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Paul Borrill

Publications and source records attributed to Paul Borrill.

At least 19 recordsLinked to original sources
arXiv2026

Why Synchronized Time is a Fiction: Daylight Saving Time, Leap Seconds, and the Guillotine Sharpened for Nothing

Civilization maintains an elaborate infrastructure devoted to the maintenance of synchronized time. Governments mandate daylight saving time. Standards bodies insert leap seconds into Coordinated Universal Time. Engineers debate leap milliseconds and leap nanoseconds. The Global Positioning System applies relativistic corrections at the nanosecond level. All of these adjustments attempt to preserve an assumption: that a single global time exists and that clocks can be made to agree upon it. This paper argues that this assumption constitutes a category mistake in the sense of Ryle (1949). We show that special and general relativity prohibit absolute simultaneity, that the one-way speed of light is conventionally defined rather than measured, and that recent experiments on indefinite causal order demonstrate nature admits correlations with no well-defined temporal sequence. We trace the consequences of this category mistake through distributed computing, where it manifests as the Forward-In-Time-Only (FITO) assumption that underlies Lamport's logical clocks (1978), the impossibility results of Fischer-Lynch-Paterson (1985), and the CAP theorem (2000). From this perspective, daylight saving time and leap seconds are not corrections to time but corrections to conventions -- they sharpen the guillotine of synchronization in preparation for executing something that does not exist.

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arXiv2026

The Bilateral Efficiency of Ethernet: Recalibrating Metcalfe and Boggs After Fifty Years

In July 1976, Metcalfe and Boggs published their foundational paper on Ethernet in Communications of the ACM. Their efficiency model -- E = (P/C)/(P/C + W*T) -- measures the fraction of Ether time carrying good forward packets under contention. For fifty years this model has framed how the community thinks about Ethernet performance. We argue it is silent on the question that matters for modern intra-rack interconnect: bilateral transaction efficiency -- the fraction of link time that produces committed agreements between sender and receiver. Metcalfe and Boggs themselves planted the seed in their EFTP "end-dally" protocol (Section 7.2.2), and the deeper anchor is older still: Abramson's Alohanet carried positive acknowledgments at the link layer -- a bilateral mechanism Metcalfe consciously removed in 1973 to obtain Ethernet's simple, ACK-free packet format. The result is a fifty-year bilateral zigzag: Aloha (bilateral) to Ethernet (unilateral) to the EFTP end-dally (bilateral) to TCP (unilateral-with-bilateral-above). We formalize bilateral efficiency, connect it to the back-to-back Shannon channel with Perfect Information Feedback, and -- scoping the claim explicitly to intra-rack distances of one meter or less -- describe how the Open Aethernet link recovers mutual knowledge at the link layer. The correction to Table 1 is not a different set of numbers. It is a different question.

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arXiv2026

The Markovianity of Time: The Category Mistake in Open Quantum Systems

The Markov approximation is arguably the most ubiquitous tool in physics, underpinning quantum master equations, stochastic processes, and -- via Shannon's channel model and Lamport's logical clocks -- the foundational assumptions of distributed computing. It is widely assumed that Markovianity inherently implies temporal asymmetry: that the Markov property is a forward-in-time-only (FITO) construct. We show that this assumption is a category mistake in the sense of Ryle (1949). Guff, Shastry, and Rocco (2025) have recently demonstrated that the Markov approximation applied to the Caldeira-Leggett model -- a paradigmatic open quantum system -- maintains time-reversal symmetry in the derived equations of motion. The resulting time-symmetric formulations of quantum Brownian motion, Lindblad master equations, and Pauli master equations describe thermalisation that can occur in two opposing temporal directions. Asymmetry arises not from the dynamics but from boundary conditions. We trace how Markovianity's assumed directionality propagated from physics through Shannon's information theory to Lamport's happens-before relation and the impossibility theorems of distributed computing (FLP, CAP, Two Generals). Each step encodes FITO as convention, then treats it as physical law -- the same category mistake repeated across domains. The Surrey result establishes that this conflation is not merely philosophically suspect but mathematically unnecessary: the most fundamental approximation used to derive irreversibility is itself time-symmetric.

