{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:ZLABNLJ7VJXOQQ67GIUSZMX57Y","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":"c810e53958757705d1cc9351582aa6e0e50af9a472503ec36bf11f71fc799d76","cross_cats_sorted":["math.AP","math.FA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.MG","submitted_at":"2025-03-23T17:55:44Z","title_canon_sha256":"6dda03e02fb69f16118ebd76d0b1ed21dd3bbea7a8cbf9cb1188745b9b92db6d"},"schema_version":"1.0","source":{"id":"2503.18157","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.18157","created_at":"2026-07-05T10:38:03Z"},{"alias_kind":"arxiv_version","alias_value":"2503.18157v1","created_at":"2026-07-05T10:38:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.18157","created_at":"2026-07-05T10:38:03Z"},{"alias_kind":"pith_short_12","alias_value":"ZLABNLJ7VJXO","created_at":"2026-07-05T10:38:03Z"},{"alias_kind":"pith_short_16","alias_value":"ZLABNLJ7VJXOQQ67","created_at":"2026-07-05T10:38:03Z"},{"alias_kind":"pith_short_8","alias_value":"ZLABNLJ7","created_at":"2026-07-05T10:38:03Z"}],"graph_snapshots":[{"event_id":"sha256:9d8f741f8848a2c0324d53ad85b3d85082ea3e78bfbf861b1afe780562c32634","target":"graph","created_at":"2026-07-05T10:38:03Z","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/2503.18157/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that every one-dimensional locally normal metric current, intended in the sense of U. Lang and S. Wenger, admits a nice integral representation through currents associated to (possibly unbounded) curves with locally finite length, generalizing the result shown by E. Paolini and E. Stepanov in the special case of Ambrosio-Kirchheim normal currents. Our result holds in Polish spaces, or more generally in complete metric spaces for 1-currents with tight support.","authors_text":"Federico Renzi, Federico Vitillaro, Luigi Ambrosio","cross_cats":["math.AP","math.FA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.MG","submitted_at":"2025-03-23T17:55:44Z","title":"The superposition principle for local 1-dimensional currents"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.18157","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:cfd79e09b3e8885b0de9b1350915443fd4ff91ec21524e8975760082470a1196","target":"record","created_at":"2026-07-05T10:38:03Z","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":"c810e53958757705d1cc9351582aa6e0e50af9a472503ec36bf11f71fc799d76","cross_cats_sorted":["math.AP","math.FA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.MG","submitted_at":"2025-03-23T17:55:44Z","title_canon_sha256":"6dda03e02fb69f16118ebd76d0b1ed21dd3bbea7a8cbf9cb1188745b9b92db6d"},"schema_version":"1.0","source":{"id":"2503.18157","kind":"arxiv","version":1}},"canonical_sha256":"cac016ad3faa6ee843df32292cb2fdfe060e273c478f933acd5c464188b4a055","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cac016ad3faa6ee843df32292cb2fdfe060e273c478f933acd5c464188b4a055","first_computed_at":"2026-07-05T10:38:03.868669Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:38:03.868669Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ODFhC37km8wuGAw0TYou5ycLaSTkZq13AaoiNAQw08CUrUoR50DzxC8NWyqm2+lZXE03SW8XAp3EPIbOInZaAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T10:38:03.869201Z","signed_message":"canonical_sha256_bytes"},"source_id":"2503.18157","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cfd79e09b3e8885b0de9b1350915443fd4ff91ec21524e8975760082470a1196","sha256:9d8f741f8848a2c0324d53ad85b3d85082ea3e78bfbf861b1afe780562c32634"],"state_sha256":"643a0425baa0705c879e0758bf50169e9c17900bf7d1a476177880371115dc51"}