{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:26YF5UHN6G5Z6XV264RZARDNTN","short_pith_number":"pith:26YF5UHN","canonical_record":{"source":{"id":"1309.4857","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-09-19T04:44:50Z","cross_cats_sorted":[],"title_canon_sha256":"76b608eb6bf1f3586b683c2a5cccd1aef4c7a9f797789b9da0a62e0c49f3b3b8","abstract_canon_sha256":"c70e1c7bebcf91c4e28152593af0042213dd63ff4f01f77012f0c4b583975922"},"schema_version":"1.0"},"canonical_sha256":"d7b05ed0edf1bb9f5ebaf72390446d9b6ce4451c9059a08264e225049580b766","source":{"kind":"arxiv","id":"1309.4857","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.4857","created_at":"2026-05-18T01:23:09Z"},{"alias_kind":"arxiv_version","alias_value":"1309.4857v1","created_at":"2026-05-18T01:23:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.4857","created_at":"2026-05-18T01:23:09Z"},{"alias_kind":"pith_short_12","alias_value":"26YF5UHN6G5Z","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"26YF5UHN6G5Z6XV2","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"26YF5UHN","created_at":"2026-05-18T12:27:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:26YF5UHN6G5Z6XV264RZARDNTN","target":"record","payload":{"canonical_record":{"source":{"id":"1309.4857","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-09-19T04:44:50Z","cross_cats_sorted":[],"title_canon_sha256":"76b608eb6bf1f3586b683c2a5cccd1aef4c7a9f797789b9da0a62e0c49f3b3b8","abstract_canon_sha256":"c70e1c7bebcf91c4e28152593af0042213dd63ff4f01f77012f0c4b583975922"},"schema_version":"1.0"},"canonical_sha256":"d7b05ed0edf1bb9f5ebaf72390446d9b6ce4451c9059a08264e225049580b766","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:09.097517Z","signature_b64":"JgW4QP3pGeNtMFw+6+kNZ6uHWvHGGE/MRsp/1jTgrErSyXFr6CLmiSTRAteFAdtYGrGlJBfdGdy5R3GTbzWZBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d7b05ed0edf1bb9f5ebaf72390446d9b6ce4451c9059a08264e225049580b766","last_reissued_at":"2026-05-18T01:23:09.097053Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:09.097053Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.4857","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:23:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SV69yIISH8R26FbmDU0Vzv/KUv9xP8xnvjazgrCdzBWBAqRAD3p/lU9kKwSwL/XrKuIy96d2aixMYnZJ5YCcBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T23:38:31.170057Z"},"content_sha256":"c18141c1e886170df586c8edf4f5f858615146cfb51622d9ea4c59332b579024","schema_version":"1.0","event_id":"sha256:c18141c1e886170df586c8edf4f5f858615146cfb51622d9ea4c59332b579024"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:26YF5UHN6G5Z6XV264RZARDNTN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A sharp Sobolev trace inequality involving the mean curvature on Riemannian manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jingang Xiong, Tianling Jin","submitted_at":"2013-09-19T04:44:50Z","abstract_excerpt":"In this paper, we examine the boundary $L^2$ term of the sharp Sobolev trace inequality $\\|u\\|_{L^{q}(\\pa M)}^2\\leq S \\|\\nabla_g u\\|_{L^2(M)}^2 +A(M,g)\\|u\\|^2_{L^2(\\pa M)}$ on Riemannian manifolds $(M,g)$ with boundaries $\\pa M$, where $q=\\frac{2(n-1)}{n-2}$, $S$ is the best constant and $A(M,g)$ is some positive constant depending only on $M$ and $g$. We obtain a sharp trace inequality involving the mean curvature in a remainder term, which would fail in general once the mean curvature is replaced by any smaller function."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.4857","kind":"arxiv","version":1},"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":"2026-05-18T01:23:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OMIX6h1Cz0l0BGf21+5Lt/F3P75+omM2pYR9Vqw2L/SlwQg6EGOBk3krKxhmPD9r08LWddwnSFe5NSEUHFHACA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T23:38:31.170406Z"},"content_sha256":"879ad83f19d68ed4f60a48e89e6730c8de387417274cf5c58828d99fb2c10be2","schema_version":"1.0","event_id":"sha256:879ad83f19d68ed4f60a48e89e6730c8de387417274cf5c58828d99fb2c10be2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/26YF5UHN6G5Z6XV264RZARDNTN/bundle.json