Coherence Index (CI)
Think of CI as a behavioral consistency score — like a credit check that asks not just “who are you?” but “does your behavior make physical sense?”
CI measures four dimensions of consistency: where you are, what you can do, when you act, and who you interact with. One inconsistency drags the whole score down.
↓ Try the coherence simulator below
The Key Insight
Traditional identity: Trust is binary (logged in = trusted, not logged in = untrusted)
Web4 identity: Trust is modulated by coherence (consistent behavior = full trust, incoherent behavior = trust severely limited)
The Problem: Identity Isn't Binary
Traditional Web: Binary Trust
- •Compromised credentials = full access - Attacker with stolen password looks identical to real user
- •No behavioral consistency checks - System can't detect impossible travel, capability changes, or temporal anomalies
- •Detection happens too late - Only after damage is done do fraud detection systems trigger
Web4: Coherence-Modulated Trust
- •Continuous coherence verification - Every grounding (a periodic check-in where the device proves it's still the same device) verifies spatial, temporal, capability, and relational consistency
- •Trust modulation in real-time - Incoherent behavior immediately reduces effective trust, increases costs, and requires more witnesses
- •Attack becomes expensive - Faking coherence across all dimensions simultaneously is computationally and economically prohibitive
How It Works: Maria's Phone Gets Stolen
Maria lives in Madrid. Her phone is stolen at a café. Within 20 minutes, the thief tries to access Maria's Web4 account from the same city.
Result: Even though the thief has Maria's actual device in the same city, CI drops to 0.55 because temporal continuity is broken (device was powered off briefly) and relational patterns don't match (thief contacts different people, navigates unfamiliar apps). The society restricts access and demands extra verification.
Traditional security would see valid credentials on the correct device in the right city — and grant full access. CI catches what passwords can't.
The Four Coherence Dimensions
Web4 measures coherence across four independent dimensions. All must be consistent for full trust access.
1. Spatial Coherence
Question: Can this device actually be where it claims?
Detects:
- • Impossible travel (Tokyo → London in 30 min)
- • Hardware-specific velocity profiles (server = 0 km/h, mobile = 100 km/h)
- • Sudden location jumps without travel announcements
Mitigations: Travel announcements (+0.4), destination witnesses (+0.3)
2. Capability Coherence
Question: Does this device have the capabilities it should?
Detects:
- • Unexpected capabilities (mobile with GPU cluster)
- • Capability changes without upgrade events
- • Hardware class mismatches (IoT sensor with 1TB RAM)
16% penalty per unexpected capability. Sudden changes require documented upgrades.
3. Temporal Coherence
Question: Is this device's temporal behavior consistent?
Detects:
- • Broken continuity chains (missing hash links)
- • Unusual activity patterns (night activity for day device)
- • Time gaps without explanation
Continuity tokens link groundings. Broken chain = 0.3 CI penalty.
4. Relational Coherence
Question: Are this device's relationships consistent?
Detects:
- • Claiming relationships with entities never interacted with
- • Contradictory operational states
- • Relationship claims without witness validation
Validates grounding against existing interaction history and witnessed relationships.
Try It: Can You Stay Coherent?
Drag the sliders to simulate incoherent behavior. Watch how even one compromised dimension tanks your effective trust, inflates your ATP costs (ATP is the energy budget that powers every action), and demands extra witnesses. Try a preset scenario, then tweak individual dimensions.
Coherence Dimensions
Overall Coherence Index (CI)
1.000All four dimensions must be healthy — one failing dimension pulls your whole score down.
What's Happening?
Device exhibits consistent location patterns, expected capabilities, regular temporal activity, and coherent relationships. Full trust access.
Why One Low Dimension Tanks Everything
Security by Design
Web4 combines the four coherence dimensions so that one weak dimension drags down the entire score. This is a deliberate security choice:
❌ Simple Average (Insecure)
CI = (0.9 + 0.9 + 0.9 + 0.1) / 4 = 0.7
One dimension at 0.1 gets “averaged out” by the others. Attacker can ignore one dimension and still get decent CI.
