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The Semantic Arrow of Time, Part II: The Semantics of Open Atomic Ethernet

Paul Borrill

TL;DR

A comparative analysis is concluded with a comparative analysis showing that OAE achieves infinite consensus number while RDMA, NVLink, and UALink remain limited to finite consensus numbers due to their FITO semantics.

Abstract

This is the second of five papers comprising The Semantic Arrow of Time. Part I established that computing's arrow of time is semantic rather than thermodynamic, and that the Forward-In-Time-Only (FITO) assumption constitutes a category mistake. This paper develops the constructive alternative. We present the semantics of Open Atomic Ethernet (OAE) links as a concrete realization of a non-FITO protocol architecture. The key insight is that causal order is not assumed a priori but created through transaction structure: the link state machine progresses through TENTATIVE to REFLECTING to COMMITTED, with the option to abort at any point before commitment. Delivery does not imply commitment; commitment requires reflective acknowledgment -- proof that information has round-tripped and been semantically validated by both endpoints. We formalize this through three frameworks. First, the OAE link state machine, a six-state finite automaton whose normative invariants guarantee that semantic corruption cannot occur at the link level. Second, Indefinite Logical Timestamps (ILT), a four-valued causal structure that admits a genuinely indefinite relation between concurrent events, resolving only after symmetric link-level exchange. Third, the Slowdown Theorem applied to links, which establishes that round-trip measurement is the minimum interaction required to establish causal order. We show that ILT is strictly more expressive than Definite Causal Order systems for reversible link protocols. We connect these results to the Knowledge Balance Principle from quantum information theory. The paper concludes with a comparative analysis showing that OAE achieves infinite consensus number while RDMA, NVLink, and UALink remain limited to finite consensus numbers due to their FITO semantics.

The Semantic Arrow of Time, Part II: The Semantics of Open Atomic Ethernet

TL;DR

A comparative analysis is concluded with a comparative analysis showing that OAE achieves infinite consensus number while RDMA, NVLink, and UALink remain limited to finite consensus numbers due to their FITO semantics.

Abstract

This is the second of five papers comprising The Semantic Arrow of Time. Part I established that computing's arrow of time is semantic rather than thermodynamic, and that the Forward-In-Time-Only (FITO) assumption constitutes a category mistake. This paper develops the constructive alternative. We present the semantics of Open Atomic Ethernet (OAE) links as a concrete realization of a non-FITO protocol architecture. The key insight is that causal order is not assumed a priori but created through transaction structure: the link state machine progresses through TENTATIVE to REFLECTING to COMMITTED, with the option to abort at any point before commitment. Delivery does not imply commitment; commitment requires reflective acknowledgment -- proof that information has round-tripped and been semantically validated by both endpoints. We formalize this through three frameworks. First, the OAE link state machine, a six-state finite automaton whose normative invariants guarantee that semantic corruption cannot occur at the link level. Second, Indefinite Logical Timestamps (ILT), a four-valued causal structure that admits a genuinely indefinite relation between concurrent events, resolving only after symmetric link-level exchange. Third, the Slowdown Theorem applied to links, which establishes that round-trip measurement is the minimum interaction required to establish causal order. We show that ILT is strictly more expressive than Definite Causal Order systems for reversible link protocols. We connect these results to the Knowledge Balance Principle from quantum information theory. The paper concludes with a comparative analysis showing that OAE achieves infinite consensus number while RDMA, NVLink, and UALink remain limited to finite consensus numbers due to their FITO semantics.
Paper Structure (17 sections, 6 theorems, 2 equations, 1 table)

This paper contains 17 sections, 6 theorems, 2 equations, 1 table.

Table of Contents

  1. Introduction
  2. Shannon's Channel Model and the Origin of fito
  3. The Atomicity Framework
  4. The oae Link State Machine
  5. Indefinite Logical Timestamps
  6. Tensor Clocks
  7. Reversible Protocol Algebra
  8. The Slowdown Theorem Applied to Links
  9. Subtime and the Invisible Structure
  10. Perfect Information Feedback
  11. The Knowledge Balance Principle at the Link Level
  12. Comparative Analysis
  13. RDMA: Completion Without Commitment
  14. NVLink: Signal-Based Ordering
  15. CXL: Cache Coherence Without Transaction Semantics
  16. ...and 2 more sections

Key Result

Theorem 5.3

ilt is strictly more expressive than dco systems in the domain of reversible link protocols.

Theorems & Definitions (13)

  • Definition 3.1: Three Failure Classes
  • Definition 3.2: Three Atomicity Dimensions
  • Definition 4.1: oae Link States
  • Definition 5.1: Four-Valued Causal Structure
  • Definition 5.2: Tensor Clock
  • Theorem 5.3: Expressiveness
  • proof : Proof sketch
  • Lemma 5.4
  • Lemma 5.5
  • Proposition 6.1: Round-Trip Minimum
  • ...and 3 more