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Asymmetric-Loss Equal-Born Test: proposal for a host laboratory and first-run equipment list

Robert James Cecil, Mark Trewick

Published Oct 26, 2026• 0 citations
Publisher

Abstract

Why this measurement is worth a bench: see section 2 of the proposal, "Why anyone should want to measure it". Contact: concursion.alebt@gmail.com. Two companion documents to the deposited paper, doi:10.5281/zenodo.22678044, and its pre-registration, osf.io/3h6yf. The question: does a 50/50 beam splitter transmit a single photon in exactly the same proportion as it transmits bright light? Standard linear optics says yes, exactly. The first run compares the two to one part in a thousand, with one source; only a calibrated attenuator changes between the bright phase and the single-photon phase. ALEBT_proposal_paper_v1_oct20.pdf: the proposal written for a host laboratory (the observable, the hypothesis, the error budget, the stages, the equipment and the open problems). ALEBT_equipment_list_v2_oct26.pdf: the first-run equipment list, with answers to the questions raised by groups we have written to (existing measurements, fibre-coupled detectors, differences between detectors).

DOI
10.5281/zenodo.23675936

Related papers

Asymmetric-Loss Equal-Born Test: a tabletop search for record-information-dependent optical loss

Robert James Cecil, Mark Trewick

Standard linear optics requires that the transmittance of an optic be independent of photon number: for a linear element the input–output relation a_out = t·a_in + r·b_in is an operator identity, so single-photon and bright-light transmission are equal as a theorem rather than as an approximation. We are not aware of a dedicated test of that equality with a controlled scatterer at the 10⁻⁴ level. We state a hypothesis in which the equality fails in the single-quantum sector by a fixed dimensionless coupling λ*, and specify the tabletop experiment that would exclude it. The observable is Δ = D_quantum − D_classical, where D is the half-difference of a two-arm log-ratio under an ABBA swap of a weak scatterer, measured once with counting detectors and once with photodiodes through identical geometry. Standard quantum mechanics fixes Δ = 0 exactly; the hypothesis predicts Δ = −λ*·(−p ln p), or −0.046·λ* at a 1% transmission deficit. The loss map is stated as a photon-number-dependent Kraus channel, K = Σ exp[−½λ*·I_R(n)]|n⟩⟨n| with P_R(n) = 1 − (1−p)^n, which is linear, completely positive, local and non-signalling; invariance of a remote marginal is verified explicitly on a two-mode squeezed vacuum to 3×10⁻¹⁷. An earlier thermal formulation of the same idea is excluded by published SNSPD efficiency data at 2 K by a factor of 2×10⁵ and is withdrawn. An attempt to derive the criterion distinguishing which optical elements incur the cost failed under independent adversarial review and is reported as a failure; the surviving readings are converted into five pre-registered experimental arms with their nulls stated in advance. A borrowed teaching bench at 780 nm reaches a total uncertainty of 2.9×10⁻⁴ per operating point at 2×10⁸ counts, giving 5σ sensitivity at λ* ≥ 0.031 and 95% exclusion to 0.013 at a 1% scatterer; an extended scan through the turnover at p = 36.8% reaches 0.0039 and 0.0016 respectively, subject to a costed high-loss error-budget row and seven stated pass criteria. Five signatures distinguish the effect from systematics, including a −p ln p scaling and a maximum located at p = 0.368. The cheapest arm needs no interferometer: the single-photon versus bright transmission of one 50/50 beam splitter at 10⁻³, which bounds one reading of the hypothesis below λ* = 0.003 in an afternoon’s run on a prepared bench. The protocol is pre-registered before any bench is borrowed. The result will be published in either direction; a null is reported as the best bound in this sector.

•Sep 9, 2026•0 citations

Asymmetric-Loss Equal-Born Test — Supplements 1 and 2: the Pre-Bench Closure with its postscripts, and the high-loss error-budget row with its adversarial referee report

Robert James Cecil, Mark Trewick

Two working documents that the deposited paper (Draft 4, v1.0; DOI 10.5281/zenodo.22678044; printed title The Asymmetric-Loss Equal-Born Test: a pre-registered search for record-information-dependent optical loss) cites and undertakes to deposit alongside it. They are deposited here as they stood on September 7, 2026, the day Draft 4 was completed, each with a dated deposit note at its head; nothing beneath the note is altered. Supplement 1 — Pre-Bench Closure (September 4, 2026), with postscript layers of September 6 and 7. The arithmetic companion to the paper. Part A runs the no-signalling check on the programme's surviving statement, finds that the normalised form permits superluminal signalling and is excluded, and records the single repair — a loss channel — that leaves the bench prediction numerically unchanged and converts the hypothesis from a nonlinear modification of the Born rule into a linear one. Part B carries the consequences into the protocol: the turnover of −p ln p at p = 1/e and the extended scan that would see it, a fourth signature, the cost of the high-loss points, the total-rate observable, the absorber control with its prediction stated in advance, and the consolidated protocol amendments. Part C makes the structural repairs: locating the branching event, the J-conservation contradiction, and the cost functional, with both candidates carried and the location of the peak left to decide between them. Part D drafts the pre-registration and scores the open tasks. The September-6 layer, headed "Postscript — September 5–6", records the two independent referee passes (one blind, one adversarial), the photon-number-dependent loss map, the derivation of the record criterion put to a third referee instructed to kill it and killed on twelve counts, the pre-registered arms and the correction of a handover error; the addendum of September 7 records the closing of the high-loss row. 17 pages. Supplement 2 — The high-p row: proposal, adversarial pass, and the row as costed (September 7, 2026). The error-budget row for the extended scan (p = 10%, 36.8%, 60% and 70%) that the paper's §9 named as the single item blocking pre-registration of the extended points, kept in the three steps by which it was reached. Appendix A is the first-pass proposal exactly as written for review, errors included. Appendix B is the report of an independent adversarial referee instructed to kill it, verbatim: eight errors and six systematics the first pass had not carried. Appendix C is the row as costed after every finding was re-derived and accepted, with the seven pass criteria written into the pre-registration. Its findings: the reach at the turnover (5σ at λ* ≥ 0.0039, 95% exclusion to 0.0016) stands only under the seven criteria; the bright-phase thermal family has the sign of the predicted anomaly and is bounded by a power-dependence test stated in advance; the far point of the scan moves from 70% to 60%; and the extended scan is research-group metrology, not teaching-laboratory work. 25 pages with its deposit note. The coloured highlights in Supplement 1 are its dated layers (rose, September 6; periwinkle, September 7; sky, the deposit note of September 16, 2026), each explained at its head. The line "Not for deposit" on the cover of Supplement 2 recorded the authors' working practice on September 7 and is superseded by the deposit note above it; the paper's Draft-4 note undertakes to deposit the document. The reconciliation document the paper also cites is the programme's working record, still being expanded, and is available from the authors.

•Sep 16, 2026•0 citations

Not at a distance, but nowhere: non-locality beyond entanglement, in twelve phenomena

