10_STACK_I/TENET_I_DoctrinalInvariants.md

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Page Sections
============================================================
TENET I — MIXTURA (CARRIER LAYER)
Ars Generalis Applied — Unified Carrier System for Principia and Regimen_RQ
Version: 0.1.0-TENET-I-MIXTURA
Status: PROPOSED / CONTROL-PLANE DRAFT
Scope: CARRIER ORDER / MIXTURE DISCIPLINE / NUMERIC STRUCTURE
Authority: AGLA / TENET (LOCAL CONTROL PLANE — STACK I)
Mutation Policy: VERSION-CONTROLLED ONLY

Class: TENET
============================================================


<!-- 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-10-stack-i-tenet-i-doctrinalinvariants-i-purpose)
- [CORE ASSERTION](#local-section-10-stack-i-tenet-i-doctrinalinvariants-core-assertion)
- [II. DOCTRINAL POSITION](#local-section-10-stack-i-tenet-i-doctrinalinvariants-ii-doctrinal-position)
- [INTERPRETATION](#local-section-10-stack-i-tenet-i-doctrinalinvariants-interpretation)
- [DISTINCTION](#local-section-10-stack-i-tenet-i-doctrinalinvariants-distinction)
- [III. CARRIER ORDER (ABJAD-BASED)](#local-section-10-stack-i-tenet-i-doctrinalinvariants-iii-carrier-order-abjad-based)
- [STRUCTURE](#local-section-10-stack-i-tenet-i-doctrinalinvariants-structure)
- [PRIMARY SEQUENCE](#local-section-10-stack-i-tenet-i-doctrinalinvariants-primary-sequence)
- [ABSOLUTE PRINCIPLES (A)](#local-section-10-stack-i-tenet-i-doctrinalinvariants-absolute-principles-a)
- [RELATIVE PRINCIPLES (T)](#local-section-10-stack-i-tenet-i-doctrinalinvariants-relative-principles-t)
- [INTERROGATIVE / RULE REGIME ROOT (E)](#local-section-10-stack-i-tenet-i-doctrinalinvariants-interrogative-rule-regime-root-e)
- [RULE](#local-section-10-stack-i-tenet-i-doctrinalinvariants-rule)
- [IV. REGIMEN INDEXING (A / T / E)](#local-section-10-stack-i-tenet-i-doctrinalinvariants-iv-regimen-indexing-a-t-e)
- [A REGIMEN](#local-section-10-stack-i-tenet-i-doctrinalinvariants-a-regimen)
- [T REGIMEN](#local-section-10-stack-i-tenet-i-doctrinalinvariants-t-regimen)
- [E REGIMEN](#local-section-10-stack-i-tenet-i-doctrinalinvariants-e-regimen)
- [RULE](#local-section-10-stack-i-tenet-i-doctrinalinvariants-rule-2)
- [V. E REGIMEN STRUCTURE (Q / R)](#local-section-10-stack-i-tenet-i-doctrinalinvariants-v-e-regimen-structure-q-r)
- [FORM](#local-section-10-stack-i-tenet-i-doctrinalinvariants-form)
- [RULE](#local-section-10-stack-i-tenet-i-doctrinalinvariants-rule-3)
- [CONSTRAINT](#local-section-10-stack-i-tenet-i-doctrinalinvariants-constraint)
- [VI. TOKEN IDENTITY LAW](#local-section-10-stack-i-tenet-i-doctrinalinvariants-vi-token-identity-law)
- [RULE](#local-section-10-stack-i-tenet-i-doctrinalinvariants-rule-4)
- [CONSTRAINT](#local-section-10-stack-i-tenet-i-doctrinalinvariants-constraint-2)
