============================================================
TENET H — MULTIPLICATIO FIGURAE QUARTAE
Ars Generalis Applied — Principial Law of Combinatory Multiplication
Version: 0.1.0-TENET-H-MULTIPLICATIO
Status: DRAFT / LOCAL CONTROL PLANE
Scope: principial definition of multiplicatio under TENET-dispatched regimes
Authority: AGLA / TENET (LOCAL CONTROL PLANE)
Class: TENET
Regime: H (MULTIPLICATIO)
Depends-On:
    • TENET A — ABSOLUTA
    • TENET T — RELATIVA
    • TENET D — PRINCIPIA DUPLEX
    • TENET I — MIXTURA
    • TENET — REGIMEN DISPATCH LAW


    • ROTAS D — OCTO ROTAE FIGURAE QUARTAE
============================================================


<!-- 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-09-stack-h-tenet-h-doctrinalinvariants-i-purpose)
- [CORE ASSERTION](#local-section-09-stack-h-tenet-h-doctrinalinvariants-core-assertion)
- [NOT:](#local-section-09-stack-h-tenet-h-doctrinalinvariants-not)
- [II. DOCTRINAL POSITION](#local-section-09-stack-h-tenet-h-doctrinalinvariants-ii-doctrinal-position)
- [FUNCTION](#local-section-09-stack-h-tenet-h-doctrinalinvariants-function)
- [DOMAIN](#local-section-09-stack-h-tenet-h-doctrinalinvariants-domain)
- [FORMAL](#local-section-09-stack-h-tenet-h-doctrinalinvariants-formal)
- [CONSTRAINT](#local-section-09-stack-h-tenet-h-doctrinalinvariants-constraint)
- [FAILURE](#local-section-09-stack-h-tenet-h-doctrinalinvariants-failure)
- [III. ROTAS DEPENDENCY LAW](#local-section-09-stack-h-tenet-h-doctrinalinvariants-iii-rotas-dependency-law)
- [ALL TOPOLOGY IS PROVIDED BY:](#local-section-09-stack-h-tenet-h-doctrinalinvariants-all-topology-is-provided-by)
- [INTERPRETATION](#local-section-09-stack-h-tenet-h-doctrinalinvariants-interpretation)
- [PROHIBITION](#local-section-09-stack-h-tenet-h-doctrinalinvariants-prohibition)
- [RULE](#local-section-09-stack-h-tenet-h-doctrinalinvariants-rule)
- [FAILURE](#local-section-09-stack-h-tenet-h-doctrinalinvariants-failure-2)
- [IV. TENET DISPATCH COMPATIBILITY](#local-section-09-stack-h-tenet-h-doctrinalinvariants-iv-tenet-dispatch-compatibility)
- [DISPATCH DOMAIN EFFECT](#local-section-09-stack-h-tenet-h-doctrinalinvariants-dispatch-domain-effect)
- [TENET A:](#local-section-09-stack-h-tenet-h-doctrinalinvariants-tenet-a)
- [TENET T:](#local-section-09-stack-h-tenet-h-doctrinalinvariants-tenet-t)
- [TENET D:](#local-section-09-stack-h-tenet-h-doctrinalinvariants-tenet-d)
- [TENET I:](#local-section-09-stack-h-tenet-h-doctrinalinvariants-tenet-i)
- [RULE](#local-section-09-stack-h-tenet-h-doctrinalinvariants-rule-2)
- [CONSTRAINT](#local-section-09-stack-h-tenet-h-doctrinalinvariants-constraint-2)
- [FAILURE](#local-section-09-stack-h-tenet-h-doctrinalinvariants-failure-3)
- [V. CHAMBER GENERATION LAW](#local-section-09-stack-h-tenet-h-doctrinalinvariants-v-chamber-generation-law)
- [CONFIGURATION DEFINITION](#local-section-09-stack-h-tenet-h-doctrinalinvariants-configuration-definition)