Ugo Lanciano

This record. Twelve phenomena, entanglement among them, read through the same non-local phase: «non-local» as not located in space and time, not as action at a distance. Reading path: Foundations: why the laws hold, 5 of 5 · before: Is mass a contained rhythm? · all themes. Common introduction to all the records of this series. The content of this record follows below. Mathematical Materiality (MM) in brief. Why are the laws of physics the same everywhere and at every instant, even though nothing forces matter to obey them? MM proposes an answer: the laws are not rules imposed on matter from the outside; rather, matter itself is made of mathematical relations. And mathematics cannot change: a relation binds two distinct terms everywhere and always. In logic, nothing exists on its own: to exist means to be in relation to another logical entity, and outside this web of relations nothing can exist, not even other universes. This reading already meets experimental measurements at two points. First, the ratio of dark to ordinary matter is read as 3√3 = 5.196; when left free in the fits, Planck and DESI DR2 data give 5.21–5.22 (as registered in record 2.44, https://doi.org/10.5281/zenodo.23329080). Second, the acceleration scale of galaxies is read as a₀ = cH₀/6, the same scale that appears in Verlinde's emergent gravity: the computed value is 1.09–1.18 × 10⁻¹⁰ m/s² against the measured value of 1.20 (record 2.46.1, https://doi.org/10.5281/zenodo.23506655). Both readings were formulated with the measurements already known; the tests to check them against future data are registered in the same records. In the first logical nexus between space and time — which became homogeneous with Einstein — there is a non-local phase, made only of a pure logical distinction: space is not time. Between the two there is no relation of quantitative calculation, only the logical entity they have in common, which is needed to make them exist with respect to each other. This level is not distant: it is present in every phase of reality, in every place and at every instant. It shows in entanglement, where two distant systems remain correlated more strongly than any explanation based on separate properties and free of faster-than-light influences allows, without anything physically travelling between them. In this non-local phase the two distinct terms, space and time, share only one logical element, which we shall call their greatest common divisor (GCD), just as the numbers 3 and 5 have only 1 in common. The local world arises when a relation is counted through this GCD: its multiples and its fractions form a matrix. Seen by an observer inside the system like us, the multiples appear as time and the fractions as space. When that same multiple is directly contained in the matrix of the point of observation, it turns into mass — that is, into concrete matter as we usually understand it. There is therefore a close link between time and mass, in full agreement with Einstein's relativity, which ties mass to spacetime. The observed objects, while being logically autonomous entities in their local relations, enter into relation with the observer through a logical diffraction — that is, a decomposition into fractions — of the observer's matrix. This reading also gives a reason for the limit of the speed of light, which in Einstein's relativity is instead taken as a starting principle. The speed of light is the fixed exchange rate between the multiples and the fractions of the same GCD, meaning how much space a single step of time is worth: exceeding it would mean, for some observer, covering space without counting time, and thus leaving the local world. Logic always starts from a logical relative, and this exchange rate has nothing absolute in itself either: it is a necessary relative which, inside the system, becomes an absolute hypothesis, the same for everyone and impossible to exceed. Outside the system, by contrast, it has no justification at all, because outside there is only non-existence: justifying something requires another term to relate it to, and out there there is none. Asking for a reason from outside is like asking what lies north of the North Pole. The same theoretical framework that reads space, time, mass and the observed objects also admits quantum mechanics. The non-local phase and the mirror-like logical reciprocity between the two ends of the nexus give a reason for the probabilistic behaviour of matter. When the observed object is large enough, its mass fixes it in the matrix of the point of observation: for this reason we see it in one precise place and at one precise instant. When instead the object falls below a certain mass threshold, the principal GCD (that of the point of observation) and the GCD of the diffraction that generates the object are forced to become equal, reflecting each other as in a mirror. At that point the object no longer occupies a single point of the spacetime generated by the observer, but spreads over several possible positions, and we observe it as probability. It is like having to describe the number 10 using only the number 1: the only way is to distribute the 1 over ten positions, one for each unit of the 10. Today we know that even objects made of thousands of atoms behave in this way, and no experiment has yet found the boundary. The idea that the passage from quantum to classical behaviour depends on mass is close to that of Penrose and Diósi; in MM the threshold is the point where the two GCDs, the principal one and that of the local diffraction, become equal. For all these reasons the universe behaves like a simulation without really being one. It follows exact rules, made of counts, everywhere and at every instant, but no machine runs them and no programmer wrote them: a structure of mathematical relations does not need to be computed in order to exist. Tegmark (2008) had already noted that such a simulation need not be run, while Vazza (2025) estimated that running it physically on a machine would require resources that the very laws of the universe do not allow. This record develops one aspect of the theoretical framework. The work is shared openly so that it can be judged by as many readers as possible: anyone who knows someone interested can pass on this single link, valid for the whole framework (with an overview in English and Italian): https://doi.org/10.5281/zenodo.23535916. The entry page, with the complete list of all records, is https://doi.org/10.5281/zenodo.22667516. To cite the framework: Lanciano, U. (2026). The number 1 in front of the mirror: Mathematical Materiality from the nexus to the cosmos. Zenodo. https://doi.org/10.5281/zenodo.23535916. The records have been deposited since 5 August 2026, each with its own date, and are released under CC BY 4.0: anyone may use them by citing the source. Objections and errors found are welcome at riverantares@gmail.com, since Zenodo has no space for comments. This record. In physics «non-locality» mostly names one fact: the correlations of entanglement. In Mathematical Materiality (MM) it is the foundation: a non-local phase, not located in space and time and present everywhere, of which the local world is the count made from a point. Here «non-local» means not located in space and time; it does not mean action at a distance. This record collects, from MM's published records and the author's premises, twelve phenomena in which MM's reading uses the same non-local phase as the reason, and shows that entanglement is the case in which it rests most directly on a measured datum, not the only one. There are no new calculations: the result is the unity of the reading. The twelve phenomena: the correlations of entanglement beyond Bell's limit, and their Tsirelson ceiling, set by the local reading (MM 2.48, 2.48.1); the same laws everywhere and always, as copies of the same nexus (MM 2.68); identical particles, as the same unit counted twice (a proposal of the AI); the objects two observers see alike, as two counts of one non-local relation (MM 2.62.1); the boundary of the local as a number of copies, not a distance (August status report, reread); probability and the Born rule (MM 2.48.1); the mass below which an object stops being at one point (MM 2.66); the present, and the loop in which the future chooses what is written (MM 2.48, 2.68.1); space and time themselves: a clock counting events without pre-assigned places runs at Einstein's proper time (MM 2.40.2); the limit of light, the same for everyone; dark matter as the ordinary matter of a second mirror, with no reciprocal non-local link to us (MM 2.44); the boundary within which a gravitating system reads only its own field, set by the Galaxy (MM 2.70). How each is set out. For every phenomenon: what is observed, with sources; how known physics reads it; what the non-local phase does; where the link comes from (already written in a deposit, a premise of the author, or a proposal of the AI); what rests on calculations already deposited; what remains open. In ten phenomena the link is already in the deposits or in the author's premises; in one it comes partly from the AI, and in one from the AI alone. Three ways organise them: copies without distance, existence through a link, and a reading that is always local and partial. What is not claimed. The non-local phase transmits no signals and no influences outside light cones. Today it has no distinct experimental signature: where MM gives numbers, they coincide with known physics (the Tsirelson bound, decoherence, wave optics) or come from readings with declared choices. The record also lists the other senses in which «non-local» appears in MM's records, so that they are not confused with this one. Where the reading is tested. Gaia DR4 in December 2026 (rules registered in MM 2.70) and the mass threshold, with a prediction dated 31 December 2035 (MM 2.66); five open questions from MM 2.68. Contents: REA

