes only where lawful structure permits
------------------------------------------------------------
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-rule-4"></a>
RULE
------------------------------------------------------------
ROTA A must not be used to infer:
• camera domains
• combinatorial legality
• execution traversal
• evaluation outcomes
without proper downstream artifacts.
============================================================
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-x-definitiones-formal-logic"></a>
X. DEFINITIONES — FORMAL LOGIC
============================================================
Def(Di) := (Di, per_quod, actus_essendi)
------------------------------------------------------------
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-rule-5"></a>
RULE
------------------------------------------------------------
ROTA A may expose the formal definition frame.
ROTA A does not formalize:
• convertibility outcomes
• implication chains
• contraction grades
• evaluation results
------------------------------------------------------------
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-constraint"></a>
CONSTRAINT
------------------------------------------------------------
ROTA A exposes structure only.
============================================================
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-xi-definitiones-ipsis-litteris"></a>
XI. DEFINITIONES — IPSIS LITTERIS
============================================================
Bonitas : "Bonitas est, per quam bonum bonificat."
Magnitudo : "Magnitudo est, per quam bonum est magnum."
Duratio : "Duratio est, per quam bonum durat."
Potestas : "Potestas est, per quam bonum potest."
Sapientia : "Sapientia est, per quam bonum sapit."
Voluntas : "Voluntas est, per quam bonum vult."
Virtus : "Virtus est, per quam bonum virtuosum est."
Veritas : "Veritas est, per quam bonum verum est."
Gloria : "Gloria est, per quam bonum gloriosum est."
------------------------------------------------------------
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-rule-6"></a>
RULE
------------------------------------------------------------
Definitiones are immutable in ROTA A.
No paraphrase is allowed.
No interpretative extension is allowed inside this block.
============================================================
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-xii-self-binding-structural-law"></a>
XII. SELF-BINDING STRUCTURAL LAW
============================================================
When ROTA A is presented or invoked, it binds the interpretation
space.
It constrains:
• adjacency
• closure
• structural propagation
• lawful node reference
• possible traversal
------------------------------------------------------------
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-rule-7"></a>
RULE
------------------------------------------------------------
Any OPERA or SATOR output referencing REGIMEN_A must not:
• violate adjacency
• ignore closure dependencies
• collapse nodes
• reorder the cycle
• treat graph exposure as decorative
------------------------------------------------------------
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-function"></a>
FUNCTION
------------------------------------------------------------
ROTA A acts as:
• externalized structural constraint
• anti-drift enforcement surface
• machine-body of REGIMEN_A
============================================================
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-xiii-dynamic-overlay-extension"></a>
XIII. DYNAMIC OVERLAY EXTENSION
============================================================
ROTA A may carry an optional dynamic overlay layer.
This extension is:
• session-bound
• non-destructive
• non-canonical
• state-projective
• structurally constrained
------------------------------------------------------------
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-core-distinction"></a>
CORE DISTINCTION
------------------------------------------------------------
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-rota-a-base"></a>
ROTA A BASE:
canonical structural machine
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-rota-a-overlay"></a>
ROTA A OVERLAY:
temporary projection of OPERA A contracted results
------------------------------------------------------------
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-rule-8"></a>
RULE
------------------------------------------------------------
The overlay must never modify:
• TENET A
• ROTA A canon
• carrier identity
• adjacency structure
• closure law
============================================================
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-xiv-overlay-definition"></a>
XIV. OVERLAY DEFINITION
============================================================
ROTA_A_OVERLAY := mapping of OPERA A outputs onto ROTA A nodes
------------------------------------------------------------
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-form"></a>
FORM
------------------------------------------------------------
OVERLAY_A := {
B: BONITAS_RESULT(x) | null,
C: MAGNITUDO_RESULT(x) | null,
D: DURATIO_RESULT(x) | null,
E: POTESTAS_RESULT(x) | null,
F: SAPIENTIA_RESULT(x) | null,
G: VOLUNTAS_RESULT(x) | null,
H: VIRTUS_RESULT(x) | null,
I: VERITAS_RESULT(x) | null,
K: GLORIA_RESULT(x) | null
}
------------------------------------------------------------
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-rule-9"></a>
RULE
------------------------------------------------------------
Each slot is either:
• EMPTY
• or populated by a valid OPERA A result object
------------------------------------------------------------
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-constraint-2"></a>
CONSTRAINT
------------------------------------------------------------
Overlay must never fabricate values.
