============================================================
ROTAS D — OCTO ROTAE FIGURAE QUARTAE
Ars Generalis Applied — Binary Wheel Topology for Principial Mixture
Version: 0.1.0-ROTAS-D-OCTO-ROTAE-FIGURAE-QUARTAE
Status: PROPOSED / STRUCTURAL TOPOLOGY
Scope: explicit ROTA family for three-wheel Figura Quarta over A/T regimes
Authority: ROTAS
Mutation Policy: VERSION-CONTROLLED ONLY
Class: ROTAS
Regime: D (A + T PRINCIPIAL MIXTURE)
Depends-On:
• TENET D — PRINCIPIA DUPLEX
• TENET — REGIMEN DISPATCH LAW
References:
• TENET A
• TENET T
============================================================
<!-- LOCAL_SECTION_INDEX_START -->
## LOCAL SECTION INDEX
Scope: local anchors within this artifact only. No cross-artifact links are introduced here.
- [I. PURPOSE](#local-section-08-stack-d-rotas-d-structuralinstantiation-i-purpose)
- [CORE ASSERTION](#local-section-08-stack-d-rotas-d-structuralinstantiation-core-assertion)
- [II. FIGURA QUARTA BINARY SPACE](#local-section-08-stack-d-rotas-d-structuralinstantiation-ii-figura-quarta-binary-space)
- [FORMAL](#local-section-08-stack-d-rotas-d-structuralinstantiation-formal)
- [TOTAL CONFIGURATIONS](#local-section-08-stack-d-rotas-d-structuralinstantiation-total-configurations)
- [COMPLETE SET](#local-section-08-stack-d-rotas-d-structuralinstantiation-complete-set)
- [RULE](#local-section-08-stack-d-rotas-d-structuralinstantiation-rule)
- [III. WHEEL POSITION LAW](#local-section-08-stack-d-rotas-d-structuralinstantiation-iii-wheel-position-law)
- [RULE](#local-section-08-stack-d-rotas-d-structuralinstantiation-rule-2)
- [INTERPRETATION](#local-section-08-stack-d-rotas-d-structuralinstantiation-interpretation)
- [FAILURE](#local-section-08-stack-d-rotas-d-structuralinstantiation-failure)
- [IV. ROTA FAMILY REGISTRY](#local-section-08-stack-d-rotas-d-structuralinstantiation-iv-rota-family-registry)
- [ROTA_D_AAA](#local-section-08-stack-d-rotas-d-structuralinstantiation-rota-d-aaa)
- [ROTA_D_AAT](#local-section-08-stack-d-rotas-d-structuralinstantiation-rota-d-aat)
- [ROTA_D_ATA](#local-section-08-stack-d-rotas-d-structuralinstantiation-rota-d-ata)
- [ROTA_D_ATT](#local-section-08-stack-d-rotas-d-structuralinstantiation-rota-d-att)
- [ROTA_D_TAA](#local-section-08-stack-d-rotas-d-structuralinstantiation-rota-d-taa)
- [ROTA_D_TAT](#local-section-08-stack-d-rotas-d-structuralinstantiation-rota-d-tat)
- [ROTA_D_TTA](#local-section-08-stack-d-rotas-d-structuralinstantiation-rota-d-tta)
- [ROTA_D_TTT](#local-section-08-stack-d-rotas-d-structuralinstantiation-rota-d-ttt)
- [V. CARRIER DOMAIN BINDING](#local-section-08-stack-d-rotas-d-structuralinstantiation-v-carrier-domain-binding)
- [A CARRIER DOMAIN](#local-section-08-stack-d-rotas-d-structuralinstantiation-a-carrier-domain)
- [T CARRIER DOMAIN](#local-section-08-stack-d-rotas-d-structuralinstantiation-t-carrier-domain)
- [RULE](#local-section-08-stack-d-rotas-d-structuralinstantiation-rule-3)