•Oct 28, 2026•0 citations

Getting used to quantum optics

Gerd Leuchs

The article reviews how to measure one and the same photon at both output ports of a beam splitter.

arXiv:1602.03019•Feb 9, 2016•4 citations

Output photon statistics for a beam splitter with input squeezed light

R.W.F. van der Plank, L.G. Suttorp

Optics Communications•Nov 1, 1994•7 citations

Pre-registration: a sidereal-modulation search in superconducting-qubit coherence (one qubit, one year)

Zachary Piech

This document fixes, before the data exist, the hypothesis, apparatus, observables, cadence, analysis, thresholds, controls, stopping rule and reporting commitment of a one-year search for a modulation of superconducting-qubit energy relaxation (T1) at the sidereal frequency, 1/(23 h 56 m 4.09 s), beyond what the solar day and its seasonal modulation can produce. Data collection began on 17 October 2026 at 16:42 UTC on qubit 9 of the IBM Heron processor ibm_fez: an eight-delay inversion-recovery T1 measurement every six hours (about 3 s of processor time each), with the device's calibration values polled hourly. The analysis is fixed in advance: a least-squares fit of a smooth drift plus sinusoids at the solar, sidereal, anti-sidereal and extended-sidereal frequencies, with the reported amplitude leakage-corrected as sqrt(A_sid^2 - A_anti^2) (Farley and Storey 1954). The pipeline was validated on synthetic data before the first measurement and recovers an injected 0.3% at 2.7-3.4 sigma while returning 0.5 sigma with nothing injected. Detection requires a leakage-corrected amplitude at or above 3 sigma, both control channels below 2 sigma, a phase stable between the two halves of the year, and survival when runs adjacent to calibrations are removed; otherwise the result is the 95% upper limit, expected near 0.3%. The search is declared inconclusive if fewer than 900 of 1460 scheduled runs succeed or the anti-sidereal control exceeds 3 sigma. An amplitude matching the known cosmic-ray anisotropy (~0.1%) is a calibration, not a discovery. Stopping rule: one year, with a six-month interim look at the controls only; a second year is pre-declared as the response to an inconclusive or 2-3 sigma outcome. The result will be reported whether it is a detection, a bound, or a failure of the apparatus. Standard physics predicts a null result at this sensitivity; the alternative hypothesis is from The Cosmic Page (doi:10.5281/zenodo.23287018, Ch. 13) and the research proposal doi:10.5281/zenodo.23201109. Included: the pre-registration (PDF and LaTeX source), the monitor script that runs on the device, the fixed analysis script, the synthetic-data validation script with its results and figure, and the README. First data point: job db9qap9gv2cc73e5tufg, 2026-10-17T16:42:19Z, T1 = 162.9 +/- 7.9 us.

