{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:J57WPMVTH4GGDDJDANFLN4I627","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":"a5e4f6ccbf14f51a9244852ddd46f83bd569a89772c5c3b1c361c6423dd2b958","cross_cats_sorted":["math.DG","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-22T11:52:53Z","title_canon_sha256":"6c0dde7e88cb70ecad66ae22f87f88a3aa304a197a72e540a295d3e5bba8821b"},"schema_version":"1.0","source":{"id":"1411.6116","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.6116","created_at":"2026-05-18T01:55:33Z"},{"alias_kind":"arxiv_version","alias_value":"1411.6116v2","created_at":"2026-05-18T01:55:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.6116","created_at":"2026-05-18T01:55:33Z"},{"alias_kind":"pith_short_12","alias_value":"J57WPMVTH4GG","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"J57WPMVTH4GGDDJD","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"J57WPMVT","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:a39b02605d410d0fce31adccd96c6f1db9941fa816d066858e59656d2bfab4af","target":"graph","created_at":"2026-05-18T01:55:33Z","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":"In this paper, we propose a method for estimating the Sobolev type embedding constant on a domain with minimally smooth boundary. We estimate the embedding constant by constructing an extension operator and computing its operator norm. We also present some examples of estimating the embedding constant for certain domains.","authors_text":"Kazuaki Tanaka, Kouta Sekine, Makoto Mizuguchi, Shin'ichi Oishi","cross_cats":["math.DG","math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-22T11:52:53Z","title":"Estimation of the Sobolev embedding constant on domains with minimally smooth boundary"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.6116","kind":"arxiv","version":2},"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":"sha256:418df5fc178bd6fa488fc16d64b8f0605fccec36932be60ae3723b413f915ce0","target":"record","created_at":"2026-05-18T01:55:33Z","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":"a5e4f6ccbf14f51a9244852ddd46f83bd569a89772c5c3b1c361c6423dd2b958","cross_cats_sorted":["math.DG","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-22T11:52:53Z","title_canon_sha256":"6c0dde7e88cb70ecad66ae22f87f88a3aa304a197a72e540a295d3e5bba8821b"},"schema_version":"1.0","source":{"id":"1411.6116","kind":"arxiv","version":2}},"canonical_sha256":"4f7f67b2b33f0c618d23034ab6f11ed7f355f83ec382ecad590814f2f9c2608d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4f7f67b2b33f0c618d23034ab6f11ed7f355f83ec382ecad590814f2f9c2608d","first_computed_at":"2026-05-18T01:55:33.288298Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:55:33.288298Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZGqeNj4ikLqc31sAeZQZMHzcPV/eXsW9MbQfPGNFHlW+WSnfJGj/3PpJhStutsXqL6clMy0uG4btfrNK9JMBBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:55:33.288988Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.6116","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:418df5fc178bd6fa488fc16d64b8f0605fccec36932be60ae3723b413f915ce0","sha256:a39b02605d410d0fce31adccd96c6f1db9941fa816d066858e59656d2bfab4af"],"state_sha256":"03b32a1671705d886b868df28b985b6952af747bed339806ff76e807c857213a"}