{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:ROSRVE3UEJU32NWPBK2SVOD37I","short_pith_number":"pith:ROSRVE3U","canonical_record":{"source":{"id":"1812.01349","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-12-04T11:46:49Z","cross_cats_sorted":[],"title_canon_sha256":"d7b2ceadde3d0d305a88b51f1f41fb8e8686db444be381a11b0ba5f8ba0c5eb8","abstract_canon_sha256":"bc350dbf32b9dcb8eed6297b50248044d79fa44ae349e459e5a88bb13711982d"},"schema_version":"1.0"},"canonical_sha256":"8ba51a93742269bd36cf0ab52ab87bfa0bd5555d743a7284d6eab4f9b5b0f695","source":{"kind":"arxiv","id":"1812.01349","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.01349","created_at":"2026-05-17T23:54:21Z"},{"alias_kind":"arxiv_version","alias_value":"1812.01349v2","created_at":"2026-05-17T23:54:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.01349","created_at":"2026-05-17T23:54:21Z"},{"alias_kind":"pith_short_12","alias_value":"ROSRVE3UEJU3","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"ROSRVE3UEJU32NWP","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"ROSRVE3U","created_at":"2026-05-18T12:32:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:ROSRVE3UEJU32NWPBK2SVOD37I","target":"record","payload":{"canonical_record":{"source":{"id":"1812.01349","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-12-04T11:46:49Z","cross_cats_sorted":[],"title_canon_sha256":"d7b2ceadde3d0d305a88b51f1f41fb8e8686db444be381a11b0ba5f8ba0c5eb8","abstract_canon_sha256":"bc350dbf32b9dcb8eed6297b50248044d79fa44ae349e459e5a88bb13711982d"},"schema_version":"1.0"},"canonical_sha256":"8ba51a93742269bd36cf0ab52ab87bfa0bd5555d743a7284d6eab4f9b5b0f695","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:21.883858Z","signature_b64":"sg+L8OKpj+OWz2vUfzn9AXPne8IaL32//oYs2Q5cx5S55c/5/F81Javjwuz0BStDKvwJYHAbp3zLRbmeTt1EBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8ba51a93742269bd36cf0ab52ab87bfa0bd5555d743a7284d6eab4f9b5b0f695","last_reissued_at":"2026-05-17T23:54:21.883288Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:21.883288Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1812.01349","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:54:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nKxZoZzR8S1++VCsK2ap6nLRcDP4LnQKfbTnEFhov89q957WBPYqbNLO6huIIJS732nWHQMd+8BPyGIv7XeECw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T20:01:15.870977Z"},"content_sha256":"1b860a7e1e333e4c84e84581bfa50d0b301647f330037c1869e5865d47887c2c","schema_version":"1.0","event_id":"sha256:1b860a7e1e333e4c84e84581bfa50d0b301647f330037c1869e5865d47887c2c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:ROSRVE3UEJU32NWPBK2SVOD37I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the First eigenvalue of the Laplace operator for Compact Spacelike submanifolds in Lorentz-Minkowski Spacetime $\\mathbb{L}^{m}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Alfonso Romero, Francisco J. Palomo","submitted_at":"2018-12-04T11:46:49Z","abstract_excerpt":"By means of a family of counter-examples, it is shown that the Reilly upper bound for the first eigenvalue of the Laplace operator for a compact submanifold in Euclidean space does not work for $n$-dimensional compact spacelike submanifolds of Lorentz-Minkowski spacetime $\\mathbb{L}^m$, $m\\geq n+2$. We develop a new suitable technique, based on an integral formula on compact spacelike sections of the light cone in $\\mathbb{L}^m$. Then, a family of extrinsic upper bounds for the first eigenvalue of the Laplace operator for a compact spacelike submanifold in $\\mathbb{L}^m$ is proved. For each on"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.01349","kind":"arxiv","version":2},"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":"2026-05-17T23:54:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n2a/hdVmuMmBH2CbokJdoGSdGHsKJmhw4qrONKAwpOY03KBHnTamh8xvT8W908ZKDLyZddWpyB5gAS4mxyoPCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T20:01:15.871593Z"},"content_sha256":"3caf7e4391814282981a348401d3869670b7400a62f0b263703d7defe0fcc720","schema_version":"1.0","event_id":"sha256:3caf7e4391814282981a348401d3869670b7400a62f0b263703d7defe0fcc720"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ROSRVE3UEJU32NWPBK2SVOD37I/bundle.json","state_url":"https://