•Oct 17, 2026•0 citations
Why this measurement is worth a bench: see section 2 of the proposal, "Why anyone should want to measure it". Contact: concursion.alebt@gmail.com. Two companion documents to the deposited paper, doi:10.5281/zenodo.22678044, and its pre-registration, osf.io/3h6yf. The question: does a 50/50 beam splitter transmit a single photon in exactly the same proportion as it transmits bright light? Standard linear optics says yes, exactly. The first run compares the two to one part in a thousand, with one source; only a calibrated attenuator changes between the bright phase and the single-photon phase. ALEBT_proposal_paper_v1_oct20.pdf: the proposal written for a host laboratory (the observable, the hypothesis, the error budget, the stages, the equipment and the open problems). ALEBT_equipment_list_v2_oct26.pdf: the first-run equipment list, with answers to the questions raised by groups we have written to (existing measurements, fibre-coupled detectors, differences between detectors).
Standard linear optics requires that the transmittance of an optic be independent of photon number: for a linear element the input–output relation a_out = t·a_in + r·b_in is an operator identity, so single-photon and bright-light transmission are equal as a theorem rather than as an approximation. We are not aware of a dedicated test of that equality with a controlled scatterer at the 10⁻⁴ level. We state a hypothesis in which the equality fails in the single-quantum sector by a fixed dimensionless coupling λ*, and specify the tabletop experiment that would exclude it. The observable is Δ = D_quantum − D_classical, where D is the half-difference of a two-arm log-ratio under an ABBA swap of a weak scatterer, measured once with counting detectors and once with photodiodes through identical geometry. Standard quantum mechanics fixes Δ = 0 exactly; the hypothesis predicts Δ = −λ*·(−p ln p), or −0.046·λ* at a 1% transmission deficit. The loss map is stated as a photon-number-dependent Kraus channel, K = Σ exp[−½λ*·I_R(n)]|n⟩⟨n| with P_R(n) = 1 − (1−p)^n, which is linear, completely positive, local and non-signalling; invariance of a remote marginal is verified explicitly on a two-mode squeezed vacuum to 3×10⁻¹⁷. An earlier thermal formulation of the same idea is excluded by published SNSPD efficiency data at 2 K by a factor of 2×10⁵ and is withdrawn. An attempt to derive the criterion distinguishing which optical elements incur the cost failed under independent adversarial review and is reported as a failure; the surviving readings are converted into five pre-registered experimental arms with their nulls stated in advance. A borrowed teaching bench at 780 nm reaches a total uncertainty of 2.9×10⁻⁴ per operating point at 2×10⁸ counts, giving 5σ sensitivity at λ* ≥ 0.031 and 95% exclusion to 0.013 at a 1% scatterer; an extended scan through the turnover at p = 36.8% reaches 0.0039 and 0.0016 respectively, subject to a costed high-loss error-budget row and seven stated pass criteria. Five signatures distinguish the effect from systematics, including a −p ln p scaling and a maximum located at p = 0.368. The cheapest arm needs no interferometer: the single-photon versus bright transmission of one 50/50 beam splitter at 10⁻³, which bounds one reading of the hypothesis below λ* = 0.003 in an afternoon’s run on a prepared bench. The protocol is pre-registered before any bench is borrowed. The result will be published in either direction; a null is reported as the best bound in this sector.
Two working documents that the deposited paper (Draft 4, v1.0; DOI 10.5281/zenodo.22678044; printed title The Asymmetric-Loss Equal-Born Test: a pre-registered search for record-information-dependent optical loss) cites and undertakes to deposit alongside it. They are deposited here as they stood on September 7, 2026, the day Draft 4 was completed, each with a dated deposit note at its head; nothing beneath the note is altered. Supplement 1 — Pre-Bench Closure (September 4, 2026), with postscript layers of September 6 and 7. The arithmetic companion to the paper. Part A runs the no-signalling check on the programme's surviving statement, finds that the normalised form permits superluminal signalling and is excluded, and records the single repair — a loss channel — that leaves the bench prediction numerically unchanged and converts the hypothesis from a nonlinear modification of the Born rule into a linear one. Part B carries the consequences into the protocol: the turnover of −p ln p at p = 1/e and the extended scan that would see it, a fourth signature, the cost of the high-loss points, the total-rate observable, the absorber control with its prediction stated in advance, and the consolidated protocol amendments. Part C makes the structural repairs: locating the branching event, the J-conservation