Finite-size entanglement-entropy coefficients in a causal set depend on the joint global-regional spectral prescription: manuscript and reproducibility package
Manuscript and complete reproducibility package for a preregistration-style numerical study of spectral truncation in causal-set spacetime entanglement entropy. Recovering continuum-compatible entanglement-entropy scaling on a causal set requires truncating the Sorkin-Johnston spectrum twice, once on the full causal set and again after restriction to the subregion. Published treatments apply both truncations at the same prescribed geometric scale. This study varies the two stages independently on nested causal diamonds in 2d Minkowski spacetime: 80 Poisson sprinklings at nominal cardinalities 500-4000 form the primary ensemble, with 10 further sprinklings at 8000 reserved for a secondary extrapolation check. Varying the regional cutoff at fixed global cutoff changes the fitted coefficient substantially and produces different compatibility classifications at the same global truncation, so the classification is a property of the joint prescription rather than of the global cutoff alone. Weight interventions that hold the retained subspace and the regional projector fixed produce slope changes that are statistically resolved yet practically equivalent within a prespecified margin. The package contains the analysis plan frozen before the production runs, both production records (5686 rows over 90 sprinklings, zero gate-failed rows), the driver, analysis and validation code, the regression and injection test suites, the frozen analysis output, a dated post-unblinding amendment with its code diff and corrected output, every supplementary analysis as a re-runnable script with its random stream recorded, the figure-generation code, a cell-level rank-retention census and reconciliation report, an eligibility census, and the environment and commands needed to regenerate every table in the manuscript. Contents are organised in seven folders: 1_frozen, 2_amendment_A1, 3_supplementary, 4_figures, 5_census_reconciliation, 6_environment, paper.MANIFEST.json lists a SHA-256 for all files and verify_manifest.py checks them. Evidentiary status. The deposit is retrospective. Hashes establish consistency between the deposited files and the production records, which embed the SHA-256 of the plan they ran under; they do not independently establish chronology. The pre-production freeze is author-reported and no independently timestamped commitment exists. Amendment A1 was made after all results and the frozen verdicts had been seen; the frozen output is the prespecified result and the corrected output is reported alongside it, never in its place. Key identifiers. Frozen analysis plan SHA-256dc6b8bdb3faa8450de3a710204ba18a72e4ed0be54639bae990d945b328a2bf5; primary production record4e3d3a58b6028531884c1de36eae15ac6d30146d1fb2599b150f898bbcf4051f; secondary production record8bf402ccc471ae9331a43d8e6f3bc383861599269922bfe89aa51f29430c5a33. Verified by extracting the archive and re-running: manifest 53/53 files, validation test suites pass, regression suite 35/35, and the frozen-path analysis reproduces every contrast and slope line of the original output.
Manuscript and complete reproducibility package for a preregistration-style numerical study of spectral truncation in causal-set spacetime entanglement entropy. Recovering continuum-compatible entanglement-entropy scaling on a causal set requires truncating the Sorkin-Johnston spectrum twice, once on the full causal set and again after restriction to the subregion. Published treatments apply both truncations at the same prescribed geometric scale. This study varies the two stages independently on nested causal diamonds in 2d Minkowski spacetime: 80 Poisson sprinklings at nominal cardinalities 500-4000 form the primary ensemble, with 10 further sprinklings at 8000 reserved for a secondary extrapolation check. Varying the regional cutoff at fixed global cutoff changes the fitted coefficient substantially and produces different compatibility classifications at the same global truncation, so the classification is a property of the joint prescription rather than of the global cutoff alone. Weight interventions that hold the retained subspace and the regional projector fixed produce slope changes that are statistically resolved yet practically equivalent within a prespecified margin. The package contains the analysis plan frozen before the production runs, both production records (5686 rows over 90 sprinklings, zero gate-failed rows), the driver, analysis and validation code, the regression and injection test suites, the frozen analysis output, a dated post-unblinding amendment with its code diff and corrected output, every supplementary analysis as a re-runnable script with its random stream recorded, the figure-generation code, a cell-level rank-retention census and reconciliation report, an eligibility census, and the environment and commands needed to regenerate every table in the manuscript. Contents are organised in seven folders: 1_frozen, 2_amendment_A1, 3_supplementary, 4_figures, 5_census_reconciliation, 6_environment, paper.MANIFEST.json lists a SHA-256 for all files and verify_manifest.py checks them. Evidentiary status. The deposit is retrospective. Hashes establish consistency between the deposited files and the production records, which embed the SHA-256 of the plan they ran under; they do not independently establish chronology. The pre-production freeze is author-reported and no independently timestamped commitment exists. Amendment A1 was made after all results and the frozen verdicts had been seen; the frozen output is the prespecified result and the corrected output is reported alongside it, never in its place. Key identifiers. Frozen analysis plan SHA-256dc6b8bdb3faa8450de3a710204ba18a72e4ed0be54639bae990d945b328a2bf5; primary production record4e3d3a58b6028531884c1de36eae15ac6d30146d1fb2599b150f898bbcf4051f; secondary production record8bf402ccc471ae9331a43d8e6f3bc383861599269922bfe89aa51f29430c5a33. Verified by extracting the archive and re-running: manifest 53/53 files, validation test suites pass, regression suite 35/35, and the frozen-path analysis reproduces every contrast and slope line of the original output.
