Measuring an absence: instrument characterization and validation architecture for a finite-window spectral programme

In memory of Mykhailo Novikov and Mykhailo Palamarchuk, killed in the war. This work is written in their memory. This paper reports the validation architecture of a single-author computational programme measuring the spectrum of Riemann zeta zeros in finite windows, and what that architecture caught. The programme's technical results are reported separately. What is reported here is the apparatus: how a finite-window spectral instrument was characterized before use, how its validation was decomposed into four stages — generator, analysis operator, statistic, inference — each with its own class of defect and its own detection method, and what happened when the validation layer was itself treated as an instrument and audited. The architecture was not designed as a methodological framework and then demonstrated on a case. Its components were introduced sequentially, each one in response to an observed failure. The defect log, deposited with the paper, contains thirty-two entries as of 9 October 2026, of which five were found by a reviewer who had not seen the work being produced and the rest inside the programme; eleven are claims withdrawn after having been stated. The log states on its first page that it is a compilation rather than a contemporaneous logbook, which fields were not recorded at the time, and which classifications are a later reading. The count moves as the programme continues, so the argument is built not on the number but on the six recurrent patterns of Section 7.4, which stabilised after the first twenty entries: none of the twelve entries since has required a seventh. The six are — a limit of one's own postulation reported as a property of the object; statistic and reference computed on different sets; a null model lacking a structure the signal possesses; multiple comparisons; drift of the input; and a claim reported without the computation that would establish it. Each is stated with the question that tests for it, because a pattern is only useful if a reader can apply it to data that are not ours and report whether the question was answerable with a number. The central argument is that when the true answer is not directly accessible, validation itself becomes a measuring instrument — and an instrument that can create, conceal, or destroy a result. Section 5 treats the least-examined case: a correct result suppressed by its own validation, which leaves no artefact available for inspection. Section 6 argues that the resulting regress is operationally bounded: the taxonomy is reusable at every level, but detection at a higher level may still require an observer who is not the author. Reported in full: what was withdrawn, why, and who found it. Four defects required a reader who was not the author — three found by one external model and one by another, all four within a single evening — and one of those four was an error inside the acceptance document written that same day to prevent errors of its own class. One pre-specified prediction failed, and Section 7.3 treats it as the most informative single result in the paper: a functional relation, broken consistently in one direction across all nine configurations, reported the direction and shape of the failure in a way that a pre-specified interval could not. A statement on the use of AI systems is included in the paper.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-10-09
DOI
https://doi.org/10.5281/zenodo.23262156
Primary Topic
Analytic Number Theory Research
Type
article
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article

Measuring an absence: instrument characterization and validation architecture for a finite-window spectral programme

Serhii Kanivets
Zenodo (CERN European Organization for Nuclear Research)
Analytic Number Theory Research
article

Measuring an absence: instrument characterization and validation architecture for a finite-window spectral programme

Serhii Kanivets
article en

Abstract

In memory of Mykhailo Novikov and Mykhailo Palamarchuk, killed in the war. This work is written in their memory. This paper reports the validation architecture of a single-author computational programme measuring the spectrum of Riemann zeta zeros in finite windows, and what that architecture caught. The programme's technical results are reported separately. What is reported here is the apparatus: how a finite-window spectral instrument was characterized before use, how its validation was decomposed into four stages — generator, analysis operator, statistic, inference — each with its own class of defect and its own detection method, and what happened when the validation layer was itself treated as an instrument and audited. The architecture was not designed as a methodological framework and then demonstrated on a case. Its components were introduced sequentially, each one in response to an observed failure. The defect log, deposited with the paper, contains thirty-two entries as of 9 October 2026, of which five were found by a reviewer who had not seen the work being produced and the rest inside the programme; eleven are claims withdrawn after having been stated. The log states on its first page that it is a compilation rather than a contemporaneous logbook, which fields were not recorded at the time, and which classifications are a later reading. The count moves as the programme continues, so the argument is built not on the number but on the six recurrent patterns of Section 7.4, which stabilised after the first twenty entries: none of the twelve entries since has required a seventh. The six are — a limit of one's own postulation reported as a property of the object; statistic and reference computed on different sets; a null model lacking a structure the signal possesses; multiple comparisons; drift of the input; and a claim reported without the computation that would establish it. Each is stated with the question that tests for it, because a pattern is only useful if a reader can apply it to data that are not ours and report whether the question was answerable with a number. The central argument is that when the true answer is not directly accessible, validation itself becomes a measuring instrument — and an instrument that can create, conceal, or destroy a result. Section 5 treats the least-examined case: a correct result suppressed by its own validation, which leaves no artefact available for inspection. Section 6 argues that the resulting regress is operationally bounded: the taxonomy is reusable at every level, but detection at a higher level may still require an observer who is not the author. Reported in full: what was withdrawn, why, and who found it. Four defects required a reader who was not the author — three found by one external model and one by another, all four within a single evening — and one of those four was an error inside the acceptance document written that same day to prevent errors of its own class. One pre-specified prediction failed, and Section 7.3 treats it as the most informative single result in the paper: a functional relation, broken consistently in one direction across all nine configurations, reported the direction and shape of the failure in a way that a pre-specified interval could not. A statement on the use of AI systems is included in the paper.

Zenodo (CERN European Organization for Nuclear Research)
Openalex Percentile: Top 4%
Analytic Number Theory Research
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