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):

1. Node Principle: A decision node only exists if some truth, trust, and energy are all non-zero.
2. Balance: Their ratio must stay within bounds; extreme imbalance destabilizes the system.
3. Integrity Conservation: Loss in one parameter must be compensated elsewhere in the network.
4. Recursive Trust: Trust cannot be carried forward blindly. it must decay and re-validate along each step.
5. 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:

1. How does recursive trust interact with existing formalisms in AI safety / alignment (e.g., corrigibility, calibration)?
2. Are there better mathematical forms for the “balance axiom” than a bounded ratio?
3. 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