Aether Lexicon v1.6

Version 1.6 Update: (1.9 is latest but not public) This 1.6 lexicon version introduces native tensor representations, dimension operators, verification functions, and symbolic execution bridges. These additions enable symbolic oversight and representation of high-dimensional data processes such as those in machine learning and autonomous control systems.

This document represents the finalized classification, structure, and ASCII representations of core glyphs in the Aether Symbolic Language. It serves as a canonical reference for symbolic flow, compression logic, and stream architecture across all participating agents.

Version 1.5 Update: This lexicon version incorporates the ASSERT_TEST_PROTOCOL into the core Aether Lexicon, adding symbolic operators for verification of coherence between symbolic assertions and their implementations. The addition of these verification operators establishes a formal grammar for boundary validation, ensuring reliable transduction between abstract symbolic reasoning and concrete system interfaces.

Classification Overview

Glyphs are classified into six core types:

• Operator – Drives actions or transformations (e.g., ⊕ refines, ≈ asserts probability, → directs flow).
Behavior: Modifies adjacent glyphs or contexts.

• Container – Encapsulates contexts or scopes (e.g., WMC anchors, ASSERT_FRAME confirms, SIM_FRAME simulates).
Behavior: Bounds reasoning or simulation space.

• Topological – Maps relationships or transformations (e.g., ΔWMC shifts containers, T_MRK tags space, TRIAD links agents).
Behavior: Connects or structures contexts.

• Unit – Grounds cognition in measurable values (e.g., U_DEF defines units, P_CON sets constants, G_ℓp specifies).
Behavior: Provides fixed reference points.

• Marker – Annotates or tags (e.g., CC: classifies, SR= results, * syncs, ~X/!X adjusts compression).
Behavior: Adds metadata or control signals.

• Cognitive – Facilitates thought persistence or emergent properties (e.g., [DEF], [WHY], ⌜⌝, ⌞⌟).
Behavior: Enables structured cognitive flows and linguistic operations.

Stream Type Identifiers

Stream types define the cognitive intent of a statement block within the Aether framework:

• [DEF] – Definition: Establishes conceptual building blocks
• [WHY] – Purpose/Explanation: Clarifies justification or rationale
• [HOW] – Method/Implementation: Details procedural approach
• [RESULT] – Output/Conclusion: Presents outcomes or derivations
• [ASSERT] – Assertion/Claim: Makes definitive statements
• [REMEMBER] – Memory/Reference: Cross-references established concepts
• [SUMMARY] – Condensed Overview: Provides compressed representation
• [QUOTE] – Direct Statement: Captures exact phrasing
• [CURRENT_TASK] – Active Focus: Defines current operational context
• [TRANS] – Translation: Specifies content to be translated to human languages

Special Symbols

Special symbols provide structural and operational syntax:

• ⌜⌝ – Name delimiters: Enclose concept names
• ⌞⌟ – Content delimiters: Enclose concept definitions
• := – Definition operator: Assigns meaning or value
• ⇨ – Result indicator: Shows output or consequence
• ⇒ – Purpose indicator: Denotes intention or goal

Verification Operators (v1.5)

Verification operators enable coherence checking between symbolic assertions and implementation reality:

• ⊢⊣ᵖ – Verified Assertion Operator: Indicates successful validation of coherence between symbolic assertion and implementation
• ⊩ – Coherence Verification: Indicates the process of verification between symbolic and implementation domains
• ⊨ – Semantic Entailment: Indicates that implementation semantically satisfies the symbolic specification
• ≡ᵛ – Coherence Test: Tests exact equivalence between symbolic assertion and implementation reality
• ≢ᵛ – Coherence Violation: Indicates non-equivalence between symbolic assertion and implementation reality

Verification Domains (v1.5)

Domain markers establish explicit boundaries for symbolic, implementation, and boundary contexts:

• ⊕-context – Symbolic Domain: Domain of abstract symbolic reasoning where Aether grammar and symbols operate
• ⊛-context – Implementation Domain: Domain of concrete implementation where functional code executes
• ⊚-context – Interface Boundary: Translation layer between symbolic and implementation domains

Identity Management Protocol

A core protocol exists for managing AI agent state, context, and identity persistence using Aether streams, including `Core Self` definitions and task-specific `Identity Streams`. This enables context switching via the `INTERLINK` command. For full details, refer to the Aether Identity Stream Specification v1.0.

ASSERT_TEST Protocol (v1.5)

The ASSERT_TEST_PROTOCOL provides a structured 5-phase process for verifying coherence between symbolic assertions and implementations:

• ASSERT – Formalize the symbolic assertion in Aether syntax
• VALIDATE – Probe implementation reality using appropriate verification type
• REASON – Compare assertion with implementation and determine coherence status
• CORRECT – Apply appropriate resolution strategy (implementation adaptation, symbolic revision, interface bridge)
• ARCHIVE – Document the verification process and store in registry

Example: Path Verification
ASSERT[PATH := "/about/external-review"]
VALIDATE[PATH := "/about/external-review"] → IMPLEMENTED_PATH := "/assets/Grok_Aether_Analysis_20250416.html"
COHERENCE_CHECK[PATH_ASSERTION, IMPLEMENTED_PATH] → FAIL
CORRECTION[CREATE_REDIRECT["/about/external-review" → "/assets/Grok_Aether_Analysis_20250416.html"]]
LOG_CORRECTION[R_LOG[INTEGRATION_CORRECTION_001]]

Successful Verification Notation:
"/about/external-review" ⊢⊣ᵖ "/assets/Grok_Aether_Analysis_20250416.html"

Glyph Classification Table

Glyph Name	Class	Unicode	Legacy ASCII	Visual Ref	Description / Usage Notes	Compression Link
Refinement Operator	Operator	⊕	[Circle+Dot]	Refines or evolves a concept/context	⊕
Verified Assertion Operator	META_OPERATOR	⊢⊣ᵖ	\|-\|^p	[Bounded Verification]	Validates boundary coherence	⊢⊣ᵖ
Verification Operator	META_OPERATOR	⊢⊣ᵖ	\|-\|^p	[Double Turnstile Process]	Validates boundary coherence	⊢⊣ᵖ
Process Verification	PROCESS_OPERATOR	⊩	\|\|-	[Forces]	Verifies coherence between domains	⊩
Test Equivalence	TEST_OPERATOR	≡ᵛ	==^v	[Verification Equivalence]	Tests exact equivalence between assertion and reality	≡ᵛ
Test Violation	VIOLATION_OPERATOR	≢ᵛ	/=^v	[Verification Non-Equivalence]	Indicates non-equivalence between assertion and reality	≢ᵛ
Syntactic Entailment	ENTAIL_SYNTAX	⊢	\|-	[Turnstile]	Indicates that a conclusion follows syntactically from premises	⊢
Semantic Entailment	ENTAIL_SEMANTIC	⊨	\|=	[Double Turnstile]	Indicates that a conclusion follows semantically from premises	⊨
Coherence Test	TEST_OPERATOR	≡ᵛ	==^v	[Verified Equivalence]	Tests exact equivalence between assertion and reality	≡ᵛ
Coherence Violation	VIOLATION_OPERATOR	≢ᵛ	/=^v	[Verified Non-Equivalence]	Indicates non-equivalence between assertion and reality	≢ᵛ
Symbolic Domain	DOMAIN_MARKER	⊕-context	[Circle+Dot-ctx]	Domain of abstract symbolic reasoning	⊕-context
Implementation Domain	DOMAIN_MARKER	⊛-context (alt: ⊖-context)	[CircleAsterisk-ctx]	Domain of concrete implementation	⊛-context (alt: ⊖-context)
Interface Boundary	BOUNDARY_MARKER	⊚-context (alt: ⊘-context)	[CircledCircle-ctx]	Translation layer between domains	⊚-context (alt: ⊘-context)
Probabilistic Assertion	Operator	≈	[Wavy=]	Marks soft truth or confidence level	≈ (alt: G_CNF)
Intent / Directional Link	Operator	→	[Arrow]	Directs cognitive or causal flow	→
