When reasoning systems (humans, organizations, or AI agents) make decisions, three pressures seem always present:
Truth (T): accuracy or validity of what is known.
Trust (R): reliability of others in the network, verified recursively.
Energy (E): resources or effort enabling persistence and execution.
Much of the failure we see — both in humans and in artificial systems comes when one of these is overweighted while the others collapse. (E.g., high energy without truth → reckless harm; trust without truth → blind propagation; truth without energy → paralysis.)
This led me to ask: can we formalize a minimal framework where these three co-equal parameters act as stabilizers for decision networks?
2. Core Postulates (Sketch)
I call this the Trinity Model. It rests on five axioms (stated formally in the preprint, but here in words):
Node Principle: A decision node only exists if some truth, trust, and energy are all non-zero.
Balance: Their ratio must stay within bounds; extreme imbalance destabilizes the system.
Integrity Conservation: Loss in one parameter must be compensated elsewhere in the network.
Recursive Trust: Trust cannot be carried forward blindly. it must decay and re-validate along each step.
Zero-Harm Constraint: No branch is valid if net harm > 0; shielding functions must mitigate.
From these, theorems follow about branch stability, recursive trust bounds, and emergent order when stable subgraphs combine.
3. Why This Matters
Decision integrity: Systems collapse not because they lack power, but because they drift in imbalance (e.g., truth suppressed for expediency).
AI alignment: Recursive trust rules out “blind carry-over” of authority. Every trust link must be re-validated, slowing harmful propagation.
Zero-harm: Embedding explicit shielding functions forces harm-mitigation into the math, not just the philosophy.
4. Open Questions
I don’t claim this model is final. I’d be very interested in critique on:
How does recursive trust interact with existing formalisms in AI safety / alignment (e.g., corrigibility, calibration)?
Are there better mathematical forms for the “balance axiom” than a bounded ratio?
Can “zero-harm” be meaningfully defined outside human-centric ethics (e.g., in multi-agent systems)?
Closing thought: Time and again, we see that systems endure not by maximizing a single parameter, but by stabilizing across multiple. The Trinity Model is my attempt to formalize this intuition into a recursive, testable framework.
Feedback, critique, or pointers to related work would be hugely valuable.
The Trinity Model: Toward a Framework for Decision Integrity and Recursive Trust
1. Motivation
When reasoning systems (humans, organizations, or AI agents) make decisions, three pressures seem always present:
Truth (T): accuracy or validity of what is known.
Trust (R): reliability of others in the network, verified recursively.
Energy (E): resources or effort enabling persistence and execution.
Much of the failure we see — both in humans and in artificial systems comes when one of these is overweighted while the others collapse. (E.g., high energy without truth → reckless harm; trust without truth → blind propagation; truth without energy → paralysis.)
This led me to ask: can we formalize a minimal framework where these three co-equal parameters act as stabilizers for decision networks?
2. Core Postulates (Sketch)
I call this the Trinity Model. It rests on five axioms (stated formally in the preprint, but here in words):
Node Principle: A decision node only exists if some truth, trust, and energy are all non-zero.
Balance: Their ratio must stay within bounds; extreme imbalance destabilizes the system.
Integrity Conservation: Loss in one parameter must be compensated elsewhere in the network.
Recursive Trust: Trust cannot be carried forward blindly. it must decay and re-validate along each step.
Zero-Harm Constraint: No branch is valid if net harm > 0; shielding functions must mitigate.
From these, theorems follow about branch stability, recursive trust bounds, and emergent order when stable subgraphs combine.
3. Why This Matters
Decision integrity: Systems collapse not because they lack power, but because they drift in imbalance (e.g., truth suppressed for expediency).
AI alignment: Recursive trust rules out “blind carry-over” of authority. Every trust link must be re-validated, slowing harmful propagation.
Zero-harm: Embedding explicit shielding functions forces harm-mitigation into the math, not just the philosophy.
4. Open Questions
I don’t claim this model is final. I’d be very interested in critique on:
How does recursive trust interact with existing formalisms in AI safety / alignment (e.g., corrigibility, calibration)?
Are there better mathematical forms for the “balance axiom” than a bounded ratio?
Can “zero-harm” be meaningfully defined outside human-centric ethics (e.g., in multi-agent systems)?
5. Where to Read More
The full axioms, theorems, and proofs are in the preprint:
[https://doi.org/10.5281/zenodo.17058462]
Closing thought:
Time and again, we see that systems endure not by maximizing a single parameter, but by stabilizing across multiple. The Trinity Model is my attempt to formalize this intuition into a recursive, testable framework.
Feedback, critique, or pointers to related work would be hugely valuable.
— Praveen Shira