{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:U6BXXTSORTIUEKJL4CV6XLVK6X","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":"578bde2ef893d79a6f37ca1a4ccc846f5bc3a0e61fb2ac67e3f468e0cb1a0b31","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-05-08T23:58:26Z","title_canon_sha256":"2606daa4dff1b84661849d6ca1edab8eb39145629d9d8dc173c3444d2b3576f3"},"schema_version":"1.0","source":{"id":"1905.03391","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.03391","created_at":"2026-05-17T23:46:40Z"},{"alias_kind":"arxiv_version","alias_value":"1905.03391v1","created_at":"2026-05-17T23:46:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.03391","created_at":"2026-05-17T23:46:40Z"},{"alias_kind":"pith_short_12","alias_value":"U6BXXTSORTIU","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"U6BXXTSORTIUEKJL","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"U6BXXTSO","created_at":"2026-05-18T12:33:30Z"}],"graph_snapshots":[{"event_id":"sha256:0ce70f594c67bfbf715fe34e2d32a27f80efc775bf07d1f301fd8a8f5c263882","target":"graph","created_at":"2026-05-17T23:46:40Z","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"},"paper":{"abstract_excerpt":"We give a discrete characterization of the trace of a class of Sobolev spaces on the Sierpinski gasket to the bottom line. This includes the L2 domain of the Laplacian as a special case. In addition, for Sobolev spaces of low orders, including the domain of the Dirichlet form, the trace spaces are Besov spaces on the line.","authors_text":"Prem Talwai, Robert S. Strichartz, Shiping Cao, Shuangping Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-05-08T23:58:26Z","title":"A Trace Theorem For Sobolev Spaces On The Sierpinski Gasket"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.03391","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":"sha256:8ce54dbf6e714ea28d0e73d5a4367d4957b478e7867a3443d67b44b0aa8d6fd6","target":"record","created_at":"2026-05-17T23:46:40Z","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":"578bde2ef893d79a6f37ca1a4ccc846f5bc3a0e61fb2ac67e3f468e0cb1a0b31","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-05-08T23:58:26Z","title_canon_sha256":"2606daa4dff1b84661849d6ca1edab8eb39145629d9d8dc173c3444d2b3576f3"},"schema_version":"1.0","source":{"id":"1905.03391","kind":"arxiv","version":1}},"canonical_sha256":"a7837bce4e8cd142292be0abebaeaaf5f5f84018d8ca503f6da14a8944dafcf8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a7837bce4e8cd142292be0abebaeaaf5f5f84018d8ca503f6da14a8944dafcf8","first_computed_at":"2026-05-17T23:46:40.114676Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:46:40.114676Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3xRepGL9Z/K+ToP+Ntbyzp3yKXoRRTM4DIIAhhaXnCAs9nmCTEtTqZA97oV/nSX5zwJ0Gpe2OIQ7B8w4NCkZBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:46:40.115411Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.03391","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8ce54dbf6e714ea28d0e73d5a4367d4957b478e7867a3443d67b44b0aa8d6fd6","sha256:0ce70f594c67bfbf715fe34e2d32a27f80efc775bf07d1f301fd8a8f5c263882"],"state_sha256":"b6d0503fc29f8706e5ac43df557274797c729a94b8f434720a0b76f32082e8c1"}