{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:LJ5TH3NVKC2IOODZFD6YHGOSYP","short_pith_number":"pith:LJ5TH3NV","canonical_record":{"source":{"id":"1307.7394","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-07-28T19:40:03Z","cross_cats_sorted":[],"title_canon_sha256":"0e8734d9eecebdf9b66f30d035aeb41d398616069d07db01c3dc966ff50e12e1","abstract_canon_sha256":"210e9144ca7859bd6177f3533ca1f277c00846e63d3370554885059e469f4320"},"schema_version":"1.0"},"canonical_sha256":"5a7b33edb550b487387928fd8399d2c3ec279edad1dd2c086c8f6a0148b8ee04","source":{"kind":"arxiv","id":"1307.7394","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.7394","created_at":"2026-05-18T03:01:10Z"},{"alias_kind":"arxiv_version","alias_value":"1307.7394v3","created_at":"2026-05-18T03:01:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.7394","created_at":"2026-05-18T03:01:10Z"},{"alias_kind":"pith_short_12","alias_value":"LJ5TH3NVKC2I","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"LJ5TH3NVKC2IOODZ","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"LJ5TH3NV","created_at":"2026-05-18T12:27:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:LJ5TH3NVKC2IOODZFD6YHGOSYP","target":"record","payload":{"canonical_record":{"source":{"id":"1307.7394","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-07-28T19:40:03Z","cross_cats_sorted":[],"title_canon_sha256":"0e8734d9eecebdf9b66f30d035aeb41d398616069d07db01c3dc966ff50e12e1","abstract_canon_sha256":"210e9144ca7859bd6177f3533ca1f277c00846e63d3370554885059e469f4320"},"schema_version":"1.0"},"canonical_sha256":"5a7b33edb550b487387928fd8399d2c3ec279edad1dd2c086c8f6a0148b8ee04","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:01:10.388463Z","signature_b64":"+cSQk4mUkJTgH1ZZq4ppBonQpNHYsltDtwJflu19AXuYFr4f+AWG1f9tEtdp9OShWiIyuKclXo5HJB299p+kBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5a7b33edb550b487387928fd8399d2c3ec279edad1dd2c086c8f6a0148b8ee04","last_reissued_at":"2026-05-18T03:01:10.387673Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:01:10.387673Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1307.7394","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:01:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FsqC7CDtr6oFR9ByBx7R4pWNM69JVqAvq7nmsKklKrsH+HX0Xs/7/jwBNGufA+wpnp/lIEeFG4oGMi8xGDraCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T15:59:08.791887Z"},"content_sha256":"de8481b8d2213f646dcbc444d108526408de5b24d6a7e799720b244c5459881b","schema_version":"1.0","event_id":"sha256:de8481b8d2213f646dcbc444d108526408de5b24d6a7e799720b244c5459881b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:LJ5TH3NVKC2IOODZFD6YHGOSYP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimal Rellich-Sobolev constants and their extremals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Roberta Musina","submitted_at":"2013-07-28T19:40:03Z","abstract_excerpt":"We prove that extremals for second order Rellich-Sobolev inequalities have constant sign. Then we show that the optimal constants in Rellich-Sobolev inequalities on a bounded domain {\\Omega} and under Navier boundary conditions do not depend on {\\Omega}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.7394","kind":"arxiv","version":3},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:01:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4PXnh85YhZQ61XQksFMO5NkGulPtfPYsyUEKByelvFCkSSBOYoZqFbprh5mmldAgzun6VXNsAgSwDe24PM62CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T15:59:08.792538Z"},"content_sha256":"632dedcc843ab104b1432a1f7ad6f7aa4ebd6c5cd836cb769e201babc34b9cf4","schema_version":"1.0","event_id":"sha256:632dedcc843ab104b1432a1f7ad6f7aa4ebd6c5cd836cb769e201babc34b9cf4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LJ5TH3NVKC2IOODZFD6YHGOSYP/bundle.json","state_url":"https://pith.