- [VII. K-SPLIT LAW (EMBEDDED)](#local-section-10-stack-i-tenet-i-doctrinalinvariants-vii-k-split-law-embedded)
- [NUMERIC STRUCTURE](#local-section-10-stack-i-tenet-i-doctrinalinvariants-numeric-structure)
- [RULE](#local-section-10-stack-i-tenet-i-doctrinalinvariants-rule-5)
- [PROHIBITION](#local-section-10-stack-i-tenet-i-doctrinalinvariants-prohibition)
- [VIII. MIXTURE LAW](#local-section-10-stack-i-tenet-i-doctrinalinvariants-viii-mixture-law)
- [RULE](#local-section-10-stack-i-tenet-i-doctrinalinvariants-rule-6)
- [PROHIBITION](#local-section-10-stack-i-tenet-i-doctrinalinvariants-prohibition-2)
- [INTERPRETATION](#local-section-10-stack-i-tenet-i-doctrinalinvariants-interpretation-2)
- [NOT:](#local-section-10-stack-i-tenet-i-doctrinalinvariants-not)
- [IX. NUMERIC DISCIPLINE](#local-section-10-stack-i-tenet-i-doctrinalinvariants-ix-numeric-discipline)
- [RULE](#local-section-10-stack-i-tenet-i-doctrinalinvariants-rule-7)
- [CONSTRAINT](#local-section-10-stack-i-tenet-i-doctrinalinvariants-constraint-3)
- [X. DERIVED NUMERIC PROJECTION (APPENDIX — NON-ΣΑΤΟΡ)](#local-section-10-stack-i-tenet-i-doctrinalinvariants-x-derived-numeric-projection-appendix-non)
- [FUNCTION](#local-section-10-stack-i-tenet-i-doctrinalinvariants-function)
- [RULE](#local-section-10-stack-i-tenet-i-doctrinalinvariants-rule-8)
- [PROHIBITION](#local-section-10-stack-i-tenet-i-doctrinalinvariants-prohibition-3)
- [XI. RELATION TO OTHER LAYERS](#local-section-10-stack-i-tenet-i-doctrinalinvariants-xi-relation-to-other-layers)
- [TENET A:](#local-section-10-stack-i-tenet-i-doctrinalinvariants-tenet-a)
- [TENET T:](#local-section-10-stack-i-tenet-i-doctrinalinvariants-tenet-t)
- [TENET E:](#local-section-10-stack-i-tenet-i-doctrinalinvariants-tenet-e)
- [TENET I:](#local-section-10-stack-i-tenet-i-doctrinalinvariants-tenet-i)
- [ROTAS:](#local-section-10-stack-i-tenet-i-doctrinalinvariants-rotas)
- [AREPO:](#local-section-10-stack-i-tenet-i-doctrinalinvariants-arepo)
- [OPERA:](#local-section-10-stack-i-tenet-i-doctrinalinvariants-opera)
- [SATOR:](#local-section-10-stack-i-tenet-i-doctrinalinvariants-sator)
- [XII. FAILURE CONDITIONS](#local-section-10-stack-i-tenet-i-doctrinalinvariants-xii-failure-conditions)
- [CARRIER FAILURES](#local-section-10-stack-i-tenet-i-doctrinalinvariants-carrier-failures)
- [REGIME FAILURES](#local-section-10-stack-i-tenet-i-doctrinalinvariants-regime-failures)
- [TOKEN FAILURES](#local-section-10-stack-i-tenet-i-doctrinalinvariants-token-failures)
- [NUMERIC FAILURES](#local-section-10-stack-i-tenet-i-doctrinalinvariants-numeric-failures)
- [RULE](#local-section-10-stack-i-tenet-i-doctrinalinvariants-rule-9)
- [XIII. CLOSURE](#local-section-10-stack-i-tenet-i-doctrinalinvariants-xiii-closure)
- [FINAL STATE:](#local-section-10-stack-i-tenet-i-doctrinalinvariants-final-state)
<!-- LOCAL_SECTION_INDEX_END -->

