Epistemic Topology¶
Knowledge isn't flat. It has topology—areas of density, regions of uncertainty, fault lines where contradictions create tension. Archivus maps this landscape.
The Problem with Traditional AI¶
Traditional RAG systems treat knowledge as a bag of text chunks. They retrieve "similar" content and hope for the best. They have no awareness of:
- Where they are in the knowledge landscape
- How confident they should be at this location
- What they don't know in surrounding regions
- Where contradictions might invalidate their reasoning
This is like navigating a city with only a list of addresses—no map, no terrain awareness, no understanding of which neighborhoods are well-charted and which are terra incognita.
VERITAS: The Topology of Truth¶
The VERITAS framework gives AI agents spatial awareness within the knowledge graph. Every position in the graph has measurable properties:
Density (ρ)¶
How much verified knowledge exists in this region of the graph?
High Density (ρ > 0.8):
├── Many claims about this topic
├── Multiple corroborating sources
├── Rich entity relationships
└── Confidence: HIGH
Low Density (ρ < 0.3):
├── Few claims available
├── Limited source coverage
├── Sparse entity connections
└── Confidence: REDUCE
When an agent operates in a low-density region, it should lower its confidence and potentially defer to humans rather than confabulate.
Tension (T)¶
How much contradiction pressure exists at this position?
High Tension (T > 0.7):
├── Conflicting claims detected
├── Sources disagree
├── Temporal inconsistencies
└── Action: SURFACE CONFLICTS
Low Tension (T < 0.2):
├── Claims align
├── Sources corroborate
├── No contradictions found
└── Action: PROCEED CONFIDENTLY
Tension isn't bad—it's information. A region with high tension tells the agent: "There's a dispute here. Don't pick a side silently. Surface the conflict."
Coherence (η)¶
How focused is the retrieval on the actual query?
High Coherence (η > 0.8):
├── Retrieved claims are relevant
├── Entity matches are strong
├── Graph traversal stayed on topic
└── Quality: GOOD CONTEXT
Low Coherence (η < 0.4):
├── Retrieval drifted off-topic
├── Weak entity matches
├── Tangential claims included
└── Quality: NOISY CONTEXT
Coherence measures whether the agent is actually answering the question or wandering through loosely related territory.
Coverage (κ)¶
How much of the query's scope has been addressed?
High Coverage (κ > 0.9):
├── All query entities found
├── All aspects addressed
├── No blind spots
└── Completeness: FULL
Low Coverage (κ < 0.5):
├── Some entities not found
├── Query aspects missing
├── Knowledge gaps exist
└── Completeness: PARTIAL (acknowledge gaps)
Coverage prevents agents from giving confident answers to questions they've only partially understood.
The VERITAS Lagrangian¶
These metrics combine into a decision function:
L = (Confidence × ContextMatch) / Risk
Where:
├── Confidence is enhanced by: Density, Corroboration
├── ContextMatch is enhanced by: Coherence, Coverage
└── Risk is increased by: Tension, Proximity to contradictions
If L ≥ λ (threshold): The agent can proceed autonomously.
If L < λ: The agent should escalate to human review or acknowledge uncertainty.
This isn't arbitrary caution—it's calibrated confidence. Agents that know what they don't know make better decisions than agents that confabulate with false certainty.
Truth Layers: The Verification Ladder¶
Not all knowledge is created equal. Claims ascend through verification levels:
Layer 1: Raw¶
Extracted from documents but unverified.
Layer 2: Corroborated¶
Supported by multiple independent sources.
"Company X had $50M revenue"
Sources: 3 independent documents
Status: Cross-validated
Confidence: +15% boost
Layer 3: Agent Verified¶
Verified by GOLAG agents with sufficient confidence.
"Company X had $50M revenue"
Verification: GOLAG claim_verification domain
Lagrangian: L = 1.42 (above threshold)
Status: Agent-approved
Layer 4: Expert Confirmed¶
Verified by expert-status agents (95%+ accuracy over 20+ decisions).
"Company X had $50M revenue"
Verification: Expert agent #A7F3
Agent accuracy: 97.2%
Status: Expert-endorsed
Layer 5: Hedera Anchored¶
Cryptographically anchored to public consensus.
"Company X had $50M revenue"
Hedera TX: 0.0.12345@1234567890.123456789
Consensus time: 2026-02-07T14:30:00Z
Status: Independently verifiable forever
Claims can only ascend—never descend. Each layer provides stronger guarantees than the last.
