{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:POYP2XUBZSVTQDK3JANJIQLAYS","short_pith_number":"pith:POYP2XUB","canonical_record":{"source":{"id":"1206.2678","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-06-12T21:47:51Z","cross_cats_sorted":[],"title_canon_sha256":"6531d77ca8ba494d63e4e01b0553dfb5f00de5cc5d94f9fba6e4d24758288763","abstract_canon_sha256":"4f108231e4e2d339222f6571306216396138ef6ac4eaa0bdc802870c3f5ce7d9"},"schema_version":"1.0"},"canonical_sha256":"7bb0fd5e81ccab380d5b481a944160c487c20ec1c9bdfdf450f6d27e61daeca8","source":{"kind":"arxiv","id":"1206.2678","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.2678","created_at":"2026-05-18T03:53:43Z"},{"alias_kind":"arxiv_version","alias_value":"1206.2678v1","created_at":"2026-05-18T03:53:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.2678","created_at":"2026-05-18T03:53:43Z"},{"alias_kind":"pith_short_12","alias_value":"POYP2XUBZSVT","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"POYP2XUBZSVTQDK3","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"POYP2XUB","created_at":"2026-05-18T12:27:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:POYP2XUBZSVTQDK3JANJIQLAYS","target":"record","payload":{"canonical_record":{"source":{"id":"1206.2678","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-06-12T21:47:51Z","cross_cats_sorted":[],"title_canon_sha256":"6531d77ca8ba494d63e4e01b0553dfb5f00de5cc5d94f9fba6e4d24758288763","abstract_canon_sha256":"4f108231e4e2d339222f6571306216396138ef6ac4eaa0bdc802870c3f5ce7d9"},"schema_version":"1.0"},"canonical_sha256":"7bb0fd5e81ccab380d5b481a944160c487c20ec1c9bdfdf450f6d27e61daeca8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:53:43.346975Z","signature_b64":"oEBW0qEJ0yzzR92aLrP91+ydFCy3iKkuBQ5FajGLeHqSP58velWfL+/PbbKgGGF77mroTSSDyofAfegcJ4g4Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7bb0fd5e81ccab380d5b481a944160c487c20ec1c9bdfdf450f6d27e61daeca8","last_reissued_at":"2026-05-18T03:53:43.346558Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:53:43.346558Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1206.2678","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":"2026-05-18T03:53:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+4pSakzi+zHqEZEDoA7PBENhUeQjcLyTOKihOi/CrshMVdQvZo9UQawdQvMKZE3RqYEzy7/FIdcFgGd6U2X2Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T20:37:29.781527Z"},"content_sha256":"a55f2f81658e801456b55cadd514109918f846514f000dcdde52be0bfbe78948","schema_version":"1.0","event_id":"sha256:a55f2f81658e801456b55cadd514109918f846514f000dcdde52be0bfbe78948"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:POYP2XUBZSVTQDK3JANJIQLAYS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"({\\kappa},{\\mu},\\u{psion}=const.)-Contact Metric Manifolds With {\\xi}(I_{M})=0","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Cengizhan Murathan, \\.Irem K\\\"upeli Erken","submitted_at":"2012-06-12T21:47:51Z","abstract_excerpt":"We give a local classification of ({\\kappa},{\\mu},\\u{psion}=const.)-contact metric manifold (M,{\\phi},{\\xi},{\\eta},g) with {\\kappa}<1 which satisfies the condition\" the Boeckx invariant function I_{M}=((1-({\\mu}/2))/(\\surd(1-{\\kappa}))) is constant along the integral curves of the characteristic vector field {\\xi}\"."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.2678","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":"2026-05-18T03:53:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RupAjithizd5W9yY4/hDTHk3PDcMLlVTroMRk8feQSEMAdI68YRIiTLPhC5CNaRF7SngdZTvzTazVt3zRaLUDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T20:37:29.781868Z"},"content_sha256":"809d0df114e2637ff65da86bbc0c6aa20d7b2b68dc464ecc432c3add939f9dcb","schema_version":"1.0","event_id":"sha256:809d0df114e2637ff65da86bbc0c6aa20d7b2b68dc464ecc432c3add939f9dcb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/POYP2XUBZSVTQDK3JANJIQLAYS/bundle.json","state_