This repository contains the computational reproducibility and verification package accompanying the frozen Version v1.0 manuscript: “Phase Curvature and Assumption-Budgeted Certification in Gravity-Mediated Entanglement.” The associated manuscript develops an operational certification framework for gravity-mediated entanglement experiments. Its central aim is to quantify when an observed entanglement signal excludes a specified neighborhood of local classical-mediator models under explicit assumptions and separately controlled nuisance channels. The package supports the manuscript’s analytical and numerical results concerning: gauge-invariant nonseparable phase curvature for diagonal two-path interactions; exact concurrence and separability-distance formulas for pure two-qubit outputs; assumption-budgeted exclusion bounds around the classical-mediator free class; primal and dual PPT/semidefinite-program certification; finite-shot confidence bounds for experimentally accessible Pauli correlators; certified residual bounds for physically compensated coherent nuisance interactions; stochastic geometry and Casimir–Polder uncertainty budgets; matter-bypass and common-auxiliary-channel bookkeeping; circular-shield mode analysis, including the azimuthal matched-null obstruction; thermal shield-channel factorization; finite-footprint high-mode suppression; an analytic positive high-mode tail bound for the shield benchmark; and a conservative outward-rounded audit of the finite numerical mode block. The frozen manuscript does not claim that a particular experimental apparatus has already closed every systematic-error channel. Quantities such as preparation error, matter-channel leakage, shield-model discrepancy, control error, and readout error remain apparatus-dependent inputs to the certification framework. Package contents The archive includes: the frozen Version v1.0 manuscript source; deterministic verification scripts for the theorem-core identities; finite-shot and Casimir–Polder statistical/geometry checks; shield-mode and analytic-tail verification; conservative floating-point interval/audit checks; submission-interface regression checks; machine-readable verification reports; and a SHA256 manifest for file-integrity verification. All verification scripts distributed with the Version v1.0 package return PASS under the documented software environment. The numerical audit is intended as a transparent reproducibility layer for the stated model calculations. It should not be interpreted as a formal interval-special-function proof or as certification of a realized experimental apparatus.
Theory of Quantum Entanglement of Particles: Multiscale Graph States, Region Geometry, Quantum Error Correction, and the Effective-Space Hypothesis Abstract This study develops a finite-dimensional, computationally testable framework for examining how multiscale graph structure organizes quantum entanglement and the accessibility of logical information. For the circulant graph family G_N, where N = 2ⁿ, n ≥ 3, and edge offsets are 1, 2, 4, …, N/2, an analytic proof establishes that the binary adjacency matrix across every contiguous block A of length L ≤ N/2 has rank L over F₂. For the associated graph states, this yields S(A) = min(L, N − L). For G₈, the study enumerates 238 proper connected vertex subsets ("tubes") and 32,640 maximal tubings and computes the entanglement entropy of every tube. Explicit bit-flip and phase-dual quantum error-correcting code embeddings are examined under specified Pauli-noise and erasure models, showing that recovery performance depends on the encoding, error model, and decoder class, not on graph-state entropy alone. The dynamical component, M1-Green, models a four-dimensional logical code coupled to eight intermediary bosonic modes and sequential collision-bin output registers. At selected resonantly matched parameter settings and T = 120/K, the computed mutual information I(Ref:R) reaches 3.9414 bits for G₈ and 3.8876 bits for C₈, below the four-bit upper bound. The study also reports a verified finite-step symmetry for C₈ in the tested setup, Petz recovery, and a numerical semidefinite-programming interval of 0.235788–0.245982 for recovery fidelity in a specified 69-dimensional output-space formulation. A one-port Page-like model, a random-unitary scrambling benchmark, and a two-sided mediated channel are treated as distinct models. The accompanying compact archive provides scripts, data tables, figures, and numerical certificates. The effective-space interpretation remains a hypothesis; global recovery optimality and independent experimental validation are not claimed. Keywords: quantum entanglement; graph states; multiscale graphs; circulant graphs; entanglement entropy; graph associahedra; quantum error correction; erasure channels; logical information recovery; collision-bin dynamics; Petz recovery map; semidefinite programming; quantum scrambling; effective geometry.