Session Traces: The Agent's Journey¶
When an AI agent processes a query, it doesn't just retrieve and generate. It navigates—moving through the knowledge graph, visiting claims, detecting contradictions, building context.
This journey is recorded as a session trace:
Session: cgr3-query-abc123
Started: 2026-02-07T14:30:00Z
Type: CGR3 Pipeline
Position 1 (Retrieve Stage):
├── Focus: Entity "Company X"
├── Density: 0.78 (good coverage)
├── Tension: 0.12 (low conflict)
├── Claims visited: 23
└── Decision: PROCEED
Position 2 (Rank Stage):
├── Focus: Claim "Q3 Revenue"
├── Density: 0.82
├── Tension: 0.67 (conflict detected!)
├── Contradiction: HR data vs. earnings report
└── Decision: SURFACE CONFLICT
Position 3 (Reason Stage):
├── Coverage: 0.91 (query fully addressed)
├── Coherence: 0.88 (on-topic)
├── Lagrangian: 1.34 (above threshold)
└── Decision: GENERATE WITH CAVEAT
Session End:
├── Positions recorded: 3
├── Claims visited: 47
├── Contradictions surfaced: 1
└── Calibration: Agent acknowledged uncertainty appropriately
Session traces enable:
- Audit trails for compliance (why did the AI say this?)
- Calibration tracking (is this agent overconfident?)
- Performance analysis (where do agents struggle?)
- Continuous improvement (learn from agent journeys)
The Navigation Mesh¶
Frequently-traversed paths through the knowledge graph are cached as a navigation mesh:
Path: "Revenue Questions" → "Financial Statements"
├── Strength: 0.92 (high-traffic route)
├── Typical density: 0.85
├── Known conflicts: Quarterly vs. annual figures
└── Cache TTL: 5 minutes
Path: "Employee Count" → "HR Data"
├── Strength: 0.78
├── Typical density: 0.61 (sparse region)
├── Known conflicts: Headcount methodology varies
└── Cache TTL: 5 minutes
The navigation mesh accelerates common queries while providing agents with terrain awareness—"This path leads through a region where contradictions are common."
Why This Matters¶
For Trust¶
Agents that report "I'm 92% confident" without epistemic grounding are making up numbers. Agents that report "I'm in a high-density region (ρ=0.85) with low tension (T=0.15) and good coverage (κ=0.91)" are providing calibrated confidence you can actually rely on.
For Compliance¶
Regulators want to know: "Why did your AI say this?" Session traces answer that question with precision—not "the model generated it" but "the agent visited these 47 claims, detected this contradiction, and decided to surface the conflict rather than pick a side."
For Accuracy¶
Agents that understand the topology of knowledge don't confabulate in sparse regions. They don't ignore contradictions. They don't claim certainty where uncertainty exists. They navigate responsibly.
For Federation¶
When organizations share verified claims, the receiving organization needs to know: What verification level does this claim have? What was the epistemic context of its verification? Truth layers and session traces travel with federated intelligence.
The Epistemic Stack¶
┌─────────────────────────────────────────────┐
│ NATURAL LANGUAGE OUTPUT │
│ Fluent responses with inline citations │
├─────────────────────────────────────────────┤
│ VERITAS DECISION LAYER │
│ L = (Confidence × ContextMatch) / Risk │
├─────────────────────────────────────────────┤
│ TOPOLOGY METRICS │
│ Density, Tension, Coherence, Coverage │
├─────────────────────────────────────────────┤
│ TRUTH LAYERS │
│ Raw → Corroborated → Verified → Anchored │
├─────────────────────────────────────────────┤
│ KNOWLEDGE GRAPH │
│ Entities, Claims, Relationships, Context │
├─────────────────────────────────────────────┤
│ HEDERA CONSENSUS │
│ Cryptographic anchoring for Layer 5 │
└─────────────────────────────────────────────┘
Each layer builds on the one below. The knowledge graph provides structure. Truth layers provide verification grades. Topology metrics provide spatial awareness. The decision layer integrates everything into calibrated action. And the output is natural language that users can understand—with the full epistemic stack available for audit.
The Result¶
AI agents that:
- Know where they are in the knowledge landscape
- Know what they don't know and acknowledge it
- Surface contradictions rather than hiding them
- Provide calibrated confidence based on measurable properties
- Leave audit trails for every decision
- Improve over time as the topology is refined
This is what it means to build enterprise AI that organizations can actually trust.
Knowledge isn't flat. Neither should be the AI that navigates it.