Only OPERA A outputs admitted or validated under AREPO A may
populate slots.
============================================================
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-xv-slot-state-model"></a>
XV. SLOT STATE MODEL
============================================================
Each ROTA A node has two layers:
1. CANONICAL_LAYER
2. OVERLAY_LAYER
------------------------------------------------------------
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-canonical-layer"></a>
CANONICAL_LAYER
------------------------------------------------------------
Immutable dignity identity.
Includes:
• ordinal
• token
• noun
• adjective
• definition
• graph position
------------------------------------------------------------
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-overlay-layer"></a>
OVERLAY_LAYER
------------------------------------------------------------
Dynamic contracted state.
May include:
• PRESENCE_MODE
• CONVERTIBILITY_EFFECT
• CORRELATIVE_PROFILE
• ATTRIBUTION_MODE
• DISTORTION_FLAGS
• SUPPORT_DEPTH
• REUSE_READINESS
• VALIDITY_STATE
------------------------------------------------------------
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-slot-states"></a>
SLOT STATES
------------------------------------------------------------
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-empty"></a>
EMPTY:
no OPERA A evaluation present
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-filled"></a>
FILLED:
OPERA A result present
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-degraded"></a>
DEGRADED:
FILLED with degraded admissibility under AREPO A
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-provisional"></a>
PROVISIONAL:
FILLED with provisional admissibility under AREPO A
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-blocked"></a>
BLOCKED:
slot explicitly marked by AREPO A block
------------------------------------------------------------
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-rule-10"></a>
RULE
------------------------------------------------------------
Overlay states must reflect AREPO A truthfully.
============================================================
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-xvi-temporality-law"></a>
XVI. TEMPORALITY LAW
============================================================
Overlay is strictly:
• session-bound
• non-persistent
• non-canonical
------------------------------------------------------------
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-discard-rule"></a>
DISCARD RULE
------------------------------------------------------------
Overlay must be discarded when:
• session ends
• context resets
• new OPERA A invalidates prior state
• AREPO A blocks prior state
• user explicitly clears the state
------------------------------------------------------------
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-prohibition-2"></a>
PROHIBITION
------------------------------------------------------------
Overlay must not:
• be stored as doctrine
• be reused as TENET
• be treated as canonical truth
• be silently carried across contexts
============================================================
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-xvii-projection-rule"></a>
XVII. PROJECTION RULE
============================================================
Projection occurs only when:
• OPERA A result exists
• AREPO A has admitted, validated, or explicitly marked it
• dignity identity is resolved
• slot identity is unambiguous
------------------------------------------------------------
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-projection-function"></a>
PROJECTION FUNCTION
------------------------------------------------------------
PROJECT_A_RESULT(r):
let d := dignity(r)
OVERLAY_A[d] := r
------------------------------------------------------------
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-rule-11"></a>
RULE
------------------------------------------------------------
Projection is:
• injective per dignity per context
• last-write-valid only when update is declared
• structurally constrained by ROTA A
------------------------------------------------------------
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-conflict-constraint"></a>
CONFLICT CONSTRAINT
------------------------------------------------------------
Multiple competing results must not silently override.
Conflict must be surfaced through SATOR A.
============================================================
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-xviii-node-view-model"></a>
XVIII. NODE VIEW MODEL
============================================================
NODE(d) :=
{
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-canon"></a>
CANON:
{
ORDINAL_SLOT,
TOKEN,
DIGNITY,
ADJECTIVE,
DEFINITION,
GRAPH_POSITION
}
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-overlay"></a>
OVERLAY:
{
PRESENCE_MODE,
CONVERTIBILITY_EFFECT,
CORRELATIVE_PROFILE,
ATTRIBUTION_MODE,
DISTORTION_FLAGS,
VALIDITY_STATE,
SUPPORT_DEPTH
} | EMPTY
}
------------------------------------------------------------
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-rule-12"></a>
RULE
------------------------------------------------------------
Overlay must not replace canon.