science/pith/LJ5TH3NVKC2IOODZFD6YHGOSYP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LJ5TH3NVKC2IOODZFD6YHGOSYP/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-28T15:59:08Z","links":{"resolver":"https://pith.science/pith/LJ5TH3NVKC2IOODZFD6YHGOSYP","bundle":"https://pith.science/pith/LJ5TH3NVKC2IOODZFD6YHGOSYP/bundle.json","state":"https://pith.science/pith/LJ5TH3NVKC2IOODZFD6YHGOSYP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LJ5TH3NVKC2IOODZFD6YHGOSYP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:LJ5TH3NVKC2IOODZFD6YHGOSYP","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":"210e9144ca7859bd6177f3533ca1f277c00846e63d3370554885059e469f4320","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-07-28T19:40:03Z","title_canon_sha256":"0e8734d9eecebdf9b66f30d035aeb41d398616069d07db01c3dc966ff50e12e1"},"schema_version":"1.0","source":{"id":"1307.7394","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.7394","created_at":"2026-05-18T03:01:10Z"},{"alias_kind":"arxiv_version","alias_value":"1307.7394v3","created_at":"2026-05-18T03:01:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.7394","created_at":"2026-05-18T03:01:10Z"},{"alias_kind":"pith_short_12","alias_value":"LJ5TH3NVKC2I","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"LJ5TH3NVKC2IOODZ","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"LJ5TH3NV","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:632dedcc843ab104b1432a1f7ad6f7aa4ebd6c5cd836cb769e201babc34b9cf4","target":"graph","created_at":"2026-05-18T03:01:10Z","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 prove that extremals for second order Rellich-Sobolev inequalities have constant sign. Then we show that the optimal constants in Rellich-Sobolev inequalities on a bounded domain {\\Omega} and under Navier boundary conditions do not depend on {\\Omega}","authors_text":"Roberta Musina","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-07-28T19:40:03Z","title":"Optimal Rellich-Sobolev constants and their extremals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.7394","kind":"arxiv","version":3},"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:de8481b8d2213f646dcbc444d108526408de5b24d6a7e799720b244c5459881b","target":"record","created_at":"2026-05-18T03:01:10Z","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":"210e9144ca7859bd6177f3533ca1f277c00846e63d3370554885059e469f4320","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-07-28T19:40:03Z","title_canon_sha256":"0e8734d9eecebdf9b66f30d035aeb41d398616069d07db01c3dc966ff50e12e1"},"schema_version":"1.0","source":{"id":"1307.7394","kind":"arxiv","version":3}},"canonical_sha256":"5a7b33edb550b487387928fd8399d2c3ec279edad1dd2c086c8f6a0148b8ee04","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5a7b33edb550b487387928fd8399d2c3ec279edad1dd2c086c8f6a0148b8ee04","first_computed_at":"2026-05-18T03:01:10.387673Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:01:10.387673Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+cSQk4mUkJTgH1ZZq4ppBonQpNHYsltDtwJflu19AXuYFr4f+AWG1f9tEtdp9OShWiIyuKclXo5HJB299p+kBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:01:10.388463Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.7394","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:de8481b8d2213f646dcbc444d108526408de5b24d6a7e799720b244c5459881b","sha256:632dedcc843ab104b1432a1f7ad6f7aa4ebd6c5cd836cb769e201babc34b9cf4"],"state_sha256":"55d7e62158025989247ab6144e9b048b694c0e879548ca48c2341ccf10718984"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ogTZZo4MsxlJmkyFLBckMSvRIHY0BKknvyXH7O+2QsSQDyWyBzAGNGJ7XGvX4kyY2tB3NfY2FTHBdCzMN46OCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T15:59:08.795804Z","bundle_sha256":"c03b000b832188bb985b36007af11f4e1e97d3497fac0ee77747d4e7ab57bc66"}}