Can cosmic-ray muons detect hidden high-Z material in unknown cargo? A plain-language summary of a one-day computational study. Quantum Clarity LLC · September 2026 Repository: muon-tomography-lab The short version We built a computer simulation to test whether a particular statistical method could detect a block of dense, heavy metal hidden inside cluttered cargo, using nothing but naturally occurring cosmic-ray particles. The simulated volume was a one-metre cube of surrogate cargo, not a full shipping container, and the hidden object in the decisive experiments was a 10 cm cube of tungsten. It worked well when the method was given an exact description of the surrounding cargo. It stopped working entirely when the cargo was unknown — even though the unknown cargo came from the same random generator as the cargo descriptions already in the method's library of possibilities. That is a negative result, and it is the point of this report. It rules out one plausible approach and identifies where the real difficulty sits. The idea Cosmic rays constantly strike the Earth's atmosphere and produce muons — heavy, electron-like particles that pass through most matter. Near sea level, integrated over all arrival directions, of order one muon lands on every square centimetre of ground every minute, day and night. Muons bend slightly as they pass through matter, and they bend much more sharply when passing through dense, heavy elements — uranium, tungsten, lead — than through steel, water, or air. So if you place particle detectors above and below a shipping container and measure how much each muon bends, you can in principle infer what is inside. This is real and not speculative. Los Alamos National Laboratory pioneered the technique in the early 2000s and working systems have been fielded. It has two appealing properties: it needs no radiation source, and dense shielding is itself strongly scattering, so the material a smuggler would add to conceal a threat can become part of the detectable signature rather than hiding it. The catch is that cosmic muons arrive at their own pace. You cannot turn up the beam. Scanning a container properly takes a long time, and port throughput is the operational bottleneck. The question we set out to answer Our original hypothesis: containers differ in how hard they are to inspect, so a system that decides for itself when it has seen enough should be able to clear easy containers quickly and spend its time on difficult ones. To test that, we first had to establish a baseline: how well does conventional detection work, and at what exposure? That baseline question consumed the entire study, because the answer kept turning out to be more complicated than expected. What we built A four-layer simulation, deliberately separated so that each layer could be tested independently: The world — cargo scenes described in metres: dozens of randomly placed blocks of steel and water, sometimes containing a hidden block of lead, tungsten, or uranium, sometimes containing a harmless dense steel block as a decoy, sometimes containing nothing unusual. The physics — muons generated with a realistic angular and energy distribution, traced through the scene, scattered according to the standard physics of multiple Coulomb scattering. The measurements — an immutable record of what a detector would see for each muon: where it entered, where it left, and how much it bent. The analysis — several different methods for turning those measurements into a verdict: threat, or no threat. The separation matters. An early version accidentally let the analysis settings change the physical scene, which invalidated a full day of results. The rebuilt version verifies by cryptographic hash that the world and the measurements are identical no matter how they are later analysed. Everything ran on a single desktop computer with one consumer graphics card. Simulating several hours of real cosmic-ray exposure takes under a second. What we tested, and what happened We worked through nine explanations in sequence. Each was killed by a test designed specifically to kill it. Hypothesis Result Maybe we just need to scan for longer No. Performance stopped improving. Maybe where muons cluster is itself informative No. Chance-level once instrument bias was removed. Maybe the heavy-metal signal is inherently weak No — the signal is strong. Maybe the problem is searching the whole container Part of it, but not all. Maybe an exact statistical model would solve it Yes, spectacularly — when the cargo was known. Maybe the cargo can be one of a known set of possibilities Appeared to work — but the method simply identified which one. Not a real test. Maybe it works on genuinely unseen cargo No. Performance fell to chance. Maybe that collapse was a numerical artefact No. It survived the correction. Maybe a second viewing angle would rescue it No measurable benefit. Two findings deserve emphasis. We measure performance with AUC, which has a