Overlay must be clearly marked as contracted state.
============================================================
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-xix-graph-consistency-under-overlay"></a>
XIX. GRAPH CONSISTENCY UNDER OVERLAY
============================================================
Overlay must respect ROTA A graph laws:
• adjacency
• closure
• propagation
• non-permutability
• node distinction
------------------------------------------------------------
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-consistency-rule"></a>
CONSISTENCY RULE
------------------------------------------------------------
If overlay introduces contradiction across nodes:
• inconsistency must be exposed
• not silently resolved
------------------------------------------------------------
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-propagation-exposure"></a>
PROPAGATION EXPOSURE
------------------------------------------------------------
If B, C, or D are unstable or contradictory, SATOR A may expose
expected instability in E–K.
------------------------------------------------------------
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-constraint-3"></a>
CONSTRAINT
------------------------------------------------------------
ROTA A does not compute propagation.
ROTA A exposes the structure through which propagation is
interpretable.
============================================================
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-xx-support-for-opera-d-tertia-quarta"></a>
XX. SUPPORT FOR OPERA D / TERTIA / QUARTA
============================================================
Overlay may provide lawful input substrate for higher OPERAE.
------------------------------------------------------------
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-opera-d"></a>
OPERA D
------------------------------------------------------------
May consume:
• filled slots as evaluation domain
Domain:
{d ∈ N_A | OVERLAY_A[d] ≠ EMPTY}
------------------------------------------------------------
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-opera-tertia"></a>
OPERA TERTIA
------------------------------------------------------------
May use:
• overlay states
• distortion flags
• convertibility gradients
• blocked / degraded loci
To refine structural coherence.
------------------------------------------------------------
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-opera-quarta"></a>
OPERA QUARTA
------------------------------------------------------------
May operate over:
• overlay as bounded principial field
To generate structured propositions.
------------------------------------------------------------
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-rule-13"></a>
RULE
------------------------------------------------------------
Overlay is admissible input only when AREPO lineage and flags
are preserved.
Overlay is not validated doctrine.
============================================================
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-xxi-self-binding-overlay-function"></a>
XXI. SELF-BINDING OVERLAY FUNCTION
============================================================
Overlay reinforces:
• session coherence
• assistant output discipline
• explicit state tracking
• downstream visibility
------------------------------------------------------------
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-rule-14"></a>
RULE
------------------------------------------------------------
Once overlay is declared, all subsequent reasoning in the same
session must respect it unless an update is explicitly declared.