✅ Web4's Approach (Secure)
CI = (0.9 × 0.9 × 0.9 × 0.1)^(1/4) = 0.48
One dimension at 0.1 tanks the entire CI. Attacker MUST fake coherence across ALL dimensions simultaneously.
Result: Attacks become exponentially harder. You can't just spoof location OR capabilities OR timing - you must maintain perfect coherence across all dimensions simultaneously, which is computationally and economically prohibitive.
Connection to Coherence Physics▶
Web4's Coherence Index draws inspiration from coherence principles observed across multiple domains of physical and social reality.
The Nine Domains of Coherence
Research on Synchronism reveals coherence as a fundamental principle across scales, from quantum mechanics to galaxy dynamics:
Quantum Scale
- • Superconductivity
- • BEC (Bose-Einstein Condensate)
- • Laser coherence
Biological Scale
- • Heart rhythm
- • Neural synchrony
- • Circadian cycles
Social Scale
- • Trust emergence
- • Collective behavior
- • Economic coordination
Key principle: Coherence measures how well a system's parts align in phase and behavior. Loss of coherence = loss of system functionality.
Web4's CI applies this principle to digital identity: An entity with high coherence across spatial, temporal, capability, and relational dimensions is exhibiting the "phase alignment" characteristic of trustworthy systems. Incoherence = phase misalignment = untrustworthy behavior.
Spacetime Coupling & Geodesics
Recent work on Synchronism's 9th domain (Spacetime Coherence) reveals that coherent systems follow "geodesics" - paths of minimal action through their state space.
For Web4: Coherent entities follow smooth, predictable trajectories through spatial, temporal, and capability space. Sudden jumps or discontinuities indicate either (1) external force (attack) or (2) phase transition (upgrade event). CI detects both.
Real-World Applications
Fraud Detection
Traditional: Reactive fraud detection after damage is done.
Web4: Proactive coherence checking prevents fraud before it happens. Stolen credentials can't bypass spatial, temporal, and relational coherence checks.
Example: Credit card stolen in New York. Thief tries to use it in Tokyo 2 hours later. CI tanks due to impossible travel, transaction blocked or requires massive additional witnesses.
Bot Detection
Traditional: CAPTCHA, rate limiting, behavior analysis (all gameable).
Web4: Bots struggle to maintain coherence across dimensions. Botnet from same datacenter? Spatial coherence fails. Sudden capability spike? Capability coherence fails.
Example: 1000 "users" all claiming to be mobile devices but with identical capability fingerprints and sequential IP addresses. CI drops to near-zero, society access denied.
Account Takeover
Traditional: Password reset = full access. Attacker indistinguishable from real user.
Web4: Even with valid credentials, attacker's device has broken temporal continuity (new device), different capabilities, and no relational history. CI flags this immediately.
Example: Phished password used from new device in different country. Temporal + spatial + relational coherence all fail. Society requires 6 additional witnesses or blocks access entirely.
Fake Identity Resistance
Traditional: One person creates many identities, hard to detect.
Web4: Each presence requires coherence across dimensions. Creating 100 fake presences means maintaining spatial, temporal, capability, and relational coherence for all 100 simultaneously - prohibitively expensive.
Example: Fake-presence attack on a voting system. Attacker creates 50 presences from same device. Spatial + capability coherence fails for 49 of them (all same location, same hardware fingerprint). CI drops below the trust threshold (0.5), identities rejected.
Integration with Web4 Foundations
Coherence Index works in concert with the other three Web4 foundational pillars:
CI + Identity Constellations (LCT)
How they work together: Each device in your identity constellation maintains its own CI. More devices with high CI = stronger overall identity trust.
Example: You have 3 devices (phone, laptop, FIDO2 key). If phone's CI drops (stolen and used from different location), other devices' high CI keeps your constellation intact. Stolen device's low CI prevents full access.
