{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:P6PQ67HWFCHS5RGYCMBUHNCZ6O","short_pith_number":"pith:P6PQ67HW","canonical_record":{"source":{"id":"1202.4589","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-02-21T10:33:21Z","cross_cats_sorted":[],"title_canon_sha256":"abec55000bb4bc9bf04452c4ed1d5d02ce19689153d762d0045f8b96fd9bea90","abstract_canon_sha256":"bf9b6b485038a14f9050eddd91ebbcb5c0862acd6f24de4b92bd8365c5c3a639"},"schema_version":"1.0"},"canonical_sha256":"7f9f0f7cf6288f2ec4d8130343b459f3b0ddf2ae40bb5715b99f79ddc0dc494d","source":{"kind":"arxiv","id":"1202.4589","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.4589","created_at":"2026-05-18T04:01:50Z"},{"alias_kind":"arxiv_version","alias_value":"1202.4589v1","created_at":"2026-05-18T04:01:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.4589","created_at":"2026-05-18T04:01:50Z"},{"alias_kind":"pith_short_12","alias_value":"P6PQ67HWFCHS","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"P6PQ67HWFCHS5RGY","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"P6PQ67HW","created_at":"2026-05-18T12:27:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:P6PQ67HWFCHS5RGYCMBUHNCZ6O","target":"record","payload":{"canonical_record":{"source":{"id":"1202.4589","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-02-21T10:33:21Z","cross_cats_sorted":[],"title_canon_sha256":"abec55000bb4bc9bf04452c4ed1d5d02ce19689153d762d0045f8b96fd9bea90","abstract_canon_sha256":"bf9b6b485038a14f9050eddd91ebbcb5c0862acd6f24de4b92bd8365c5c3a639"},"schema_version":"1.0"},"canonical_sha256":"7f9f0f7cf6288f2ec4d8130343b459f3b0ddf2ae40bb5715b99f79ddc0dc494d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:01:50.340537Z","signature_b64":"Q1srDqvbJ9NyEePIlPlMsx6EnBVy8UfEzOEKF32IX+7SySiqRdwBEOhRmBXNsKNUM4yevYIK+d8w7UhSZHg/DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7f9f0f7cf6288f2ec4d8130343b459f3b0ddf2ae40bb5715b99f79ddc0dc494d","last_reissued_at":"2026-05-18T04:01:50.339845Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:01:50.339845Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1202.4589","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":"2026-05-18T04:01:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M8ele6/DacYlp8gaDP6CUiHTyqQHiQvJl7HgSOjUByAJPA2LloQjJwmVEQTtrM7Vvk6ilxBdUzTS+ZhbiSB3Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T21:50:51.926629Z"},"content_sha256":"f2e6fdda390f9d5c75c7afcc23c75f45169826b281ab51d2ad922b4e10a7d64e","schema_version":"1.0","event_id":"sha256:f2e6fdda390f9d5c75c7afcc23c75f45169826b281ab51d2ad922b4e10a7d64e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:P6PQ67HWFCHS5RGYCMBUHNCZ6O","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On spacelike surfaces in 4-dimensional Lorentz-Minkowski spacetime through a lightcone","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":"2012-02-21T10:33:21Z","abstract_excerpt":"On any spacelike surface in a lightcone of four dimensional Lorentz-Minkowski space a distinguished smooth function is considered. It is shown how both extrinsic and intrinsic geometry of such a surface is codified by this function. The existence of a local maximum is assumed to decide when the spacelike surface must be totally umbilical, deriving a Liebmann type result. Two remarkable families of examples of spacelike surfaces in a lightcone are explicitly constructed. Finally, several results which involve the first eigenvalue of the Laplace operator of a compact spacelike surface in a light"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.4589","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":"2026-05-18T04:01:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Pr1mAu9TSfZEO7t00CNEtiPTYkN7LwyoDoX8WQPDBCBPsAxJz6E/1yb+DgVuiMg19cildNcmh+6gOMCSyVHDBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T21:50:51.927351Z"},"content_sha256":"0a4fc5c75d80235f6bf80d0a81577973eb319dde3535f040e2478803fb64e39d","schema_version":"1.0","event_id":"sha256:0a4fc5c75d80235f6bf80d0a81577973eb319dde3535f040e2478803fb64e39d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P6PQ67HWFCHS5RGYCMBUHNCZ6O/bundle.json","state_url":"https