direct meaning: given one volume that contains a hidden object and one that does not, AUC is the fraction of the time the method ranks them the right way round. An AUC of 1.0 is perfect, 0.5 is a coin flip. The information is really there. When we told the analysis exactly where the hidden object was and asked only "is this dense or not," it reached AUC 0.97. The physics carries the signal. Finding it is the hard part. When the same analysis had to search the volume without being told where to look, it fell to AUC 0.72. And when the surrounding cargo was unknown as well, it fell to AUC 0.45–0.52 — no better than guessing. We then tried to break our own conclusion, and could not. The statistical model contained no allowance for detector measurement error, which can make such a method wildly overconfident and could by itself have produced the collapse. We added a realistic allowance — 1 milliradian of angular error, 1 millimetre of position error — declared the correction and its pass/fail threshold in advance, and reran. The overconfidence disappeared as intended: the score scale fell by a factor of six. The collapse did not. Blind performance stayed at AUC 0.47–0.50. That is what makes the conclusion below a finding rather than a numerical artefact. What this means Within this model, the decisive unresolved bottleneck is neither the strength of the physical signal nor the length of the scan. It is that the method must work out what the ordinary cargo looks like and whether something dangerous is hidden inside it at the same time — and those two problems interfere with each other. (That is a statement about this study. It does not establish that physics or exposure could never be limiting in a higher-fidelity system.) An analysis given a perfect description of the benign cargo performs superbly. The same analysis, facing cargo it has never seen, cannot separate "this is an unusual but harmless load" from "this contains something dense." That reframes the research question. The interesting problem is not "how do we scan more cleverly" or "where should we point the detector." It is: How can a detector reason about essentially unlimited variation in ordinary cargo without needing an exact description of it? That is a substantially harder statistical problem, and we did not solve it. What this study does not show These limits are as important as the findings. It does not show that muon tomography does not work. Working systems exist and are fielded. This study examined one specific analysis method inside one specific simulation. It does not show that no method can handle unknown cargo. It shows that this method required the true cargo to be present in its library of possibilities, and failed when it was not. The method was not trained in the machine-learning sense; it averaged over sixteen explicit cargo hypotheses. Better approaches may well exist; we did not test them. The physics was never checked against an independent simulator. We used a fast approximation throughout. Validating it against Geant4, the standard particle-physics simulation package, is the obvious next step and was not done. Every number here is conditional on that approximation being adequate. The final test used a very short exposure — about 500 usable muon tracks, roughly nine seconds of real-world scanning through a one-square-metre aperture. That budget was chosen for reasons that later proved partly artefactual. A longer-exposure test was authorised in advance only if intermediate results cleared a threshold; they did not, so it was not run. The simulated cargo was simple — rectangular blocks of four materials, from a single random generator, inside a one-metre cube rather than a full-scale container. Real cargo is not. The detector was idealised: no efficiency losses, no absorption modelling, and scattering treated as the only measurable effect. Why publish a negative result Because the specific thing that failed here is something people generally assume works. The step from "this method works when the background is known" to "this method works in the field" looks small and is routinely taken without checking. We checked, and the step does not hold. Anyone planning to build on this kind of approach can now spend their effort on the part that is actually hard. The study also documents its own errors. Several conclusions were retracted mid-study when a check failed: a bug that let analysis settings alter the simulated world; a scoring routine that silently discarded unmeasurable cases and reported perfect accuracy as a result; a comparison that unknowingly handicapped one side; a statistical test that was numerically meaningless. Each was found by a test built to find it, and each is documented in the repository alongside the correction. The falsification trail is the contribution. The negative answer is what it produced. Reproducing this All
Amit Brahmbhatt· Zenodo (CERN European Organi...· 0 citations
