{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:RF45GC5AIIXOA5LSYHTESVP7ZT","short_pith_number":"pith:RF45GC5A","schema_version":"1.0","canonical_sha256":"8979d30ba0422ee07572c1e64955ffccc086f6ececc326842b4b3e3f0f1eb335","source":{"kind":"arxiv","id":"1212.4817","version":3},"attestation_state":"computed","paper":{"title":"Canonical connection on contact manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.SG","authors_text":"Rui Wang, Yong-Geun Oh","submitted_at":"2012-12-19T20:24:58Z","abstract_excerpt":"We introduce a canonical affine connection on the contact manifold $(Q,\\xi)$, which is associated to each contact triad $(Q,\\lambda,J)$ where $\\lambda$ is a contact form and $J:\\xi \\to \\xi$ is an endomorphism with $J^2 = -id$ compatible to $d\\lambda$. We call it the \\emph{contact triad connection} of $(Q,\\lambda,J)$ and prove its existence and uniqueness. The connection is canonical in that the pull-back connection $\\phi^*\\nabla$ of a triad connection $\\nabla$ becomes the triad connection of the pull-back triad $(Q, \\phi^*\\lambda, \\phi^*J)$ for any diffeomorphism $\\phi:Q \\to Q$ satisfying $\\ph"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1212.4817","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2012-12-19T20:24:58Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"7712ed6e27433e3010dec7a0f2888527b7fe62a9cc01f0418deba3a6e7d7cba6","abstract_canon_sha256":"35a7201438fe8e2f38484a9228e8994c4c49fbcc493faad0467036aea6b70d70"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:15.171696Z","signature_b64":"pyxz47Y7QzhJ4hT+KvHsotuhMcw10tAXhER4vdaErFPOtibmo+YsPKsh50pxC7WUMJy11IXDaj7OLE0/NNzmDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8979d30ba0422ee07572c1e64955ffccc086f6ececc326842b4b3e3f0f1eb335","last_reissued_at":"2026-05-18T01:12:15.171247Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:15.171247Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Canonical connection on contact manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.SG","authors_text":"Rui Wang, Yong-Geun Oh","submitted_at":"2012-12-19T20:24:58Z","abstract_excerpt":"We introduce a canonical affine connection on the contact manifold $(Q,\\xi)$, which is associated to each contact triad $(Q,\\lambda,J)$ where $\\lambda$ is a contact form and $J:\\xi \\to \\xi$ is an endomorphism with $J^2 = -id$ compatible to $d\\lambda$. We call it the \\emph{contact triad connection} of $(Q,\\lambda,J)$ and prove its existence and uniqueness. The connection is canonical in that the pull-back connection $\\phi^*\\nabla$ of a triad connection $\\nabla$ becomes the triad connection of the pull-back triad $(Q, \\phi^*\\lambda, \\phi^*J)$ for any diffeomorphism $\\phi:Q \\to Q$ satisfying $\\ph"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.4817","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1212.4817","created_at":"2026-05-18T01:12:15.171301+00:00"},{"alias_kind":"arxiv_version","alias_value":"1212.4817v3","created_at":"2026-05-18T01:12:15.171301+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.4817","created_at":"2026-05-18T01:12:15.171301+00:00"},{"alias_kind":"pith_short_12","alias_value":"RF45GC5AIIXO","created_at":"2026-05-18T12:27:20.899486+00:00"},{"alias_kind":"pith_short_16","alias_value":"RF45GC5AIIXOA5LS","created_at":"2026-05-18T12:27:20.899486+00:00"},{"alias_kind":"pith_short_8","alias_value":"RF45GC5A","created_at":"2026-05-18T12:27:20.899486+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/RF45GC5AIIXOA5LSYHTESVP7ZT","json":"https://pith.science/pith/RF45GC5AIIXOA5LSYHTESVP7ZT.json","graph_json":"https://pith.science/api/pith-number/RF45GC5AIIXOA5LSYHTESVP7ZT/graph.json","events_json":"https://pith.science/api/pith-number/RF45GC5AIIXOA5LSYHTESVP7ZT/events.json","paper":"https://pith.science/paper/RF45GC5A"},"agent_actions":{"view_html":"https://pith.science/pith/RF45GC5AIIXOA5LSYHTESVP7ZT","download_json":"https://pith.science/pith/RF45GC5AIIXOA5LSYHTESVP7ZT.json","view_paper":"https://pith.science/paper/RF45GC5A","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1212.4817&json=true","fetch_graph":"https://pith.science/api/pith-number/RF45GC5AIIXOA5LSYHTESVP7ZT/graph.json","fetch_events":"https://pith.science/api/pith-number/RF45GC5AIIXOA5LSYHTESVP7ZT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RF45GC5AIIXOA5LSYHTESVP7ZT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RF45GC5AIIXOA5LSYHTESVP7ZT/action/storage_attestation","attest_author":"https://pith.science/pith/RF45GC5AIIXOA5LSYHTESVP7ZT/action/author_attestation","sign_citation":"https://pith.science/pith/RF45GC5AIIXOA5LSYHTESVP7ZT/action/citation_signature","submit_replication":"https://pith.science/pith/RF45GC5AIIXOA5LSYHTESVP7ZT/action/replication_record"}},"created_at":"2026-05-18T01:12:15.171301+00:00","updated_at":"2026-05-18T01:12:15.171301+00:00"}