{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:RVIHWVRNPWAN4WD64J6SGTH5W4","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"9645758d882efb991f7631e9928f99fe6f58ea7a66250510cc7d54738d7702bf","cross_cats_sorted":["math.AP","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2025-03-04T13:18:04Z","title_canon_sha256":"a9f5d61fae31c6261e159217b3aa91a1ab8a7133c2d7e5a514e3bbb37021c5ac"},"schema_version":"1.0","source":{"id":"2503.02596","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.02596","created_at":"2026-07-05T10:24:09Z"},{"alias_kind":"arxiv_version","alias_value":"2503.02596v1","created_at":"2026-07-05T10:24:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.02596","created_at":"2026-07-05T10:24:09Z"},{"alias_kind":"pith_short_12","alias_value":"RVIHWVRNPWAN","created_at":"2026-07-05T10:24:09Z"},{"alias_kind":"pith_short_16","alias_value":"RVIHWVRNPWAN4WD6","created_at":"2026-07-05T10:24:09Z"},{"alias_kind":"pith_short_8","alias_value":"RVIHWVRN","created_at":"2026-07-05T10:24:09Z"}],"graph_snapshots":[{"event_id":"sha256:96d0607d0f5de3ed0bc68fb2640a68f5ea6789c89deb207a31249b7f9e2a3541","target":"graph","created_at":"2026-07-05T10:24:09Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2503.02596/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We investigate the first-order differential calculus over extended metric-topological measure spaces. The latter are quartets $\\mathbb X=(X,\\tau,{\\sf d},\\mathfrak m)$, given by an extended metric space $(X,{\\sf d})$ together with a weaker topology $\\tau$ (satisfying suitable compatibility conditions) and a finite Radon measure $\\mathfrak m$ on $(X,\\tau)$. The class of extended metric-topological measure spaces encompasses all metric measure spaces and many infinite-dimensional metric-measure structures, such as abstract Wiener spaces. In this framework, we study the following classes of object","authors_text":"Enrico Pasqualetto, Janne Taipalus","cross_cats":["math.AP","math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2025-03-04T13:18:04Z","title":"Derivations and Sobolev functions on extended metric-measure spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.02596","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:4f8ba9e6cfda3deeedb55eb6e018017eceee8921edcfd8e27002e551f1094f81","target":"record","created_at":"2026-07-05T10:24:09Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"9645758d882efb991f7631e9928f99fe6f58ea7a66250510cc7d54738d7702bf","cross_cats_sorted":["math.AP","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2025-03-04T13:18:04Z","title_canon_sha256":"a9f5d61fae31c6261e159217b3aa91a1ab8a7133c2d7e5a514e3bbb37021c5ac"},"schema_version":"1.0","source":{"id":"2503.02596","kind":"arxiv","version":1}},"canonical_sha256":"8d507b562d7d80de587ee27d234cfdb7358b3d69c1157ebd6f933fe33b30f885","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8d507b562d7d80de587ee27d234cfdb7358b3d69c1157ebd6f933fe33b30f885","first_computed_at":"2026-07-05T10:24:09.334939Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:24:09.334939Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6uHY4rTGHSf8V0cdyHmIebdwF4g0bASAOeqzSF908lltmwIqoVvcPhHTJYGXBRvwGBA2LY3uJzrTsL6Tit5OAg==","signature_status":"signed_v1","signed_at":"2026-07-05T10:24:09.337269Z","signed_message":"canonical_sha256_bytes"},"source_id":"2503.02596","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4f8ba9e6cfda3deeedb55eb6e018017eceee8921edcfd8e27002e551f1094f81","sha256:96d0607d0f5de3ed0bc68fb2640a68f5ea6789c89deb207a31249b7f9e2a3541"],"state_sha256":"407a128813d0e39f3cd46451fc4a9a27ec1613986b067d7705608ed5192f0249"}