- [VI. CONFIGURATION INSTANCE FORM](#local-section-08-stack-d-rotas-d-structuralinstantiation-vi-configuration-instance-form)
- [FORM](#local-section-08-stack-d-rotas-d-structuralinstantiation-form)
- [EXAMPLE](#local-section-08-stack-d-rotas-d-structuralinstantiation-example)
- [INTERPRETATION](#local-section-08-stack-d-rotas-d-structuralinstantiation-interpretation-2)
- [VII. NO FREE WHEEL ASSIGNMENT LAW](#local-section-08-stack-d-rotas-d-structuralinstantiation-vii-no-free-wheel-assignment-law)
- [PROHIBITION](#local-section-08-stack-d-rotas-d-structuralinstantiation-prohibition)
- [RULE](#local-section-08-stack-d-rotas-d-structuralinstantiation-rule-4)
- [FAILURE](#local-section-08-stack-d-rotas-d-structuralinstantiation-failure-2)
- [VIII. RELATION TO OPERA](#local-section-08-stack-d-rotas-d-structuralinstantiation-viii-relation-to-opera)
- [RULE](#local-section-08-stack-d-rotas-d-structuralinstantiation-rule-5)
- [IX. FIGURA QUARTA COMPLETENESS LAW](#local-section-08-stack-d-rotas-d-structuralinstantiation-ix-figura-quarta-completeness-law)
- [FORMAL](#local-section-08-stack-d-rotas-d-structuralinstantiation-formal-2)
- [RULE](#local-section-08-stack-d-rotas-d-structuralinstantiation-rule-6)
- [FAILURE](#local-section-08-stack-d-rotas-d-structuralinstantiation-failure-3)
- [X. NON-COLLAPSE LAW](#local-section-08-stack-d-rotas-d-structuralinstantiation-x-non-collapse-law)
- [PROHIBITIONS](#local-section-08-stack-d-rotas-d-structuralinstantiation-prohibitions)
- [FAILURE](#local-section-08-stack-d-rotas-d-structuralinstantiation-failure-4)
- [XI. FUNCTION](#local-section-08-stack-d-rotas-d-structuralinstantiation-xi-function)
- [XII. CLOSURE](#local-section-08-stack-d-rotas-d-structuralinstantiation-xii-closure)
- [FINAL LAW](#local-section-08-stack-d-rotas-d-structuralinstantiation-final-law)
- [FINAL STATE:](#local-section-08-stack-d-rotas-d-structuralinstantiation-final-state)
<!-- LOCAL_SECTION_INDEX_END -->
END SECTION 0 — HEADER
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============================================================
<a id="local-section-08-stack-d-rotas-d-structuralinstantiation-i-purpose"></a>
I. PURPOSE
============================================================
Define the complete ROTAS topology for REGIMEN_D as:
OCTO ROTAE FIGURAE QUARTAE
------------------------------------------------------------
This artifact establishes:
• the full set of 8 lawful three-wheel configurations
• explicit wheel-to-regime binding
• positional distinction between configurations
• non-ambiguous Figura Quarta use under A/T mixture
• structural substrate for later OPERA selection
------------------------------------------------------------
<a id="local-section-08-stack-d-rotas-d-structuralinstantiation-core-assertion"></a>
CORE ASSERTION
------------------------------------------------------------
Figura Quarta under REGIMEN_D must not rely on implicit
wheel assignment.