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arXiv2026

The Forward-In-Time-Only Assumption in SmartNIC Resource Management: A Critique of Wave and the Case for Bilateral Interaction

The datacenter industry is converging on SmartNIC-based resource management. Wave (Humphries et al., ASPLOS '25) demonstrates the practical feasibility of offloading kernel thread scheduling, memory management, and RPC stacks to the ARM cores of Intel's Mount Evans Infrastructure Processing Unit (IPU). The engineering is careful and the results are honest: without Wave's PCIe latency mitigations, offloaded workloads degrade by 350%. We argue that this 350% degradation is not an engineering problem to be optimized away but a diagnostic symptom of a deeper architectural issue: Wave's communication model is Forward-In-Time-Only (FITO). Every interaction between host and SmartNIC is a unidirectional message -- event forward, decision back -- creating a temporal vulnerability window in which decisions can become stale before they are enforced. Wave's entire optimization stack (write-combining page table entries, prestaging, prefetching, atomic transaction abort) exists to hide or tolerate this window. We apply the FITO diagnostic to Wave's architecture systematically, identify the category mistake it inherits from Lamport's happened-before and Shannon's channel model, and show how Open Atomic Ethernet's bilateral swap primitive -- implemented on the same Intel IPU hardware -- dissolves the latency, atomicity, and timeout problems without engineering around them. The SmartNIC is the right location for resource management; what is missing is the right communication primitive at that location.

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arXiv2026

Link Wars: The Semantic Crisis. Is the debate over or is it just beginning?

For fifty years, networking has fragmented whenever new workloads exposed hidden assumptions about time, ordering, failure, and trust. This paper argues that the current interconnect landscape -- NVLink, UALink, Ultra Ethernet, AELink/Aethernet, TTPoE, and classical RDMA -- suffers from a semantic crisis: vendor-specific divergence disguised as optimization. We trace this crisis to the Forward-In-Time-Only (FITO) category mistake embedded in every major fabric stack, and show how each pathology -- aspirational RDMA completion, fire-and-forget GPU semantics, opaque proprietary stacks, incompatible multi-cloud ordering, universal fencing -- arises from the same failure to define explicit, testable link semantics from APIs to bits on the wire. We conjecture that RDMA achieves reliability through universal fencing that collapses concurrency into serialized checkpoints, and that precise minimal semantics can maintain correctness without global barriers, as superscalar architectures separated execution from retirement. We describe how Open Atomic Ethernet (OAE) under the Open Compute Project addresses the crisis through bilateral transaction primitives with explicit ordering, completion, and failure visibility. Drawing on Helland's analysis of scalable OLTP isolation (the "BIG DEAL"), we show the crisis pervades the entire stack. We assess whether convergence on a single open standard is still possible or whether fragmentation is now structural.

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arXiv2026

Background and Intellectual Development: Supplementary Material for the Category Mistake Papers

This supplement documents the intellectual trajectory that led to the Category Mistake framework and the Forward-In-Time-Only (FITO) analysis presented in our recent arXiv papers. The ideas crystallized over fifteen years of research, conversation, and engineering practice -- beginning with a 2014 Stanford EE380 lecture on the physics of time in computing, sharpened through a 2016 email exchange with Leslie Lamport following a Papers We Love presentation of his seminal 1978 paper, and matured through the development of Open Atomic Ethernet (OAE). This document traces the concept development from its origins in the physics of entanglement and background-free time, through the recognition that Lamport's "happened-before" relation embeds a category mistake, to the practical engineering consequences documented in "Why iCloud Fails" and "What Distributed Computing Got Wrong." It is intended as archival supplementary material for future arXiv submission.

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arXiv2026

The Semantic Arrow of Time, Part III: RDMA and the Completion Fallacy

This is the third of five papers comprising The Semantic Arrow of Time. Parts I and II identified computing's hidden semantic arrow of time, the FITO category mistake, and presented the constructive alternative: the OAE link state machine with its mandatory reflecting phase. This paper examines what happens when those principles are violated at industrial scale. Remote Direct Memory Access (RDMA) is the highest-performance data movement technology in production, deployed across Meta's 24,000-GPU clusters, Google's data centers, and Microsoft's Azure infrastructure. We argue that RDMA's completion semantics contain a category mistake: they guarantee placement (data written to a remote NIC buffer) but not commitment (data semantically integrated by the receiving application). We call this the completion fallacy. We document the fallacy through seven temporal stages of an RDMA Write operation, showing that the gap between completion signal and application semantic satisfaction can be arbitrarily large. We trace consequences through four case studies: Meta's RoCE fabric, Google's 1RMA redesign, Microsoft's DCQCN failures, and SDR-RDMA partial completions. A comparative analysis shows CXL 3.0, NVLink, and UALink each address parts of the completion fallacy but none eliminates it entirely. Only a protocol architecture with a mandatory reflecting phase can close the gap between delivery and commitment.

