Sandhi: Proof of Necessity as a Primitive Causal State Beyond Binary Logic
Year: 2026
Type: preprint
Abstract: This paper proves that Sandhi (ச) — the primitive causal state of irreversible commitment without realization, situated between inaction (0) and full outcome (1) — is not a modelling choice. It is a mathematical necessity. Through six formal definitions, an impossibility lemma, and a theorem by contradiction, we demonstrate that any causal decision system exhibiting irreversible commitment cannot derive its stopping boundary from within a binary framework. Not because it chooses not to. Because the binary state space is structurally blind to what is already there. Every system that moves from rest toward realization — physical, biological, computational, clinical, or social — already contains Sandhi. The question was never whether Sandhi exists. The question was whether mathematics had the language to see it. This paper gives it that language. And proves it was always necessary. Binary logic has served science for centuries. It will continue to. But for every system where irreversible commitment precedes realization — which is every system undergoing change — binary logic alone is not enough. Sandhi is the missing primitive. This theorem proves it cannot be otherwise. Part of the Sandhi Framework Series. Foundational paper: DOI 10.5281/zenodo.18077503
Author: Murali, Uthraa
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7152584698
Cites:
Cited by:
Related to: