{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:4X5TYGXBWPTUBV3WVBG6RSPON6","short_pith_number":"pith:4X5TYGXB","canonical_record":{"source":{"id":"1803.05509","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-03-15T00:29:16Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"a3bd9ecb38936d9c0a4dcb62191dd89c472e34814983c3e077dd71de6d045436","abstract_canon_sha256":"2504ba467af35ee027fdbafa0bc22e12c3a09cb9ea221736d1aa2dc6b1b3b7d0"},"schema_version":"1.0"},"canonical_sha256":"e5fb3c1ae1b3e740d776a84de8c9ee6faccfb05717117a56e7330b89ebf1be1a","source":{"kind":"arxiv","id":"1803.05509","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.05509","created_at":"2026-05-17T23:47:40Z"},{"alias_kind":"arxiv_version","alias_value":"1803.05509v2","created_at":"2026-05-17T23:47:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.05509","created_at":"2026-05-17T23:47:40Z"},{"alias_kind":"pith_short_12","alias_value":"4X5TYGXBWPTU","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"4X5TYGXBWPTUBV3W","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"4X5TYGXB","created_at":"2026-05-18T12:32:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:4X5TYGXBWPTUBV3WVBG6RSPON6","target":"record","payload":{"canonical_record":{"source":{"id":"1803.05509","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-03-15T00:29:16Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"a3bd9ecb38936d9c0a4dcb62191dd89c472e34814983c3e077dd71de6d045436","abstract_canon_sha256":"2504ba467af35ee027fdbafa0bc22e12c3a09cb9ea221736d1aa2dc6b1b3b7d0"},"schema_version":"1.0"},"canonical_sha256":"e5fb3c1ae1b3e740d776a84de8c9ee6faccfb05717117a56e7330b89ebf1be1a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:40.120098Z","signature_b64":"N+XNJaCKxuPApKYIMG/jAAqJz3IRTAAgMn5866//Loz2mn8TZ792v1vhBiyaEFWOpmchPjZ4U78f1VjbCSpABA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e5fb3c1ae1b3e740d776a84de8c9ee6faccfb05717117a56e7330b89ebf1be1a","last_reissued_at":"2026-05-17T23:47:40.119583Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:40.119583Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.05509","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":"2026-05-17T23:47:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2TkN+6HILrZnpcMT7ML/IBkVey2S9ZEujRH4LHfn63+aE7XCNfCIhYGBZ2fA3VqutrO1T6bsdXBTYeYk2XFBCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-31T13:28:22.113470Z"},"content_sha256":"f9a590691242ef94e0a6fab128824cbafb2e54b9ab97161ef9aae257216e8e79","schema_version":"1.0","event_id":"sha256:f9a590691242ef94e0a6fab128824cbafb2e54b9ab97161ef9aae257216e8e79"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:4X5TYGXBWPTUBV3WVBG6RSPON6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Geometric momentum and angular momentum for charge-monopole system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"quant-ph","authors_text":"Q. H. Liu, S. F. Xiao","submitted_at":"2018-03-15T00:29:16Z","abstract_excerpt":"For a charge-monopole pair, though the definition of the orbital angular momentum is different from the usual one, and the transverse part of the momentum that includes the vector potential as an additive term turns out to be the so-called geometric momentum that is under intensive study recently. For the charge is constrained on the spherical surface with monopole at the origin, the commutation relations between all components of geometric momentum and the orbital angular momentum satisfy the $so(3,1)$ algebra. With construction of the geometrically infinitesimal displacement operator based o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.05509","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":"2026-05-17T23:47:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G++6X3ot9vXLlhkkb1Y0dnP8C8QluEvrHkgrw6MK5JeBcs04HUPALFblPfQ8TLsJQzWdKSk6YQo17QEj1XRMBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-31T13:28:22.113884Z"},"content_sha256":"06b218a816c8cfdaa6f371b671d86895fff4ce8b4278cf69259df0c7c67dc48b","schema_version":"1.0","event_id":"sha256:06b218a816c8cfdaa6f371b671d86895fff4ce8b4278cf69259df0c7c67dc48b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4X5TYGXBWPTUBV3WVBG6RSPON6/bundle.json","state_url":"