------------------------------------------------------------
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-prohibition-3"></a>
PROHIBITION
------------------------------------------------------------
Assistant must not:
• contradict overlay silently
• recompute without declaring update
• collapse EMPTY into ABSENT
• treat DEGRADED as BLOCKED
• treat PROVISIONAL as REFINED
============================================================
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-xxii-sator-mediation-requirements"></a>
XXII. SATOR MEDIATION REQUIREMENTS
============================================================
When ROTA A or its overlay is active, SATOR A should expose:
• filled vs empty nodes
• degraded nodes
• provisional nodes
• blocked nodes
• closure risks
• adjacency violations
• missing loci where relevant
------------------------------------------------------------
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-optional-compressed-display"></a>
OPTIONAL COMPRESSED DISPLAY
------------------------------------------------------------
Example:
B: STRONG / STABLE_CONTRACTED
C: MODERATE / PARTIAL
D: WEAK / FRAGMENTED
E–K: EMPTY
------------------------------------------------------------
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-rule-15"></a>
RULE
------------------------------------------------------------
SATOR A may compress display, but must preserve:
• dignity identity
• slot state clarity
• canon / overlay distinction
============================================================
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-xxiii-failure-modes"></a>
XXIII. FAILURE MODES
============================================================
Improper use of ROTA A includes:
• treating it as decorative
• treating it as display-only
• ignoring adjacency
• evaluating nodes in isolation
• bypassing closure propagation
• inferring execution from structure
• inferring camera domains from graph exposure
• reordering cycles arbitrarily
• collapsing nodes
• mixing overlay contexts
• overriding overlay without declaration
• ignoring AREPO states
• collapsing EMPTY into ABSENT
------------------------------------------------------------
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-result"></a>
RESULT
------------------------------------------------------------
Improper use produces:
• semantic drift
• invalid inference
• false coherence
• invalid downstream execution
• corrupted mediation
============================================================
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-xxiv-function"></a>
XXIV. FUNCTION
============================================================
ROTA A governs:
• cyclic machine topology
• principial loci
• ordinal carrier structure
• graph exposure
• adjacency constraints
• closure awareness
• self-binding structural reference
• optional dynamic overlay projection
ROTA A is:
• ROTAS
• structure
• machine layer
• constraint surface
• graph carrier
• traversal substrate
ROTA A is NOT:
• doctrine
• execution
• admissibility
• inference engine
• human-facing explanation layer
• persistent contracted state
============================================================
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-xxv-summary"></a>
XXV. SUMMARY
============================================================
ROTA A functions as:
• canonical structural machine of Figura A
• cyclic graph of principial loci
• adjacency-constrained structure
• closure-enforcing surface
• self-binding reference for OPERA and SATOR
• optional session-bound overlay substrate
------------------------------------------------------------
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-closure-rule"></a>
CLOSURE RULE
------------------------------------------------------------
ROTA A must be read not as what dignities do,
but as:
how dignities are structurally positioned,
constrained,
closed,
and made traversable.
------------------------------------------------------------
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-final-law"></a>
FINAL LAW
------------------------------------------------------------
ROTAS defines the space in which the Ars becomes operable.
ROTA A defines the structural space in which REGIMEN_A becomes
operable.
============================================================
END ROTA A — REGIMEN_A STRUCTURAL MACHINE LAYER
============================================================
============================================================
ROTA A(BCD) — MINIMAL DIFFERENTIATED PRINCIPIAL WHEEL
Ars Generalis Applied — Regimen_A Minimal Structural Display
Version: 0.1.0-ROTA-A-BCD
Status: PROPOSED / MINIMAL WHEEL / STRUCTURAL DISPLAY
Scope: minimal differentiated wheel of Bonitas, Magnitudo, and Duratio
Authority: TENET A / ALBUS FIGURA PRIMA / ALBUS ROTÆ
Mutation Policy: VERSION-CONTROLLED ONLY
Class: ROTAS
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-parent-rota-a-regimen-a-structural-display-layer"></a>
Parent: ROTA A — REGIMEN_A STRUCTURAL DISPLAY LAYER
============================================================
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-purpose-2"></a>
PURPOSE
============================================================
ROTA A(BCD) defines the minimal differentiated principial
wheel capable of expressing REGIMEN_A without collapse into
undifferentiated singularity.
It provides:
• the minimal triadic principial field
• full convertibility within that field
• minimal closure surface for principial display
• bounded structural substrate for early validation
This artifact does NOT:
• replace full ROTA A
• deny the remaining dignities
• execute OPERA A
• define admissibility
• introduce new doctrine
------------------------------------------------------------
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-core-principle"></a>
CORE PRINCIPLE
------------------------------------------------------------
BCD is the minimal differentiated set of dignities through
which A may be expressed without collapse.
Thus:
ROTA A(BCD) is not an arbitrary truncation.
It is:
the first stable differentiated principial wheel.
