{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:GBNPQDAPPI2WKG7QJE5LCZJEXE","short_pith_number":"pith:GBNPQDAP","canonical_record":{"source":{"id":"1610.08867","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-10-27T16:20:46Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"69f793e4d1f413ac76567a33dfa8e47e71d1b3d26782e31c203a259ec60fd880","abstract_canon_sha256":"cc8024e91a66ea2b44ada4306556fcc754fa7565dba1bb5fb4545ec22ebe914c"},"schema_version":"1.0"},"canonical_sha256":"305af80c0f7a35651bf0493ab16524b90dfedf39a9856a7dde97c8df0bb1a093","source":{"kind":"arxiv","id":"1610.08867","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.08867","created_at":"2026-05-18T00:00:32Z"},{"alias_kind":"arxiv_version","alias_value":"1610.08867v3","created_at":"2026-05-18T00:00:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.08867","created_at":"2026-05-18T00:00:32Z"},{"alias_kind":"pith_short_12","alias_value":"GBNPQDAPPI2W","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"GBNPQDAPPI2WKG7Q","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"GBNPQDAP","created_at":"2026-05-18T12:30:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:GBNPQDAPPI2WKG7QJE5LCZJEXE","target":"record","payload":{"canonical_record":{"source":{"id":"1610.08867","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-10-27T16:20:46Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"69f793e4d1f413ac76567a33dfa8e47e71d1b3d26782e31c203a259ec60fd880","abstract_canon_sha256":"cc8024e91a66ea2b44ada4306556fcc754fa7565dba1bb5fb4545ec22ebe914c"},"schema_version":"1.0"},"canonical_sha256":"305af80c0f7a35651bf0493ab16524b90dfedf39a9856a7dde97c8df0bb1a093","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:00:32.943623Z","signature_b64":"iLqXugAobtiJJC2iHysvh2X3SRqqkFv+aJbvl0QWz7PEczXYuhkWnh9JhX8wSFkIzE+NHvKlnvzSk14w16XFBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"305af80c0f7a35651bf0493ab16524b90dfedf39a9856a7dde97c8df0bb1a093","last_reissued_at":"2026-05-18T00:00:32.943143Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:00:32.943143Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.08867","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:00:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3k5SONZjd/tVqLT8faQi6zkTTs5YaLGnX6VI+T9voPuafe9Dgpjq/a281aMiMJqT9ZC6xCElnM7yX0upwF12Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T17:15:49.779779Z"},"content_sha256":"40ef8f14e28c7509c4114d2c1b67fff0f2cd0e7016a94fc3719cfedbbdf3e144","schema_version":"1.0","event_id":"sha256:40ef8f14e28c7509c4114d2c1b67fff0f2cd0e7016a94fc3719cfedbbdf3e144"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:GBNPQDAPPI2WKG7QJE5LCZJEXE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Constant mean curvature foliation of domains of dependence in $AdS_{3}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.DG","authors_text":"Andrea Tamburelli","submitted_at":"2016-10-27T16:20:46Z","abstract_excerpt":"We prove that, given an acausal curve $\\Gamma$ in the boundary at infinity of $AdS_{3}$ which is the graph of a quasi-symmetric homeomorphism $\\phi$, there exists a unique foliation of its domain of dependence $D(\\Gamma)$ by constant mean curvature surfaces with bounded second fundamental form. Moreover, these surfaces provide a family of quasi-conformal extensions of $\\phi$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.08867","kind":"arxiv","version":3},"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":"2026-05-18T00:00:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1QfT272c2GmG//xfj254CJpzffwYJpPh2DsRdOZKSvDPJOAk0zsPjR6cPWTXQXP3pl/yrkkLlArM13ZX0ORrBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T17:15:49.780111Z"},"content_sha256":"30b054f0436f5049eb4a101f710cab6fdd9f3980fd60b52a44686a19e60745f4","schema_version":"1.0","event_id":"sha256:30b054f0436f5049eb4a101f710cab6fdd9f3980fd60b52a44686a19e60745f4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GBNPQDAPPI2WKG7QJE5LCZJEXE/bundle.json","state_url":"https://