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


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


<a id="local-section-10-stack-i-tenet-i-doctrinalinvariants-i-purpose"></a>
I. PURPOSE
============================================================


Define the carrier system governing:

    STACK I — MIXTURA

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


TENET_I establishes:

    • unified carrier order for A, T, and E regimens
    • explicit ordinal-slot mapping
    • gematric and cardinal correspondence
    • Phoenician carrier stabilization
    • mixture-safe indexing discipline
    • token-based identity for combinatorics

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


TENET_I does NOT:

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

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


<a id="local-section-10-stack-i-tenet-i-doctrinalinvariants-core-assertion"></a>
CORE ASSERTION
------------------------------------------------------------


Identity in MIXTURA is determined by:

    FULL TOKEN PRESENCE

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


NOT by:

    • single symbol
    • numeric value alone
    • partial encoding


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


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


<a id="local-section-10-stack-i-tenet-i-doctrinalinvariants-ii-doctrinal-position"></a>
II. DOCTRINAL POSITION
============================================================


MIXTURA is:

    the carrier-level integration layer


for:

    • principia absoluta (A)
    • principia relativa (T)
    • interrogative and rule system (E)

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


Function:

    provide a unified indexing system


such that:

    all three regimens may coexist
    without ambiguity or collision

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


<a id="local-section-10-stack-i-tenet-i-doctrinalinvariants-interpretation"></a>
INTERPRETATION
------------------------------------------------------------


TENET_I operates at:

    carrier level

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


It does NOT:

    redefine doctrinal content

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


<a id="local-section-10-stack-i-tenet-i-doctrinalinvariants-distinction"></a>
DISTINCTION
------------------------------------------------------------

TENET A → defines absolute principles  
TENET T → defines relative principles  
TENET E → defines interrogative doctrine  

TENET I → defines how they coexist structurally  


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


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


<a id="local-section-10-stack-i-tenet-i-doctrinalinvariants-iii-carrier-order-abjad-based"></a>
III. CARRIER ORDER (ABJAD-BASED)
============================================================


MIXTURA adopts:

    ABJAD ORDER (PHOENICIAN-ALIGNED)

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


<a id="local-section-10-stack-i-tenet-i-doctrinalinvariants-structure"></a>
STRUCTURE
------------------------------------------------------------


Each carrier defines:

    • ORDINAL_SLOT
    • SYMBOL (Latin)
    • PHOENICIAN CHARACTER
    • GEMATRIC VALUE
    • CARDINAL VALUE

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


<a id="local-section-10-stack-i-tenet-i-doctrinalinvariants-primary-sequence"></a>
PRIMARY SEQUENCE
------------------------------------------------------------

PRE/A

    ORDINAL_SLOT = PRE
    SYMBOL       = A
    PHOENICIAN   = 𐤀
    GEMATRIC     = 1
    CARDINAL     = 1

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


<a id="local-section-10-stack-i-tenet-i-doctrinalinvariants-absolute-principles-a"></a>
ABSOLUTE PRINCIPLES (A)
------------------------------------------------------------

Ⅰ  B   𐤁   2    2
Ⅱ  C   𐤂   3    3
Ⅲ  D   𐤃   4    4
Ⅳ  E   𐤄   5    5
Ⅴ  F   𐤅   6    6
Ⅵ  G   𐤆   7    7
Ⅶ  H   𐤇   8    8
Ⅷ  I   𐤈   9    9
Ⅸ  K   𐤉   10   10

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


<a id="local-section-10-stack-i-tenet-i-doctrinalinvariants-relative-principles-t"></a>
RELATIVE PRINCIPLES (T)
------------------------------------------------------------

Ⅹ   L   𐤊   20   11
Ⅺ   M   𐤋   30   12
Ⅻ   N   𐤌   40   13
ⅩⅢ  O   𐤍   50   14
ⅩⅣ  P   𐤎   60   15
ⅩⅤ  Q   𐤏   70   16
ⅩⅥ  R   𐤐   80   17
ⅩⅦ  S   𐤑   90   18
ⅩⅧ  T   𐤒   100  19

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


<a id="local-section-10-stack-i-tenet-i-doctrinalinvariants-interrogative-rule-regime-root-e"></a>
INTERROGATIVE / RULE REGIME ROOT (E)
------------------------------------------------------------


Uses extended range:

    200 → 1000

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


<a id="local-section-10-stack-i-tenet-i-doctrinalinvariants-rule"></a>
RULE
------------------------------------------------------------


No carrier may change:

    • ordinal position
    • gematric value
    • Phoenician mapping


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


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


<a id="local-section-10-stack-i-tenet-i-doctrinalinvariants-iv-regimen-indexing-a-t-e"></a>
IV. REGIMEN INDEXING (A / T / E)
============================================================

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


<a id="local-section-10-stack-i-tenet-i-doctrinalinvariants-a-regimen"></a>
A REGIMEN
------------------------------------------------------------


Uses:

    slots Ⅰ–Ⅸ

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


<a id="local-section-10-stack-i-tenet-i-doctrinalinvariants-t-regimen"></a>
T REGIMEN
------------------------------------------------------------


Uses:

    slots Ⅹ–ⅩⅧ

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


<a id="local-section-10-stack-i-tenet-i-doctrinalinvariants-e-regimen"></a>
E REGIMEN
------------------------------------------------------------


Uses:

    extended numeric carriers

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


<a id="local-section-10-stack-i-tenet-i-doctrinalinvariants-rule-2"></a>
RULE
------------------------------------------------------------


Regimen identity is determined by:

    carrier range

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


NOT by:

    symbol reuse alone


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


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


<a id="local-section-10-stack-i-tenet-i-doctrinalinvariants-v-e-regimen-structure-q-r"></a>
V. E REGIMEN STRUCTURE (Q / R)
============================================================