url":"https://pith.science/pith/POYP2XUBZSVTQDK3JANJIQLAYS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/POYP2XUBZSVTQDK3JANJIQLAYS/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":"2026-06-22T20:37:29Z","links":{"resolver":"https://pith.science/pith/POYP2XUBZSVTQDK3JANJIQLAYS","bundle":"https://pith.science/pith/POYP2XUBZSVTQDK3JANJIQLAYS/bundle.json","state":"https://pith.science/pith/POYP2XUBZSVTQDK3JANJIQLAYS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/POYP2XUBZSVTQDK3JANJIQLAYS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:POYP2XUBZSVTQDK3JANJIQLAYS","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":"4f108231e4e2d339222f6571306216396138ef6ac4eaa0bdc802870c3f5ce7d9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-06-12T21:47:51Z","title_canon_sha256":"6531d77ca8ba494d63e4e01b0553dfb5f00de5cc5d94f9fba6e4d24758288763"},"schema_version":"1.0","source":{"id":"1206.2678","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.2678","created_at":"2026-05-18T03:53:43Z"},{"alias_kind":"arxiv_version","alias_value":"1206.2678v1","created_at":"2026-05-18T03:53:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.2678","created_at":"2026-05-18T03:53:43Z"},{"alias_kind":"pith_short_12","alias_value":"POYP2XUBZSVT","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"POYP2XUBZSVTQDK3","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"POYP2XUB","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:809d0df114e2637ff65da86bbc0c6aa20d7b2b68dc464ecc432c3add939f9dcb","target":"graph","created_at":"2026-05-18T03:53:43Z","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 give a local classification of ({\\kappa},{\\mu},\\u{psion}=const.)-contact metric manifold (M,{\\phi},{\\xi},{\\eta},g) with {\\kappa}<1 which satisfies the condition\" the Boeckx invariant function I_{M}=((1-({\\mu}/2))/(\\surd(1-{\\kappa}))) is constant along the integral curves of the characteristic vector field {\\xi}\".","authors_text":"Cengizhan Murathan, \\.Irem K\\\"upeli Erken","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-06-12T21:47:51Z","title":"({\\kappa},{\\mu},\\u{psion}=const.)-Contact Metric Manifolds With {\\xi}(I_{M})=0"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.2678","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:a55f2f81658e801456b55cadd514109918f846514f000dcdde52be0bfbe78948","target":"record","created_at":"2026-05-18T03:53:43Z","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":"4f108231e4e2d339222f6571306216396138ef6ac4eaa0bdc802870c3f5ce7d9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-06-12T21:47:51Z","title_canon_sha256":"6531d77ca8ba494d63e4e01b0553dfb5f00de5cc5d94f9fba6e4d24758288763"},"schema_version":"1.0","source":{"id":"1206.2678","kind":"arxiv","version":1}},"canonical_sha256":"7bb0fd5e81ccab380d5b481a944160c487c20ec1c9bdfdf450f6d27e61daeca8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7bb0fd5e81ccab380d5b481a944160c487c20ec1c9bdfdf450f6d27e61daeca8","first_computed_at":"2026-05-18T03:53:43.346558Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:53:43.346558Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oEBW0qEJ0yzzR92aLrP91+ydFCy3iKkuBQ5FajGLeHqSP58velWfL+/PbbKgGGF77mroTSSDyofAfegcJ4g4Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:53:43.346975Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.2678","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a55f2f81658e801456b55cadd514109918f846514f000dcdde52be0bfbe78948","sha256:809d0df114e2637ff65da86bbc0c6aa20d7b2b68dc464ecc432c3add939f9dcb"],"state_sha256":"d5160502cd8a46fb5f28a21efeb3e1b75cf2b28f49023f8fc0bd5c3a0b3d10c3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CQHocRnwI3prSPRr5nrxpc2Q/eyEP/g4KpUKay2aUxxIIeGJzkuZMcfCJGkM/9bzOhzrlNGmpZo9aigandm6Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T20:37:29.783790Z","bundle_sha256":"101b5e613681cb3453a2cf1aafd75aab12eb8fb37973161d487662012d263966"}}