Draft preprint. Not submitted to a venue. Quantum compiler benchmarks are used to accept or reject changes to production transpilers, but the compilers they measure are stochastic. At the pinned revision of IBM's Benchpress benchmark suite, its Qiskit gym compiles without passing seed_transpiler, so every gate count it reports is one draw from an unmeasured distribution — while the BQSKit gym in the same repository does seed its compiler. We quantify the consequence as finite-sample decision risk: the probability that a regression verdict computed from k runs per version disagrees with the verdict implied by the long-run mean of the same measurement. On bv_n140 mapped to a heavy-hex lattice, measured over 400 seeds per version across 21 OS processes, the change from Qiskit 1.4.3 to 2.0.0 has a long-run mean of +5.37% (95% CI +4.27% to +6.50%). The suite's own protocol — three unseeded runs per version — reports it as a ≥+10% regression 24.4% of the time (95% CI 19.5–31.1%). A disjoint 200-seed sample across ten fresh processes reproduces this at 22.6%. Twenty runs per version, roughly 40 hours of compute, still leaves 3.7%. A pre-registered replication across 39 circuits is reported in full: the analysis code was committed before the data existed, and the commit ordering is included in this archive as COMMIT_TIMESTAMPS.txt. The pre-registered primary endpoint is 12 of 26 eligible circuits (46.2%, Wilson 95% CI 28.8–64.5%), reported alongside a cluster-robust interval of [17.4%, 81.0%] that reflects algorithm-family clustering. What this archive contains: the paper, the complete analysis and measurement code, and all 41,790 raw per-seed measurements. verify.py re-runs six checks — the toolchain pin, the test suite, the numeric inventory, the replication artifact, a proof of a withdrawn analytical claim, and a recomputation of every quantitative claim in the manuscript against the text — in about two minutes. Four claims from earlier phases of this work were withdrawn on the record after adversarial review, and the withdrawals remain in the repository with the evidence that defeated them. Passing seed_transpiler removes false positives on the circuits tested but was worse on three of four circuits exhibiting false negatives, and is not presented as a general remedy. Changes in v2 (2026-09-10). This version corrects two overstatements carried by the v1 manuscript and adds one new pre-registered result. No measurement changed, and no reported figure moved. Withdrawn. v1 stated that Benchpress sets no transpiler seed anywhere. That is narrowed to the claim the evidence supports: at the pinned revision, the Qiskit gym compiles without passing seed_transpiler — while the sibling BQSKit gym does seed its compiler, and six further gyms were not assessed. v1 also stated that the work identifies the mechanism that governs the effect. The paper now reports what predicts the risk and explicitly declines to call that association a compiler mechanism. Added: a pre-registered cross-machine determinism control. All 216 per-seed gate counts are identical across two physical machines with different CPU vendors (AMD64 AuthenticAMD, 16 cores, Python 3.10.10; Intel64 GenuineIntel, 8 cores, Python 3.10.21), over all three Qiskit versions including the 1.4.3 → 2.0.0 pair the primary study uses. The design was committed before the second machine existed and inherits the frozen six-circuit, twelve-seed selection, so it introduces no selection freedom. Stated scope limit: both machines ran rustworkx 0.18.1, so this cannot separate “the CPU does not matter” from “the graph library was identical, so the CPU never had the opportunity to matter”. The primary 200-seed study itself ran on one machine. Also in this archive. The settled-question ledger now holds 33 entries, each naming the attack, who made it, the command that settled it and the result; it includes three rounds of external adversarial audit of the cross-machine comparator itself, in which fourteen defects were found in the checking instrument and none in the measurements. The cross-machine evidence, its pre-registration, the comparator and its property-based fuzz tests are included. The numeric inventory now records a provenance tier per figure (29 re-derived from raw per-seed files, 12 read from a summary table, 5 not applicable). verify.py now runs six checks rather than five, the sixth recomputing every quantitative claim in the manuscript and comparing it to the text. Two reproducibility defects in the README were fixed: a shallow clone that could not reach the pinned Benchpress revision, and a missing environment without which the primary 1.4.3 → 2.0.0 study could not be reproduced at all.