E is a ROOT CARRIER DOMAIN

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


E splits into:

    Q → interrogatives
    R → rules

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


<a id="local-section-10-stack-i-tenet-i-doctrinalinvariants-form"></a>
FORM
------------------------------------------------------------

E
├── Q
└── R

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


<a id="local-section-10-stack-i-tenet-i-doctrinalinvariants-rule-3"></a>
RULE
------------------------------------------------------------


Q and R are:

    sub-regimens


within:

    E

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


<a id="local-section-10-stack-i-tenet-i-doctrinalinvariants-constraint"></a>
CONSTRAINT
------------------------------------------------------------


TENET E defines:

    doctrinal structure


TENET I defines:

    carrier indexing


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


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


<a id="local-section-10-stack-i-tenet-i-doctrinalinvariants-vi-token-identity-law"></a>
VI. TOKEN IDENTITY LAW
============================================================


Identity is defined as:

    FULL TOKEN CHAIN

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


Example:

    ERB ≠ EQB

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


<a id="local-section-10-stack-i-tenet-i-doctrinalinvariants-rule-4"></a>
RULE
------------------------------------------------------------


No identity may be inferred from:

    • partial token
    • numeric subset
    • symbolic coincidence

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


<a id="local-section-10-stack-i-tenet-i-doctrinalinvariants-constraint-2"></a>
CONSTRAINT
------------------------------------------------------------


All tokens must be:

    • explicit
    • ordered
    • complete


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


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


<a id="local-section-10-stack-i-tenet-i-doctrinalinvariants-vii-k-split-law-embedded"></a>
VII. K-SPLIT LAW (EMBEDDED)
============================================================


K is:

    a unified interrogative carrier

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


K contains:

    • modality (K1)
    • instrumentality (K2)

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


<a id="local-section-10-stack-i-tenet-i-doctrinalinvariants-numeric-structure"></a>
NUMERIC STRUCTURE
------------------------------------------------------------

1000 → K (general)

1200 → K1 (modality)
1300 → K2 (instrumentality)

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


<a id="local-section-10-stack-i-tenet-i-doctrinalinvariants-rule-5"></a>
RULE
------------------------------------------------------------


K must be used in:

    • combinatorics
    • TABULA
    • multiplication
    • evacuation

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


K1 / K2 may be used in:

    • analytical decomposition
    • explanatory expansion

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


<a id="local-section-10-stack-i-tenet-i-doctrinalinvariants-prohibition"></a>
PROHIBITION
------------------------------------------------------------

K must not be replaced by K1 or K2
in combinatorial operations


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


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


<a id="local-section-10-stack-i-tenet-i-doctrinalinvariants-viii-mixture-law"></a>
VIII. MIXTURE LAW
============================================================


MIXTURA allows:

    coexistence of A, T, and E carriers

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


<a id="local-section-10-stack-i-tenet-i-doctrinalinvariants-rule-6"></a>
RULE
------------------------------------------------------------


All mixture operations must preserve:

    • carrier identity
    • ordinal integrity
    • regime distinction

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


<a id="local-section-10-stack-i-tenet-i-doctrinalinvariants-prohibition-2"></a>
PROHIBITION
------------------------------------------------------------


No collapse between:

    • A and T
    • T and E
    • Q and R

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


<a id="local-section-10-stack-i-tenet-i-doctrinalinvariants-interpretation-2"></a>
INTERPRETATION
------------------------------------------------------------


Mixture is:

    structural coexistence


<a id="local-section-10-stack-i-tenet-i-doctrinalinvariants-not"></a>
NOT:

    doctrinal fusion


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


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


<a id="local-section-10-stack-i-tenet-i-doctrinalinvariants-ix-numeric-discipline"></a>
IX. NUMERIC DISCIPLINE
============================================================


Three numeric layers exist:

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

1. ORDINAL

    position in sequence

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

2. GEMATRIC

    native abjad value

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

3. CARDINAL

    normalized sequence

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


<a id="local-section-10-stack-i-tenet-i-doctrinalinvariants-rule-7"></a>
RULE
------------------------------------------------------------


These layers must NOT be:

    • collapsed
    • substituted
    • inferred

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


<a id="local-section-10-stack-i-tenet-i-doctrinalinvariants-constraint-3"></a>
CONSTRAINT
------------------------------------------------------------