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arXiv2026

The Semantic Arrow of Time, Part IV: Why Transactions Fail

This is the fourth of five papers comprising The Semantic Arrow of Time. Parts I-III established that computing's hidden arrow of time is semantic rather than thermodynamic, that bilateral transaction protocols create causal order through a mandatory reflecting phase, and that RDMA's completion semantics implement the FITO category mistake at industrial scale. This paper traces the consequences of the FITO category mistake beyond the data center, into systems people use every day. We examine three domains where forward-only temporal assumptions destroy meaning: file synchronization, where cloud platforms silently delete user content because last-writer-wins cannot represent distributed causality; email, where timestamp-based ordering produces phantom messages, causality violations, and stuck synchronization; and memory--both human and artificial--where reconstructive processes that operate without transactional guarantees produce systematic semantic corruption. In each domain, we identify the same structural pattern: a system that commits state changes forward in time without a reflecting phase, and that therefore cannot distinguish between successful semantic integration and mere temporal succession. The pattern is not coincidental. It is the FITO category mistake operating at different scales: bytes in a NIC buffer, files in a cloud, messages in an inbox, engrams in a hippocampus, tokens in a transformer. We conclude that the semantic arrow of time is violated whenever a system treats the forward flow of information as sufficient evidence of meaning. Part V will show how the Leibniz Bridge provides a unified framework for closing this gap across all five domains.

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arXiv2026

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

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.

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arXiv2026

The Ghost in the Datacenter: Link Flapping, Topology Knowledge Failures, and the FITO Category Mistake

A link changes state faster than knowledge of that change can reach every component that acts on it. During the interval in between, some observer operates on a topology that no longer exists. We call that mismatch a ghost: for observer i, a ghost exists whenever the connectivity state on which i acts differs from the connectivity actually available to it. Ghosts appear wherever this delay does -- PCIe and UCIe, NVLink and NVSwitch, Ethernet and Thunderbolt, IP and BGP. What the mechanisms we survey have in common is narrower than a shared ancestry: in each, failure state is at some point inferred from absence, elapsed time, probing, or eventual convergence, and absence alone does not distinguish delay from loss, partition, or endpoint failure. We survey the scale of the problem with production data from Meta, ByteDance, Google and Alibaba, and reproduce an industry scaling projection -- attributed, and not our own measurement -- under which a fabric of more than ten million optical links sees an aggregate flap roughly every 48 seconds. The mitigations surveyed reduce the interval, often substantially, but each retains a period in which failure state is inferred rather than established. We then examine Open Aethernet (OAE), whose distinctive move is asymmetric: a completed transaction yields positive, mutually held evidence, while absence of completion is not treated as identification of a failure but recorded as an explicit IN-DOUBT state, resolved by corroboration where the topology permits. We are explicit about what this does not claim. OAE does not eliminate uncertainty; it makes it first-class. It does not repair a hard partition; detection is not repair; its detector latency is uncharacterised; triangle coverage is assumed rather than proved; we report no OAE measurement; and we do not claim common knowledge in the epistemic-logic sense.

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arXiv2026

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

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.

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arXiv2026

Why Atomicity Matters to AI/ML Infrastructure: Snapshots, Firmware Updates, and the Cost of the Forward-In-Time-Only Category Mistake