contradiction, and the cost functional, with both candidates carried and the location of the peak left to decide between them. Part D drafts the pre-registration and scores the open tasks. The September-6 layer, headed "Postscript — September 5–6", records the two independent referee passes (one blind, one adversarial), the photon-number-dependent loss map, the derivation of the record criterion put to a third referee instructed to kill it and killed on twelve counts, the pre-registered arms and the correction of a handover error; the addendum of September 7 records the closing of the high-loss row. 17 pages. Supplement 2 — The high-p row: proposal, adversarial pass, and the row as costed (September 7, 2026). The error-budget row for the extended scan (p = 10%, 36.8%, 60% and 70%) that the paper's §9 named as the single item blocking pre-registration of the extended points, kept in the three steps by which it was reached. Appendix A is the first-pass proposal exactly as written for review, errors included. Appendix B is the report of an independent adversarial referee instructed to kill it, verbatim: eight errors and six systematics the first pass had not carried. Appendix C is the row as costed after every finding was re-derived and accepted, with the seven pass criteria written into the pre-registration. Its findings: the reach at the turnover (5σ at λ* ≥ 0.0039, 95% exclusion to 0.0016) stands only under the seven criteria; the bright-phase thermal family has the sign of the predicted anomaly and is bounded by a power-dependence test stated in advance; the far point of the scan moves from 70% to 60%; and the extended scan is research-group metrology, not teaching-laboratory work. 25 pages with its deposit note. The coloured highlights in Supplement 1 are its dated layers (rose, September 6; periwinkle, September 7; sky, the deposit note of September 16, 2026), each explained at its head. The line "Not for deposit" on the cover of Supplement 2 recorded the authors' working practice on September 7 and is superseded by the deposit note above it; the paper's Draft-4 note undertakes to deposit the document. The reconciliation document the paper also cites is the programme's working record, still being expanded, and is available from the authors.
This record. Twelve phenomena, entanglement among them, read through the same non-local phase: «non-local» as not located in space and time, not as action at a distance. Reading path: Foundations: why the laws hold, 5 of 5 · before: Is mass a contained rhythm? · all themes. Common introduction to all the records of this series. The content of this record follows below. Mathematical Materiality (MM) in brief. Why are the laws of physics the same everywhere and at every instant, even though nothing forces matter to obey them? MM proposes an answer: the laws are not rules imposed on matter from the outside; rather, matter itself is made of mathematical relations. And mathematics cannot change: a relation binds two distinct terms everywhere and always. In logic, nothing exists on its own: to exist means to be in relation to another logical entity, and outside this web of relations nothing can exist, not even other universes. This reading already meets experimental measurements at two points. First, the ratio of dark to ordinary matter is read as 3√3 = 5.196; when left free in the fits, Planck and DESI DR2 data give 5.21–5.22 (as registered in record 2.44, https://doi.org/10.5281/zenodo.23329080). Second, the acceleration scale of galaxies is read as a₀ = cH₀/6, the same scale that appears in Verlinde's emergent gravity: the computed value is 1.09–1.18 × 10⁻¹⁰ m/s² against the measured value of 1.20 (record 2.46.1, https://doi.org/10.5281/zenodo.23506655). Both readings were formulated with the measurements already known; the tests to check them against future data are registered in the same records. In the first logical nexus between space and time — which became homogeneous with Einstein — there is a non-local phase, made only of a pure logical distinction: space is not time. Between the two there is no relation of quantitative calculation, only the logical entity they have in common, which is needed to make them exist with respect to each other. This level is not distant: it is present in every phase of reality, in every place and at every instant. It shows in entanglement, where two distant systems remain correlated more strongly than any explanation based on separate properties and free of faster-than-light influences allows, without anything physically travelling between them. In this non-local phase the two distinct terms, space and time, share only one logical element, which we shall call their greatest common divisor (GCD), just as the numbers 3 and 5 have only 1 in common. The local world arises when a relation is counted