{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:OZ2IADOJ7VKUZ2NOK6NMWLNRQT","short_pith_number":"pith:OZ2IADOJ","canonical_record":{"source":{"id":"1512.07163","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-22T17:20:47Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"db01b500ab8a107e6a17f73f30e8f4d5dfcffaaf8b26df9c1fa632a078f61fa8","abstract_canon_sha256":"2dea6758cf5702ba084141c5e91e2dd1475e959d614bfb27bf399713d962ab7b"},"schema_version":"1.0"},"canonical_sha256":"7674800dc9fd554ce9ae579acb2db184d2db980d598ca525d63b4c3d917bc451","source":{"kind":"arxiv","id":"1512.07163","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.07163","created_at":"2026-05-18T01:23:52Z"},{"alias_kind":"arxiv_version","alias_value":"1512.07163v1","created_at":"2026-05-18T01:23:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.07163","created_at":"2026-05-18T01:23:52Z"},{"alias_kind":"pith_short_12","alias_value":"OZ2IADOJ7VKU","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"OZ2IADOJ7VKUZ2NO","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"OZ2IADOJ","created_at":"2026-05-18T12:29:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:OZ2IADOJ7VKUZ2NOK6NMWLNRQT","target":"record","payload":{"canonical_record":{"source":{"id":"1512.07163","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-22T17:20:47Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"db01b500ab8a107e6a17f73f30e8f4d5dfcffaaf8b26df9c1fa632a078f61fa8","abstract_canon_sha256":"2dea6758cf5702ba084141c5e91e2dd1475e959d614bfb27bf399713d962ab7b"},"schema_version":"1.0"},"canonical_sha256":"7674800dc9fd554ce9ae579acb2db184d2db980d598ca525d63b4c3d917bc451","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:52.746158Z","signature_b64":"D/VZ8DR1J6Rf7pdAdoUIVYH9bEIWZtjzXzjQ9beyAxmNyncYNbifXx5gRI4AHA0kpPp0NN/Ak1/o4lIhHLvAAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7674800dc9fd554ce9ae579acb2db184d2db980d598ca525d63b4c3d917bc451","last_reissued_at":"2026-05-18T01:23:52.745395Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:52.745395Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.07163","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":"2026-05-18T01:23:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nY+JIJEyCxnWE7XhRAuUrlb9SxubgwICyJ7HrgCJV31JUCfOzvbcohRo/lTDJkgDYORG5XhHKyKvpn2xqeWFCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T03:34:42.993602Z"},"content_sha256":"e1d73ee1de61446588f117f6e8ca8b6ae0e4fd24855e637fc985a59d8d846b7c","schema_version":"1.0","event_id":"sha256:e1d73ee1de61446588f117f6e8ca8b6ae0e4fd24855e637fc985a59d8d846b7c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:OZ2IADOJ7VKUZ2NOK6NMWLNRQT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A sharp Trudinger-Moser inequality on any bounded and convex planar domain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.AP","authors_text":"Guozhen Lu, Qiaohua Yang","submitted_at":"2015-12-22T17:20:47Z","abstract_excerpt":"Wang and Ye conjectured in [22]:\n  Let $\\Omega$ be a regular, bounded and convex domain in $\\mathbb{R}^{2}$. There exists a finite constant $C({\\Omega})>0$ such that \\[ \\int_{\\Omega}e^{\\frac{4\\pi u^{2}}{H_{d}(u)}}dxdy\\le C(\\Omega),\\;\\;\\forall u\\in C^{\\infty}_{0}(\\Omega), \\] where $H_{d}=\\int_{\\Omega}|\\nabla u|^{2}dxdy-\\frac{1}{4}\\int_{\\Omega}\\frac{u^{2}}{d(z,\\partial\\Omega)^{2}}dxdy$ and $d(z,\\partial\\Omega)=\\min\\limits_{z_{1}\\in\\partial\\Omega}|z-z_{1}|$.}\n  The main purpose of this paper is to confirm that this conjecture indeed holds for any bounded and convex domain in $\\mathbb{R}^{2}$ via "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.07163","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":"2026-05-18T01:23:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RRPw56Yg6xITyqZmZVnq95dEXXcsgSGgaf46IhUzggs9nrJuH3f2ntaIItFfxjBlSnoIDOcS6kDjcbUfsCovCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T03:34:42.994292Z"},"content_sha256":"63ab62e3f7f3421c7da4abaac6f2a9b67ae777932dbd68aa7fb9b686382d61b4","schema_version":"1.0","event_id":"sha256:63ab62e3f7f3421c7da4abaac6f2a9b67ae777932dbd68aa7fb9b686382d61b4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OZ2IADOJ7VKUZ2NOK6NMWLNRQT/bundle.json","state_url":"https://pith.science/pith/OZ2IADOJ7VKUZ2NOK6NMWLNRQT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OZ2IADOJ7VKUZ2NOK6NMWLNRQT/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":"2026-06-04T03:34:42Z","links":{"resolver":"https://pith.science/pith/OZ2IADOJ7VKUZ2NOK6NMWLNRQT","bundle":"https://pith.science/pith/OZ2IADOJ7VKUZ2NOK6NMWLNRQT/bundle.json","state":"https://pith.science/pith/OZ2IADOJ7VKUZ2NOK6NMWLNRQT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OZ2IADOJ7VKUZ2NOK6NMWLNRQT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:OZ2IADOJ7VKUZ2NOK6NMWLNRQT","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":"2dea6758cf5702ba084141c5e91e2dd1475e959d614bfb27bf399713d962ab7b","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-22T17:20:47Z","title_canon_sha256":"db01b500ab8a107e6a17f73f30e8f4d5dfcffaaf8b26df9c1fa632a078f61fa8"},"schema_version":"1.0","source":{"id":"1512.07163","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.07163","created_at":"2026-05-18T01:23:52Z"},{"alias_kind":"arxiv_version","alias_value":"1512.07163v1","created_at":"2026-05-18T01:23:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.07163","created_at":"2026-05-18T01:23:52Z"},{"alias_kind":"pith_short_12","alias_value":"OZ2IADOJ7VKU","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"OZ2IADOJ7VKUZ2NO","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"OZ2IADOJ","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:63ab62e3f7f3421c7da4abaac6f2a9b67ae777932dbd68aa7fb9b686382d61b4","target":"graph","created_at":"2026-05-18T01:23:52Z","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":"Wang and Ye conjectured in [22]:\n  Let $\\Omega$ be a regular, bounded and convex domain in $\\mathbb{R}^{2}$. There exists a finite constant $C({\\Omega})>0$ such that \\[ \\int_{\\Omega}e^{\\frac{4\\pi u^{2}}{H_{d}(u)}}dxdy\\le C(\\Omega),\\;\\;\\forall u\\in C^{\\infty}_{0}(\\Omega), \\] where $H_{d}=\\int_{\\Omega}|\\nabla u|^{2}dxdy-\\frac{1}{4}\\int_{\\Omega}\\frac{u^{2}}{d(z,\\partial\\Omega)^{2}}dxdy$ and $d(z,\\partial\\Omega)=\\min\\limits_{z_{1}\\in\\partial\\Omega}|z-z_{1}|$.}\n  The main purpose of this paper is to confirm that this conjecture indeed holds for any bounded and convex domain in $\\mathbb{R}^{2}$ via ","authors_text":"Guozhen Lu, Qiaohua Yang","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-22T17:20:47Z","title":"A sharp Trudinger-Moser inequality on any bounded and convex planar domain"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.07163","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:e1d73ee1de61446588f117f6e8ca8b6ae0e4fd24855e637fc985a59d8d846b7c","target":"record","created_at":"2026-05-18T01:23:52Z","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":"2dea6758cf5702ba084141c5e91e2dd1475e959d614bfb27bf399713d962ab7b","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-22T17:20:47Z","title_canon_sha256":"db01b500ab8a107e6a17f73f30e8f4d5dfcffaaf8b26df9c1fa632a078f61fa8"},"schema_version":"1.0","source":{"id":"1512.07163","kind":"arxiv","version":1}},"canonical_sha256":"7674800dc9fd554ce9ae579acb2db184d2db980d598ca525d63b4c3d917bc451","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7674800dc9fd554ce9ae579acb2db184d2db980d598ca525d63b4c3d917bc451","first_computed_at":"2026-05-18T01:23:52.745395Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:52.745395Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"D/VZ8DR1J6Rf7pdAdoUIVYH9bEIWZtjzXzjQ9beyAxmNyncYNbifXx5gRI4AHA0kpPp0NN/Ak1/o4lIhHLvAAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:52.746158Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.07163","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e1d73ee1de61446588f117f6e8ca8b6ae0e4fd24855e637fc985a59d8d846b7c","sha256:63ab62e3f7f3421c7da4abaac6f2a9b67ae777932dbd68aa7fb9b686382d61b4"],"state_sha256":"7f9b4793f9f476d481ee930ab732c20bbeba47496f1f09582d89b80770547a0f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HayDCk87BFNmLZ5UewTA2yeJJ8DbKyA3ExblxYRwfdJhnKhv9Zaa7zdmN3EDyNqe0ZU+Rj1Pm0gsppuhgMiADg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T03:34:42.998549Z","bundle_sha256":"b64e6dca700314773583d7b1e9ddac41cf4b977a21bb3ee45a4ce573ae34fde0"}}