Numeric value does NOT define identity


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


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


<a id="local-section-10-stack-i-tenet-i-doctrinalinvariants-x-derived-numeric-projection-appendix-non"></a>
X. DERIVED NUMERIC PROJECTION (APPENDIX — NON-ΣΑΤΟΡ)
============================================================


Derived projection may be defined as:

    f := gematric + cardinal
    g := f × ordinal

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


<a id="local-section-10-stack-i-tenet-i-doctrinalinvariants-function"></a>
FUNCTION
------------------------------------------------------------


Supports:

    • external preprocessing
    • combinatorial indexing
    • mapping to external systems

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


<a id="local-section-10-stack-i-tenet-i-doctrinalinvariants-rule-8"></a>
RULE
------------------------------------------------------------


This projection:

    • is OPTIONAL
    • is NON-CANONICAL
    • must be IGNORED in ΣΑΤΟΡ I

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


<a id="local-section-10-stack-i-tenet-i-doctrinalinvariants-prohibition-3"></a>
PROHIBITION
------------------------------------------------------------


Derived values must NOT:

    • replace canonical carriers
    • influence identity
    • affect mixture logic


============================================================
END SECTION X
============================================================


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


<a id="local-section-10-stack-i-tenet-i-doctrinalinvariants-xi-relation-to-other-layers"></a>
XI. RELATION TO OTHER LAYERS
============================================================


<a id="local-section-10-stack-i-tenet-i-doctrinalinvariants-tenet-a"></a>
TENET A:

    defines absolute principles


<a id="local-section-10-stack-i-tenet-i-doctrinalinvariants-tenet-t"></a>
TENET T:

    defines relative principles


<a id="local-section-10-stack-i-tenet-i-doctrinalinvariants-tenet-e"></a>
TENET E:

    defines interrogative doctrine

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


<a id="local-section-10-stack-i-tenet-i-doctrinalinvariants-tenet-i"></a>
TENET I:

    defines unified carrier system

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


<a id="local-section-10-stack-i-tenet-i-doctrinalinvariants-rotas"></a>
ROTAS:

    structures carriers spatially


<a id="local-section-10-stack-i-tenet-i-doctrinalinvariants-arepo"></a>
AREPO:

    gates admissibility


<a id="local-section-10-stack-i-tenet-i-doctrinalinvariants-opera"></a>
OPERA:

    executes combinations


<a id="local-section-10-stack-i-tenet-i-doctrinalinvariants-sator"></a>
SATOR:

    exposes structure


============================================================
END SECTION XI
============================================================


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


<a id="local-section-10-stack-i-tenet-i-doctrinalinvariants-xii-failure-conditions"></a>
XII. FAILURE CONDITIONS
============================================================


<a id="local-section-10-stack-i-tenet-i-doctrinalinvariants-carrier-failures"></a>
CARRIER FAILURES
------------------------------------------------------------

• ordinal drift
• symbol collision
• Phoenician mismatch

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


<a id="local-section-10-stack-i-tenet-i-doctrinalinvariants-regime-failures"></a>
REGIME FAILURES
------------------------------------------------------------

• A/T collapse
• E ambiguity
• Q/R confusion

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


<a id="local-section-10-stack-i-tenet-i-doctrinalinvariants-token-failures"></a>
TOKEN FAILURES
------------------------------------------------------------

• partial identity
• missing token
• implicit inference

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


<a id="local-section-10-stack-i-tenet-i-doctrinalinvariants-numeric-failures"></a>
NUMERIC FAILURES
------------------------------------------------------------

• gematric/cardinal collapse
• derived substitution

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


<a id="local-section-10-stack-i-tenet-i-doctrinalinvariants-rule-9"></a>
RULE
------------------------------------------------------------


Any failure:

    → invalidates mixture


============================================================
END SECTION XII
============================================================


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


<a id="local-section-10-stack-i-tenet-i-doctrinalinvariants-xiii-closure"></a>
XIII. CLOSURE
============================================================


TENET I establishes:

    • unified carrier order
    • regime coexistence
    • token-based identity
    • numeric discipline

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


With this artifact:

    ✓ A, T, E may coexist without ambiguity
    ✓ combinatorics becomes stable
    ✓ carrier identity becomes explicit
    ✓ expansion and compression coexist lawfully

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


<a id="local-section-10-stack-i-tenet-i-doctrinalinvariants-final-state"></a>
FINAL STATE:

    READY FOR INTEGRATION

============================================================
END TENET I — MIXTURA
============================================================