Can cosmic-ray muons detect hidden high-Z material in unknown cargo? A plain-language summary of a one-day computational study. Quantum Clarity LLC · September 2026 Repository: muon-tomography-lab The short version We built a computer simulation to test whether a particular statistical method could detect a block of dense, heavy metal hidden inside cluttered cargo, using nothing but naturally occurring cosmic-ray particles. The simulated volume was a one-metre cube of surrogate cargo, not a full shipping container, and the hidden object in the decisive experiments was a 10 cm cube of tungsten. It worked well when the method was given an exact description of the surrounding cargo. It stopped working entirely when the cargo was unknown — even though the unknown cargo came from the same random generator as the cargo descriptions already in the method's library of possibilities. That is a negative result, and it is the point of this report. It rules out one plausible approach and identifies where the real difficulty sits. The idea Cosmic rays constantly strike the Earth's atmosphere and produce muons — heavy, electron-like particles that pass through most matter. Near sea level, integrated over all arrival directions, of order one muon lands on every square centimetre of ground every minute, day and night. Muons bend slightly as they pass through matter, and they bend much more sharply when passing through dense, heavy elements — uranium, tungsten, lead — than through steel, water, or air. So if you place particle detectors above and below a shipping container and measure how much each muon bends, you can in principle infer what is inside. This is real and not speculative. Los Alamos National Laboratory pioneered the technique in the early 2000s and working systems have been fielded. It has two appealing properties: it needs no radiation source, and dense shielding is itself strongly scattering, so the material a smuggler would add to conceal a threat can become part of the detectable signature rather than hiding it. The catch is that cosmic muons arrive at their own pace. You cannot turn up the beam. Scanning a container properly takes a long time, and port throughput is the operational bottleneck. The question we set out to answer Our original hypothesis: containers differ in how hard they are to inspect, so a system that decides for itself when it has seen enough should be able to clear easy containers quickly and spend its time on difficult ones. To test that, we first had to establish a baseline: how well does conventional detection work, and at what exposure? That baseline question consumed the entire study, because the answer kept turning out to be more complicated than expected. What we built A four-layer simulation, deliberately separated so that each layer could be tested independently: The world — cargo scenes described in metres: dozens of randomly placed blocks of steel and water, sometimes containing a hidden block of lead, tungsten, or uranium, sometimes containing a harmless dense steel block as a decoy, sometimes containing nothing unusual. The physics — muons generated with a realistic angular and energy distribution, traced through the scene, scattered according to the standard physics of multiple Coulomb scattering. The measurements — an immutable record of what a detector would see for each muon: where it entered, where it left, and how much it bent. The analysis — several different methods for turning those measurements into a verdict: threat, or no threat. The separation matters. An early version accidentally let the analysis settings change the physical scene, which invalidated a full day of results. The rebuilt version verifies by cryptographic hash that the world and the measurements are identical no matter how they are later analysed. Everything ran on a single desktop computer with one consumer graphics card. Simulating several hours of real cosmic-ray exposure takes under a second. What we tested, and what happened We worked through nine explanations in sequence. Each was killed by a test designed specifically to kill it. Hypothesis Result Maybe we just need to scan for longer No. Performance stopped improving. Maybe where muons cluster is itself informative No. Chance-level once instrument bias was removed. Maybe the heavy-metal signal is inherently weak No — the signal is strong. Maybe the problem is searching the whole container Part of it, but not all. Maybe an exact statistical model would solve it Yes, spectacularly — when the cargo was known. Maybe the cargo can be one of a known set of possibilities Appeared to work — but the method simply identified which one. Not a real test. Maybe it works on genuinely unseen cargo No. Performance fell to chance. Maybe that collapse was a numerical artefact No. It survived the correction. Maybe a second viewing angle would rescue it No measurable benefit. Two findings deserve emphasis. We measure performance with AUC, which has a direct meaning: given one