https://pith.science/pith/4X5TYGXBWPTUBV3WVBG6RSPON6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4X5TYGXBWPTUBV3WVBG6RSPON6/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":"2026-07-31T13:28:22Z","links":{"resolver":"https://pith.science/pith/4X5TYGXBWPTUBV3WVBG6RSPON6","bundle":"https://pith.science/pith/4X5TYGXBWPTUBV3WVBG6RSPON6/bundle.json","state":"https://pith.science/pith/4X5TYGXBWPTUBV3WVBG6RSPON6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4X5TYGXBWPTUBV3WVBG6RSPON6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:4X5TYGXBWPTUBV3WVBG6RSPON6","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":"2504ba467af35ee027fdbafa0bc22e12c3a09cb9ea221736d1aa2dc6b1b3b7d0","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-03-15T00:29:16Z","title_canon_sha256":"a3bd9ecb38936d9c0a4dcb62191dd89c472e34814983c3e077dd71de6d045436"},"schema_version":"1.0","source":{"id":"1803.05509","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.05509","created_at":"2026-05-17T23:47:40Z"},{"alias_kind":"arxiv_version","alias_value":"1803.05509v2","created_at":"2026-05-17T23:47:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.05509","created_at":"2026-05-17T23:47:40Z"},{"alias_kind":"pith_short_12","alias_value":"4X5TYGXBWPTU","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"4X5TYGXBWPTUBV3W","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"4X5TYGXB","created_at":"2026-05-18T12:32:05Z"}],"graph_snapshots":[{"event_id":"sha256:06b218a816c8cfdaa6f371b671d86895fff4ce8b4278cf69259df0c7c67dc48b","target":"graph","created_at":"2026-05-17T23:47:40Z","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":"For a charge-monopole pair, though the definition of the orbital angular momentum is different from the usual one, and the transverse part of the momentum that includes the vector potential as an additive term turns out to be the so-called geometric momentum that is under intensive study recently. For the charge is constrained on the spherical surface with monopole at the origin, the commutation relations between all components of geometric momentum and the orbital angular momentum satisfy the $so(3,1)$ algebra. With construction of the geometrically infinitesimal displacement operator based o","authors_text":"Q. H. Liu, S. F. Xiao","cross_cats":["hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-03-15T00:29:16Z","title":"Geometric momentum and angular momentum for charge-monopole system"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.05509","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:f9a590691242ef94e0a6fab128824cbafb2e54b9ab97161ef9aae257216e8e79","target":"record","created_at":"2026-05-17T23:47:40Z","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":"2504ba467af35ee027fdbafa0bc22e12c3a09cb9ea221736d1aa2dc6b1b3b7d0","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-03-15T00:29:16Z","title_canon_sha256":"a3bd9ecb38936d9c0a4dcb62191dd89c472e34814983c3e077dd71de6d045436"},"schema_version":"1.0","source":{"id":"1803.05509","kind":"arxiv","version":2}},"canonical_sha256":"e5fb3c1ae1b3e740d776a84de8c9ee6faccfb05717117a56e7330b89ebf1be1a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e5fb3c1ae1b3e740d776a84de8c9ee6faccfb05717117a56e7330b89ebf1be1a","first_computed_at":"2026-05-17T23:47:40.119583Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:40.119583Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"N+XNJaCKxuPApKYIMG/jAAqJz3IRTAAgMn5866//Loz2mn8TZ792v1vhBiyaEFWOpmchPjZ4U78f1VjbCSpABA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:40.120098Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.05509","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f9a590691242ef94e0a6fab128824cbafb2e54b9ab97161ef9aae257216e8e79","sha256:06b218a816c8cfdaa6f371b671d86895fff4ce8b4278cf69259df0c7c67dc48b"],"state_sha256":"70451ab480783b36fadad9a2c55d02464c67ed14e3e230b667e6bc6d60e0d6e8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UlSRU3fzlukcSq/OL2JRZIEGdgj4DaF56AdBy8aYJN8t6NfFtQNpiXkUcOGL81Vy3w3gIl+6VQ7xPaSEwWb4Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-31T13:28:22.119259Z","bundle_sha256":"092e260e0e22099db64a095d3cea21048892462d7803959007746b35222a5548"}}