through this GCD: its multiples and its fractions form a matrix. Seen by an observer inside the system like us, the multiples appear as time and the fractions as space. When that same multiple is directly contained in the matrix of the point of observation, it turns into mass — that is, into concrete matter as we usually understand it. There is therefore a close link between time and mass, in full agreement with Einstein's relativity, which ties mass to spacetime. The observed objects, while being logically autonomous entities in their local relations, enter into relation with the observer through a logical diffraction — that is, a decomposition into fractions — of the observer's matrix. This reading also gives a reason for the limit of the speed of light, which in Einstein's relativity is instead taken as a starting principle. The speed of light is the fixed exchange rate between the multiples and the fractions of the same GCD, meaning how much space a single step of time is worth: exceeding it would mean, for some observer, covering space without counting time, and thus leaving the local world. Logic always starts from a logical relative, and this exchange rate has nothing absolute in itself either: it is a necessary relative which, inside the system, becomes an absolute hypothesis, the same for everyone and impossible to exceed. Outside the system, by contrast, it has no justification at all, because outside there is only non-existence: justifying something requires another term to relate it to, and out there there is none. Asking for a reason from outside is like asking what lies north of the North Pole. The same theoretical framework that reads space, time, mass and the observed objects also admits quantum mechanics. The non-local phase and the mirror-like logical reciprocity between the two ends of the nexus give a reason for the probabilistic behaviour of matter. When the observed object is large enough, its mass fixes it in the matrix of the point of observation: for this reason we see it in one precise place and at one precise instant. When instead the object falls below a certain mass threshold, the principal GCD (that of the point of observation) and the GCD of the diffraction that generates the object are forced to become equal, reflecting each other as in a mirror. At that point the object no longer occupies a single point of the spacetime generated by the observer, but spreads over several possible positions, and we observe it as probability. It is like having to describe the number 10 using only the number 1: the only way is to distribute the 1 over ten positions, one for each unit of the 10. Today we know that even objects made of thousands of atoms behave in this way, and no experiment has yet found the boundary. The idea that the passage from quantum to classical behaviour depends on mass is close to that of Penrose and Diósi; in MM the threshold is the point where the two GCDs, the principal one and that of the local diffraction, become equal. For all these reasons the universe behaves like a simulation without really being one. It follows exact rules, made of counts, everywhere and at every instant, but no machine runs them and no programmer wrote them: a structure of mathematical relations does not need to be computed in order to exist. Tegmark (2008) had already noted that such a simulation need not be run, while Vazza (2025) estimated that running it physically on a machine would require resources that the very laws of the universe do not allow. This record develops one aspect of the theoretical framework. The work is shared openly so that it can be judged by as many readers as possible: anyone who knows someone interested can pass on this single link, valid for the whole framework (with an overview in English and Italian): https://doi.org/10.5281/zenodo.23535916. The entry page, with the complete list of all records, is https://doi.org/10.5281/zenodo.22667516. To cite the framework: Lanciano, U. (2026). The number 1 in front of the mirror: Mathematical Materiality from the nexus to the cosmos. Zenodo. https://doi.org/10.5281/zenodo.23535916. The records have been deposited since 5 August 2026, each with its own date, and are released under CC BY 4.0: anyone may use them by citing the source. Objections and errors found are welcome at riverantares@gmail.com, since Zenodo has no space for comments. This record. In physics «non-locality» mostly names one fact: the correlations of entanglement. In Mathematical Materiality (MM) it is the foundation: a non-local phase, not located in space and time and present everywhere, of which the local world is the count made from a point. Here «non-local» means not located in space and time; it does not mean action at a distance. This record collects, from MM's published records and the author's premises, twelve