pith.science/pith/ROSRVE3UEJU32NWPBK2SVOD37I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ROSRVE3UEJU32NWPBK2SVOD37I/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":"2026-05-30T20:01:15Z","links":{"resolver":"https://pith.science/pith/ROSRVE3UEJU32NWPBK2SVOD37I","bundle":"https://pith.science/pith/ROSRVE3UEJU32NWPBK2SVOD37I/bundle.json","state":"https://pith.science/pith/ROSRVE3UEJU32NWPBK2SVOD37I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ROSRVE3UEJU32NWPBK2SVOD37I/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:ROSRVE3UEJU32NWPBK2SVOD37I","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":"bc350dbf32b9dcb8eed6297b50248044d79fa44ae349e459e5a88bb13711982d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-12-04T11:46:49Z","title_canon_sha256":"d7b2ceadde3d0d305a88b51f1f41fb8e8686db444be381a11b0ba5f8ba0c5eb8"},"schema_version":"1.0","source":{"id":"1812.01349","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.01349","created_at":"2026-05-17T23:54:21Z"},{"alias_kind":"arxiv_version","alias_value":"1812.01349v2","created_at":"2026-05-17T23:54:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.01349","created_at":"2026-05-17T23:54:21Z"},{"alias_kind":"pith_short_12","alias_value":"ROSRVE3UEJU3","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"ROSRVE3UEJU32NWP","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"ROSRVE3U","created_at":"2026-05-18T12:32:50Z"}],"graph_snapshots":[{"event_id":"sha256:3caf7e4391814282981a348401d3869670b7400a62f0b263703d7defe0fcc720","target":"graph","created_at":"2026-05-17T23:54:21Z","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":"By means of a family of counter-examples, it is shown that the Reilly upper bound for the first eigenvalue of the Laplace operator for a compact submanifold in Euclidean space does not work for $n$-dimensional compact spacelike submanifolds of Lorentz-Minkowski spacetime $\\mathbb{L}^m$, $m\\geq n+2$. We develop a new suitable technique, based on an integral formula on compact spacelike sections of the light cone in $\\mathbb{L}^m$. Then, a family of extrinsic upper bounds for the first eigenvalue of the Laplace operator for a compact spacelike submanifold in $\\mathbb{L}^m$ is proved. For each on","authors_text":"Alfonso Romero, Francisco J. Palomo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-12-04T11:46:49Z","title":"On the First eigenvalue of the Laplace operator for Compact Spacelike submanifolds in Lorentz-Minkowski Spacetime $\\mathbb{L}^{m}$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.01349","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":"sha256:1b860a7e1e333e4c84e84581bfa50d0b301647f330037c1869e5865d47887c2c","target":"record","created_at":"2026-05-17T23:54:21Z","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":"bc350dbf32b9dcb8eed6297b50248044d79fa44ae349e459e5a88bb13711982d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-12-04T11:46:49Z","title_canon_sha256":"d7b2ceadde3d0d305a88b51f1f41fb8e8686db444be381a11b0ba5f8ba0c5eb8"},"schema_version":"1.0","source":{"id":"1812.01349","kind":"arxiv","version":2}},"canonical_sha256":"8ba51a93742269bd36cf0ab52ab87bfa0bd5555d743a7284d6eab4f9b5b0f695","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8ba51a93742269bd36cf0ab52ab87bfa0bd5555d743a7284d6eab4f9b5b0f695","first_computed_at":"2026-05-17T23:54:21.883288Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:21.883288Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sg+L8OKpj+OWz2vUfzn9AXPne8IaL32//oYs2Q5cx5S55c/5/F81Javjwuz0BStDKvwJYHAbp3zLRbmeTt1EBg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:21.883858Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.01349","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1b860a7e1e333e4c84e84581bfa50d0b301647f330037c1869e5865d47887c2c","sha256:3caf7e4391814282981a348401d3869670b7400a62f0b263703d7defe0fcc720"],"state_sha256":"ad274cd931fadce94dedc4c89573e25844d0ab1062cf124ca53295217544a006"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U+uMt6+Hw4T9LR+KLiByKhSuk8Bgad1No8uuWfzK8qjv3Lk4haOEKTp+FilA10Wx13i4cVU6/Y2i5/hIf1STDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T20:01:15.876006Z","bundle_sha256":"49098e190acbc3d49ccf17292d77ae457973e4241a5f914484868cae52fb271b"}}