Version 2: pre-registration addendum for Phase D Outcome of the registered gate (G0) The G0 gate failed for every dataset, window family and null. No twin built from independent error mechanisms with circuit-local supports reproduces the bulk of the window-count distributions in the public data from Google Willow, Google Sycamore or Rigetti. For larger codes the twin cannot even be simulated. As the protocol requires, hypotheses H1–H3 are therefore not tested. This version adds pre-registration addendum 1. It fixes the analyses run instead, before either touches the test halves: • Model-free certificate (T3), on the test halves. It covers every registered configuration that has a circuit (the Google archives and Rigetti D6e). Windows are whole-patch windows of 1 and of 5 rounds, separated by one unused round, and the disjointness of their fault-location sets is checked from each circuit. Each stratum (archive, code family, code distance, window family) gets a premise curve ε_lo(k) on the grid k = c·j, j = 1–16, with Bonferroni correction at family-wise α = 0.05.• Threshold values for the certificate. ε* = 7.4 × 10⁻⁴ (Fowler, PRL 109, 180502, 2012) is the primary value; 2.73 × 10⁻⁵ (Aliferis, Gottesman and Preskill, QIC 6, 97, 2006) is a sensitivity check. Certificates against ε* are computed for surface-code strata only. Repetition-code, colour-code and stability strata get premise curves only.• Bursts. The primary analysis uses all windows; a secondary one excludes the windows flagged by the frozen burst classifier. B1/B2 event rates are reported descriptively.• Cat-qubit case study (exploratory). The model-based premise meter is applied to the AWS cat-qubit (D4) distance-3 configurations whose twin was simulable in G0. It reports R(k) intervals and k_cert, with the H1 reading (consistent if R_hi ≤ 3 for all k ≤ k_cert). It is labelled exploratory because D4's own G0 verdict is a fail. Status of the data when version 2 was created G0, which uses only the bulk bins, has run on the test halves. Its stored histograms include tail bins, but no tail statistic has been computed or examined. Both new analyses were dry-run on fit halves as pipeline checks. One choice was made after that dry run, and it is recorded in the addendum: ε* certificates were limited to surface-code strata, and strata were split by code family. The dry run had shown repetition-code and stability strata crossing ε* at k = c, i.e. at their base error rate, where Fowler's surface-code theorem does not apply. The model-based certification horizon is not computed, because it needs a twin tail. Files added in version 2 • phaseD_addendum.json: the machine-readable addendum. SHA-256: a458bcb40aa474d94a882a563a38a1a152d7bfb4404df9299f99fb020ab78834• ADDENDUM.md: the readable version of the addendum.• qpremise_code_phaseD_ade59b0.zip: the code that will run. The addendum's code_sha256 (794122ae1557c009664127e1c2e6b109781d5a71efcc566bc637b991c0403ab6) can be recomputed from it as the SHA-256 over the files matching qpremise/**/*.py, phaseD/scripts/*.py and phaseC/scripts/run_g0.py, taken in path order: each file's relative path, then its bytes with LF line endings.• SHA256SUMS_addendum.txt: checksums of the three files above. The version 1 files are unchanged. The original registration text follows. ──────────────────────────── Version 1 registration (2026-10-01) What this registers The analysis protocol of the premise meter. It tests whether public quantum-error-correction syndrome data agree with an independent-noise "twin" fitted to the same data. It also measures how far each dataset can certify the local-stochastic premise of the threshold theorem. Every analysis choice is fixed in frozen_protocol.json:• configuration eligibility, and the pre-registered subset in g0_selection.json;• the interleaved fit/test split;• the window families;• twin construction: candidate mechanisms from each circuit, an exact parity-moment fit, and a signed quasi-probability simulation with local weights;• the G0 gate decision rule;• the burst classifiers B1 and B2 with their validation targets;• the excess-tail-ratio interval and the certification-horizon conditions;• the model-free certificate's window rule. qpremise_code_at_freeze_79dbf14.zip holds the analysis code at the freeze. The