VECTOR AUTHORITY SPECIFICATION v1.0

Authority: Succinct Authority Domain: VectorAuthority.com Status: CANONICAL Date: 2026-01-18

PURPOSE

Vector Authority defines the universal mathematical foundation for structured data across all domains. It specifies how to decompose any domain into orthogonal axes, address points in the resulting coordinate space, and project views onto subspaces.

This specification is domain-agnostic. Construction, marketing, legal, medical, and any other vertical inherit these rules while defining their own axes.

CORE PRINCIPLES

Data exists without interpretation — Coordinates are addresses, not meanings
Axes are orthogonal — No axis can be derived from another
Coordinates are unique — Each point in the space has exactly one address
Projections are views — Modules/features are slices of the space, not separate data

DEFINITIONS

Term	Definition
Axis	An independent, measurable dimension of the data space
Coordinate	A specific point in the space, defined by values on each axis
Projection	A view of the space that collapses or filters axes
Sparsity	The property that most coordinates in the space are empty
Orthogonal	Two axes are orthogonal if knowing one tells you nothing about the other
Derived	A value calculated from coordinates, not a true axis

AXIS REQUIREMENTS

For a dimension to qualify as a true axis:

Requirement	Test
Independent	Cannot be calculated from other axes
Measurable	Has discrete or continuous values
Orthogonal	Does not correlate with other axes
Universal	Applies to all entities in the domain
Stable	Values do not change based on observer

True Axis Examples

Domain	True Axes
Construction	Thickness, Substrate, Rating, Density, Method
Marketing	Contact, Campaign, Channel, Time, Outcome
Legal	Party, Document, Clause, Status, Date

Non-Axis Examples (Derived/Calculated)

Value	Why Not an Axis
Segment	Derived from Contact attributes
Score	Calculated from multiple axes
Total	Aggregation across coordinates
Rank	Relative to other coordinates

COORDINATE NOTATION

Format

[L1].[L2].[L3].[L4].[L5]

Structure

Level	Name	Function	Cardinality
L1	Category	Industry vertical	Low (10s)
L2	Domain	Functional area	Medium (100s)
L3	Entity	Discrete object	High (1000s)
L4	Attribute	Property of entity	Medium (100s)
L5	State	Validation status	Low (10s)

Depth Limit

Maximum: 5 levels. No exceptions.

Rationale: Beyond 5 levels adds navigation burden without semantic value. If more specificity is needed, add axes (width) not levels (depth).

Examples

Construction.Roofing.Assembly.RValue.Validated
Construction.Roofing.Assembly.Thickness.Pending
Marketing.Contacts.Lead.Score.Qualified
Marketing.Campaigns.Email.Status.Sent
Legal.Contracts.NDA.Term.Executed
Medical.Patients.Diagnosis.ICD10.Confirmed

COORDINATE SPACE

Definition

The coordinate space is the Cartesian product of all axes:

Space = A1 × A2 × A3 × ... × An

Where each Ai is the set of valid values for axis i.

Dimensionality

Domain	Typical Axes	Space Size
Construction Materials	20	10^20 theoretical
Marketing Events	8	10^12 theoretical
Legal Documents	12	10^15 theoretical

Sparsity

Real data occupies a tiny fraction of the theoretical space:

Density = Occupied Coordinates / Total Possible Coordinates

Typical density: 10^-6 to 10^-12 (extremely sparse)

This sparsity enables efficient storage via sparse matrix representations.

PROJECTION RULES

Projections reduce dimensionality by:

Fixing — Hold one axis constant
Collapsing — Ignore an axis entirely
Aggregating — Sum/count across an axis

Projection Notation

π[axes](Space) = Projected subspace

Examples:
π[Contact](MarketingSpace) = All contacts (Module M01)
π[Campaign](MarketingSpace) = All campaigns (Module M06)
π[Time, Outcome](MarketingSpace) = Time series of outcomes (Reports)

Module-to-Projection Mapping

Module	Projection	Axes Shown
All Contacts	π[Contact]	Contact only
Campaigns	π[Campaign, Status]	Campaign + Status
Reports	π[Time, Outcome, Value]	Aggregated metrics
Revenue	π[Contact, Value]	Attribution