- [FORMAL](#local-section-09-stack-h-tenet-h-doctrinalinvariants-formal-2)
- [RULE](#local-section-09-stack-h-tenet-h-doctrinalinvariants-rule-3)
- [MULTIPLICATION EFFECT](#local-section-09-stack-h-tenet-h-doctrinalinvariants-multiplication-effect)
- [CONSTRAINT](#local-section-09-stack-h-tenet-h-doctrinalinvariants-constraint-3)
- [FAILURE](#local-section-09-stack-h-tenet-h-doctrinalinvariants-failure-4)
- [VI. PRINCIPIAL CONSTRAINTS](#local-section-09-stack-h-tenet-h-doctrinalinvariants-vi-principial-constraints)
- [1. NON-CREATION](#local-section-09-stack-h-tenet-h-doctrinalinvariants-1-non-creation)
- [2. NON-COLLAPSE](#local-section-09-stack-h-tenet-h-doctrinalinvariants-2-non-collapse)
- [3. RELATIONAL PRESERVATION](#local-section-09-stack-h-tenet-h-doctrinalinvariants-3-relational-preservation)
- [4. ORDINAL CONTINUITY](#local-section-09-stack-h-tenet-h-doctrinalinvariants-4-ordinal-continuity)
- [5. DOMAIN CONSISTENCY](#local-section-09-stack-h-tenet-h-doctrinalinvariants-5-domain-consistency)
- [FAILURE](#local-section-09-stack-h-tenet-h-doctrinalinvariants-failure-5)
- [VII. MULTIPLICATIO MODES (PRINCIPIAL VIEW)](#local-section-09-stack-h-tenet-h-doctrinalinvariants-vii-multiplicatio-modes-principial-view)
- [MODES](#local-section-09-stack-h-tenet-h-doctrinalinvariants-modes)
- [MULTIPLICATIO_OA:](#local-section-09-stack-h-tenet-h-doctrinalinvariants-multiplicatio-oa)
- [MULTIPLICATIO_PL:](#local-section-09-stack-h-tenet-h-doctrinalinvariants-multiplicatio-pl)
- [MULTIPLICATIO_CT:](#local-section-09-stack-h-tenet-h-doctrinalinvariants-multiplicatio-ct)
- [MULTIPLICATIO_RT:](#local-section-09-stack-h-tenet-h-doctrinalinvariants-multiplicatio-rt)
- [RULE](#local-section-09-stack-h-tenet-h-doctrinalinvariants-rule-4)
- [CONSTRAINT](#local-section-09-stack-h-tenet-h-doctrinalinvariants-constraint-4)
- [FAILURE](#local-section-09-stack-h-tenet-h-doctrinalinvariants-failure-6)
- [VIII. LIMITS](#local-section-09-stack-h-tenet-h-doctrinalinvariants-viii-limits)
- [TENET H ONLY:](#local-section-09-stack-h-tenet-h-doctrinalinvariants-tenet-h-only)
- [PROHIBITION](#local-section-09-stack-h-tenet-h-doctrinalinvariants-prohibition-2)
- [IX. RELATION TO OTHER CLASSES](#local-section-09-stack-h-tenet-h-doctrinalinvariants-ix-relation-to-other-classes)
- [TENET:](#local-section-09-stack-h-tenet-h-doctrinalinvariants-tenet)
- [ROTAS D:](#local-section-09-stack-h-tenet-h-doctrinalinvariants-rotas-d)
- [AREPO H:](#local-section-09-stack-h-tenet-h-doctrinalinvariants-arepo-h)
- [OPERA H:](#local-section-09-stack-h-tenet-h-doctrinalinvariants-opera-h)
- [SATOR H:](#local-section-09-stack-h-tenet-h-doctrinalinvariants-sator-h)
- [RULE](#local-section-09-stack-h-tenet-h-doctrinalinvariants-rule-5)
- [X. CLOSURE](#local-section-09-stack-h-tenet-h-doctrinalinvariants-x-closure)
- [FINAL LAW](#local-section-09-stack-h-tenet-h-doctrinalinvariants-final-law)
- [FINAL STATE:](#local-section-09-stack-h-tenet-h-doctrinalinvariants-final-state)
<!-- LOCAL_SECTION_INDEX_END -->