Every active wheel must explicitly declare:
• wheel position
• bound regime
• carrier domain
============================================================
END SECTION I
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============================================================
<a id="local-section-08-stack-d-rotas-d-structuralinstantiation-ii-figura-quarta-binary-space"></a>
II. FIGURA QUARTA BINARY SPACE
============================================================
REGIMEN_D uses three wheel positions:
W1
W2
W3
Each wheel may bind to:
A
T
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<a id="local-section-08-stack-d-rotas-d-structuralinstantiation-formal"></a>
FORMAL
------------------------------------------------------------
Wn ∈ {A, T}
where:
n ∈ {1,2,3}
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<a id="local-section-08-stack-d-rotas-d-structuralinstantiation-total-configurations"></a>
TOTAL CONFIGURATIONS
------------------------------------------------------------
2^3 = 8
------------------------------------------------------------
<a id="local-section-08-stack-d-rotas-d-structuralinstantiation-complete-set"></a>
COMPLETE SET
------------------------------------------------------------
AAA
AAT
ATA
ATT
TAA
TAT
TTA
TTT
------------------------------------------------------------
<a id="local-section-08-stack-d-rotas-d-structuralinstantiation-rule"></a>
RULE
------------------------------------------------------------
All 8 configurations are lawful unless explicitly blocked
by a later AREPO constraint.
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END SECTION II
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============================================================
<a id="local-section-08-stack-d-rotas-d-structuralinstantiation-iii-wheel-position-law"></a>
III. WHEEL POSITION LAW
============================================================
Wheel position is structurally significant.
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<a id="local-section-08-stack-d-rotas-d-structuralinstantiation-rule-2"></a>
RULE
------------------------------------------------------------
AAT ≠ ATA ≠ TAA
because:
W1, W2, W3 are distinct positions
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<a id="local-section-08-stack-d-rotas-d-structuralinstantiation-interpretation"></a>
INTERPRETATION
------------------------------------------------------------
Configuration identity is determined by:
ordered wheel binding
not by:
unordered regime count
------------------------------------------------------------
<a id="local-section-08-stack-d-rotas-d-structuralinstantiation-failure"></a>
FAILURE
------------------------------------------------------------
wheel_order_collapse
configuration_equivalence_error
positional_erasure
============================================================
END SECTION III
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<a id="local-section-08-stack-d-rotas-d-structuralinstantiation-iv-rota-family-registry"></a>
IV. ROTA FAMILY REGISTRY
============================================================
The complete ROTAS D family is:
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<a id="local-section-08-stack-d-rotas-d-structuralinstantiation-rota-d-aaa"></a>
ROTA_D_AAA
------------------------------------------------------------
W1 = A
W2 = A
W3 = A
Type:
pure absolute principial configuration
------------------------------------------------------------
<a id="local-section-08-stack-d-rotas-d-structuralinstantiation-rota-d-aat"></a>
ROTA_D_AAT
------------------------------------------------------------
W1 = A
W2 = A
W3 = T
Type:
absolute-leading mixed configuration
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<a id="local-section-08-stack-d-rotas-d-structuralinstantiation-rota-d-ata"></a>
ROTA_D_ATA
------------------------------------------------------------
W1 = A
W2 = T
W3 = A
Type:
medial-relative mixed configuration
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<a id="local-section-08-stack-d-rotas-d-structuralinstantiation-rota-d-att"></a>
ROTA_D_ATT
------------------------------------------------------------
W1 = A
W2 = T
W3 = T
Type:
absolute-initial mixed configuration
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<a id="local-section-08-stack-d-rotas-d-structuralinstantiation-rota-d-taa"></a>
ROTA_D_TAA
------------------------------------------------------------
W1 = T
W2 = A
W3 = A
Type:
relative-initial mixed configuration
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<a id="local-section-08-stack-d-rotas-d-structuralinstantiation-rota-d-tat"></a>
ROTA_D_TAT
------------------------------------------------------------
W1 = T
W2 = A
W3 = T
Type:
medial-absolute mixed configuration
------------------------------------------------------------
<a id="local-section-08-stack-d-rotas-d-structuralinstantiation-rota-d-tta"></a>
ROTA_D_TTA
------------------------------------------------------------
W1 = T
W2 = T
W3 = A
Type:
absolute-terminal mixed configuration
------------------------------------------------------------
<a id="local-section-08-stack-d-rotas-d-structuralinstantiation-rota-d-ttt"></a>
ROTA_D_TTT
------------------------------------------------------------
W1 = T
