[Paper Review] The Semantic Arrow of Time, Part V: The Leibniz Bridge -- Toward a Unified Theory of Semantic Time

Paul Borrill|arXiv (Cornell University)|Mar 5, 2026

Distributed systems and fault tolerance0 citations

TL;DR

This final paper introduces the Leibniz Bridge, a mutual-information conservation principle that unifies philosophical, protocol, and physical aspects of semantic time, replacing fito with a bilateral, reflection-enabled framework.

ABSTRACT

This is the final paper in the five-part series The Semantic Arrow of Time. Part I identified the FITO category mistake -- treating forward temporal flow as sufficient for establishing meaning. Part II presented the constructive alternative: the OAE link state machine with its mandatory reflecting phase. Part III showed the FITO fallacy operating at industrial scale in RDMA completion semantics. Part IV traced the same pattern through file synchronization, email, human memory, and language model hallucination. This paper closes the series by constructing the Leibniz Bridge: a unified framework that connects the philosophical foundations (Leibniz's Identity of Indiscernibles, as formalized by Spekkens), the protocol engineering (OAE's bilateral transaction structure), and the physical substrate (indefinite causal order in quantum mechanics). The bridge rests on a single principle: mutual information conservation -- the requirement that every causal exchange preserve the total information accessible to both endpoints, with the direction of time emerging not from axiom but from entropy production when a reversible exchange commits. We show that this principle dissolves the apparent impossibility of the FLP, Two Generals, and CAP theorems by revealing them as theorems about FITO systems, not about physics. We present the triangle network as the minimal topology for semantic consistency without centralized coordination. We conclude with open questions and a reflection on what distributed computing looks like when the FITO assumption is dropped.

Motivation & Objective

• Identify the foundational commitment that replaces the fito category mistake in semantic time.
• Unify philosophical foundations (Leibniz Identity of Indiscernibles, Spekkens’ principle) with protocol engineering (oae) and physics (indefinite causal order) through mutual information conservation.
• Elucidate how bilateral exchange with a reflecting phase prevents semantic corruption in distributed systems.
• Show how the triangle network enables semantic consistency without centralized coordination.
• Outline open questions and the potential impact on distributed computing when fito is dropped.

Proposed method

• Define the Leibniz Bridge as mutual information conservation for bilateral causal exchanges.
• Map the principle across three communities: computer science, networking, and physics.
• Describe the oae link state machine with its mandatory reflecting phase and the role of knowledge balance.
• Introduce the Alternating Causality framework and the reversible causal principle as information-conservation laws.
• Present the triangle network as the minimal topology for semantic consistency and discuss scale independence.

Experimental results

Research questions

• RQ1 What is the foundational principle that replaces fito to prevent semantic category mistakes?
• RQ2 How does mutual information conservation connect Leibniz–Spekkens foundations, oae protocol engineering, and indefinite causal order in physics?
• RQ3 Can the triangle network provide semantic consistency without centralized coordination in distributed systems?
• RQ4 What open questions remain about formalizing semantic time and its relation to existing impossibility theorems?
• RQ5 How might bilateral reflecting phases influence deployment in memory, language models, and distributed protocols?

Key findings

• Mutual information conservation is proposed as the core principle tying philosophical, engineering, and physical perspectives.
• A bilateral exchange with a mandatory reflecting phase closes the informational loop and preserves I(A;B).
• The completion signal that ignores information conservation is identified as a source of semantic corruption in several domains (rdma, file sync, email, memory, LLMs).
• The triangle network is presented as the minimal topology to maintain semantic consistency without a central coordinator.
• Impossibility theorems (FLP, Two Generals, CAP) are reframed as theorems about fito systems, not physics, under the Leibniz Bridge.