END SECTION 0 — HEADER
============================================================


============================================================


<a id="local-section-09-stack-h-tenet-h-doctrinalinvariants-i-purpose"></a>
I. PURPOSE
============================================================


Define the principial foundation governing:

    MULTIPLICATIO FIGURAE QUARTAE

------------------------------------------------------------


TENET H establishes:

    • multiplicatio as principial operation
    • combinatory behavior of chambers
    • interaction of carriers under multiplication
    • dependency on TENET-dispatched regimes
    • structural reliance on ROTAS D

------------------------------------------------------------


<a id="local-section-09-stack-h-tenet-h-doctrinalinvariants-core-assertion"></a>
CORE ASSERTION
------------------------------------------------------------


Multiplicatio is:

    principial combination
    of chamber-structured carriers


under:

    TENET-dispatched domains

------------------------------------------------------------


TENET H defines:

    what multiplicatio IS


<a id="local-section-09-stack-h-tenet-h-doctrinalinvariants-not"></a>
NOT:

    how it executes (OPERA)
    how it is structured (ROTAS)
    how it is admitted (AREPO)
    how it is exposed (SATOR)

============================================================
END SECTION I
============================================================


============================================================


<a id="local-section-09-stack-h-tenet-h-doctrinalinvariants-ii-doctrinal-position"></a>
II. DOCTRINAL POSITION
============================================================


REGIMEN H is:

    the combinatory multiplication regime of the Ars

------------------------------------------------------------


<a id="local-section-09-stack-h-tenet-h-doctrinalinvariants-function"></a>
FUNCTION
------------------------------------------------------------


Multiplicatio:

    combines structured chambers
    into higher-order configurations

------------------------------------------------------------


<a id="local-section-09-stack-h-tenet-h-doctrinalinvariants-domain"></a>
DOMAIN
------------------------------------------------------------


Multiplicatio operates over:

    chambers defined in Figura Quarta

------------------------------------------------------------


<a id="local-section-09-stack-h-tenet-h-doctrinalinvariants-formal"></a>
FORMAL
------------------------------------------------------------


Given:

    C := set of chambers


Multiplicatio produces:

    C' := combinatory transformation of C

------------------------------------------------------------


<a id="local-section-09-stack-h-tenet-h-doctrinalinvariants-constraint"></a>
CONSTRAINT
------------------------------------------------------------

Multiplicatio does not create carriers.


It:

    recombines existing carriers

------------------------------------------------------------


<a id="local-section-09-stack-h-tenet-h-doctrinalinvariants-failure"></a>
FAILURE
------------------------------------------------------------

carrier_creation
structure_invention
domain_extension

============================================================
END SECTION II
============================================================


============================================================


<a id="local-section-09-stack-h-tenet-h-doctrinalinvariants-iii-rotas-dependency-law"></a>
III. ROTAS DEPENDENCY LAW
============================================================

REGIMEN H does not define an independent ROTAS layer.

------------------------------------------------------------


<a id="local-section-09-stack-h-tenet-h-doctrinalinvariants-all-topology-is-provided-by"></a>
ALL TOPOLOGY IS PROVIDED BY:

    ROTAS D — OCTO ROTAE FIGURAE QUARTAE

------------------------------------------------------------


ROTAS D defines:

    • chamber topology
    • wheel structure (W1, W2, W3)
    • carrier placement rules
    • configuration space

------------------------------------------------------------


<a id="local-section-09-stack-h-tenet-h-doctrinalinvariants-interpretation"></a>
INTERPRETATION
------------------------------------------------------------


TENET H assumes:


    chambers are already:

        • constructed
        • ordered
        • topologically valid

------------------------------------------------------------


<a id="local-section-09-stack-h-tenet-h-doctrinalinvariants-prohibition"></a>
PROHIBITION
------------------------------------------------------------


REGIMEN H must NOT:

    • define ROTAS H
    • alter chamber topology
    • reinterpret wheel structure
    • introduce alternative combinatory spaces

------------------------------------------------------------


<a id="local-section-09-stack-h-tenet-h-doctrinalinvariants-rule"></a>
RULE
------------------------------------------------------------


All multiplicatio must be:

    ROTAS D-bound

------------------------------------------------------------


<a id="local-section-09-stack-h-tenet-h-doctrinalinvariants-failure-2"></a>
FAILURE
------------------------------------------------------------

topology_override
rota_redefinition
structure_drift

============================================================
END SECTION III
============================================================


============================================================


<a id="local-section-09-stack-h-tenet-h-doctrinalinvariants-iv-tenet-dispatch-compatibility"></a>
IV. TENET DISPATCH COMPATIBILITY
============================================================


Multiplicatio is conditioned by:

    selected_tenet

------------------------------------------------------------


<a id="local-section-09-stack-h-tenet-h-doctrinalinvariants-dispatch-domain-effect"></a>
DISPATCH DOMAIN EFFECT
------------------------------------------------------------


<a id="local-section-09-stack-h-tenet-h-doctrinalinvariants-tenet-a"></a>
TENET A:

    multiplicatio over A-only carriers

------------------------------------------------------------


<a id="local-section-09-stack-h-tenet-h-doctrinalinvariants-tenet-t"></a>
TENET T:

    multiplicatio over T-only carriers

------------------------------------------------------------


<a id="local-section-09-stack-h-tenet-h-doctrinalinvariants-tenet-d"></a>
TENET D:

    multiplicatio over A + T
    within principial interaction

------------------------------------------------------------


<a id="local-section-09-stack-h-tenet-h-doctrinalinvariants-tenet-i"></a>
TENET I:

    multiplicatio over A + T + E
    under operator influence

------------------------------------------------------------


<a id="local-section-09-stack-h-tenet-h-doctrinalinvariants-rule-2"></a>
RULE
------------------------------------------------------------


Multiplicatio must preserve:

    the domain defined by selected_tenet

------------------------------------------------------------


<a id="local-section-09-stack-h-tenet-h-doctrinalinvariants-constraint-2"></a>
CONSTRAINT
------------------------------------------------------------


No multiplicatio may:

    • exceed TENET domain
    • introduce non-admissible carriers
    • collapse regime distinctions

------------------------------------------------------------


<a id="local-section-09-stack-h-tenet-h-doctrinalinvariants-failure-3"></a>
FAILURE
------------------------------------------------------------

tenet_domain_violation
regime_collapse
operator_misplacement

============================================================
END SECTION IV
============================================================


============================================================


<a id="local-section-09-stack-h-tenet-h-doctrinalinvariants-v-chamber-generation-law"></a>
V. CHAMBER GENERATION LAW
============================================================


Multiplicatio operates over:

    configurations of chambers

------------------------------------------------------------


<a id="local-section-09-stack-h-tenet-h-doctrinalinvariants-configuration-definition"></a>
CONFIGURATION DEFINITION
------------------------------------------------------------


A configuration produces:

    exactly 9 triadic chambers

------------------------------------------------------------


<a id="local-section-09-stack-h-tenet-h-doctrinalinvariants-formal-2"></a>
FORMAL
------------------------------------------------------------

CONFIGURATION :=

    {C₁, C₂, ..., C₉}

------------------------------------------------------------


<a id="local-section-09-stack-h-tenet-h-doctrinalinvariants-rule-3"></a>
RULE
------------------------------------------------------------


Each chamber must:

