Faster Than Light, According to the Arithmetic: code and analysis for two failure modes of streaming latency measurement

Abstract

Code, analysis and manuscript for a study of two failure modes of sub-millisecond streaming latency benchmarking, both governed by one ratio: the instrument's timescale over the interval being measured. Mode A (negative spans): a latency assembled from two stamps written by two threads can come out negative. The acknowledgment-referenced span is a proxy rather than a causal chain, because the broker's append precedes both branches and neither branch precedes the other; a negative value therefore does not prove impossible physics, it proves the reference stamp cannot serve as the origin of that event's interval. Applied as a sign check to every run, that rule rejected 1,321 of 2,266, including every run behind a statistically clean result we were about to publish. Over 738,730 events the acknowledgment-referenced span goes negative 62,264 times while the send-referenced span, which is a genuine chain, never does, on one clock by construction. The mechanism is scheduling, not clock skew, established by manipulation: real-time priority on the stamping threads collapses the rate 7 to 80x at fixed utilisation, and two core geometries at identical utilisation differ by 2.07x. Mode B (deletion): the OpenMessaging Benchmark silently deletes every sample whose millisecond-quantised difference is not positive. Across 223 instrumented runs it computed its reported distribution from 0.36% to 100% of the samples it took, reporting the same median either way. Retention obeys a grid law in the reduced fraction of send interval over timestamp quantum, confirmed by a pre-registered payload manipulation, reproduced by a 200-line Python harness with no JVM, and measured across two clocks. The sign channel caught 41,403 genuine one-tick negatives being absorbed by the same guard. What changed in v2.7. A co-author, a title, and the first sustained pass at explaining the system before making claims about it. (1) David Gregg joins as an author, and the record takes the manuscript's new title — both of which this record had wrong until now. (2) The system is drawn before any claim is made about it: a figure inside the first two pages showing which threads do the benchmark's work, which record times, and how the two groups interact. A companion figure that had drawn a single producer lane for eight rounds, contradicting the project's own pre-registration, now separates the two stamping threads. (3) The word interval is retired for the timing sense and flight defined in its place, ahead of its first use. (4) Mode B is generalised: the failure is a quantum destroying a sample, of which the OpenMessaging Benchmark's positivity guard is one mechanism. An audit of the harnesses practitioners actually run — SPECjms2007, the Kafka bundled tools, RabbitMQ PerfTest, nats bench and Redpanda rpk — records what each does about resolution and sign. (5) The 1/D law is stated where it is argued: the displacement is a scheduling quantity and does not grow because a message travelled further, so the relative error falls as 1/T, and two identical systems whose clients stamp in different places are separated by the difference of their lags. The exposure curve now reaches below the crossover at which the displacement exceeds the path it is a correction to — which is where published sub-millisecond broker medians sit — and the curve is stated to apply to acknowledgment-referenced spans only, a harness that subtracts a send stamp being off it entirely. (6) One estimate changed. Unlike v2.6, this release moves a number: ρ(D, A) was computed from a variance identity on three separately binned, edge-truncated margins, did not conserve, and was not bounded — returning |ρ| > 1 on five of seventy conditions. It is now a windowed Pearson correlation on paired co-moments, with excluded pairs counted rather than dropped in silence. (7) Author biographies; the manuscript held at twelve pages with the displaced material in a supplement that grew to 49; and every quantity in the exposure discussion moved out of the prose and into the emitter, so the sentence a reader quotes and the table it summarises can no longer disagree. The test suite is now 3,866 tests at 100% branch coverage, up from 3,650. The archive contains the instrumentation, every campaign script and ledger, the analysis suite that recomputes the manuscript's numbers from committed data and fails if paper and data disagree, the manuscript, and its supplement. A SHA256SUMS manifest lists every file in the archive so any single file can be verified independently of the zip. Data note. No StatsBomb event data is redistributed. Replay plans derived from it are excluded from this record and regenerable byte-for-byte from a pinned upstream commit with the included scripts. Licence carve-out. The code is released under the MIT Licence, and the data compilation and documentation in this record under CC BY 4.0. The manuscript files (paper.pdf, paper.tex, supplement.pdf, supplement.tex) are © the authors, are expressly not released under CC BY, and are included here as a data complement pending journal publication. This record is not a preprint venue; the preprint is on arXiv and will be linked as a related identifier on announcement.