{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:Z44HN5X5F3GL23UJEPGOJ462XQ","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":"b85ccebca92f60448f47c76d384a17d980a82559369731f0c1a2289b318cc6cf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-06-10T15:33:45Z","title_canon_sha256":"1914e9931ead6052af1eb574efe13ae0412e6079c8a106f55282e86312170f56"},"schema_version":"1.0","source":{"id":"1306.2231","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.2231","created_at":"2026-05-18T00:56:51Z"},{"alias_kind":"arxiv_version","alias_value":"1306.2231v1","created_at":"2026-05-18T00:56:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.2231","created_at":"2026-05-18T00:56:51Z"},{"alias_kind":"pith_short_12","alias_value":"Z44HN5X5F3GL","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"Z44HN5X5F3GL23UJ","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"Z44HN5X5","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:f69c2ee88a7d0ee032841def4a1c321514c707095b1648b1b91446bc600ff1c1","target":"graph","created_at":"2026-05-18T00:56:51Z","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 characterize functions of finite energy in the plane in terms of their traces on the lines that make up \"graph paper\" with squares of side length $mn$ for all $n$, and certain $\\12-$order Sobolev norms on the graph paper lines. We also obtain analogous results for functions of finite energy on two classical fractals: the Sierpinski gasket and the Sierpinski carpet.","authors_text":"Robert S. Strichartz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-06-10T15:33:45Z","title":"\"Graph Paper\" Trace Characterizations of Functions of Finite Energy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.2231","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":"sha256:17f66cc5b23b9dd80402c555fb0cfa9d2752aade9a596dafe188231bf51cc5f5","target":"record","created_at":"2026-05-18T00:56:51Z","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":"b85ccebca92f60448f47c76d384a17d980a82559369731f0c1a2289b318cc6cf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-06-10T15:33:45Z","title_canon_sha256":"1914e9931ead6052af1eb574efe13ae0412e6079c8a106f55282e86312170f56"},"schema_version":"1.0","source":{"id":"1306.2231","kind":"arxiv","version":1}},"canonical_sha256":"cf3876f6fd2eccbd6e8923cce4f3dabc36f19cd332f98f4fcb976277e28194b5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cf3876f6fd2eccbd6e8923cce4f3dabc36f19cd332f98f4fcb976277e28194b5","first_computed_at":"2026-05-18T00:56:51.839350Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:56:51.839350Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zcmPBDFJTqAG6C0bGnSpVpYCyBlnHZdnCyD2eKCicmlTH75UQxLfgGr/t5gnrTCdt2Ls5mhvmNu6PtrtTqwWDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:56:51.840015Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.2231","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:17f66cc5b23b9dd80402c555fb0cfa9d2752aade9a596dafe188231bf51cc5f5","sha256:f69c2ee88a7d0ee032841def4a1c321514c707095b1648b1b91446bc600ff1c1"],"state_sha256":"e305cd94dff95c709f607099d406dd7838191e6f1395b6a1c90c0eb21e311182"}