    • contain 3 carriers (W1, W2, W3)
    • preserve ordinal alignment
    • preserve carrier typing

------------------------------------------------------------


<a id="local-section-09-stack-h-tenet-h-doctrinalinvariants-multiplication-effect"></a>
MULTIPLICATION EFFECT
------------------------------------------------------------


Multiplicatio transforms:

    one or more configurations


into:

    new chamber sets

------------------------------------------------------------


<a id="local-section-09-stack-h-tenet-h-doctrinalinvariants-constraint-3"></a>
CONSTRAINT
------------------------------------------------------------


Generated chambers must:

    • remain within ROTAS D topology
    • remain within TENET domain
    • preserve carrier lineage

------------------------------------------------------------


<a id="local-section-09-stack-h-tenet-h-doctrinalinvariants-failure-4"></a>
FAILURE
------------------------------------------------------------

invalid_chamber_count
carrier_overflow
topology_violation
ordinal_loss

============================================================
END SECTION V
============================================================


============================================================


<a id="local-section-09-stack-h-tenet-h-doctrinalinvariants-vi-principial-constraints"></a>
VI. PRINCIPIAL CONSTRAINTS
============================================================


Multiplicatio is governed by:

------------------------------------------------------------


<a id="local-section-09-stack-h-tenet-h-doctrinalinvariants-1-non-creation"></a>
1. NON-CREATION
------------------------------------------------------------

No new carriers may be introduced.

------------------------------------------------------------


<a id="local-section-09-stack-h-tenet-h-doctrinalinvariants-2-non-collapse"></a>
2. NON-COLLAPSE
------------------------------------------------------------


Carriers must not:

    • merge
    • lose identity

------------------------------------------------------------


<a id="local-section-09-stack-h-tenet-h-doctrinalinvariants-3-relational-preservation"></a>
3. RELATIONAL PRESERVATION
------------------------------------------------------------


Relations between carriers must:

    remain interpretable

------------------------------------------------------------


<a id="local-section-09-stack-h-tenet-h-doctrinalinvariants-4-ordinal-continuity"></a>
4. ORDINAL CONTINUITY
------------------------------------------------------------


Ordinal structure must:

    remain traceable

------------------------------------------------------------


<a id="local-section-09-stack-h-tenet-h-doctrinalinvariants-5-domain-consistency"></a>
5. DOMAIN CONSISTENCY
------------------------------------------------------------


All results must:

    remain within selected_tenet

------------------------------------------------------------


<a id="local-section-09-stack-h-tenet-h-doctrinalinvariants-failure-5"></a>
FAILURE
------------------------------------------------------------

carrier_collapse
identity_loss
relation_break
ordinal_discontinuity
domain_violation

============================================================
END SECTION VI
============================================================


============================================================


<a id="local-section-09-stack-h-tenet-h-doctrinalinvariants-vii-multiplicatio-modes-principial-view"></a>
VII. MULTIPLICATIO MODES (PRINCIPIAL VIEW)
============================================================


TENET H recognizes multiplicatio modes as:

    principial variants

------------------------------------------------------------


<a id="local-section-09-stack-h-tenet-h-doctrinalinvariants-modes"></a>
MODES
------------------------------------------------------------


<a id="local-section-09-stack-h-tenet-h-doctrinalinvariants-multiplicatio-oa"></a>
MULTIPLICATIO_OA:

    ordinal-aligned combination

------------------------------------------------------------


<a id="local-section-09-stack-h-tenet-h-doctrinalinvariants-multiplicatio-pl"></a>
MULTIPLICATIO_PL:

    position-locked combination

------------------------------------------------------------


<a id="local-section-09-stack-h-tenet-h-doctrinalinvariants-multiplicatio-ct"></a>
MULTIPLICATIO_CT:

    Cartesian expansion

------------------------------------------------------------


<a id="local-section-09-stack-h-tenet-h-doctrinalinvariants-multiplicatio-rt"></a>
MULTIPLICATIO_RT:

    transformational combination

------------------------------------------------------------


<a id="local-section-09-stack-h-tenet-h-doctrinalinvariants-rule-4"></a>
RULE
------------------------------------------------------------


All modes must:

    • respect TENET constraints
    • respect ROTAS D topology
    • preserve carrier identity

------------------------------------------------------------


<a id="local-section-09-stack-h-tenet-h-doctrinalinvariants-constraint-4"></a>
CONSTRAINT
------------------------------------------------------------


Mode selection does not:

    alter principial law

------------------------------------------------------------


<a id="local-section-09-stack-h-tenet-h-doctrinalinvariants-failure-6"></a>
FAILURE
------------------------------------------------------------

mode_principial_violation
topology_inconsistency
carrier_distortion

============================================================
END SECTION VII
============================================================


============================================================


<a id="local-section-09-stack-h-tenet-h-doctrinalinvariants-viii-limits"></a>
VIII. LIMITS
============================================================


TENET H does NOT:

    • define execution procedure (OPERA)
    • define admissibility (AREPO)
    • define topology (ROTAS)
    • define mediation (SATOR)

------------------------------------------------------------


<a id="local-section-09-stack-h-tenet-h-doctrinalinvariants-tenet-h-only"></a>
TENET H ONLY:

    defines principial constraints of multiplicatio

------------------------------------------------------------


<a id="local-section-09-stack-h-tenet-h-doctrinalinvariants-prohibition-2"></a>
PROHIBITION
------------------------------------------------------------


TENET H must not:

    • perform combination
    • select configurations
    • resolve TENET dispatch
    • evaluate results

============================================================
END SECTION VIII
============================================================


============================================================


<a id="local-section-09-stack-h-tenet-h-doctrinalinvariants-ix-relation-to-other-classes"></a>
IX. RELATION TO OTHER CLASSES
============================================================


<a id="local-section-09-stack-h-tenet-h-doctrinalinvariants-tenet"></a>
TENET:

    defines multiplicatio principles

------------------------------------------------------------


<a id="local-section-09-stack-h-tenet-h-doctrinalinvariants-rotas-d"></a>
ROTAS D:

    defines combinatory topology

------------------------------------------------------------


<a id="local-section-09-stack-h-tenet-h-doctrinalinvariants-arepo-h"></a>
AREPO H:

    gates admissibility

------------------------------------------------------------


<a id="local-section-09-stack-h-tenet-h-doctrinalinvariants-opera-h"></a>
OPERA H:

    executes multiplicatio

------------------------------------------------------------


<a id="local-section-09-stack-h-tenet-h-doctrinalinvariants-sator-h"></a>
SATOR H:

    exposes results

------------------------------------------------------------


<a id="local-section-09-stack-h-tenet-h-doctrinalinvariants-rule-5"></a>
RULE
------------------------------------------------------------


TENET H is:

    binding for AREPO H and OPERA H

============================================================
END SECTION IX
============================================================


============================================================


<a id="local-section-09-stack-h-tenet-h-doctrinalinvariants-x-closure"></a>
X. CLOSURE
============================================================


TENET H establishes:

    the principial law of multiplicatio
    under Figura Quarta

------------------------------------------------------------


<a id="local-section-09-stack-h-tenet-h-doctrinalinvariants-final-law"></a>
FINAL LAW
------------------------------------------------------------


Multiplicatio is valid only if:

    • chamber structure is ROTAS D-compliant
    • TENET domain is preserved
    • carrier identity is maintained
    • ordinal continuity is traceable

------------------------------------------------------------


<a id="local-section-09-stack-h-tenet-h-doctrinalinvariants-final-state"></a>
FINAL STATE:

    DRAFT / READY FOR ITERATION

============================================================
END TENET H — MULTIPLICATIO FIGURAE QUARTAE
============================================================