STORAGE MODEL

Key-Value Representation

Each occupied coordinate is a key-value pair:

KEY: [L1].[L2].[L3].[L4].[L5]
VALUE: { payload }

Lookup Complexity

Operation	Complexity	Notes
Point lookup	O(1)	Direct address
Axis scan	O(n)	n = values on axis
Projection	O(k)	k = occupied coordinates
Full scan	O(k)	k << total space

Storage Formats

Format	Extension	Use Case
JSON	.va.json	Data interchange
Binary	.va.bin	High performance
Markdown	.va.md	Documentation

SCHEMA DEFINITION

Each domain must declare its axes:

{
  "schema": {
    "domain": "Construction",
    "version": "1.0",
    "axes": [
      {
        "id": "L1",
        "name": "Category",
        "type": "enum",
        "values": ["Roofing", "Waterproofing", "Fireproofing", "Insulation"]
      },
      {
        "id": "L2",
        "name": "Domain",
        "type": "enum",
        "values": ["Assembly", "Component", "Accessory", "System"]
      },
      {
        "id": "L3",
        "name": "Entity",
        "type": "string",
        "pattern": "^[A-Z][a-zA-Z0-9]+$"
      },
      {
        "id": "L4",
        "name": "Attribute",
        "type": "enum",
        "values": ["Thickness", "RValue", "Rating", "Density", "Method"]
      },
      {
        "id": "L5",
        "name": "State",
        "type": "enum",
        "values": ["Draft", "Pending", "Validated", "Rejected", "Archived"]
      }
    ],
    "depth_limit": 5
  }
}

VALIDATION RULES

Code	Rule
VA.01	Coordinate depth MUST NOT exceed schema depth_limit
VA.02	Each level value MUST conform to axis type/pattern
VA.03	Axes MUST be orthogonal (no derivable axes)
VA.04	Coordinates MUST be unique within the space
VA.05	Projections MUST reference valid axes
VA.06	Schema MUST declare all axes before use

INVARIANTS

Code	Invariant
IV.01	Axis count is unlimited (width)
IV.02	Coordinate depth is limited to 5 (depth)
IV.03	Empty coordinates are not stored
IV.04	Coordinates are case-sensitive
IV.05	Schema is immutable after declaration
IV.06	Projections do not modify underlying data

DOMAIN INHERITANCE

All domain kernels inherit Vector Authority rules:

VECTOR AUTHORITY (This Spec)
│
├── Construction Kernel
│   └── 20 material axes
│
├── Marketing Kernel
│   └── 8 event axes
│
├── Legal Kernel
│   └── 12 document axes
│
└── [Future Domains]
    └── Domain-specific axes

Each domain:

Declares its axes per this spec
Follows coordinate notation
Respects depth limit
Implements projections for modules

CROSS-DOMAIN QUERIES

When data spans domains, prefix with domain identifier:

Construction:Roofing.Assembly.RValue.Validated
Marketing:Contact.Campaign.Email.Opened

The colon separates domain from coordinate.

FILE FORMAT

Document Structure

VECTOR AUTHORITY DOCUMENT
│
├── HEADER
│   ├── version
│   ├── domain
│   ├── created_by
│   └── signature
│
├── SCHEMA
│   └── axes[]
│
├── DATA
│   └── coordinates[]
│
├── PROJECTIONS
│   └── views[]
│
└── AUDIT
    └── event_log[]

Extensions

Extension	Description
.va.json	Vector Authority data document
.va.md	Vector Authority specification
.va.html	Vector Authority rendered view

REFERENCES

SuccinctAuthority.com — Philosophical foundation
ValidKernel.com — Validation infrastructure
CanonicalKernel.com — Frozen vocabulary
LDSKernel.com — Lefebvre Data Standard

VERSION HISTORY

Version	Date	Changes
1.0	2026-01-18	Initial specification

Issued by: Armand Lefebvre
Date: 2026-01-18
Authority: SuccinctAuthority.com / VectorAuthority.com