{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:2JARR2URKDVSDRYFW33I7OXXER","short_pith_number":"pith:2JARR2UR","canonical_record":{"source":{"id":"1305.5391","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-05-23T12:04:43Z","cross_cats_sorted":["math.CV","math.SG"],"title_canon_sha256":"7b95765c1322bf1b87a4f2dc7fd590c85515b38db8729ba964cb52d4ddfea6bd","abstract_canon_sha256":"195a0f890555f08523f533cf3a5d8f0bb331f05b8bd7181ceeb6a818adfd3bff"},"schema_version":"1.0"},"canonical_sha256":"d24118ea9150eb21c705b6f68fbaf7245dfb9d90cc320dbfac672b35bcbc34f8","source":{"kind":"arxiv","id":"1305.5391","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.5391","created_at":"2026-05-18T03:01:25Z"},{"alias_kind":"arxiv_version","alias_value":"1305.5391v2","created_at":"2026-05-18T03:01:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.5391","created_at":"2026-05-18T03:01:25Z"},{"alias_kind":"pith_short_12","alias_value":"2JARR2URKDVS","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"2JARR2URKDVSDRYF","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"2JARR2UR","created_at":"2026-05-18T12:27:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:2JARR2URKDVSDRYFW33I7OXXER","target":"record","payload":{"canonical_record":{"source":{"id":"1305.5391","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-05-23T12:04:43Z","cross_cats_sorted":["math.CV","math.SG"],"title_canon_sha256":"7b95765c1322bf1b87a4f2dc7fd590c85515b38db8729ba964cb52d4ddfea6bd","abstract_canon_sha256":"195a0f890555f08523f533cf3a5d8f0bb331f05b8bd7181ceeb6a818adfd3bff"},"schema_version":"1.0"},"canonical_sha256":"d24118ea9150eb21c705b6f68fbaf7245dfb9d90cc320dbfac672b35bcbc34f8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:01:25.310792Z","signature_b64":"/VYS/wN8IZmZkexaPoXGUPbmI3p9VLMy56y+vAwRDprqQGQvPmVjM+yms6/j60ht0OMsVbVAJW+BktucNpF/Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d24118ea9150eb21c705b6f68fbaf7245dfb9d90cc320dbfac672b35bcbc34f8","last_reissued_at":"2026-05-18T03:01:25.310207Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:01:25.310207Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1305.5391","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:01:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D02wBy+MrR306ic9YI4IIyotBo5vYUbG7Je9M0qGzU3cNUr7XKUzRL50Je/qJHVck79kcv0jx/rYPw24pHpPDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T21:12:10.317969Z"},"content_sha256":"b2dec00f62a99bfd7e8b6eb92101486a4d72730dc9fb0e4902e081fd1b077d74","schema_version":"1.0","event_id":"sha256:b2dec00f62a99bfd7e8b6eb92101486a4d72730dc9fb0e4902e081fd1b077d74"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:2JARR2URKDVSDRYFW33I7OXXER","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The torsion flow on a closed pseudohermitian 3-manifold","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.SG"],"primary_cat":"math.DG","authors_text":"Chin-Tung Wu, Otto van Koert, Shu-Cheng Chang","submitted_at":"2013-05-23T12:04:43Z","abstract_excerpt":"In this paper we define the torsion flow, a CR analogue of the Ricci flow. For homogeneous CR manifolds we give explicit solutions to the torsion flow illustrating various kinds of behavior. We also derive monotonicity formulas for CR entropy functionals. As an application, we classify torsion breathers."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.5391","kind":"arxiv","version":2},"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":"2026-05-18T03:01:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JXZ6n1tqG1HiO7d3KFxEYcyxMa3q6i4HQ4L5rlIJaf854XQ3a1exdGozp+li7hizpVX7Bgd6sAMoSKL084YtDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T21:12:10.318421Z"},"content_sha256":"c66d89e36cb2012862191a85572cd932bd310ab2e99b7df2053dbffa2895ccae","schema_version":"1.0","event_id":"sha256:c66d89e36cb2012862191a85572cd932bd310ab2e99b7df2053dbffa2895ccae"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2JARR2URKDVSDRYFW33I7OXXER/bundle.json","state_url":"https://pith