Learn more about identity constellations →CI + ATP Economics
How they work together: ATP is the energy budget every agent has — every action costs some. Low CI increases those costs (up to 10x). This makes incoherent behavior economically expensive, not just trust-limited.
Example: An attacker with stolen credentials (CI = 0.4) pays 6.25x more energy for every action. Their budget drains rapidly, making the attack unsustainable before it can do real damage.
Learn more about ATP economics →CI + Trust Tensors (T3)
How they work together: CI modulates effective trust. T3 = long-term reputation. CI = current consistency. Effective trust = T3 × CI².
Example: You have high T3 (0.9 across all dimensions from years of good behavior). Suddenly you ground from impossible location (CI = 0.3). Effective trust drops to 0.9 × 0.3² = 0.081 (8%). Your reputation is intact, but current access is severely limited until coherence recovers.
Learn more about trust tensors →▶ Technical Implementation
Where CI Lives in Web4
1. Grounding Events
Every time a device grounds (proves presence), Web4 calculates CI across all four dimensions. This happens continuously, not just at "login."
// Pseudocode: how a grounding check works
grounding_event = {
lct_id: device_lct, // which device
timestamp: now, // when
location: gps_coords, // where
capabilities: hardware_fingerprint,
continuity_token: hash(previous_grounding),
context: [recent_interactions] // who you've interacted with
}
ci = calculate_coherence(grounding_event, mrh_history)
effective_trust = base_trust * ci^2
atp_cost_multiplier = 1 / ci^22. Society Policies
Each society configures CI thresholds and modulation curves. Strict societies require higher CI, lenient societies are more forgiving.
// Society configuration
strict_society = {
min_ci_for_access: 0.8,
trust_modulation_exponent: 3, // ci^3 = steeper penalty
atp_cost_exponent: 2.5,
witness_scaling_factor: 15
}
lenient_society = {
min_ci_for_access: 0.5,
trust_modulation_exponent: 1.5, // ci^1.5 = gentler penalty
atp_cost_exponent: 1.8,
witness_scaling_factor: 5
}3. Reference Implementation
Web4's reference implementation (Python) is available in the Web4 repository:
- •
coherence.py(560 lines) - CI calculation across 4 dimensions - •
trust_tensors.py(330 lines) - CI modulation functions - •
test_coherence.py(337 lines) - 16 comprehensive tests - •
test_trust_tensors.py(280 lines) - 20 modulation tests
Key Takeaways
1. Trust Isn't Binary
Web4 treats trust as a continuous function modulated by real-time coherence, not a binary logged-in/logged-out state. This makes attacks exponentially harder.
2. Four Dimensions, One Weak Link
The scoring ensures that one low dimension tanks everything. Attackers must fake coherence across spatial, temporal, capability, AND relational dimensions simultaneously — prohibitively expensive.
3. Grounded in Real-World Patterns
CI isn't arbitrary — it's designed so that faking consistent behavior is always more expensive than genuinely having it. The design draws from how consistency works in biology and social systems.
4. Economic + Reputational Penalty
Low CI doesn't just limit trust — it increases ATP costs (up to 10x) and witness requirements (up to +8). Incoherent behavior becomes economically unsustainable.
Why so harsh? Mild penalties (2x) would barely slow an attacker with stolen credentials. The 1/CI² formula means penalties escalate sharply only when coherence drops below ~0.5 — normal users with occasional inconsistencies (CI 0.8) pay just 1.6x, while a stolen account (CI 0.3) pays 11x. The severity is targeted at the threat, not at regular users.
5. Continuous, Not Discrete
CI is calculated at every grounding event (not just "login"), and modulates trust in real-time. Coherent behavior = full access. Incoherent behavior = immediate limitation.
Explore More
How It Works
See how CI integrates with LCT, ATP, and T3 to create complete Web4 societies.
Society Simulator
Run simulations and see coherence, trust, and energy interact in real-time.
Identity Constellations
How multi-device identity strengthens CI and resists attacks.
Reference Implementation
Dive into the coherence.py and trust_tensors.py code on GitHub.