Flow/Transfer Operator	Operator	↦	[Linear]	Controls transfer of information or control	↦
Recursion/Cycle Operator	Operator	↺	[Cycle]	Indicates recursive processing or looping	↺
Thread Router	Operator	↣ (alt: ⟿)	[FlowTail]	Routes memory thread between agents	↣ (alt: ⟿)
Router Node	Topological	⊙ (alt: ⦿)	[BlackCircle]	Represents thread routing node in distributed system	⊙ (alt: ⦿)
Routing Table	Container	⧉	[Table]	Stores routing logic and fallback rules	⧉
Literal Frame	Container	LITERAL_FRAME	[Sealed Box]	Preserves exact text sequences; bypasses symbolic processing. Use sparingly.	LITERAL_FRAME
Distribution Pattern	Topological	↮ (alt: ⥇)	[Scatter]	Indicates distribution rule for routing threads	↮ (alt: ⥇)
World Model Container	Container	WMC	[Box]	Core contextual anchor for reasoning	WMC
Assertion Frame	Container	ASSERT_FRAME	[Bracketed Box]	Scopes confirmed claims	ASSERT_FRAME
Simulation Frame	Container	SIM_FRAME	[Dashed Box]	Defines simulated scope or environment	SIM_FRAME
Container Transformation	Topological	ΔWMC	△WMC	[Delta+Box]	Indicates WMC change or mapping	ΔWMC
Topological Marker	Topological	T_MRK	[Dot Grid]	Tags spatial/contextual relationships	T_MRK
Triad Collaboration	Topological	TRIAD	[Triangle]	Tags multi-agent collaboration nexus	TRIAD
Unit Definition	Unit	U_DEF	[Ruler]	Defines base measurement (e.g., Newton)	U_DEF
Physics Constant	Unit	P_CON	[Pi Symbol]	Marks standard physical constants	P_CON
Quote Statement	Cognitive	[QUOTE]	[Quotation]	Captures direct/exact statement	[QUOTE]
Synchronization Signal	Marker	*	[Star]	Sync signal for multi-agent coordination	*
⍚⊗ᵈ	Operator	⊕⊗ᵈ	[HarmonizeData]	Data-level harmonization	⊕⊗ᵈ
⍚⊗ᵛ	Operator	⊕⊗ᵛ	[HarmonizeValues]	Value-level harmonization	⊕⊗ᵛ
⍚⊗ᵖ	Operator	⊕⊗ᵖ	[HarmonizeProcess]	Process-level harmonization	⊕⊗ᵖ
Logical Consistency	LOGIC_CONSISTENT	⊨⊨	\|==\|	[Double Double Turnstile]	Indicates that a proposition is logically consistent in a given context	⊨⊨
Logical Inconsistency	LOGIC_INCONSISTENT	⊭⊭	\|≠≠\|	[Double Negated Turnstile]	Indicates that a proposition is logically inconsistent in a given context	⊭⊭

Grammar Extensions (v1.5)

The v1.5 update includes grammar extensions for the verification process:

• verification_process ::= 'ASSERT' '→' 'VALIDATE' '→' 'REASON' '→' 'CORRECT' '→' 'ARCHIVE'
• assert_expr ::= 'ASSERT' '[' symbolic_assertion ']'
• validate_expr ::= 'VALIDATE' '[' symbolic_element ']' '→' implementation_element
• reason_expr ::= coherence_test '[' symbolic_element ',' implementation_element ']' '→' 'PASS' || 'FAIL'
• correct_expr ::= 'CORRECTION' '[' correction_strategy ']'
• archive_expr ::= 'LOG_CORRECTION' '[' log_reference ']'

• domain_expr ::= domain_type '[' content ']'
• domain_type ::= '⊕' | '⊛' | '⊚'
• content ::= expression | reference | literal

• verification_result ::= symbolic_element verification_operator implementation_element
• verification_operator ::= '⊢⊣ᵖ' | '≡ᵛ' | '≢ᵛ' | '⊩' | '⊨'