protocol's code_sha256 can be recomputed from it: the SHA-256 over every qpremise/**/*.py file in path order, each file's relative path followed by its bytes with LF line endings. Hypotheses analysed after this registration (on test halves only) H1. After removing windows flagged by the frozen burst classifier, the excess tail ratio R(k) = P_obs(K ≥ k) / P_twin(K ≥ k) has an upper 95% confidence bound ≤ 3 for all k ≤ k_cert. Failure: a lower bound > 3 that replicates on the held-out half. H2. Including burst windows, R(k) > 10 for k ≥ k_b in at least one dataset, and a burst-mixture model fitted to the flagged windows predicts the published repetition-code error floor within a factor of 10. H3. The empirical horizon (power ≥ 0.8 at α = 0.05 against a factor-5 excess) agrees with the exact binomial computation within ±1. At least one dataset certifies k ≥ 10 in whole-patch windows. These are evaluated only on (dataset, window family) pairs that pass the G0 gate under both the stationary (N1) and drift-aware (N5) twins. The model-free certificate (T3) does not depend on the twin. Its threshold ε* is fixed before any certificate is computed. Timing and what had been seen Frozen 2026-10-01 17:31 IST (git commit 79dbf14). Before the freeze, only fit halves had been analysed. The G0 gate (bulk of the window-count distributions only; decision rule frozen) began on the test halves minutes after the freeze. When this record was created, no tail statistic (R(k), H1–H3, burst rates, certificates) had been computed from the test halves, and their tail bins had not been examined. The planned cloud-hardware contrast experiment (H4, H5) is not part of this registration and will be registered separately before any hardware run. Full details are in PREREGISTRATION.md. Protocol SHA-256: 5f7458cfdbe0e203fd9e2bf5d579703509c8374bae53096c37f8f1530540707a
La première partie de ce mémoire traite de l'intrication quantique (entropie de Von Neumann) dans certains systèmes bidimensionnels. Il s'agit de fonctions d'onde de type Rokhsar-Kivelson (RK), construites à partir des poids de Boltzmann d'un modèle classique (modèle de dimères, de vertex ou de spins d'Ising par exemple). Nous montrons comment le spectre des matrices densité réduites de ces états s'obtient à partir des probabilités du modèle classique sous-jacent. Cette observation permet de calculer numériquement l'entropie d'intrication dans de grands systèmes, et en particulier de tester la présence de constantes sous-dominantes universelles dans le cas d'un liquide (de dimères) topologique de type Z_2 (construction de Kitaev-Preskill & Levin-Wen) et dans le cas d'une fonction d'onde critique (dimères sur réseaux bipartites).Si le système est un cylindre infiniment long et que le sous-système considéré est un demi-cylindre infini, le spectre de la matrice densité réduite peut se calculer plus simplement encore, par matrice de transfert. L'entropie d'intrication entre les deux moitiés du système apparaît alors comme l'entropie de Shannon associée aux probabilités des différentes configurations des degrés de liberté qui se trouvent à la frontière (un cercle). Ceci nous conduit à considérer l'entropie de Shannon (et ses généralisations de type Rényi)d'une fonction d'onde à N corps en tant que telle – indépendamment de son lien éventuel avec l'intrication quantique d'un état RK en dimension supérieure. Nous étudions les contributions universelles de cette entropie dans trois cas:1) les liquides de Tomonaga-Luttinger, cadre dans lequel nous établissons un lien entre l'entropie de Shannon-Rényi et des problèmes de théories conformes avec bords, et calculons exactement les termes universels de l'entropie en fonction du paramètre de Luttinger et de l'indice de Rényi;2) la chaîne d'Ising critique en champ transverse, pour laquelle nos simulations numériques montrent la présence d'une transition de phase à n=1 (indice de Rényi), qui reste mal comprise théoriquement, et pour laquelle une approche par méthode des répliques semble inadaptée;et enfin 3) des systèmes bidimensionnels avec symétrie continue spontanément brisée, où nous expliquons par un argument dechamp libre (et de tour d'états) la présence de termes en log(L) dans l'entropie, comme récemment observé par simulations Monte-Carlo quantique.