{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:NI3JL6EMGMH4VSY57ECMCICZQH","short_pith_number":"pith:NI3JL6EM","canonical_record":{"source":{"id":"1312.2724","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2013-12-10T09:28:51Z","cross_cats_sorted":["math-ph","math.GT","math.MP"],"title_canon_sha256":"b2c77126671ae310727331527c55931e9a8837473e52e069a37187606697ccb3","abstract_canon_sha256":"6ad1bce54050114f01246da75173882d2a40ab766ab0d0d7a8fcfd7c4ea6f3b6"},"schema_version":"1.0"},"canonical_sha256":"6a3695f88c330fcacb1df904c1205981c50c07817f3f2391186c7bd601166c9e","source":{"kind":"arxiv","id":"1312.2724","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.2724","created_at":"2026-05-18T01:26:58Z"},{"alias_kind":"arxiv_version","alias_value":"1312.2724v4","created_at":"2026-05-18T01:26:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.2724","created_at":"2026-05-18T01:26:58Z"},{"alias_kind":"pith_short_12","alias_value":"NI3JL6EMGMH4","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"NI3JL6EMGMH4VSY5","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"NI3JL6EM","created_at":"2026-05-18T12:27:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:NI3JL6EMGMH4VSY57ECMCICZQH","target":"record","payload":{"canonical_record":{"source":{"id":"1312.2724","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2013-12-10T09:28:51Z","cross_cats_sorted":["math-ph","math.GT","math.MP"],"title_canon_sha256":"b2c77126671ae310727331527c55931e9a8837473e52e069a37187606697ccb3","abstract_canon_sha256":"6ad1bce54050114f01246da75173882d2a40ab766ab0d0d7a8fcfd7c4ea6f3b6"},"schema_version":"1.0"},"canonical_sha256":"6a3695f88c330fcacb1df904c1205981c50c07817f3f2391186c7bd601166c9e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:26:58.511748Z","signature_b64":"s3vmmYCGbXaKO1qrHWbBYIfEc6ojA0TVh07YNcjygpdqV2zJcExWBlnNFcAaa1swtOJAkV3TU8q7Q246KwuEDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6a3695f88c330fcacb1df904c1205981c50c07817f3f2391186c7bd601166c9e","last_reissued_at":"2026-05-18T01:26:58.511069Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:26:58.511069Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1312.2724","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:26:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FCgGKotsYgBDEqwT4pIw7c4UdS+fRGlhAtJtlRIE7d1z1rJOhuW6r5e8s1j2Yls/vy/UkFcxqedkHxO86KgbAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T15:22:54.532947Z"},"content_sha256":"a30790eefe42b18869af288d2a4c24258d44446a46402c2dff25201c3526a829","schema_version":"1.0","event_id":"sha256:a30790eefe42b18869af288d2a4c24258d44446a46402c2dff25201c3526a829"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:NI3JL6EMGMH4VSY57ECMCICZQH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Maximal surfaces in anti-de Sitter 3-manifolds with particles","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.GT","math.MP"],"primary_cat":"math.DG","authors_text":"J\\'er\\'emy Toulisse","submitted_at":"2013-12-10T09:28:51Z","abstract_excerpt":"We prove the existence of a unique maximal surface in each anti-de Sitter (AdS) convex Globally Hyperbolic Maximal (GHM) manifold with particles (that is, with conical singularities along time-like lines) for cone angles less than $\\pi$. We interpret this result in terms of Teichm\\\"uller theory, and prove the existence of a unique minimal Lagrangian diffeomorphism isotopic to the identity between two hyperbolic surfaces with cone singularities when the cone angles are the same for both surfaces and are less than $\\pi$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.2724","kind":"arxiv","version":4},"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":"2026-05-18T01:26:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xCwimWENTRUNGy14tECz4RMDjEQutfiG4T/3ghFl7GpQS9DZrBbA+xpwa0ttrawjOwCneK6ckkQVhUq5v6ltDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T15:22:54.533295Z"},"content_sha256":"5abb1377598e25b13e79194fe3bef0c0ce62f1388a3a763dcd54ac0db7edfdf4","schema_version":"1.0","event_id":"sha256:5abb1377598e25b13e79194fe3bef0c0ce62f1388a3a763dcd54ac0db7edfdf4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NI3JL6EMGMH4VSY57ECMCICZQH/bundle.json","state_url":"https://