","state_url":"https://pith.science/pith/26YF5UHN6G5Z6XV264RZARDNTN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/26YF5UHN6G5Z6XV264RZARDNTN/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":"2026-06-26T23:38:31Z","links":{"resolver":"https://pith.science/pith/26YF5UHN6G5Z6XV264RZARDNTN","bundle":"https://pith.science/pith/26YF5UHN6G5Z6XV264RZARDNTN/bundle.json","state":"https://pith.science/pith/26YF5UHN6G5Z6XV264RZARDNTN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/26YF5UHN6G5Z6XV264RZARDNTN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:26YF5UHN6G5Z6XV264RZARDNTN","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":"c70e1c7bebcf91c4e28152593af0042213dd63ff4f01f77012f0c4b583975922","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-09-19T04:44:50Z","title_canon_sha256":"76b608eb6bf1f3586b683c2a5cccd1aef4c7a9f797789b9da0a62e0c49f3b3b8"},"schema_version":"1.0","source":{"id":"1309.4857","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.4857","created_at":"2026-05-18T01:23:09Z"},{"alias_kind":"arxiv_version","alias_value":"1309.4857v1","created_at":"2026-05-18T01:23:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.4857","created_at":"2026-05-18T01:23:09Z"},{"alias_kind":"pith_short_12","alias_value":"26YF5UHN6G5Z","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"26YF5UHN6G5Z6XV2","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"26YF5UHN","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:879ad83f19d68ed4f60a48e89e6730c8de387417274cf5c58828d99fb2c10be2","target":"graph","created_at":"2026-05-18T01:23:09Z","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 examine the boundary $L^2$ term of the sharp Sobolev trace inequality $\\|u\\|_{L^{q}(\\pa M)}^2\\leq S \\|\\nabla_g u\\|_{L^2(M)}^2 +A(M,g)\\|u\\|^2_{L^2(\\pa M)}$ on Riemannian manifolds $(M,g)$ with boundaries $\\pa M$, where $q=\\frac{2(n-1)}{n-2}$, $S$ is the best constant and $A(M,g)$ is some positive constant depending only on $M$ and $g$. We obtain a sharp trace inequality involving the mean curvature in a remainder term, which would fail in general once the mean curvature is replaced by any smaller function.","authors_text":"Jingang Xiong, Tianling Jin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-09-19T04:44:50Z","title":"A sharp Sobolev trace inequality involving the mean curvature on Riemannian manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.4857","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:c18141c1e886170df586c8edf4f5f858615146cfb51622d9ea4c59332b579024","target":"record","created_at":"2026-05-18T01:23:09Z","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":"c70e1c7bebcf91c4e28152593af0042213dd63ff4f01f77012f0c4b583975922","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-09-19T04:44:50Z","title_canon_sha256":"76b608eb6bf1f3586b683c2a5cccd1aef4c7a9f797789b9da0a62e0c49f3b3b8"},"schema_version":"1.0","source":{"id":"1309.4857","kind":"arxiv","version":1}},"canonical_sha256":"d7b05ed0edf1bb9f5ebaf72390446d9b6ce4451c9059a08264e225049580b766","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d7b05ed0edf1bb9f5ebaf72390446d9b6ce4451c9059a08264e225049580b766","first_computed_at":"2026-05-18T01:23:09.097053Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:09.097053Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JgW4QP3pGeNtMFw+6+kNZ6uHWvHGGE/MRsp/1jTgrErSyXFr6CLmiSTRAteFAdtYGrGlJBfdGdy5R3GTbzWZBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:09.097517Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.4857","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c18141c1e886170df586c8edf4f5f858615146cfb51622d9ea4c59332b579024","sha256:879ad83f19d68ed4f60a48e89e6730c8de387417274cf5c58828d99fb2c10be2"],"state_sha256":"72c278d85ddb11748da75f23deedb264a436ef02f66512c6d324892bf3d35a3b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n6/owlM+ojMLmWatQxrNSEkq/lxu1w2oA8lHXGXA61gxfDPEU/qIOZCUI8rjcEFBia9wUra0azjc2E1cZ4dWAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T23:38:31.172302Z","bundle_sha256":"06ebfad5e49d993c8dc2b18e87faaceb5b75f5c9813794f1c009364bededba17"}}