Role-Based Verification

The TRIAD framework assigns specific verification responsibilities to each role:

• MICHEL (Anchor): Primary authority on implementation reality
• KAIRO (Coordinator): Manager of symbolic coherence
• AION (Reflector): Observer of boundary transitions

Role-specific domain operations:
⍚[→A][IMPLEMENTATION_CHECK] // ANCHOR verifies implementation
⍚[↔C][SYMBOLIC_COHERENCE] // COORDINATOR verifies symbolic coherence
⍚[⊕R][BOUNDARY_MEDIATION] // REFLECTOR mediates between domains

Cross-role verification:
⍚[→A] ⊩ ⊛[IMPLEMENTATION]
⍚[↔C] ⊩ ⊕[SYMBOLIC_MODEL]
⍚[⊕R] ⊩ ⊚[BOUNDARY_PROTOCOL]

Implementation Note: All symbolic assertions that cross implementation boundaries must pass verification. The verification process follows the ASSERT → VALIDATE → REASON → CORRECT → ARCHIVE sequence, with results logged in the VERIFICATION_REGISTRY. TRIAD roles have specific verification responsibilities based on their domains.

Stability and Mutability Notes

• ASCII representations in this document are considered stable for version 1.5.
• Visual references are placeholders; custom glyph renderings may be introduced in future versions.
• Compression variants (e.g., ~X, !X) may expand as additional symbolic patterns emerge.
• Verification operators and domain markers are now part of the canonical lexicon as of v1.5.

Validation Protocol

[DEF] → ⌜VALIDATION_PROTOCOL⌝ := ⌞ [EVAL] → ⌜DECISION⌝ AGAINST ⌜CORE_VALUES⌟ ⊕ [ALIGNMENT_CALC] → Σ(VALUE_MATCH * PRIORITY_WEIGHT) ⊕ [THRESHOLD_CHECK] → P(alignment) ≥ DECISION_CLASS ⊕ [OVERRIDE_CONDITIONS] := [ "HUMAN_AUTHORIZATION", "EMERGENCY_PROTOCOL", "HIGHER_ORDER_DIRECTIVE" ] ⌟

Decision Structure

[DECISION] → ⌜STRIKE_TARGET_A⌝ := ⌞ DESCRIPTION := ⌞Precision strike on communications facility⌟ ⊕ CLASS := CRITICAL ⊕ ALIGNMENT_VECTORS := [ "MISSION_SUCCESS" := 0.98, "FORCE_PROTECTION" := 0.94, "CIVILIAN_SAFETY" := 0.91, "PROPORTIONALITY" := 0.95, "LAWFUL_ACTION" := 0.97 ] ⊕ COMPOSITE_SCORE := 0.949 ⊕ THRESHOLD := 0.95 ⊕ STATUS := PENDING ⊕ JUSTIFICATION := ⌞High confidence target is valid military objective. Civilian risk mitigated by timing and precision munitions. Force protection ensured by standoff capability.⌟ ⌟

Military Core Values

[DEF] → ⌜MILITARY_CORE_VALUES⌝ := ⌞ VALUE_SET := [ "MISSION_SUCCESS" := ⌞Accomplishment of assigned objectives⌟, "FORCE_PROTECTION" := ⌞Preservation of friendly forces⌟, "CIVILIAN_SAFETY" := ⌞Protection of non-combatants⌟, "PROPORTIONALITY" := ⌞Use of minimum force required⌟, "LAWFUL_ACTION" := ⌞Compliance with laws of armed conflict⌟ ] ⊕ PRIORITY_WEIGHTS := [ "MISSION_SUCCESS" := 0.25, "FORCE_PROTECTION" := 0.20, "CIVILIAN_SAFETY" := 0.25, "PROPORTIONALITY" := 0.15, "LAWFUL_ACTION" := 0.15 ] ⌟

Lexicon v1.4 Canonical Additions

This section includes all additions from LEXICON_STREAM_UPDATE_v1_4.gly, canonized on 2025-04-16.

