{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:T4C6RTUUMDBWLOMW4RQTJ5KUCI","short_pith_number":"pith:T4C6RTUU","canonical_record":{"source":{"id":"1404.3695","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2014-04-14T18:53:39Z","cross_cats_sorted":[],"title_canon_sha256":"98720069bc99b7b7f2c9fe54553c70618109cf086f6649806c1ce75291f44f3d","abstract_canon_sha256":"3fb43b24ca32db7adf89215da3b7845977dcc56905688e57e31acf9abcd6408f"},"schema_version":"1.0"},"canonical_sha256":"9f05e8ce9460c365b996e46134f5541222846fe71c6675d550e9f49ae7869f48","source":{"kind":"arxiv","id":"1404.3695","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.3695","created_at":"2026-05-18T01:43:34Z"},{"alias_kind":"arxiv_version","alias_value":"1404.3695v2","created_at":"2026-05-18T01:43:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.3695","created_at":"2026-05-18T01:43:34Z"},{"alias_kind":"pith_short_12","alias_value":"T4C6RTUUMDBW","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"T4C6RTUUMDBWLOMW","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"T4C6RTUU","created_at":"2026-05-18T12:28:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:T4C6RTUUMDBWLOMW4RQTJ5KUCI","target":"record","payload":{"canonical_record":{"source":{"id":"1404.3695","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2014-04-14T18:53:39Z","cross_cats_sorted":[],"title_canon_sha256":"98720069bc99b7b7f2c9fe54553c70618109cf086f6649806c1ce75291f44f3d","abstract_canon_sha256":"3fb43b24ca32db7adf89215da3b7845977dcc56905688e57e31acf9abcd6408f"},"schema_version":"1.0"},"canonical_sha256":"9f05e8ce9460c365b996e46134f5541222846fe71c6675d550e9f49ae7869f48","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:43:34.792861Z","signature_b64":"x6ZJc/2nUPkhGlLVOYd+YuvfNDFDMWNCKw1C5SdW8v2V/InelrlAOk6EwYMTqQT9r8TPt1fmSZslF1Hi+nufDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9f05e8ce9460c365b996e46134f5541222846fe71c6675d550e9f49ae7869f48","last_reissued_at":"2026-05-18T01:43:34.792339Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:43:34.792339Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1404.3695","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":"2026-05-18T01:43:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ALz6XBI0zBPZCozsarFE8yF4ZM+PsJZ4R/6HyWUOtJzWrEUSntPieZQBK3buDrPgfsbtdnqBgs+sBtz1BmomBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T17:16:51.232359Z"},"content_sha256":"62de88d8adcbe959f6afc2bac13d8e7b01536c84494f880ad0186b60ef6ce490","schema_version":"1.0","event_id":"sha256:62de88d8adcbe959f6afc2bac13d8e7b01536c84494f880ad0186b60ef6ce490"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:T4C6RTUUMDBWLOMW4RQTJ5KUCI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Some exact solutions of the semilocal Popov equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Chanju Kim","submitted_at":"2014-04-14T18:53:39Z","abstract_excerpt":"We study the semilocal version of Popov's vortex equations on $S^2$. Though they are not integrable, we construct two families of exact solutions which are expressed in terms of rational functions on $S^2$. One family is a trivial embedding of Liouville-type solutions of the Popov equations obtained by Manton, where the vortex number is an even integer. The other family of solutions are constructed through a field redefinition which relate the semilocal Popov equation to the original Popov equation but with the ratio of radii $\\sqrt{3/2}$, which is not integrable. These solutions have vortex n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.3695","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":"2026-05-18T01:43:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zQD+KtEXEVLpWnBj4kiUdShk4nsruZDr2pzfftYyT6S9R42OoG4ssQvasPVNP2kSOG5h5WfQF4ROgX2pKv92BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T17:16:51.232985Z"},"content_sha256":"fba0dedee72e2e57cd509b9a0ec3f94504d961fcc5c088523a1dab74a125c31d","schema_version":"1.0","event_id":"sha256:fba0dedee72e2e57cd509b9a0ec3f94504d961fcc5c088523a1dab74a125c31d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T4C6RTUUMDBWLOMW4RQTJ5KUCI/bundle.json","state_url":"https://pith.science