Large-scale AI/ML training systems depend on two assumptions that are rarely examined: (1) that checkpoints represent atomic snapshots of global training state, and (2) that infrastructure updates can be applied without inducing mixed-protocol cluster states. Both assumptions are instances of a deeper structural error: the Forward-In-Time-Only (FITO) category mistake, which confuses protocol convergence properties with temporal predicates. We formalize this confusion as a type error: the identification of a temporal snapshot $\mathsf{Snap}(t)$ with a convergence property $\mathsf{Conv}(\mathcal{P},e)$. We model checkpoint execution in a process-algebraic framework and prove that under asynchronous composition with crash-recovery failures, no temporal instant can serve as an atomicity boundary. We reformulate checkpoint inconsistency on an epoch lattice and show that atomicity is a measure-zero event whose complement grows exponentially with the number of independent persistence domains. We formalize mixed-epoch recovery as a type violation in the optimization algebra and show that the resulting update is not a valid step of any standard optimizer. For firmware fleet updates, we strengthen the known consensus-hardness result: atomic deployment requires not merely agreement but common knowledge of the epoch transition, which is strictly unattainable in asynchronous systems with unreliable communication. We conclude by sketching a bilateral convergence protocol, inspired by Open Atomic Ethernet, that achieves $\mathsf{Conv}(\mathcal{P},e)$ without requiring $\mathsf{Snap}(t)$ -- replacing the FITO assumption with constraint semantics.

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arXiv2026

Bisynchronous FIFOs and the FITO Category Mistake: Silicon-Proven Interaction Primitives for Distributed Coordination

Bisynchronous FIFOs -- hardware buffers that mediate data transfer between independent clock domains without a shared global timebase -- have been designed, formally verified, and commercially deployed in silicon for over four decades. We survey this literature from Chapiro's 1984 GALS thesis through Cummings's Gray-code pointer techniques, Chelcea and Nowick's mixed-timing interfaces, Greenstreet's STARI protocol, and the 2015 NVIDIA pausible bisynchronous FIFO, and argue that this body of work constitutes a silicon-proven existence proof against the Forward-In-Time-Only (FITO) assumption that pervades distributed systems. The central claim is that interaction-based synchronization primitives -- handshakes, mutual exclusion, and causal flow control -- can replace timestamp-based coordination at the most demanding levels of digital engineering, directly undermining the FITO assumption in protocols such as PTP, TSN, and conventional Ethernet. We draw a structural parallel between on-chip bisynchronous coordination and the Open Atomic Ethernet (OAE) architecture, and identify the handshake -- not the timestamp -- as the fundamental primitive for coordination between independent causal domains.

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arXiv2026

Unix Tools and the FITO Category Mistake: Crash Consistency and the Protocol Nature of Persistence

Unix tools such as ls, cp, mv, and rename expose a filesystem abstraction that appears to present a single, authoritative state evolving through atomic transitions. This abstraction is false. We present a systematic Forward-In-Time-Only (FITO) analysis demonstrating that the assumption of instantaneous atomic state transitions constitutes a category mistake at every layer of the computing stack -- from ext4 journaling and delayed allocation, through fsync failure semantics, NVMe Flush/FUA device behavior, and Linux restartable sequences, down to the x86-64 CPU's own inability to guarantee atomic supervisor entry under Non-Maskable Interrupts. We prove a formal impossibility result: no syscall-based persistence primitive can define a commit boundary under failure, because the syscall return value is consistent with multiple materially different persistence states across Linux filesystems. We identify cross-layer temporal assumption leakage as the structural mechanism by which the category mistake propagates, and show that the entire storage stack forms a recursive chain of non-atomic dependencies whose apparent atomicity reflects mathematical impossibility (Herlihy, 1991), not merely engineering deficiency. An appendix documents the real-world consequences: cascading cloud outages at Google, AWS, Meta, and Cloudflare driven by retry amplification; database corruption from fsync failures in PostgreSQL, etcd, and MySQL; silent data corruption at CERN, NetApp, and Meta; AI training waste consuming 12--43% of compute budgets at scale; and financial system failures totaling billions of dollars annually. These consequences trace to a single structural cause: systems designed around the FITO assumption, compensating for its failure with retry-and-recover protocols that amplify the very failures they attempt to mask.

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arXiv2026

Message Passing Without Temporal Direction: Constraint Semantics and the FITO Category Mistake

Message passing is widely assumed to be a fundamental primitive of distributed systems. This paper argues that conventional message systems embed a category mistake: they misinterpret logical dependency relations as temporal propagation processes. This error arises from an implicit Forward-In-Time-Only (FITO) assumption, which treats causality as intrinsically directed along a temporal axis. We formalize FITO as the imposition of a partial order over events and show that clocks, scheduling, and message propagation are representational artifacts rather than ontological primitives. We then reformulate interaction in terms of symmetric constraint relations, identify the minimal substrate of interaction independent of temporal direction, and prove an equivalence theorem: under mild assumptions, a broad class of message-passing executions can be represented as constraint satisfaction problems, and conversely, constraint satisfaction instances can be realized as message-passing protocols. We connect the result to Lamport clocks, Hewitt actors, Pratt pomsets, category theory, relativity, and indefinite causal order, and interpret engineering consequences for reflective and reversible link architectures such as Open Atomic Ethernet.