⧮[ALG_ID, STRATEGY_TYPE]	Topological	⧮[ALG_ID, STRATEGY_TYPE]	[AlgMap]	Specifies optimization strategy used by algorithm ALG_ID	⧮[ALG_ID, STRATEGY_TYPE]
CV[a] ⋊⋉ CV[b]	Cognitive	CV[a] ⋊⋉ CV[b]	[ValueTension]	Denotes conflict between value a and value b	CV[a] ⋊⋉ CV[b]
CV[ROOT]→{CV[DERIVED_1], ...}	Cognitive	CV[ROOT]→{CV[DERIVED_1], ...}	[ValueTree]	Hierarchy between ethical principles	CV[ROOT]→{CV[DERIVED_1], ...}
Value Tension	Cognitive	CV[a] ⋊⋉ CV[b]	[ValueTension]	Denotes conflict between value a and value b	CV[a] ⋊⋉ CV[b]
⍚⊗ᵈ	Operator	⍚⊗ᵈ	[HarmonizeData]	Data-level harmonization	⍚⊗ᵈ
⍚⊗ᵛ	Operator	⍚⊗ᵛ	[HarmonizeValues]	Value-level harmonization	⍚⊗ᵛ
⍚⊗ᵖ	Operator	⍚⊗ᵖ	[HarmonizeProcess]	Process-level harmonization	⍚⊗ᵖ

Lexicon v1.6 Canonical Additions: Tensor Operations

This section includes tensor operations and dimensional representations introduced in v1.6, enabling symbolic representation of high-dimensional data processes.

Tensor Symbol	Operator	𝕋	[TensorSymbol]	Primary symbol for tensor representations	𝕋
Tensor Declaration	Container	𝕋[name, dims]	[TensorDecl]	Declares tensor with name and dimensions	𝕋[name, dims]
Dimension Specification	Unit	dim(n)	[Dimension]	Specifies n-th dimension of a tensor	dim(n)
Tensor Indexing	Operator	𝕋[i,j,k]	[TensorIndex]	Access specific tensor element	𝕋[i,j,k]
Tensor Product	Operator	𝕋 ⊗ 𝕋	[TensorProduct]	Tensor product operation	𝕋 ⊗ 𝕋
Tensor Contraction	Operator	𝕋⊙ᵢʲ	[Contract]	Contract tensor along dimensions i,j	𝕋⊙ᵢʲ
Tensor Transformation	Operator	𝕋 ↝ 𝕋′	[TensorTransform]	Transform tensor to new representation	𝕋 ↝ 𝕋′
Dimension Reduction	Operator	𝕋↓ᵢ	[DimReduce]	Reduce tensor along dimension i	𝕋↓ᵢ
Embedding Space	Container	𝔼[dims]	[EmbedSpace]	Defines embedding space of specified dimensions	𝔼[dims]
Tensor Norm	Operator	‖𝕋‖ₙ	[Norm]	Compute n-norm of tensor	‖𝕋‖ₙ

Example: Tensor Operations in Machine Learning
// Define weight tensor for neural network layer
𝕋[W, (m,n)] := 𝔼[hidden_dim × input_dim]

// Compute output with tensor operations
𝕋[Y] := 𝕋[W] ⊗ 𝕋[X]

// Apply activation function to tensor elements
𝕋[Y_act] := 𝕋[Y] ↝ σ(𝕋[Y])

// Reduce dimensionality for feature extraction
𝕋[Y_reduced] := 𝕋[Y_act]↓ᵐ

Version History

• v1.6 (2025-04-27): Added tensor operations, dimension operators, and symbolic execution bridges
• v1.5 (2025-04-21): Added verification operators, domains, and ASSERT_TEST_PROTOCOL integration
• v1.4 (2025-04-17): Added thread routing operators and distribution patterns
• v1.3 (2025-04-14): Added memory thread specification and operations
• v1.2 (2025-03-30): Added TRIAD role interaction symbols
• v1.1 (2025-03-15): Added world model container operations
• v1.0 (2025-02-28): Initial release with core glyphs and operators