{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T10:59:22Z","timestamp":1790852362878,"version":"4.1.0"},"reference-count":18,"publisher":"AIP Publishing","issue":"13","content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2026,10,7]]},"abstract":"<jats:p>Persistent homology provides multiscale structural descriptors for disordered particle systems, but state-to-state comparisons require consistent treatment of characteristic length scales, periodic boundaries, and statistical uncertainty. We define a lift-consistent local H1 observable under periodic boundary conditions (PBCs), normalize its longest finite persistence lifetime by the PBC mean nearest-neighbor distance, and compare states using the ratio RA\/B of state-averaged dimensionless lifetimes. Confidence intervals for R are obtained by nonparametric bootstrap for independent configurations and circular moving-block bootstrap for serially dependent trajectories. For the public N = 44 glass-forming benchmark, R0.32\/1.0 = 0.914\u200953 with a 95% confidence interval [0.905\u200917, 0.923\u200997], resolving a residual difference below unity. The local-PBC observable is unchanged over the validated range 2.0 \u2264 \u03b1 \u2264 3.4. Comparison with the raw local lifetime shows that normalization increases the departure from unity by 0.021\u200960, so it is interpreted as dimensionless local-length rescaling rather than correction of a specific contraction mechanism. A filled-disk\/ring calibration resolves a prescribed H1 contrast. For DFTB SiO2 trajectories, the pressure ratios are 0.517\u200988, 0.377\u200901, and 0.728\u200900, with all 95% confidence intervals excluding unity. The framework, therefore, supports statistically consistent local-topology comparisons across thermodynamic states while treating periodic winding and sampling dependence explicitly.<\/jats:p>","DOI":"10.1063\/5.0349045","type":"journal-article","created":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T10:40:46Z","timestamp":1790851246000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":0,"title":["Periodic-boundary-aware normalized persistent homology for glass-forming liquids: A simulation methodology"],"prefix":"10.1063","volume":"165","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3539-2334","authenticated-orcid":false,"given":"Zhenpeng","family":"Li","sequence":"first","affiliation":[{"name":"School of Information, Lijiang Culture and Tourism College , Lijiang,","place":["China"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2026,10,1]]},"reference":[{"key":"2026100106404207000_c1","doi-asserted-by":"publisher","first-page":"1924","DOI":"10.1126\/science.267.5206.1924","article-title":"Formation of glasses from liquids and biopolymers","volume":"267","year":"1995","journal-title":"Science"},{"key":"2026100106404207000_c2","doi-asserted-by":"publisher","first-page":"259","DOI":"10.1038\/35065704","article-title":"Supercooled liquids and the glass transition","volume":"410","year":"2001","journal-title":"Nature"},{"key":"2026100106404207000_c3","doi-asserted-by":"publisher","first-page":"587","DOI":"10.1103\/RevModPhys.83.587","article-title":"Theoretical perspective on the glass transition and amorphous materials","volume":"83","year":"2011","journal-title":"Rev. Mod. Phys."},{"key":"2026100106404207000_c4","doi-asserted-by":"publisher","first-page":"1935","DOI":"10.1126\/science.267.5206.1935","article-title":"A topographic view of supercooled liquids and glass formation","volume":"267","year":"1995","journal-title":"Science"},{"key":"2026100106404207000_c5","doi-asserted-by":"publisher","first-page":"511","DOI":"10.1007\/s00454-002-2885-2","article-title":"Topological persistence and simplification","volume":"28","year":"2002","journal-title":"Discrete Comput. Geom."},{"key":"2026100106404207000_c6","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1090\/S0273-0979-07-01191-3","article-title":"Barcodes: The persistent topology of data","volume":"45","year":"2008","journal-title":"Bull. Am. Math. Soc."