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Two pre-registered tests of an exact ladder ratio

José Casado Martínez

Published Aug 24, 2026• 0 citations
Publisher

Abstract

Results paper — the prediction is refuted, and published as promised. P18 (DOI 10.5281/zenodo.21801251) committed in advance to an exact ladder ratio (√(3/8)=0.612372 per rung in amplitude; 3/8 in trace) in two independent planes, with thresholds and nulls frozen and OpenTimestamps-anchored (SHA-256 prefix 8615c386) before either test ran. Both tests have now run. T1 (angular, virgin window ℓ=20..29, sealed instrument b1a1121d): rung ratios ~1 (|ratio|=1.079, outside 0.6124±0.05); a free ratio wins at Δ=5.1≥3. T2 (temporal, frozen 11,100,220-byte decay-counting snapshot, ordinal census, clock-preserving block null): the two resolvable levels give a trace ratio of +2.19 (device-signature-deflated +1.92; deflator frozen pre-judgment), outside 0.375±0.05. Per the binding table: prediction refuted; the framework's ladder remains an internal construct without observable shadow in these planes. Incidental finding, reported separately: the sealed instrument's own pre-registered detection threshold was exceeded in the virgin window — the axis-alignment chain continues through ℓ=20..29 (p=0.0033) with no decay (ratio ~1): the phenomenon extends, and the predicted decay law is not its law. A pre-registered E-mode test is sealed; the E data remain unexamined at deposit time. [ES] Paper de resultados: la predicción queda refutada en sus dos planos y se publica tal cual, como P18 prometió. Hallazgo incidental aparte: la cadena de alineamiento continúa en la ventana virgen sin decaer (p=0,0033). Integrity: PDF SHA-256 2094364ad745650e... · source 0efc8ffb22ebf7f5...; both OTS-anchored before deposit; .ots archived here. Pre-registration 8615c386, instrument b1a1121d, data snapshot 3ce29d7c, deflator 5ecd09d7 — all OTS-anchored before their respective uses.