volume that contains a hidden object and one that does not, AUC is the fraction of the time the method ranks them the right way round. An AUC of 1.0 is perfect, 0.5 is a coin flip. The information is really there. When we told the analysis exactly where the hidden object was and asked only "is this dense or not," it reached AUC 0.97. The physics carries the signal. Finding it is the hard part. When the same analysis had to search the volume without being told where to look, it fell to AUC 0.72. And when the surrounding cargo was unknown as well, it fell to AUC 0.45–0.52 — no better than guessing. We then tried to break our own conclusion, and could not. The statistical model contained no allowance for detector measurement error, which can make such a method wildly overconfident and could by itself have produced the collapse. We added a realistic allowance — 1 milliradian of angular error, 1 millimetre of position error — declared the correction and its pass/fail threshold in advance, and reran. The overconfidence disappeared as intended: the score scale fell by a factor of six. The collapse did not. Blind performance stayed at AUC 0.47–0.50. That is what makes the conclusion below a finding rather than a numerical artefact. What this means Within this model, the decisive unresolved bottleneck is neither the strength of the physical signal nor the length of the scan. It is that the method must work out what the ordinary cargo looks like and whether something dangerous is hidden inside it at the same time — and those two problems interfere with each other. (That is a statement about this study. It does not establish that physics or exposure could never be limiting in a higher-fidelity system.) An analysis given a perfect description of the benign cargo performs superbly. The same analysis, facing cargo it has never seen, cannot separate "this is an unusual but harmless load" from "this contains something dense." That reframes the research question. The interesting problem is not "how do we scan more cleverly" or "where should we point the detector." It is: How can a detector reason about essentially unlimited variation in ordinary cargo without needing an exact description of it? That is a substantially harder statistical problem, and we did not solve it. What this study does not show These limits are as important as the findings. It does not show that muon tomography does not work. Working systems exist and are fielded. This study examined one specific analysis method inside one specific simulation. It does not show that no method can handle unknown cargo. It shows that this method required the true cargo to be present in its library of possibilities, and failed when it was not. The method was not trained in the machine-learning sense; it averaged over sixteen explicit cargo hypotheses. Better approaches may well exist; we did not test them. The physics was never checked against an independent simulator. We used a fast approximation throughout. Validating it against Geant4, the standard particle-physics simulation package, is the obvious next step and was not done. Every number here is conditional on that approximation being adequate. The final test used a very short exposure — about 500 usable muon tracks, roughly nine seconds of real-world scanning through a one-square-metre aperture. That budget was chosen for reasons that later proved partly artefactual. A longer-exposure test was authorised in advance only if intermediate results cleared a threshold; they did not, so it was not run. The simulated cargo was simple — rectangular blocks of four materials, from a single random generator, inside a one-metre cube rather than a full-scale container. Real cargo is not. The detector was idealised: no efficiency losses, no absorption modelling, and scattering treated as the only measurable effect. Why publish a negative result Because the specific thing that failed here is something people generally assume works. The step from "this method works when the background is known" to "this method works in the field" looks small and is routinely taken without checking. We checked, and the step does not hold. Anyone planning to build on this kind of approach can now spend their effort on the part that is actually hard. The study also documents its own errors. Several conclusions were retracted mid-study when a check failed: a bug that let analysis settings alter the simulated world; a scoring routine that silently discarded unmeasurable cases and reported perfect accuracy as a result; a comparison that unknowingly handicapped one side; a statistical test that was numerically meaningless. Each was found by a test built to find it, and each is documented in the repository alongside the correction. The falsification trail is the contribution. The negative answer is what it produced. Reproducing this All
Amit Brahmbhatt· Zenodo (CERN European Organi...· 0 citations