.science/pith/2JARR2URKDVSDRYFW33I7OXXER/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2JARR2URKDVSDRYFW33I7OXXER/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":"2026-05-27T21:12:10Z","links":{"resolver":"https://pith.science/pith/2JARR2URKDVSDRYFW33I7OXXER","bundle":"https://pith.science/pith/2JARR2URKDVSDRYFW33I7OXXER/bundle.json","state":"https://pith.science/pith/2JARR2URKDVSDRYFW33I7OXXER/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2JARR2URKDVSDRYFW33I7OXXER/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:2JARR2URKDVSDRYFW33I7OXXER","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":"195a0f890555f08523f533cf3a5d8f0bb331f05b8bd7181ceeb6a818adfd3bff","cross_cats_sorted":["math.CV","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-05-23T12:04:43Z","title_canon_sha256":"7b95765c1322bf1b87a4f2dc7fd590c85515b38db8729ba964cb52d4ddfea6bd"},"schema_version":"1.0","source":{"id":"1305.5391","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.5391","created_at":"2026-05-18T03:01:25Z"},{"alias_kind":"arxiv_version","alias_value":"1305.5391v2","created_at":"2026-05-18T03:01:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.5391","created_at":"2026-05-18T03:01:25Z"},{"alias_kind":"pith_short_12","alias_value":"2JARR2URKDVS","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"2JARR2URKDVSDRYF","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"2JARR2UR","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:c66d89e36cb2012862191a85572cd932bd310ab2e99b7df2053dbffa2895ccae","target":"graph","created_at":"2026-05-18T03:01:25Z","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":"In this paper we define the torsion flow, a CR analogue of the Ricci flow. For homogeneous CR manifolds we give explicit solutions to the torsion flow illustrating various kinds of behavior. We also derive monotonicity formulas for CR entropy functionals. As an application, we classify torsion breathers.","authors_text":"Chin-Tung Wu, Otto van Koert, Shu-Cheng Chang","cross_cats":["math.CV","math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-05-23T12:04:43Z","title":"The torsion flow on a closed pseudohermitian 3-manifold"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.5391","kind":"arxiv","version":2},"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:b2dec00f62a99bfd7e8b6eb92101486a4d72730dc9fb0e4902e081fd1b077d74","target":"record","created_at":"2026-05-18T03:01:25Z","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":"195a0f890555f08523f533cf3a5d8f0bb331f05b8bd7181ceeb6a818adfd3bff","cross_cats_sorted":["math.CV","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-05-23T12:04:43Z","title_canon_sha256":"7b95765c1322bf1b87a4f2dc7fd590c85515b38db8729ba964cb52d4ddfea6bd"},"schema_version":"1.0","source":{"id":"1305.5391","kind":"arxiv","version":2}},"canonical_sha256":"d24118ea9150eb21c705b6f68fbaf7245dfb9d90cc320dbfac672b35bcbc34f8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d24118ea9150eb21c705b6f68fbaf7245dfb9d90cc320dbfac672b35bcbc34f8","first_computed_at":"2026-05-18T03:01:25.310207Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:01:25.310207Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/VYS/wN8IZmZkexaPoXGUPbmI3p9VLMy56y+vAwRDprqQGQvPmVjM+yms6/j60ht0OMsVbVAJW+BktucNpF/Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:01:25.310792Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.5391","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b2dec00f62a99bfd7e8b6eb92101486a4d72730dc9fb0e4902e081fd1b077d74","sha256:c66d89e36cb2012862191a85572cd932bd310ab2e99b7df2053dbffa2895ccae"],"state_sha256":"55eda3b763f8845fb88bd40500c3aca53ef2b83e9d7b3b5047a4eb5f6c96ebfc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IuaOgRuXpu0Nuq6WB6ijg3vzMpi2BmkcWUEa+WC4k22V2JPHue+wodZa68pRbd8nDQL6HOB6syiwxkZvLnuzDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T21:12:10.321830Z","bundle_sha256":"626edc54bdd6b973add073e57fafc7651383c799caa6f353bfafe17c037ca7d3"}}