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arXiv2026

The Semantic Arrow of Time, Part I: From Eddington to Ethernet

This is the first of five papers comprising The Semantic Arrow of Time. The argument begins with a claim: computing's arrow of time is semantic, not thermodynamic. The direction in which meaning is preserved or destroyed across transactions is not a consequence of the second law but of design choices embedded in protocol architectures since Shannon's 1948 channel model. These choices encode the Forward-In-Time-Only (FITO) assumption -- the commitment that causation is irreversible, acyclic, and globally monotonic. We trace this assumption from Eddington's 1927 coinage of "the arrow of time," through the Boltzmann--Loschmidt debate, to contemporary philosophy of physics: Price's time-symmetric ontology, Smolin's temporal naturalism, Rovelli's relational quantum mechanics, and Roberts's analysis of time-reversal symmetry. We show that fundamental physics is time-symmetric at the microscopic level, that the thermodynamic arrow emerges from boundary conditions rather than fundamental law, and that recent demonstrations of indefinite causal order confirm nature admits correlations with no well-defined temporal ordering. We then identify the category mistake (Ryle, 1949): computing inherited Newton's absolute background time -- via Shannon, Lamport, and the impossibility theorems -- and encoded it as a semantic primitive. The FITO assumption is not a law of nature but a design choice, and recognizing this dissolves apparent constraints that have shaped forty years of distributed systems theory. Subsequent papers develop the constructive alternative through link semantics, RDMA, transaction failures, and the Leibniz Bridge framework.

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arXiv2026

Lamport's Arrow of Time: The Category Mistake in Logical Clocks

Lamport's 1978 paper introduced the happens-before relation and logical clocks, freeing distributed systems from dependence on synchronized physical clocks. This is widely understood as a move away from Newtonian absolute time. We argue that Lamport's formalism retains a deeper and largely unexamined assumption: that causality induces a globally well-defined directed acyclic graph (DAG) over events -- a forward-in-time-only (FITO) structure that functions as an arrow of time embedded at the semantic level. Following Ryle's analysis of category mistakes, we show that this assumption conflates an epistemic construct (the logical ordering of messages) with an ontic claim (that physical causality is globally acyclic and monotonic). We trace this conflation through Shannon's channel model, TLA+, Bell's theorem, and the impossibility results of Fischer-Lynch-Paterson and Brewer's CAP theorem. We then show that special and general relativity permit only local causal structure, and that recent work on indefinite causal order demonstrates that nature admits correlations with no well-defined causal ordering. We propose that mutual information conservation, rather than temporal precedence, provides a more fundamental primitive for distributed consistency.

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arXiv2026

Engineered Simultaneity: The Physical Impossibility of Consolidated Price Discovery Across Spacelike-Separated Exchanges

We define \emph{engineered simultaneity}: the construction of a system that requires temporal comparison of events at spacelike-separated locations, implements this comparison via an implicit simultaneity convention, and represents the result as an objective measurement rather than a conventional choice. We show that the National Best Bid and Offer (NBBO) -- the regulatory cornerstone of U.S. equity markets -- is an instance of engineered simultaneity. The NBBO requires determining ``current'' prices across exchanges whose spatial separation places their price events outside each other's light cones. Special relativity proves that the temporal ordering of such events is frame-dependent: there exist inertial reference frames in which the NBBO differs from the value reported by the Securities Information Processor. The impossibility is not approximate; it is exact and unavoidable within the causal structure of Minkowski spacetime. General relativity compounds the impossibility: gravitational time dilation introduces frame-rate discrepancies between exchanges at different altitudes, and recent work on indefinite causal order in quantum information theory undermines the premise of a fixed causal structure altogether. We formalize the special-relativistic argument using the causal precedence relation, connect it to Lamport's theorem on distributed ordering, and note that approximately \$5~billion per year in latency arbitrage profits are extracted from the gap between the NBBO's implicit simultaneity convention and physical reality.

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