://pith.science/pith/P6PQ67HWFCHS5RGYCMBUHNCZ6O/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P6PQ67HWFCHS5RGYCMBUHNCZ6O/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":"2026-05-30T21:50:51Z","links":{"resolver":"https://pith.science/pith/P6PQ67HWFCHS5RGYCMBUHNCZ6O","bundle":"https://pith.science/pith/P6PQ67HWFCHS5RGYCMBUHNCZ6O/bundle.json","state":"https://pith.science/pith/P6PQ67HWFCHS5RGYCMBUHNCZ6O/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P6PQ67HWFCHS5RGYCMBUHNCZ6O/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:P6PQ67HWFCHS5RGYCMBUHNCZ6O","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":"bf9b6b485038a14f9050eddd91ebbcb5c0862acd6f24de4b92bd8365c5c3a639","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-02-21T10:33:21Z","title_canon_sha256":"abec55000bb4bc9bf04452c4ed1d5d02ce19689153d762d0045f8b96fd9bea90"},"schema_version":"1.0","source":{"id":"1202.4589","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.4589","created_at":"2026-05-18T04:01:50Z"},{"alias_kind":"arxiv_version","alias_value":"1202.4589v1","created_at":"2026-05-18T04:01:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.4589","created_at":"2026-05-18T04:01:50Z"},{"alias_kind":"pith_short_12","alias_value":"P6PQ67HWFCHS","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"P6PQ67HWFCHS5RGY","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"P6PQ67HW","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:0a4fc5c75d80235f6bf80d0a81577973eb319dde3535f040e2478803fb64e39d","target":"graph","created_at":"2026-05-18T04:01:50Z","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":"On any spacelike surface in a lightcone of four dimensional Lorentz-Minkowski space a distinguished smooth function is considered. It is shown how both extrinsic and intrinsic geometry of such a surface is codified by this function. The existence of a local maximum is assumed to decide when the spacelike surface must be totally umbilical, deriving a Liebmann type result. Two remarkable families of examples of spacelike surfaces in a lightcone are explicitly constructed. Finally, several results which involve the first eigenvalue of the Laplace operator of a compact spacelike surface in a light","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":"2012-02-21T10:33:21Z","title":"On spacelike surfaces in 4-dimensional Lorentz-Minkowski spacetime through a lightcone"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.4589","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:f2e6fdda390f9d5c75c7afcc23c75f45169826b281ab51d2ad922b4e10a7d64e","target":"record","created_at":"2026-05-18T04:01:50Z","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":"bf9b6b485038a14f9050eddd91ebbcb5c0862acd6f24de4b92bd8365c5c3a639","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-02-21T10:33:21Z","title_canon_sha256":"abec55000bb4bc9bf04452c4ed1d5d02ce19689153d762d0045f8b96fd9bea90"},"schema_version":"1.0","source":{"id":"1202.4589","kind":"arxiv","version":1}},"canonical_sha256":"7f9f0f7cf6288f2ec4d8130343b459f3b0ddf2ae40bb5715b99f79ddc0dc494d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7f9f0f7cf6288f2ec4d8130343b459f3b0ddf2ae40bb5715b99f79ddc0dc494d","first_computed_at":"2026-05-18T04:01:50.339845Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:01:50.339845Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Q1srDqvbJ9NyEePIlPlMsx6EnBVy8UfEzOEKF32IX+7SySiqRdwBEOhRmBXNsKNUM4yevYIK+d8w7UhSZHg/DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:01:50.340537Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.4589","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f2e6fdda390f9d5c75c7afcc23c75f45169826b281ab51d2ad922b4e10a7d64e","sha256:0a4fc5c75d80235f6bf80d0a81577973eb319dde3535f040e2478803fb64e39d"],"state_sha256":"1afaac1f43794608b163b62958b130bd2b8589a15ea46d0a04d47d3aaf046648"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e8wug+yw4YnT/JfoxxRI6OTS1BpMO/VGa7TV9R2fbku+3jpSgysVavCiYYZMmn9cOhvjAsE84zl2dHB67lGIAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T21:50:51.931517Z","bundle_sha256":"badffa27a35e600794e54d15915c19dd327384da62bba9e460f9a168f4b0824a"}}