pith.science/pith/GBNPQDAPPI2WKG7QJE5LCZJEXE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GBNPQDAPPI2WKG7QJE5LCZJEXE/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":"2026-06-21T17:15:49Z","links":{"resolver":"https://pith.science/pith/GBNPQDAPPI2WKG7QJE5LCZJEXE","bundle":"https://pith.science/pith/GBNPQDAPPI2WKG7QJE5LCZJEXE/bundle.json","state":"https://pith.science/pith/GBNPQDAPPI2WKG7QJE5LCZJEXE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GBNPQDAPPI2WKG7QJE5LCZJEXE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:GBNPQDAPPI2WKG7QJE5LCZJEXE","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":"cc8024e91a66ea2b44ada4306556fcc754fa7565dba1bb5fb4545ec22ebe914c","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-10-27T16:20:46Z","title_canon_sha256":"69f793e4d1f413ac76567a33dfa8e47e71d1b3d26782e31c203a259ec60fd880"},"schema_version":"1.0","source":{"id":"1610.08867","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.08867","created_at":"2026-05-18T00:00:32Z"},{"alias_kind":"arxiv_version","alias_value":"1610.08867v3","created_at":"2026-05-18T00:00:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.08867","created_at":"2026-05-18T00:00:32Z"},{"alias_kind":"pith_short_12","alias_value":"GBNPQDAPPI2W","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"GBNPQDAPPI2WKG7Q","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"GBNPQDAP","created_at":"2026-05-18T12:30:15Z"}],"graph_snapshots":[{"event_id":"sha256:30b054f0436f5049eb4a101f710cab6fdd9f3980fd60b52a44686a19e60745f4","target":"graph","created_at":"2026-05-18T00:00:32Z","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 that, given an acausal curve $\\Gamma$ in the boundary at infinity of $AdS_{3}$ which is the graph of a quasi-symmetric homeomorphism $\\phi$, there exists a unique foliation of its domain of dependence $D(\\Gamma)$ by constant mean curvature surfaces with bounded second fundamental form. Moreover, these surfaces provide a family of quasi-conformal extensions of $\\phi$.","authors_text":"Andrea Tamburelli","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-10-27T16:20:46Z","title":"Constant mean curvature foliation of domains of dependence in $AdS_{3}$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.08867","kind":"arxiv","version":3},"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":"sha256:40ef8f14e28c7509c4114d2c1b67fff0f2cd0e7016a94fc3719cfedbbdf3e144","target":"record","created_at":"2026-05-18T00:00:32Z","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":"cc8024e91a66ea2b44ada4306556fcc754fa7565dba1bb5fb4545ec22ebe914c","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-10-27T16:20:46Z","title_canon_sha256":"69f793e4d1f413ac76567a33dfa8e47e71d1b3d26782e31c203a259ec60fd880"},"schema_version":"1.0","source":{"id":"1610.08867","kind":"arxiv","version":3}},"canonical_sha256":"305af80c0f7a35651bf0493ab16524b90dfedf39a9856a7dde97c8df0bb1a093","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"305af80c0f7a35651bf0493ab16524b90dfedf39a9856a7dde97c8df0bb1a093","first_computed_at":"2026-05-18T00:00:32.943143Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:00:32.943143Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iLqXugAobtiJJC2iHysvh2X3SRqqkFv+aJbvl0QWz7PEczXYuhkWnh9JhX8wSFkIzE+NHvKlnvzSk14w16XFBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:00:32.943623Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.08867","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:40ef8f14e28c7509c4114d2c1b67fff0f2cd0e7016a94fc3719cfedbbdf3e144","sha256:30b054f0436f5049eb4a101f710cab6fdd9f3980fd60b52a44686a19e60745f4"],"state_sha256":"59eb078d266a6e361fde674223b95c5087e72925e2bf96b05f4b0a323bad6814"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"efjfUzS9QwmOPQeatlVgYnuknqfWulhmLoNoUjAwxZGHAQ8ngXSBLGj1F8styqo0hmaB2T44GwcbATQ0S9edDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T17:15:49.781957Z","bundle_sha256":"f038f145ea089d856121db36e70b18078224466a104ec378e9c5b1021dc8e52f"}}