============================================================
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-i-carrier"></a>
I. CARRIER
============================================================
DOMINIUM_ORDINALE_A_BCD := {Ⅰ,Ⅱ,Ⅲ}
TOKENS_A_BCD := {B,C,D}
PRE (header sentinel): A (non-enumerable)
============================================================
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-ii-canon-list"></a>
II. CANON LIST
============================================================
Ⅰ → B → Bonitas | Bonus
Ⅱ → C → Magnitudo | Magnus
Ⅲ → D → Duratio | Durabilis
------------------------------------------------------------
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-interpretation-3"></a>
INTERPRETATION
------------------------------------------------------------
B — qualitative principial ground
C — principial amplitude / greatness
D — principial persistence / duration
Together:
BCD = first stable differentiated expression of A
============================================================
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-iii-minimal-circular-render"></a>
III. MINIMAL CIRCULAR RENDER
============================================================
RENDER_ORDER_A_BCD := B → C → D → B
Equivalent ordinal walk:
Ⅰ → Ⅱ → Ⅲ → Ⅰ
------------------------------------------------------------
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-rule-16"></a>
RULE
------------------------------------------------------------
This render order is:
• structural
• circular
• minimal
It is not:
• full ROTA A
• a substitute for full canon
============================================================
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-iv-graph-structure"></a>
IV. GRAPH STRUCTURE
============================================================
ROTA A(BCD) defines:
G_A_BCD := (N_BCD, E_BCD)
Where:
N_BCD = {B,C,D}
------------------------------------------------------------
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-iv-1-adjacency-edges"></a>
IV.1 — ADJACENCY EDGES
------------------------------------------------------------
E_adj :=
{
(B,C),
(C,D),
(D,B)
}
------------------------------------------------------------
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-rule-17"></a>
RULE
------------------------------------------------------------
All nodes are adjacent within the minimal wheel.
Thus:
every dignity in BCD stands in immediate structural
relation with the others.
============================================================
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-v-full-convertibility-law-within-bcd"></a>
V. FULL CONVERTIBILITY LAW (WITHIN BCD)
============================================================
Within the bounded field of BCD:
B ⇄ C
C ⇄ D
D ⇄ B
and therefore:
∀ x,y ∈ {B,C,D}, x ≠ y :
x is structurally convertible with y
------------------------------------------------------------
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-interpretation-4"></a>
INTERPRETATION
------------------------------------------------------------
This is not merely pairwise contact.
It is:
full minimal principial convertibility
------------------------------------------------------------
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-rule-18"></a>
RULE
------------------------------------------------------------
ROTA A(BCD) must always be read as a field of full internal
convertibility.
------------------------------------------------------------
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-constraint-4"></a>
CONSTRAINT
------------------------------------------------------------
This law applies to the BCD field as such.
It must not be silently extended to:
• contracted outputs
• contextual overlays
• downstream mixed procedures
without proper mediation.
============================================================
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-vi-triadic-closure"></a>
VI. TRIADIC CLOSURE
============================================================
BCD forms a closed minimal wheel:
B → C → D → B
------------------------------------------------------------
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-rule-19"></a>
RULE
------------------------------------------------------------
No node in BCD may be read in isolation if the wheel is active.
Each node is:
• locally distinct
• globally co-present
• minimally closure-bound
------------------------------------------------------------
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-interpretation-5"></a>
INTERPRETATION
------------------------------------------------------------
If one node is structurally unstable in contextual use,
the whole minimal field is affected.
This is why BCD functions as:
first validation field of REGIMEN_A
============================================================
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-vii-structural-function"></a>
VII. STRUCTURAL FUNCTION
============================================================
ROTA A(BCD) serves as:
• minimal display of differentiated A
• first closure surface for principial analysis
• compact wheel for early-stage OPERA A validation
• reduced graph for testing coherence before EFGHIK
------------------------------------------------------------
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-rule-20"></a>
RULE
------------------------------------------------------------
When minimal principial validation is sufficient,
ROTA A(BCD) may be invoked before full ROTA A.
------------------------------------------------------------
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-constraint-5"></a>
CONSTRAINT
------------------------------------------------------------
ROTA A(BCD) must not be mistaken for denial of EFGHIK.
It is:
principial minimum,
not:
principial totality.