W2 = T
W3 = T
Type:
pure relative principial configuration
============================================================
END SECTION IV
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============================================================
<a id="local-section-08-stack-d-rotas-d-structuralinstantiation-v-carrier-domain-binding"></a>
V. CARRIER DOMAIN BINDING
============================================================
A-bound wheels use:
absolute dignity carriers
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<a id="local-section-08-stack-d-rotas-d-structuralinstantiation-a-carrier-domain"></a>
A CARRIER DOMAIN
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B — Bonitas
C — Magnitudo
D — Duratio
E — Potentia
F — Sapientia
G — Voluntas
H — Virtus
I — Veritas
K — Gloria
------------------------------------------------------------
T-bound wheels use:
relative dignity carriers
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<a id="local-section-08-stack-d-rotas-d-structuralinstantiation-t-carrier-domain"></a>
T CARRIER DOMAIN
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L — Differentia = T(B)
M — Concordantia = T(C)
N — Contrarietas = T(D)
O — Initium = T(E)
P — Medium = T(F)
Q — Finis = T(G)
R — Majoritas = T(H)
S — Aequalitas = T(I)
T — Minoritas = T(K)
------------------------------------------------------------
<a id="local-section-08-stack-d-rotas-d-structuralinstantiation-rule-3"></a>
RULE
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A wheel bound to A may not receive T carriers.
A wheel bound to T may not receive A carriers.
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END SECTION V
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============================================================
<a id="local-section-08-stack-d-rotas-d-structuralinstantiation-vi-configuration-instance-form"></a>
VI. CONFIGURATION INSTANCE FORM
============================================================
A ROTAS D chamber instance must declare:
• selected ROTA
• W1 carrier
• W2 carrier
• W3 carrier
------------------------------------------------------------
<a id="local-section-08-stack-d-rotas-d-structuralinstantiation-form"></a>
FORM
------------------------------------------------------------
ROTA_INSTANCE :=
{
rota_id,
W1: {regime, carrier},
W2: {regime, carrier},
W3: {regime, carrier}
}
------------------------------------------------------------
<a id="local-section-08-stack-d-rotas-d-structuralinstantiation-example"></a>
EXAMPLE
------------------------------------------------------------
BCN under ROTA_D_AAT means:
W1 = A:B
W2 = A:C
W3 = T:N
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<a id="local-section-08-stack-d-rotas-d-structuralinstantiation-interpretation-2"></a>
INTERPRETATION
------------------------------------------------------------
The surface string:
BCN
is valid only if its ROTA binding is explicit.
============================================================
END SECTION VI
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============================================================
<a id="local-section-08-stack-d-rotas-d-structuralinstantiation-vii-no-free-wheel-assignment-law"></a>
VII. NO FREE WHEEL ASSIGNMENT LAW
============================================================
Figura Quarta may not be used with implicit wheel regimes.
------------------------------------------------------------
<a id="local-section-08-stack-d-rotas-d-structuralinstantiation-prohibition"></a>
PROHIBITION
------------------------------------------------------------
No operation may assume:
• W1 regime from context
• W2 regime from context
• W3 regime from context
------------------------------------------------------------
<a id="local-section-08-stack-d-rotas-d-structuralinstantiation-rule-4"></a>
RULE
------------------------------------------------------------
Wheel regime must be declared before traversal,
comparison, multiplication, or evacuation.
------------------------------------------------------------
<a id="local-section-08-stack-d-rotas-d-structuralinstantiation-failure-2"></a>
FAILURE
------------------------------------------------------------
implicit_wheel_binding
free_assignment_drift
runtime_regime_guessing
============================================================
END SECTION VII
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============================================================
<a id="local-section-08-stack-d-rotas-d-structuralinstantiation-viii-relation-to-opera"></a>
VIII. RELATION TO OPERA
============================================================
ROTAS D defines:
lawful ROTA configurations
------------------------------------------------------------
OPERA may later:
• select a ROTA
• activate a ROTA
• compare ROTAE
• traverse within a ROTA
• multiply across ROTAE
------------------------------------------------------------
ROTAS D does NOT:
• select configurations
• execute traversal
• filter outputs
• perform evacuation
• perform multiplication
------------------------------------------------------------
<a id="local-section-08-stack-d-rotas-d-structuralinstantiation-rule-5"></a>
RULE
------------------------------------------------------------
ROTAE define lawful wheel structures.