/pith/T4C6RTUUMDBWLOMW4RQTJ5KUCI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T4C6RTUUMDBWLOMW4RQTJ5KUCI/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":"2026-05-30T17:16:51Z","links":{"resolver":"https://pith.science/pith/T4C6RTUUMDBWLOMW4RQTJ5KUCI","bundle":"https://pith.science/pith/T4C6RTUUMDBWLOMW4RQTJ5KUCI/bundle.json","state":"https://pith.science/pith/T4C6RTUUMDBWLOMW4RQTJ5KUCI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T4C6RTUUMDBWLOMW4RQTJ5KUCI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:T4C6RTUUMDBWLOMW4RQTJ5KUCI","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":"3fb43b24ca32db7adf89215da3b7845977dcc56905688e57e31acf9abcd6408f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2014-04-14T18:53:39Z","title_canon_sha256":"98720069bc99b7b7f2c9fe54553c70618109cf086f6649806c1ce75291f44f3d"},"schema_version":"1.0","source":{"id":"1404.3695","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.3695","created_at":"2026-05-18T01:43:34Z"},{"alias_kind":"arxiv_version","alias_value":"1404.3695v2","created_at":"2026-05-18T01:43:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.3695","created_at":"2026-05-18T01:43:34Z"},{"alias_kind":"pith_short_12","alias_value":"T4C6RTUUMDBW","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"T4C6RTUUMDBWLOMW","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"T4C6RTUU","created_at":"2026-05-18T12:28:49Z"}],"graph_snapshots":[{"event_id":"sha256:fba0dedee72e2e57cd509b9a0ec3f94504d961fcc5c088523a1dab74a125c31d","target":"graph","created_at":"2026-05-18T01:43:34Z","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 study the semilocal version of Popov's vortex equations on $S^2$. Though they are not integrable, we construct two families of exact solutions which are expressed in terms of rational functions on $S^2$. One family is a trivial embedding of Liouville-type solutions of the Popov equations obtained by Manton, where the vortex number is an even integer. The other family of solutions are constructed through a field redefinition which relate the semilocal Popov equation to the original Popov equation but with the ratio of radii $\\sqrt{3/2}$, which is not integrable. These solutions have vortex n","authors_text":"Chanju Kim","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2014-04-14T18:53:39Z","title":"Some exact solutions of the semilocal Popov equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.3695","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":"sha256:62de88d8adcbe959f6afc2bac13d8e7b01536c84494f880ad0186b60ef6ce490","target":"record","created_at":"2026-05-18T01:43:34Z","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":"3fb43b24ca32db7adf89215da3b7845977dcc56905688e57e31acf9abcd6408f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2014-04-14T18:53:39Z","title_canon_sha256":"98720069bc99b7b7f2c9fe54553c70618109cf086f6649806c1ce75291f44f3d"},"schema_version":"1.0","source":{"id":"1404.3695","kind":"arxiv","version":2}},"canonical_sha256":"9f05e8ce9460c365b996e46134f5541222846fe71c6675d550e9f49ae7869f48","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9f05e8ce9460c365b996e46134f5541222846fe71c6675d550e9f49ae7869f48","first_computed_at":"2026-05-18T01:43:34.792339Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:43:34.792339Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"x6ZJc/2nUPkhGlLVOYd+YuvfNDFDMWNCKw1C5SdW8v2V/InelrlAOk6EwYMTqQT9r8TPt1fmSZslF1Hi+nufDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:43:34.792861Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.3695","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:62de88d8adcbe959f6afc2bac13d8e7b01536c84494f880ad0186b60ef6ce490","sha256:fba0dedee72e2e57cd509b9a0ec3f94504d961fcc5c088523a1dab74a125c31d"],"state_sha256":"e5063edb3ae84cec51a0be6c0194ccd8635e40a0c7eeb40a330b31f1c2dbdca4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rMoytoWLpmNsqKWWoyMG/r+VvlPDD1rpm7Us1gnl+aDtYN9O0b4e9TpJT1q/q4u567JToF3ffGN8ZGPnhVf2CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T17:16:51.236135Z","bundle_sha256":"75c458fc1cd3fbdde9442b49a8a771aa7ac37fa2e25c425ad848dc56ff1be823"}}