DOI
10.5281/zenodo.22078006

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Results paper — the prediction is refuted, and published as promised. P18 (DOI 10.5281/zenodo.21801251) committed in advance to an exact ladder ratio (√(3/8)=0.612372 per rung in amplitude; 3/8 in trace) in two independent planes, with thresholds and nulls frozen and OpenTimestamps-anchored (SHA-256 prefix 8615c386) before either test ran. Both tests have now run. T1 (angular, virgin window ℓ=20..29, sealed instrument b1a1121d): rung ratios ~1 (|ratio|=1.079, outside 0.6124±0.05); a free ratio wins at Δ=5.1≥3. T2 (temporal, frozen 11,100,220-byte decay-counting snapshot, ordinal census, clock-preserving block null): the two resolvable levels give a trace ratio of +2.19 (device-signature-deflated +1.92; deflator frozen pre-judgment), outside 0.375±0.05. Per the binding table: prediction refuted; the framework's ladder remains an internal construct without observable shadow in these planes. Incidental finding, reported separately: the sealed instrument's own pre-registered detection threshold was exceeded in the virgin window — the axis-alignment chain continues through ℓ=20..29 (p=0.0033) with no decay (ratio ~1): the phenomenon extends, and the predicted decay law is not its law. A pre-registered E-mode test is sealed; the E data remain unexamined at deposit time. [ES] Paper de resultados: la predicción queda refutada en sus dos planos y se publica tal cual, como P18 prometió. Hallazgo incidental aparte: la cadena de alineamiento continúa en la ventana virgen sin decaer (p=0,0033). Integrity: PDF SHA-256 2094364ad745650e... · source 0efc8ffb22ebf7f5...; both OTS-anchored before deposit; .ots archived here. Pre-registration 8615c386, instrument b1a1121d, data snapshot 3ce29d7c, deflator 5ecd09d7 — all OTS-anchored before their respective uses.
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This note reports the outcome of the test pre-registered in DOI 10.5281/zenodo.23047418, applying its observables, step rule and decision criteria without modification. Using standard quantum mechanics for the ideal Rydberg-blockade (PXP) chain as the benchmark, Prediction 2, that the post-quench density settles with the universal ratio −1/φ², is refuted: the ratios are fixed by a slowly decaying oscillation about an offset centre, as a centre-and-amplitude decomposition shows exactly. Prediction 1, the spatial correlation ratio −1/φ² at infinite temperature, holds exactly in theory and awaits laboratory confirmation. The qualitative picture is corroborated: the transition is gradual, with unity exact throughout while local coherence fades. The residual ~5% amplitude loss per half-swing is shown not to be structural, since a small Hamiltonian deformation removes it. A near-hit at the first step is reported as post hoc and not counted. Includes the note, LaTeX source and a reproducibility script.
This note records a prediction before any experimental data are examined. It is a pre-registration, deposited so that the prediction and its test criteria are fixed in advance. In the ENSO Framework, the reciprocal pair (r, 1/r) under the Fibonacci law preserves unity exactly at every step while settling onto its fixed point (φ, 1/φ). Successive deviations from the fixed point stand in the ratio −1/φ² ≈ −0.382. That ratio is set by the law's two eigenvalues and has no free parameter. The same matrix is the transfer matrix of the nearest-neighbour Rydberg-blockade constraint, whose allowed configurations form the Fibonacci Hilbert space studied in Rydberg atom arrays. Two predictions follow: Prediction 1 (atemporal and spatial). Connected density correlations in the infinite-temperature blockaded chain alternate with ratio −1/φ² per site, and the bulk density is 1/(1+φ²). Standard statistical mechanics predicts the same, so this serves as a calibration of the identification, not as a discriminator. Prediction 2 (conjectural and discriminating). The same ratio governs how the chain settles after a Néel quench, universally across Rabi frequency, system size and lattice spacing. A built-in control requires next-nearest-neighbour blockade to give a different, non-alternating signature. Decision criteria (supports, refutes, inconclusive), the author's prior and the analysis procedure are all stated before any data are consulted. The upload includes the note (PDF and LaTeX source) and a reproducibility script that computes every number in it for ideal chains (8/8 checks).
Erase the apparent carrier. Recover the qubit from its halo. Then ask a different clock. This preregistration separates an ordinary quantum-memory qualification from a distinct timing test. Test A evolves a logical qubit through a frozen local channel, physically resets its original carrier, and asks whether a finite surrounding window can recover it. Test B asks whether that independently reconstructed channel fidelity controls a separate timing-covariance frontier. Test A: where is the recoverable channel? Ri(ω)=∣0⟩ ⁣⟨0∣i⊗Tr⁡iω, \mathcal R_i(\omega)=|0\rangle\!\langle0|_i\otimes\operatorname{Tr}_i\omega, Ri​(ω)=∣0⟩⟨0∣i​⊗Tri​ω, Qdel=2Favg(Ndel,id⁡)−1,Fedel=1+3Qdel4. Q_{\rm del}=2F_{\rm avg}(\mathcal N_{\rm del},\operatorname{id})-1, \qquad \boxed{F_e^{\rm del}=\frac{1+3Q_{\rm del}}4.} Qdel​=2Favg​(Ndel​,id)−1,Fedel​=41+3Qdel​​.​ Target-only and every smaller halo subwindow remain optimized counterfactuals. A physical reset, sham reset, hidden-record injection, boundary ladder, and complete terminal record are required before the recovery layer qualifies. Test B: does the memory verifier intertwine with an independent timing projector? W†MeW=Palign,ηT=Tr⁡(ρPalign), \boxed{W^\dagger M_eW=P_{\rm align}}, \qquad \eta_T=\operatorname{Tr}(\rho P_{\rm align}), W†Me​W=Palign​​,ηT​=Tr(ρPalign​), UT⋆=inf⁡2det⁡ΣTΩ. \mathcal U_T^\star =\inf 2\sqrt{\det\Sigma_{T\Omega}}. UT⋆​=inf2detΣTΩ​​. On the certified canonical branch, the sealed QTT target is ηT=Fedel,UT⋆=1−Fedel. \boxed{ \eta_T=F_e^{\rm del}, \qquad \mathcal U_T^\star=1-F_e^{\rm del}. } ηT​=Fedel​,UT⋆​=1−Fedel​.​ No complement coefficient is fitted. Five fidelity corridors, a radius/depth ladder, one-third untouched holdouts, topology twins, full covariance, global five-sigma decisions, at least 95% planned power, and transfer to a second record technology are frozen before data. The external computation is a feasibility anchor, not the timing target An, Cao, and Cui report carrier-deletion recovery in a local kicked-Ising memory. Their result qualifies the plausibility of Test A. Their reported Q=0.516Q=0.516Q=0.516 is explicitly forbidden from constructing Test B. The public source archive lacks the exact arrays and scripts, so exact replication remains pending. Five terminal outcomes INELIGIBLE_NO_THEORY_VERDICT REGISTERED_QTT_CONSEQUENCE_FALSIFIED QTT_CANDIDATE QUALIFIED_OTHER_OR_CROSS_CHANNEL_ANOMALY AMBIGUOUS_OR_UNDERPOWERED Any failed eligibility gate terminates without a theory verdict. A positive result requires the full multirung shape, not one selected point. An off-target anomaly is preserved rather than discarded or used as a post-hoc rescue. Immutable protocol seal eb0640b25c1d0bde56cacc7f25d9ce4304594833e4aa937ed50293a1faafc849 This is a separate sealed extension. It changes no target, threshold, classifier, protocol hash, or file in the parent test under concept DOI 10.5281/zenodo.21902885. Public anchors Completed-record fan-out and timing-access framework Observation as Access Quantum Traction Theory: Main Book External finite-window recovery paper The PDF is the default preview. The reconstruction archive contains the sealed JSON, classifier, eighteen-gate and raw-terminal templates, Stage-0 handoff, verifier, external audit, adversarial review, metadata, and checksums.