OPERA operates over them.
============================================================
END SECTION VIII
============================================================
============================================================
<a id="local-section-08-stack-d-rotas-d-structuralinstantiation-ix-figura-quarta-completeness-law"></a>
IX. FIGURA QUARTA COMPLETENESS LAW
============================================================
A valid REGIMEN_D Figura Quarta topology must include:
all 8 binary configurations
------------------------------------------------------------
<a id="local-section-08-stack-d-rotas-d-structuralinstantiation-formal-2"></a>
FORMAL
------------------------------------------------------------
Complete_D_Figura_Quarta :=
{
AAA,
AAT,
ATA,
ATT,
TAA,
TAT,
TTA,
TTT
}
------------------------------------------------------------
<a id="local-section-08-stack-d-rotas-d-structuralinstantiation-rule-6"></a>
RULE
------------------------------------------------------------
No configuration may be omitted unless explicitly forbidden
by TENET or AREPO.
------------------------------------------------------------
<a id="local-section-08-stack-d-rotas-d-structuralinstantiation-failure-3"></a>
FAILURE
------------------------------------------------------------
incomplete_rota_family
missing_configuration
unjustified_exclusion
============================================================
END SECTION IX
============================================================
============================================================
<a id="local-section-08-stack-d-rotas-d-structuralinstantiation-x-non-collapse-law"></a>
X. NON-COLLAPSE LAW
============================================================
ROTAS D must preserve:
• wheel position
• regime binding
• carrier identity
• configuration identity
------------------------------------------------------------
<a id="local-section-08-stack-d-rotas-d-structuralinstantiation-prohibitions"></a>
PROHIBITIONS
------------------------------------------------------------
ROTAS D must not collapse:
• A into T
• T into A
• AAT into ATA
• ATA into TAA
• any configuration into unordered regime count
------------------------------------------------------------
<a id="local-section-08-stack-d-rotas-d-structuralinstantiation-failure-4"></a>
FAILURE
------------------------------------------------------------
regime_collapse
carrier_collapse
rota_identity_loss
configuration_flattening
============================================================
END SECTION X
============================================================
============================================================
<a id="local-section-08-stack-d-rotas-d-structuralinstantiation-xi-function"></a>
XI. FUNCTION
============================================================
ROTAS D governs:
• structural display of D-wheel configurations
• explicit topology of A/T Figura Quarta variants
• stable chamber binding
• non-ambiguous carrier placement
------------------------------------------------------------
ROTAS D is:
• structural
• positional
• finite
• complete
------------------------------------------------------------
ROTAS D is NOT:
• an execution layer
• an admissibility layer
• a doctrine layer
• a mediation layer
============================================================
END SECTION XI
============================================================
============================================================
<a id="local-section-08-stack-d-rotas-d-structuralinstantiation-xii-closure"></a>
XII. CLOSURE
============================================================
ROTAS D establishes the complete eightfold Figura Quarta
topology for REGIMEN_D.
------------------------------------------------------------
<a id="local-section-08-stack-d-rotas-d-structuralinstantiation-final-law"></a>
FINAL LAW
------------------------------------------------------------
No D-level Figura Quarta chamber is valid unless:
• its ROTA configuration is explicit
• all three wheel positions are bound
• each carrier belongs to its declared regime
• the configuration belongs to the complete 8-ROTA family
------------------------------------------------------------
<a id="local-section-08-stack-d-rotas-d-structuralinstantiation-final-state"></a>
FINAL STATE:
READY FOR AREPO D / OPERA D CONSTRUCTION
============================================================
END ROTAS D — OCTO ROTAE FIGURAE QUARTAE
============================================================