DOI: 10.5281/zenodo.22283967Record set: EC-MECH campaign (EC-MECH-001 pilot + EC-MECH-002)Related to: EC-STORAGE-001, DOI 10.5281/zenodo.21299091 Research question: Can the coherence lifetime of an entangled multi-qubit state be predicted from the measured coherence losses of its individual qubits? Plain language summary When several qubits are entangled together, how fast does the entangled state lose its coherence compared with the qubits measured one at a time? The textbook expectation, if each qubit's noise is its own private business, is that the losses simply add up. This record tests that expectation directly on IBM hardware, and reports two experiments: one that returned ABSTAIN under its own preregistered rules rather than supporting a scientific conclusion, and a redesigned successor that did produce one. The first experiment failed for an instructive reason. Its quality gate asked whether the measured decay curves looked like clean exponentials, when the question that actually mattered was whether the decay rate had been pinned down precisely. Those are different things, and for shallow decays they come apart badly. Five measurements whose rates were known to within 4–6% were discarded because their curves were too flat for the goodness-of-fit statistic to work with. Under the frozen rules that cascaded into an ABSTAIN on every downstream question. The verdict stands unamended. Diagnosing that failure exposed a second and more serious problem: the single-qubit reference measurements had been performed in a different noise environment from the entangled measurements they were being compared against. The redesigned experiment fixed both problems and added a dedicated probe of the environment mismatch itself. The result: once the environments were matched, the discrepancies during plain idling became substantially smaller — especially for the 4- and 6-qubit states — but the preregistered precision was still insufficient to establish additivity. Under a standard error-suppression pulse sequence, additivity was rejected at all three sizes. And the dedicated probe confirmed the environment mismatch was real, not merely a theoretical worry. Total hardware cost: 241 seconds across both experiments. Background: an unsupported claim, entered into the record EC-STORAGE-001 (DOI 10.5281/zenodo.21299091) recorded a pre-registration miss — a bare-arm coherence witness crossing at 9.0 µs against a registered 10–30 µs band — and explained it by asserting that the payload resided in weight-4 stabilizer correlations "whose coherences decay at the sum of constituent rates." That explanation does not close numerically against data in the same deposit. The selected qubits had reported T₂ of 178–368 µs. A sum-of-rates model over four such qubits predicts a joint coherence time of roughly 45–60 µs; the measured value was 8.81 ± 0.30 µs. The stated model over-predicts by a factor of roughly 5–7. The claim was therefore a hypothesis written in the grammar of a derivation. It is entered in the adjudication ledger as UNSUPPORTED, and the EC-MECH campaign was constructed to either repair it or retract it. This deposit does not resolve it in EC-STORAGE-001's favour, and readers of that record should treat the mechanism sentence as withdrawn pending a direct test on the encrypted-cloning encoding itself. What we did Both experiments ran on ibm_kingston (156-qubit IBM Heron processor) on a connected 6-qubit chain, physical qubits [14, 15, 19, 35, 34, 33], selected by a frozen policy from the same-day calibration snapshot with no manual override. Neither experiment uses, requires, or reproduces the encrypted-cloning protocol. They test the underlying physics assumption in isolation, using GHZ states and idle delays only. No proprietary components are involved, and the deposited code is fully self-contained. EC-MECH-001 (pilot) — rate additivity Nested GHZ states on the first k qubits (k = 2, 4, 6) were idled for τ ∈ [0, 45] µs and their weight-k coherence read out via parity oscillation. In parallel, all six qubits were prepared in |+⟩ and idled simultaneously to obtain per-qubit in-situ dephasing rates. The frozen predicate compared the fitted GHZ decay rate Γ_k against the sum Σ Γᵢ of the measured single-qubit rates. 320 circuits, 1024 shots each, one job, 93 s QPU. EC-MECH-002 — coherence-function additivity The successor abandons fitted rates entirely. For any family, define c(τ) = C(τ) / C(0) χ(τ) = −ln c(τ) Under independent local phase noise, the GHZ phase is the sum of the local phases, so the coherence factorises exactly: χ_S(τ) = Σ_{i∈S} χ_i(τ) This identity assumes nothing about decay shape — exponential, Gaussian, stretched, and non-Markovian decays all satisfy it. The scientific object is the residual Δ_S(τ) = χ_S(τ) − Σ χᵢ(τ), adjudicated through the scale-free ratio r_S(τ) = Δ_S(τ) / Σ χᵢ(τ) as a preregistered equivalence test with margin |r| ≤ 0.15, using simultaneous 95% confidence intervals (Bonferroni, n = 8, z = 2.734). CI wholly inside the margin → ACCEPT; wholly outside → REJECT; overlapping the boundary → ABSTAIN. Two design repairs distinguish it from the pilot: No R² gate, no fitted rate, no assumed decay law. Matched noise environments. Every non-target chain qubit is pinned in |0⟩ — including the GHZ spectators at k < 6 — rather than left in |+⟩. This matters because a GHZ block is immune to intra-block ZZ coupling: |0…0⟩ and |1…1⟩ are both +1 eigenstates of Z_iZ_j, so the relative phase carrying the coherence is untouched. In the pilot, the single-qubit reference was exposed to neighbour-state-dependent dephasing consistent with this mechanism, while GHZ symmetry cancels intra-block static ZZ — biasing the prediction high. Single-qubit controls use a two-colour scheme on the chain (targets {14, 19, 34}, then {15, 35, 33}) so every target has all chain neighbours pinned. τ = 0 is oversampled at 4096 shots because it is the shared normaliser and its uncertainty enters every χ, inducing covariance that is carried explicitly in the analysis. Design parameters (frozen). Normalisation point τ = 0 at 4096 shots, never adjudicated. Eight informative τ points at 1024 shots each: 12, 18, 20, 22, 25, 28, 35, 45 µs The grid is pilot-informed and deliberately non-uniform: the low end starts at 12 µs because the D_min = 0.10 denominator gate would exclude earlier times once neighbour pinning reduces the local χ, and five of the eight points are clustered in the 18–28 µs window to resolve structure in Δ(τ) there. See the evidence ceiling for what this costs. Arms: bare (plain delay) and dd (symmetric XY4, one cycle). Four phase points per sweep, spanning one full period of the weight-k oscillation. Runtime dynamical decoupling and twirling disabled, so the arms are defined solely by the circuits. Diagnostic family diagPlus on the bare arm at τ ∈ {12, 25, 45} µs — all three exact members of the primary grid, so no interpolation is performed. Circuit execution order randomised under frozen seed 20260902. 376 circuits, 520,192 shots, one job, 148 s QPU against a preregistered estimate of ~139 s (6.1% error). Driver provenance. The EC-MECH-002 driver was hardened after the EC-MECH-001 pilot and before the EC-MECH-002 freeze. The hardening bound submission to the freeze manifest and to the binding layout report (removing hand-entered qubit chains), replaced diagnostic interpolation with exact grid indexing, added randomised circuit execution order under a frozen seed, and added a drift-robustness case to the offline validator. All of it predates the freeze; the deposited digest covers the hardened files, and no change was made after data was seen. Results EC-MECH-001 — ABSTAIN (frozen, unamended) All six weight predicates returned ABSTAIN. Cause: five single-qubit component fits failed the frozen R² ≥ 0.90 gate (bare q15 = 0.883, q33 = 0.873; DD q15 = 0.893, q19 = 0.871, q33 = 0.859) despite relative rate uncertainties of 3.7–5.5%. Because q15 participates from k = 2 onward, the failure cascaded into every weight. All 18 fits in the run had σ(Γ)/Γ ≤ 0.064. R² measures the fraction of variance in log C explained by the line; when a decay is shallow the true variance is small and ordinary scatter consumes a large share of it. R² was the wrong gate. The pilot did establish, as observation rather than verdict, that in-situ dephasing under simultaneous idling ran ~2.4–4.3× faster than the reported T₂ on every qubit (e.g. q35: 67.4 µs in situ against 292.9 µs reported). EC-MECH-002 — primary adjudication Arm k usable τ median r χ²/dof p Verdict bare 2 7 −0.217 2.40 0.0185 ABSTAIN bare 4 8 −0.014 0.62 0.7625 ABSTAIN bare 6 8 −0.087 1.16 0.3166 ABSTAIN dd 2 7 −0.396 5.46 <0.0001 REJECT dd 4 8 −0.213 5.36 <0.0001 REJECT dd 6 8 −0.206 6.90 <0.0001 REJECT Negative r means the GHZ state retains coherence better than the independently measured single-qubit coherences predict. The bare ABSTAINs are not a proof of independence. The equivalence predicate was built precisely so that "we could not reject zero" cannot be reported as "we demonstrated independence." At k = 4 and k = 6 the residual is small (−0.014, −0.087) and the confidence intervals straddle the ±0.15 boundary; the correct statement is that a positive equivalence claim was not supported at the preregistered precision. k = 2 warrants extra caution in both arms. It is the only weight that lost a τ point to the denominator gate, and because r = χ_S/D − 1 with the smallest denominator, it amplifies any bias in D more than the other weights. Its values (−0.217 bare, −0.396 DD) are the most extreme on the board and the least reliable. ZZ diagnostic (preregistered as diagnostic, excluded from the predicate) A dedicated family reproduced the pilot's all-|+⟩ environment to test whether intra-chain ZZ coupling really was contaminating the reference. The preregistered qualitative prediction was excess χ > 0
Amit Brahmbhatt· Zenodo (CERN European Organi...· 0 citations