pith.science/pith/NI3JL6EMGMH4VSY57ECMCICZQH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NI3JL6EMGMH4VSY57ECMCICZQH/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":"2026-06-21T15:22:54Z","links":{"resolver":"https://pith.science/pith/NI3JL6EMGMH4VSY57ECMCICZQH","bundle":"https://pith.science/pith/NI3JL6EMGMH4VSY57ECMCICZQH/bundle.json","state":"https://pith.science/pith/NI3JL6EMGMH4VSY57ECMCICZQH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NI3JL6EMGMH4VSY57ECMCICZQH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:NI3JL6EMGMH4VSY57ECMCICZQH","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":"6ad1bce54050114f01246da75173882d2a40ab766ab0d0d7a8fcfd7c4ea6f3b6","cross_cats_sorted":["math-ph","math.GT","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2013-12-10T09:28:51Z","title_canon_sha256":"b2c77126671ae310727331527c55931e9a8837473e52e069a37187606697ccb3"},"schema_version":"1.0","source":{"id":"1312.2724","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.2724","created_at":"2026-05-18T01:26:58Z"},{"alias_kind":"arxiv_version","alias_value":"1312.2724v4","created_at":"2026-05-18T01:26:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.2724","created_at":"2026-05-18T01:26:58Z"},{"alias_kind":"pith_short_12","alias_value":"NI3JL6EMGMH4","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"NI3JL6EMGMH4VSY5","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"NI3JL6EM","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:5abb1377598e25b13e79194fe3bef0c0ce62f1388a3a763dcd54ac0db7edfdf4","target":"graph","created_at":"2026-05-18T01:26:58Z","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 the existence of a unique maximal surface in each anti-de Sitter (AdS) convex Globally Hyperbolic Maximal (GHM) manifold with particles (that is, with conical singularities along time-like lines) for cone angles less than $\\pi$. We interpret this result in terms of Teichm\\\"uller theory, and prove the existence of a unique minimal Lagrangian diffeomorphism isotopic to the identity between two hyperbolic surfaces with cone singularities when the cone angles are the same for both surfaces and are less than $\\pi$.","authors_text":"J\\'er\\'emy Toulisse","cross_cats":["math-ph","math.GT","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2013-12-10T09:28:51Z","title":"Maximal surfaces in anti-de Sitter 3-manifolds with particles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.2724","kind":"arxiv","version":4},"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:a30790eefe42b18869af288d2a4c24258d44446a46402c2dff25201c3526a829","target":"record","created_at":"2026-05-18T01:26:58Z","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":"6ad1bce54050114f01246da75173882d2a40ab766ab0d0d7a8fcfd7c4ea6f3b6","cross_cats_sorted":["math-ph","math.GT","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2013-12-10T09:28:51Z","title_canon_sha256":"b2c77126671ae310727331527c55931e9a8837473e52e069a37187606697ccb3"},"schema_version":"1.0","source":{"id":"1312.2724","kind":"arxiv","version":4}},"canonical_sha256":"6a3695f88c330fcacb1df904c1205981c50c07817f3f2391186c7bd601166c9e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6a3695f88c330fcacb1df904c1205981c50c07817f3f2391186c7bd601166c9e","first_computed_at":"2026-05-18T01:26:58.511069Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:26:58.511069Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"s3vmmYCGbXaKO1qrHWbBYIfEc6ojA0TVh07YNcjygpdqV2zJcExWBlnNFcAaa1swtOJAkV3TU8q7Q246KwuEDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:26:58.511748Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.2724","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a30790eefe42b18869af288d2a4c24258d44446a46402c2dff25201c3526a829","sha256:5abb1377598e25b13e79194fe3bef0c0ce62f1388a3a763dcd54ac0db7edfdf4"],"state_sha256":"91532b4ae8988fb8d341b86fbfb764f577b4767beadf9641e6b04f23270fee48"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z7pby3XUrgGqkCQ8Fb64Obgchs3DlCrX3/rl/WOhb9EO/SFb2fc60iGQXqu56dLQGkStApPyAw5OvXQTln6zCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T15:22:54.535401Z","bundle_sha256":"9c752ae55d1ba245773e3f6a2b2eedd8874443916096892c7b0737d5df9942c1"}}