phenomena in which MM's reading uses the same non-local phase as the reason, and shows that entanglement is the case in which it rests most directly on a measured datum, not the only one. There are no new calculations: the result is the unity of the reading. The twelve phenomena: the correlations of entanglement beyond Bell's limit, and their Tsirelson ceiling, set by the local reading (MM 2.48, 2.48.1); the same laws everywhere and always, as copies of the same nexus (MM 2.68); identical particles, as the same unit counted twice (a proposal of the AI); the objects two observers see alike, as two counts of one non-local relation (MM 2.62.1); the boundary of the local as a number of copies, not a distance (August status report, reread); probability and the Born rule (MM 2.48.1); the mass below which an object stops being at one point (MM 2.66); the present, and the loop in which the future chooses what is written (MM 2.48, 2.68.1); space and time themselves: a clock counting events without pre-assigned places runs at Einstein's proper time (MM 2.40.2); the limit of light, the same for everyone; dark matter as the ordinary matter of a second mirror, with no reciprocal non-local link to us (MM 2.44); the boundary within which a gravitating system reads only its own field, set by the Galaxy (MM 2.70). How each is set out. For every phenomenon: what is observed, with sources; how known physics reads it; what the non-local phase does; where the link comes from (already written in a deposit, a premise of the author, or a proposal of the AI); what rests on calculations already deposited; what remains open. In ten phenomena the link is already in the deposits or in the author's premises; in one it comes partly from the AI, and in one from the AI alone. Three ways organise them: copies without distance, existence through a link, and a reading that is always local and partial. What is not claimed. The non-local phase transmits no signals and no influences outside light cones. Today it has no distinct experimental signature: where MM gives numbers, they coincide with known physics (the Tsirelson bound, decoherence, wave optics) or come from readings with declared choices. The record also lists the other senses in which «non-local» appears in MM's records, so that they are not confused with this one. Where the reading is tested. Gaia DR4 in December 2026 (rules registered in MM 2.70) and the mass threshold, with a prediction dated 31 December 2035 (MM 2.66); five open questions from MM 2.68. Contents: REA
This document fixes, before the data exist, the hypothesis, apparatus, observables, cadence, analysis, thresholds, controls, stopping rule and reporting commitment of a one-year search for a modulation of superconducting-qubit energy relaxation (T1) at the sidereal frequency, 1/(23 h 56 m 4.09 s), beyond what the solar day and its seasonal modulation can produce. Data collection began on 17 October 2026 at 16:42 UTC on qubit 9 of the IBM Heron processor ibm_fez: an eight-delay inversion-recovery T1 measurement every six hours (about 3 s of processor time each), with the device's calibration values polled hourly. The analysis is fixed in advance: a least-squares fit of a smooth drift plus sinusoids at the solar, sidereal, anti-sidereal and extended-sidereal frequencies, with the reported amplitude leakage-corrected as sqrt(A_sid^2 - A_anti^2) (Farley and Storey 1954). The pipeline was validated on synthetic data before the first measurement and recovers an injected 0.3% at 2.7-3.4 sigma while returning 0.5 sigma with nothing injected. Detection requires a leakage-corrected amplitude at or above 3 sigma, both control channels below 2 sigma, a phase stable between the two halves of the year, and survival when runs adjacent to calibrations are removed; otherwise the result is the 95% upper limit, expected near 0.3%. The search is declared inconclusive if fewer than 900 of 1460 scheduled runs succeed or the anti-sidereal control exceeds 3 sigma. An amplitude matching the known cosmic-ray anisotropy (~0.1%) is a calibration, not a discovery. Stopping rule: one year, with a six-month interim look at the controls only; a second year is pre-declared as the response to an inconclusive or 2-3 sigma outcome. The result will be reported whether it is a detection, a bound, or a failure of the apparatus. Standard physics predicts a null result at this sensitivity; the alternative hypothesis is from The Cosmic Page (doi:10.5281/zenodo.23287018, Ch. 13) and the research proposal doi:10.5281/zenodo.23201109. Included: the pre-registration (PDF and LaTeX source), the monitor script that runs on the device, the fixed analysis script, the synthetic-data validation script with its results and figure, and the README. First data point: job db9qap9gv2cc73e5tufg, 2026-10-17T16:42:19Z, T1 = 162.9 +/- 7.9 us.