{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:OGJIOEED7AJPEKREK7WNRJY5D6","short_pith_number":"pith:OGJIOEED","schema_version":"1.0","canonical_sha256":"7192871083f812f22a2457ecd8a71d1fb4b7561d4dd0ff1889b3f294a9125b1c","source":{"kind":"arxiv","id":"1105.1995","version":2},"attestation_state":"computed","paper":{"title":"Integrals and Potentials of Differential 1-forms on the Sierpinski Gasket","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT","math.MG"],"primary_cat":"math.FA","authors_text":"Daniele Guido, Fabio Cipriani, Jean-Luc Sauvageot, Tommaso Isola","submitted_at":"2011-05-10T16:51:14Z","abstract_excerpt":"We provide a definition of integral, along paths in the Sierpinski gasket K, for differential smooth 1-forms associated to the standard Dirichlet form K. We show how this tool can be used to study the potential theory on K. In particular, we prove: i) a de Rham reconstruction of a 1-form from its periods around lacunas in K; ii) a Hodge decomposition of 1-forms with respect to the Hilbertian energy norm; iii) the existence of potentials of smooth 1-forms on a suitable covering space of K. We finally show that this framework provides versions of the de Rham duality theorem for the fractal K."},"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":"1105.1995","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-05-10T16:51:14Z","cross_cats_sorted":["math.KT","math.MG"],"title_canon_sha256":"4ba144d18005ecb8ad36b010c7e1dcd2a2aa519c17bd9ff10f4fea1ade5d9f52","abstract_canon_sha256":"553b7f50b1239c3817e8f484a9601ba1d23c57789b882e36c448983545ccdf59"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:29:37.839181Z","signature_b64":"98z1Xv7L2jYdEqeAsaLouXi8Zlb3zf6axpwE/Kzg8mC6GgGPNHcZUi2Z3R0lldmoVfjgH6eDCVxJSPdhPzN0Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7192871083f812f22a2457ecd8a71d1fb4b7561d4dd0ff1889b3f294a9125b1c","last_reissued_at":"2026-05-18T03:29:37.838440Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:29:37.838440Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Integrals and Potentials of Differential 1-forms on the Sierpinski Gasket","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT","math.MG"],"primary_cat":"math.FA","authors_text":"Daniele Guido, Fabio Cipriani, Jean-Luc Sauvageot, Tommaso Isola","submitted_at":"2011-05-10T16:51:14Z","abstract_excerpt":"We provide a definition of integral, along paths in the Sierpinski gasket K, for differential smooth 1-forms associated to the standard Dirichlet form K. We show how this tool can be used to study the potential theory on K. In particular, we prove: i) a de Rham reconstruction of a 1-form from its periods around lacunas in K; ii) a Hodge decomposition of 1-forms with respect to the Hilbertian energy norm; iii) the existence of potentials of smooth 1-forms on a suitable covering space of K. We finally show that this framework provides versions of the de Rham duality theorem for the fractal K."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.1995","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":""},"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":"1105.1995","created_at":"2026-05-18T03:29:37.838559+00:00"},{"alias_kind":"arxiv_version","alias_value":"1105.1995v2","created_at":"2026-05-18T03:29:37.838559+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.1995","created_at":"2026-05-18T03:29:37.838559+00:00"},{"alias_kind":"pith_short_12","alias_value":"OGJIOEED7AJP","created_at":"2026-05-18T12:26:37.096874+00:00"},{"alias_kind":"pith_short_16","alias_value":"OGJIOEED7AJPEKRE","created_at":"2026-05-18T12:26:37.096874+00:00"},{"alias_kind":"pith_short_8","alias_value":"OGJIOEED","created_at":"2026-05-18T12:26:37.096874+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/OGJIOEED7AJPEKREK7WNRJY5D6","json":"https://pith.science/pith/OGJIOEED7AJPEKREK7WNRJY5D6.json","graph_json":"https://pith.science/api/pith-number/OGJIOEED7AJPEKREK7WNRJY5D6/graph.json","events_json":"https://pith.science/api/pith-number/OGJIOEED7AJPEKREK7WNRJY5D6/events.json","paper":"https://pith.science/paper/OGJIOEED"},"agent_actions":{"view_html":"https://pith.science/pith/OGJIOEED7AJPEKREK7WNRJY5D6","download_json":"https://pith.science/pith/OGJIOEED7AJPEKREK7WNRJY5D6.json","view_paper":"https://pith.science/paper/OGJIOEED","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1105.1995&json=true","fetch_graph":"https://pith.science/api/pith-number/OGJIOEED7AJPEKREK7WNRJY5D6/graph.json","fetch_events":"https://pith.science/api/pith-number/OGJIOEED7AJPEKREK7WNRJY5D6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OGJIOEED7AJPEKREK7WNRJY5D6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OGJIOEED7AJPEKREK7WNRJY5D6/action/storage_attestation","attest_author":"https://pith.science/pith/OGJIOEED7AJPEKREK7WNRJY5D6/action/author_attestation","sign_citation":"https://pith.science/pith/OGJIOEED7AJPEKREK7WNRJY5D6/action/citation_signature","submit_replication":"https://pith.science/pith/OGJIOEED7AJPEKREK7WNRJY5D6/action/replication_record"}},"created_at":"2026-05-18T03:29:37.838559+00:00","updated_at":"2026-05-18T03:29:37.838559+00:00"}