{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:DL5JBERM6Y4XUI6G5L5DLWMNAT","short_pith_number":"pith:DL5JBERM","schema_version":"1.0","canonical_sha256":"1afa90922cf6397a23c6eafa35d98d04ffccce4246ffd0c245c9c1905b74c24a","source":{"kind":"arxiv","id":"2502.03691","version":2},"attestation_state":"computed","paper":{"title":"Nonlinear Beurling-Deny criteria","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Simon Puchert","submitted_at":"2025-02-06T00:51:35Z","abstract_excerpt":"This short note introduces a simple symmetric contraction property for functionals. This property clearly characterizes Dirichlet forms in the linear case. We show that it also characterizes Dirichlet forms in the non-linear case. Furthermore, we use this property to gain a new perspective on criteria of Cipriani / Grillo as well as Brigati / Hartarsky."},"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":"2502.03691","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2025-02-06T00:51:35Z","cross_cats_sorted":[],"title_canon_sha256":"31936f548452a33df74c3ed5ae980e966fbeb398fccfb728fa035f31e0ba6d41","abstract_canon_sha256":"343df8226624093485d3d3e2897757d5773fa84ebbfc83fe64b290eb2b066f33"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:16:54.752730Z","signature_b64":"pRZVxUvjTWmT8mVh3HnwAz+V9Mw8GjdgWaYvawJnO/pVvnBKyMbU24Xv2bMNSzfioQHY+o3auDFBmiAVb0YnDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1afa90922cf6397a23c6eafa35d98d04ffccce4246ffd0c245c9c1905b74c24a","last_reissued_at":"2026-07-05T11:16:54.752214Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:16:54.752214Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Nonlinear Beurling-Deny criteria","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Simon Puchert","submitted_at":"2025-02-06T00:51:35Z","abstract_excerpt":"This short note introduces a simple symmetric contraction property for functionals. This property clearly characterizes Dirichlet forms in the linear case. We show that it also characterizes Dirichlet forms in the non-linear case. Furthermore, we use this property to gain a new perspective on criteria of Cipriani / Grillo as well as Brigati / Hartarsky."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.03691","kind":"arxiv","version":2},"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/2502.03691/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":"2502.03691","created_at":"2026-07-05T11:16:54.752273+00:00"},{"alias_kind":"arxiv_version","alias_value":"2502.03691v2","created_at":"2026-07-05T11:16:54.752273+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.03691","created_at":"2026-07-05T11:16:54.752273+00:00"},{"alias_kind":"pith_short_12","alias_value":"DL5JBERM6Y4X","created_at":"2026-07-05T11:16:54.752273+00:00"},{"alias_kind":"pith_short_16","alias_value":"DL5JBERM6Y4XUI6G","created_at":"2026-07-05T11:16:54.752273+00:00"},{"alias_kind":"pith_short_8","alias_value":"DL5JBERM","created_at":"2026-07-05T11:16:54.752273+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2507.03426","citing_title":"Nonlinear resistance forms","ref_index":27,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/DL5JBERM6Y4XUI6G5L5DLWMNAT","json":"https://pith.science/pith/DL5JBERM6Y4XUI6G5L5DLWMNAT.json","graph_json":"https://pith.science/api/pith-number/DL5JBERM6Y4XUI6G5L5DLWMNAT/graph.json","events_json":"https://pith.science/api/pith-number/DL5JBERM6Y4XUI6G5L5DLWMNAT/events.json","paper":"https://pith.science/paper/DL5JBERM"},"agent_actions":{"view_html":"https://pith.science/pith/DL5JBERM6Y4XUI6G5L5DLWMNAT","download_json":"https://pith.science/pith/DL5JBERM6Y4XUI6G5L5DLWMNAT.json","view_paper":"https://pith.science/paper/DL5JBERM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2502.03691&json=true","fetch_graph":"https://pith.science/api/pith-number/DL5JBERM6Y4XUI6G5L5DLWMNAT/graph.json","fetch_events":"https://pith.science/api/pith-number/DL5JBERM6Y4XUI6G5L5DLWMNAT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DL5JBERM6Y4XUI6G5L5DLWMNAT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DL5JBERM6Y4XUI6G5L5DLWMNAT/action/storage_attestation","attest_author":"https://pith.science/pith/DL5JBERM6Y4XUI6G5L5DLWMNAT/action/author_attestation","sign_citation":"https://pith.science/pith/DL5JBERM6Y4XUI6G5L5DLWMNAT/action/citation_signature","submit_replication":"https://pith.science/pith/DL5JBERM6Y4XUI6G5L5DLWMNAT/action/replication_record"}},"created_at":"2026-07-05T11:16:54.752273+00:00","updated_at":"2026-07-05T11:16:54.752273+00:00"}