{"data":[{"id":"https://doi.org/10.5281/zenodo.20721893","type":"works","attributes":{"doi":"10.5281/zenodo.20721893","identifier":"https://doi.org/10.5281/zenodo.20721893","url":"https://zenodo.org/doi/10.5281/zenodo.20721893","author":[{"given":"EUGENE","family":"CATRAMBONE"}],"title":"The Balance Ridge Instrument: An Interactive Test of the Record-Stability Conjecture on the Riemann Sphere","container-title":"Zenodo","description":"This record deposits the Balance Ridge instrument (blaschke_balance_ridge.html) and its companion instrument note. The instrument is a standalone browser-based tool (no installation required) that renders the record-stability field S_n and the discrete Lagrangian descriptor field MD_p for Blaschke quotient maps on the Riemann sphere, providing a live, computable test of the Balance Ridge Conjecture: that the high-balance layer {S_n \u003e 0.9} converges to the Julia set as N -\u003e infinity, with surface area shrinking to zero.\n\nTwo test configurations are reported in the note. In the degree-1 configuration (1 root, 1 pole) the balance layer occupies 2.47% of the sphere at N=24, 0.16% at N=48, and 0.00% at N=96. In the degree-3 default configuration (3 roots, 1 pole) convergence is faster: 1.67% at N=12, 0.02% at N=24, and 0.00% at N=48. Both runs are consistent with the conjecture. Three explicit failure conditions are stated. The instrument is released as open software under CC BY 4.0.\n\nThis is a companion to the Computable Records paper (doi:10.5281/zenodo.20662285) and the Signature of Registration paper (doi:10.5281/zenodo.20650285). Comments welcome.\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\nVersion 2 — corrections. The measured data remain unchanged from v1; the following errors have been corrected.\n\n\n\nMap degree labels corrected. A Blaschke quotient with r roots and p poles has degree r + p as a rational map of the sphere, not max(r, p). The test configurations are therefore relabeled: the 1-root/1-pole configuration is degree 2 (previously mislabeled degree 1), and the 3-root/1-pole default configuration is degree 4 (previously mislabeled degree 3). The degree readout in the accompanying instrument file (blaschke_balance_ridge.html) is fixed accordingly; the updated HTML is included in this version.\n\nConjecture statement corrected. The Balance Ridge Conjecture is now quoted verbatim from the Computable Records paper (ridge-set convergence in Hausdorff distance to J(f) ∪ R(f)). The area-threshold measurement reported here is now correctly presented as an operational proxy of that conjecture, not as the conjecture itself.\n\nReference corrected. The García-Garrido citation now points to the correct source for the Julia-set result: V. J. García-Garrido, “Unveiling the fractal structure of Julia sets with Lagrangian descriptors,” Communications in Nonlinear Science and Numerical Simulation, vol. 91, 105417, 2020. https://doi.org/10.1016/j.cnsns.2020.105417\n\nWording tightened. \"Confirm the framework prediction\" changed to \"are consistent with the framework prediction,\" matching the abstract; the higher-degree failure condition now reads degree ≥ 5, since degrees 2 and 4 are tested here.\n\nLayout. Figures now appear in Section 4 rather than after the acknowledgments.\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n \n\n\n\n\n\n ","resource-type-subtype":"","data-center-id":"cern.zenodo","member-id":"cern","resource-type-id":"software","version":null,"license":"https://creativecommons.org/licenses/by/4.0/legalcode","schema-version":"4","results":[],"related-identifiers":[],"related-items":[],"citation-count":2,"citations-over-time":[{"year":"2026","total":2}],"view-count":0,"views-over-time":[],"download-count":0,"downloads-over-time":[],"published":"2026","registered":"2026-06-16T18:00:06Z","checked":null,"updated":"2026-06-16T18:00:06Z","media":[],"xml":"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"},"relationships":{"data-center":{"data":{"id":"cern.zenodo","type":"data-centers"}},"member":{"data":{"id":"cern","type":"members"}},"resource-type":{"data":{"id":"software","type":"resource-types"}}}}],"meta":{"resource-types":[{"id":"software","title":"Software","count":936898}],"registered":[{"id":"2026","title":"2026","count":159174},{"id":"2025","title":"2025","count":185688},{"id":"2024","title":"2024","count":128413},{"id":"2023","title":"2023","count":111392},{"id":"2022","title":"2022","count":97322},{"id":"2021","title":"2021","count":80116},{"id":"2020","title":"2020","count":57599},{"id":"2019","title":"2019","count":39115},{"id":"2018","title":"2018","count":29321},{"id":"2017","title":"2017","count":27994}],"providers":[{"id":"cern","title":"CERN - European Organization for Nuclear Research","count":854200},{"id":"otjm","title":"Figshare Internal","count":38101},{"id":"ocean","title":"Code Ocean","count":9039},{"id":"doe","title":"Department of Energy (DOE)","count":5828},{"id":"nihod","title":"National Institutes of Health, Office of the Director (NIH OD)","count":4538},{"id":"purdue","title":"Purdue University West Lafayette","count":4212},{"id":"xklm","title":"Deutsches Forschungszentrum für Künstliche Intelligenz GmbH","count":2770},{"id":"kim","title":"Knowledgebase of Interatomic Models","count":2336},{"id":"scpr","title":"4TU.ResearchData","count":1197},{"id":"stdp","title":"ETH Zurich","count":1076}],"data-centers":[{"id":"cern.zenodo","title":"Zenodo","count":854172},{"id":"figshare.ars","title":"figshare Academic Research System","count":38073},{"id":"ocean.ocean","title":"Code Ocean","count":9039},{"id":"doe.osti","title":"DOE Office of Scientific and Technical Information (OSTI) Repository","count":5828},{"id":"nihod.bioc","title":"NCI BioConductor","count":4494},{"id":"purdue.hubzero","title":"HubZero","count":4212},{"id":"xklm.wejabm","title":"European Language Grid","count":2770},{"id":"kim.openkim","title":"Open Knowledgebase of Interatomic Models (OpenKIM)","count":2336},{"id":"delft.data4tu","title":"4TU.ResearchData","count":1197},{"id":"brainl.iu","title":"brainlife.io","count":1002}],"affiliations":[{"id":"ror.org/052gg0110","title":"University of Oxford","count":781},{"id":"ror.org/02e2c7k09","title":"Delft University of Technology","count":770},{"id":"ror.org/05a28rw58","title":"ETH Zurich","count":700},{"id":"ror.org/05591te55","title":"Ludwig-Maximilians-Universität München","count":654},{"id":"ror.org/04t3en479","title":"Karlsruhe Institute of Technology","count":627},{"id":"ror.org/02jx3x895","title":"University College London","count":545},{"id":"ror.org/035a68863","title":"United States Geological Survey","count":529},{"id":"ror.org/04xfq0f34","title":"RWTH Aachen University","count":512},{"id":"ror.org/02kkvpp62","title":"Technical University of Munich","count":483},{"id":"ror.org/042nb2s44","title":"Massachusetts Institute of Technology","count":458}],"total":936898,"total-pages":10000,"page":1}}