},{"key":"2026100106404207000_c7","doi-asserted-by":"publisher","first-page":"7035","DOI":"10.1073\/pnas.1520877113","article-title":"Hierarchical structures of amorphous solids characterized by persistent homology","volume":"113","year":"2016","journal-title":"Proc. Natl. Acad. Sci. U. S. A."},{"key":"2026100106404207000_c8","doi-asserted-by":"publisher","first-page":"98","DOI":"10.1038\/s43246-020-00100-3","article-title":"Structural changes during glass formation extracted by computational homology with machine learning","volume":"1","year":"2020","journal-title":"Commun. Mater."},{"key":"2026100106404207000_c9","doi-asserted-by":"publisher","first-page":"100123","DOI":"10.1016\/j.nocx.2022.100123","article-title":"Persistent homology: A tool to understand medium-range order glass structure","volume":"16","year":"2022","journal-title":"J.\u00a0Non-Cryst. Solids: X"},{"key":"2026100106404207000_c10","doi-asserted-by":"publisher","first-page":"1376","DOI":"10.1103\/PhysRevLett.73.1376","article-title":"Scaling behavior in the \u03b2-relaxation regime of a supercooled Lennard-Jones mixture","volume":"73","year":"1994","journal-title":"Phys. Rev. Lett."},{"key":"2026100106404207000_c11","doi-asserted-by":"publisher","first-page":"4626","DOI":"10.1103\/PhysRevE.51.4626","article-title":"Testing mode-coupling theory for a supercooled binary Lennard-Jones mixture I: The van Hove correlation function","volume":"51","year":"1995","journal-title":"Phys. Rev. E"},{"key":"2026100106404207000_c12","unstructured":"L. Grenioux , L.Galliano, L.Berthier, G.Biroli, and M.Gabri\u00e9 (2025). \u201cEquilibrium samples from inverse power law and Kob-Andersen glassy systems,\u201d Zenodo. https:\/\/doi.org\/10.5281\/zenodo.17966995"},{"key":"2026100106404207000_c13","first-page":"167","article-title":"The Gudhi library: Simplicial complexes and persistent homology","volume-title":"Mathematical Software \u2013 ICMS 2014","year":"2014"},{"key":"2026100106404207000_c14","doi-asserted-by":"publisher","first-page":"62","DOI":"10.1038\/s41586-021-03918-0","article-title":"Percolation transitions in compressed SiO2 glasses","volume":"599","year":"2021","journal-title":"Nature"},{"key":"2026100106404207000_c15","unstructured":"A. Hasmy , S.Ispas, and B.Hehlen (2021). \u201cDFTB study of silica glass under pressure (figures\/samples trajectories),\u201d Zenodo, https:\/\/doi.org\/10.5281\/zenodo.5056541"},{"key":"2026100106404207000_c16","doi-asserted-by":"publisher","first-page":"627","DOI":"10.1126\/science.287.5453.627","article-title":"Three-dimensional direct imaging of structural relaxation near the colloidal glass transition","volume":"287","year":"2000","journal-title":"Science"},{"key":"2026100106404207000_c17","doi-asserted-by":"publisher","first-page":"3829","DOI":"10.1038\/ncomms4829","article-title":"Structural signatures of dynamic heterogeneities in monolayers of colloidal ellipsoids","volume":"5","year":"2014","journal-title":"Nat. Commun."},{"key":"2026100106404207000_c18","doi-asserted-by":"publisher","first-page":"340","DOI":"10.1038\/320340a0","article-title":"Phase behaviour of concentrated suspensions of nearly hard colloidal spheres","volume":"320","year":"1986","journal-title":"Nature"}],"container-title":["The Journal of Chemical Physics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pubs.aip.org\/aip\/jcp\/article-pdf\/doi\/10.1063\/5.0349045\/21156988\/134110_1_5.0349045.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/pubs.aip.org\/aip\/jcp\/article-pdf\/doi\/10.1063\/5.0349045\/21156988\/134110_1_5.0349045.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T10:40:50Z","timestamp":1790851250000},"score":1,"resource":{"primary":{"URL":"https:\/\/pubs.aip.org\/jcp\/article\/165\/13\/134110\/3405658\/Periodic-boundary-aware-normalized-persistent"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,10,1]]},"references-count":18,"journal-issue":{"issue":"13","published-print":{"date-parts":[[2026,10,7]]}},"URL":"https:\/\/doi.org\/10.1063\/5.0349045","relation":{},"ISSN":["0021-9606","1089-7690"],"issn-type":[{"value":"0021-9606","type":"print"},{"value":"1089-7690","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2026,10,7]]},"published":{"date-parts":[[2026,10,1]]},"article-number":"134110"}}