DOI: 10.5281/zenodo.22283967Record set: EC-MECH campaign (EC-MECH-001 pilot + EC-MECH-002)Related to: EC-STORAGE-001, DOI 10.5281/zenodo.21299091 Research question: Can the coherence lifetime of an entangled multi-qubit state be predicted from the measured coherence losses of its individual qubits? Plain language summary When several qubits are entangled together, how fast does the entangled state lose its coherence compared with the qubits measured one at a time? The textbook expectation, if each qubit's noise is its own private business, is that the losses simply add up. This record tests that expectation directly on IBM hardware, and reports two experiments: one that returned ABSTAIN under its own preregistered rules rather than supporting a scientific conclusion, and a redesigned successor that did produce one. The first experiment failed for an instructive reason. Its quality gate asked whether the measured decay curves looked like clean exponentials, when the question that actually mattered was whether the decay rate had been pinned down precisely. Those are different things, and for shallow decays they come apart badly. Five measurements whose rates were known to within 4–6% were discarded because their curves were too flat for the goodness-of-fit statistic to work with. Under the frozen rules that cascaded into an ABSTAIN on every downstream question. The verdict stands unamended. Diagnosing that failure exposed a second and more serious problem: the single-qubit reference measurements had been performed in a different noise environment from the entangled measurements they were being compared against. The redesigned experiment fixed both problems and added a dedicated probe of the environment mismatch itself. The result: once the environments were matched, the discrepancies during plain idling became substantially smaller — especially for the 4- and 6-qubit states — but the preregistered precision was still insufficient to establish additivity. Under a standard error-suppression pulse sequence, additivity was rejected at all three sizes. And the dedicated probe confirmed the environment mismatch was real, not merely a theoretical worry. Total hardware cost: 241 seconds across both experiments. Background: an unsupported claim, entered into the record EC-STORAGE-001 (DOI 10.5281/zenodo.21299091) recorded a pre-registration miss — a bare-arm coherence witness crossing at 9.0 µs against a registered 10–30 µs band — and explained it by asserting that the payload resided in weight-4 stabilizer correlations "whose coherences decay at the sum of constituent rates." That explanation does not close numerically against data in the same deposit. The selected qubits had reported T₂ of 178–368 µs. A sum-of-rates model over four such qubits predicts a joint coherence time of roughly 45–60 µs; the measured value was 8.81 ± 0.30 µs. The stated model over-predicts by a factor of roughly 5–7. The claim was therefore a hypothesis written in the grammar of a derivation. It is entered in the adjudication ledger as UNSUPPORTED, and the EC-MECH campaign was constructed to either repair it or retract it. This deposit does not resolve it in EC-STORAGE-001's favour, and readers of that record should treat the mechanism sentence as withdrawn pending a direct test on the encrypted-cloning encoding itself. What we did Both experiments ran on ibm_kingston (156-qubit IBM Heron processor) on a connected 6-qubit chain, physical qubits [14, 15, 19, 35, 34, 33], selected by a frozen policy from the same-day calibration snapshot with no manual override. Neither experiment uses, requires, or reproduces the encrypted-cloning protocol. They test the underlying physics assumption in isolation, using GHZ states and idle delays only. No proprietary components are involved, and the deposited code is fully self-contained. EC-MECH-001 (pilot) — rate additivity Nested GHZ states on the first k qubits (k = 2, 4, 6) were idled for τ ∈ [0, 45] µs and their weight-k coherence read out via parity oscillation. In parallel, all six qubits were prepared in |+⟩ and idled simultaneously to obtain per-qubit in-situ dephasing rates. The frozen predicate compared the fitted GHZ decay rate Γ_k against the sum Σ Γᵢ of the measured single-qubit rates. 320 circuits, 1024 shots each, one job, 93 s QPU. EC-MECH-002 — coherence-function additivity The successor abandons fitted rates entirely. For any family, define c(τ) = C(τ) / C(0) χ(τ) = −ln c(τ) Under independent local phase noise, the GHZ phase is the sum of the local phases, so the coherence factorises exactly: χ_S(τ) = Σ_{i∈S} χ_i(τ) This identity assumes nothing about decay shape — exponential, Gaussian, stretched, and non-Markovian decays all satisfy it. The scientific object is the residual Δ_S(τ) = χ_S(τ) − Σ χᵢ(τ), adjudicated through the scale-free ratio r_S(τ) = Δ_S(τ) / Σ χᵢ(τ) as a preregistered equivalence test with margin |r| ≤ 0.15, using simultaneous 95% confidence intervals (Bonferroni, n = 8, z = 2.734). CI wholly inside the margin → ACCEPT; wholly outside → REJECT; overlapping the boundary → ABSTAIN. Two design repairs distinguish it from the pilot: No R² gate, no fitted rate, no assumed decay law. Matched noise environments. Every non-target chain qubit is pinned in |0⟩ — including the GHZ spectators at k < 6 — rather than left in |+⟩. This matters because a GHZ block is immune to intra-block ZZ coupling: |0…0⟩ and |1…1⟩ are both +1 eigenstates of Z_iZ_j, so the relative phase carrying the coherence is untouched. In the pilot, the single-qubit reference was exposed to neighbour-state-dependent dephasing consistent with this mechanism, while GHZ symmetry cancels intra-block static ZZ — biasing the prediction high. Single-qubit controls use a two-colour scheme on the chain (targets {14, 19, 34}, then {15, 35, 33}) so every target has all chain neighbours pinned. τ = 0 is oversampled at 4096 shots because it is the shared normaliser and its uncertainty enters every χ, inducing covariance that is carried explicitly in the analysis. Design parameters (frozen). Normalisation point τ = 0 at 4096 shots, never adjudicated. Eight informative τ points at 1024 shots each: 12, 18, 20, 22, 25, 28, 35, 45 µs The grid is pilot-informed and deliberately non-uniform: the low end starts at 12 µs because the D_min = 0.10 denominator gate would exclude earlier times once neighbour pinning reduces the local χ, and five of the eight points are clustered in the 18–28 µs window to resolve structure in Δ(τ) there. See the evidence ceiling for what this costs. Arms: bare (plain delay) and dd (symmetric XY4, one cycle). Four phase points per sweep, spanning one full period of the weight-k oscillation. Runtime dynamical decoupling and twirling disabled, so the arms are defined solely by the circuits. Diagnostic family diagPlus on the bare arm at τ ∈ {12, 25, 45} µs — all three exact members of the primary grid, so no interpolation is performed. Circuit execution order randomised under frozen seed 20260902. 376 circuits, 520,192 shots, one job, 148 s QPU against a preregistered estimate of ~139 s (6.1% error). Driver provenance. The EC-MECH-002 driver was hardened after the EC-MECH-001 pilot and before the EC-MECH-002 freeze. The hardening bound submission to the freeze manifest and to the binding layout report (removing hand-entered qubit chains), replaced diagnostic interpolation with exact grid indexing, added randomised circuit execution order under a frozen seed, and added a drift-robustness case to the offline validator. All of it predates the freeze; the deposited digest covers the hardened files, and no change was made after data was seen. Results EC-MECH-001 — ABSTAIN (frozen, unamended) All six weight predicates returned ABSTAIN. Cause: five single-qubit component fits failed the frozen R² ≥ 0.90 gate (bare q15 = 0.883, q33 = 0.873; DD q15 = 0.893, q19 = 0.871, q33 = 0.859) despite relative rate uncertainties of 3.7–5.5%. Because q15 participates from k = 2 onward, the failure cascaded into every weight. All 18 fits in the run had σ(Γ)/Γ ≤ 0.064. R² measures the fraction of variance in log C explained by the line; when a decay is shallow the true variance is small and ordinary scatter consumes a large share of it. R² was the wrong gate. The pilot did establish, as observation rather than verdict, that in-situ dephasing under simultaneous idling ran ~2.4–4.3× faster than the reported T₂ on every qubit (e.g. q35: 67.4 µs in situ against 292.9 µs reported). EC-MECH-002 — primary adjudication Arm k usable τ median r χ²/dof p Verdict bare 2 7 −0.217 2.40 0.0185 ABSTAIN bare 4 8 −0.014 0.62 0.7625 ABSTAIN bare 6 8 −0.087 1.16 0.3166 ABSTAIN dd 2 7 −0.396 5.46 <0.0001 REJECT dd 4 8 −0.213 5.36 <0.0001 REJECT dd 6 8 −0.206 6.90 <0.0001 REJECT Negative r means the GHZ state retains coherence better than the independently measured single-qubit coherences predict. The bare ABSTAINs are not a proof of independence. The equivalence predicate was built precisely so that "we could not reject zero" cannot be reported as "we demonstrated independence." At k = 4 and k = 6 the residual is small (−0.014, −0.087) and the confidence intervals straddle the ±0.15 boundary; the correct statement is that a positive equivalence claim was not supported at the preregistered precision. k = 2 warrants extra caution in both arms. It is the only weight that lost a τ point to the denominator gate, and because r = χ_S/D − 1 with the smallest denominator, it amplifies any bias in D more than the other weights. Its values (−0.217 bare, −0.396 DD) are the most extreme on the board and the least reliable. ZZ diagnostic (preregistered as diagnostic, excluded from the predicate) A dedicated family reproduced the pilot's all-|+⟩ environment to test whether intra-chain ZZ coupling really was contaminating the reference. The preregistered qualitative prediction was excess χ > 0
Amit Brahmbhatt· Zenodo (CERN European Organi...· 0 citations
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