{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:2NH67ID2X4HUI6QRPLPASUYJIG","short_pith_number":"pith:2NH67ID2","schema_version":"1.0","canonical_sha256":"d34fefa07abf0f447a117ade095309418e3ceae620edda679e6a0449c8b0f54f","source":{"kind":"arxiv","id":"2606.02846","version":1},"attestation_state":"computed","paper":{"title":"Cheeger Inequalities for the Persistent Laplacian","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Magnus Bakke Botnan, Rui Dong","submitted_at":"2026-06-01T20:10:48Z","abstract_excerpt":"We study Cheeger-type inequalities for persistent Laplacians associated with inclusions of simplicial complexes $\\mathcal{K}\\hookrightarrow \\mathcal{L}$. We introduce a persistent up $p$-Laplacian $\\Delta_{q,p,\\mathrm{up}}^{\\mathcal{K},\\mathcal{L}}$ for $p\\geq 1$. For $p=2$, this recovers the usual persistent up Laplacian, while for $p=1$ it yields a nonzero persistent Cheeger constant $\\varphi_q^{\\mathcal{K},\\mathcal{L}}$. We prove a Cheeger-type inequality relating $\\varphi_q^{\\mathcal{K},\\mathcal{L}}$ to the smallest nonzero eigenvalue of $\\Delta_{q,\\mathrm{up}}^{\\mathcal{K},\\mathcal{L}}$. "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2606.02846","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AT","submitted_at":"2026-06-01T20:10:48Z","cross_cats_sorted":[],"title_canon_sha256":"7c90d71ac8615a2cfd4ca43390c7ee4e3bfe0272da637e8f69ccd5dca8107d0d","abstract_canon_sha256":"7d4c56d35b20e8b86245cfbba687fd212d4317bb564e1538d7eff7543957dbc3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-03T01:05:24.460032Z","signature_b64":"yL47EMp4gBBWOIkJoTrpED/CId/IwRzsWvwMvq7UAuEj8VpiRR2h4RgaeRbbImG5ePILNnH8CfJs9je+N85SDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d34fefa07abf0f447a117ade095309418e3ceae620edda679e6a0449c8b0f54f","last_reissued_at":"2026-06-03T01:05:24.459660Z","signature_status":"signed_v1","first_computed_at":"2026-06-03T01:05:24.459660Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cheeger Inequalities for the Persistent Laplacian","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Magnus Bakke Botnan, Rui Dong","submitted_at":"2026-06-01T20:10:48Z","abstract_excerpt":"We study Cheeger-type inequalities for persistent Laplacians associated with inclusions of simplicial complexes $\\mathcal{K}\\hookrightarrow \\mathcal{L}$. We introduce a persistent up $p$-Laplacian $\\Delta_{q,p,\\mathrm{up}}^{\\mathcal{K},\\mathcal{L}}$ for $p\\geq 1$. For $p=2$, this recovers the usual persistent up Laplacian, while for $p=1$ it yields a nonzero persistent Cheeger constant $\\varphi_q^{\\mathcal{K},\\mathcal{L}}$. We prove a Cheeger-type inequality relating $\\varphi_q^{\\mathcal{K},\\mathcal{L}}$ to the smallest nonzero eigenvalue of $\\Delta_{q,\\mathrm{up}}^{\\mathcal{K},\\mathcal{L}}$. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.02846","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.02846/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2606.02846","created_at":"2026-06-03T01:05:24.459715+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.02846v1","created_at":"2026-06-03T01:05:24.459715+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.02846","created_at":"2026-06-03T01:05:24.459715+00:00"},{"alias_kind":"pith_short_12","alias_value":"2NH67ID2X4HU","created_at":"2026-06-03T01:05:24.459715+00:00"},{"alias_kind":"pith_short_16","alias_value":"2NH67ID2X4HUI6QR","created_at":"2026-06-03T01:05:24.459715+00:00"},{"alias_kind":"pith_short_8","alias_value":"2NH67ID2","created_at":"2026-06-03T01:05:24.459715+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2NH67ID2X4HUI6QRPLPASUYJIG","json":"https://pith.science/pith/2NH67ID2X4HUI6QRPLPASUYJIG.json","graph_json":"https://pith.science/api/pith-number/2NH67ID2X4HUI6QRPLPASUYJIG/graph.json","events_json":"https://pith.science/api/pith-number/2NH67ID2X4HUI6QRPLPASUYJIG/events.json","paper":"https://pith.science/paper/2NH67ID2"},"agent_actions":{"view_html":"https://pith.science/pith/2NH67ID2X4HUI6QRPLPASUYJIG","download_json":"https://pith.science/pith/2NH67ID2X4HUI6QRPLPASUYJIG.json","view_paper":"https://pith.science/paper/2NH67ID2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.02846&json=true","fetch_graph":"https://pith.science/api/pith-number/2NH67ID2X4HUI6QRPLPASUYJIG/graph.json","fetch_events":"https://pith.science/api/pith-number/2NH67ID2X4HUI6QRPLPASUYJIG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2NH67ID2X4HUI6QRPLPASUYJIG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2NH67ID2X4HUI6QRPLPASUYJIG/action/storage_attestation","attest_author":"https://pith.science/pith/2NH67ID2X4HUI6QRPLPASUYJIG/action/author_attestation","sign_citation":"https://pith.science/pith/2NH67ID2X4HUI6QRPLPASUYJIG/action/citation_signature","submit_replication":"https://pith.science/pith/2NH67ID2X4HUI6QRPLPASUYJIG/action/replication_record"}},"created_at":"2026-06-03T01:05:24.459715+00:00","updated_at":"2026-06-03T01:05:24.459715+00:00"}