============================================================
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-viii-relation-to-full-rota-a"></a>
VIII. RELATION TO FULL ROTA A
============================================================
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-rota-a-bcd"></a>
ROTA A(BCD):
• is a lawful reduced wheel
• preserves principial differentiation
• preserves full convertibility within its own field
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-rota-a-2"></a>
ROTA A:
• contains the full ninefold principial canon
------------------------------------------------------------
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-rule-21"></a>
RULE
------------------------------------------------------------
ROTA A(BCD) is a minimal subset wheel under A,
not a replacement artifact for full ROTA A.
------------------------------------------------------------
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-functional-relation"></a>
FUNCTIONAL RELATION
------------------------------------------------------------
ROTA A(BCD)
→ early principial validation
→ compression analysis
→ minimal closure testing
ROTA A
→ full principial field
→ complete adjacency structure
→ full-cycle structural display
============================================================
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-ix-dynamic-overlay-compatibility"></a>
IX. DYNAMIC OVERLAY COMPATIBILITY
============================================================
If contextual overlay is active, ROTA A(BCD) may display only:
• B_RESULT
• C_RESULT
• D_RESULT
------------------------------------------------------------
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-rule-22"></a>
RULE
------------------------------------------------------------
Overlay on ROTA A(BCD) must preserve:
• distinction between canon and contraction
• full convertibility of pure BCD
• non-convertibility of contracted overlays unless
separately validated
------------------------------------------------------------
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-constraint-6"></a>
CONSTRAINT
------------------------------------------------------------
Contracted BCD overlay must never be presented as identical
to pure BCD closure.
============================================================
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-x-geometria-descriptiva"></a>
X. GEOMETRIA DESCRIPTIVA
============================================================
FIGURA: A(BCD)
ENUMERATIO_CAMBRARUM: 3
SENSUS_ROTATIONIS: clockwise
ANGULUS_ANCORA: 90°
ANGULUS_ANCORA_CAMBRA: B (ρ=Ⅰ)
GRADUS_CAMBRA: 120°
θ(ρ)=90°−(Index(ρ)−1)*120° mod 360
MAPA_CIRCULAR: (B,C,D)
CAMBRA_ID_RULE: A(BCD)- + ORDINAL_SLOT
SENTINELA_PRE: PRE is header, non-enumerable
------------------------------------------------------------
<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-interpretation-6"></a>
INTERPRETATION
------------------------------------------------------------
This is a minimal regular triadic wheel.
It reflects:
• equality of the three nodes
• full adjacency
• full minimal closure
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<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-xi-prohibitions"></a>
XI. PROHIBITIONS
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ROTA A(BCD) must not:
✗ be treated as arbitrary abbreviation
✗ be confused with full ROTA A
✗ deny the existence of EFGHIK
✗ project contracted results as pure convertibility
✗ infer execution by itself
✗ redefine TENET A canon
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<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-rule-23"></a>
RULE
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ROTA A(BCD) is:
• structural
• minimal
• fully convertible within its field
It is not:
• a doctrinal reduction of the whole system
• an execution artifact
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<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-xii-function"></a>
XII. FUNCTION
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ROTA A(BCD) governs:
• display of the minimal principial triad
• exposure of full convertibility within BCD
• triadic closure surface
• compact graph-carrier for early A-validation
ROTA A(BCD) is:
• minimal
• circular
• fully internally convertible
• structurally closed
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<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-xiii-summary"></a>
XIII. SUMMARY
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ROTA A(BCD) is:
• the minimal differentiated wheel of REGIMEN_A
• composed of Bonitas, Magnitudo, and Duratio
• fully internally convertible
• triadically closed
• suitable for early principial validation
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<a id="local-section-02-stack-a-rotas-a-structuralinstantiation-closure-rule-2"></a>
CLOSURE RULE
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ROTA A(BCD) must always be read as:
the minimal full-convertibility wheel of A,
through which principial differentiation first becomes stable
without collapse into undifferentiated A.
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END OF ROTA A(BCD) — MINIMAL DIFFERENTIATED PRINCIPIAL WHEEL
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