{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:KSFY7WTPWZCRFHZ4BRJBYMU3JT","short_pith_number":"pith:KSFY7WTP","canonical_record":{"source":{"id":"1110.1423","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-10-07T02:21:04Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"115f0331cb313f660cf661bdea9742987e047875ae9b244a18f49f6874b36008","abstract_canon_sha256":"bf43e36e79347fcb08eb6d40355cb1c8fc05124e003342e95fe43c15bcd925f7"},"schema_version":"1.0"},"canonical_sha256":"548b8fda6fb645129f3c0c521c329b4cd6be2bdb1f1cfa5ab3690ccbcbaac5b9","source":{"kind":"arxiv","id":"1110.1423","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.1423","created_at":"2026-05-18T03:20:45Z"},{"alias_kind":"arxiv_version","alias_value":"1110.1423v2","created_at":"2026-05-18T03:20:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.1423","created_at":"2026-05-18T03:20:45Z"},{"alias_kind":"pith_short_12","alias_value":"KSFY7WTPWZCR","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"KSFY7WTPWZCRFHZ4","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"KSFY7WTP","created_at":"2026-05-18T12:26:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:KSFY7WTPWZCRFHZ4BRJBYMU3JT","target":"record","payload":{"canonical_record":{"source":{"id":"1110.1423","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-10-07T02:21:04Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"115f0331cb313f660cf661bdea9742987e047875ae9b244a18f49f6874b36008","abstract_canon_sha256":"bf43e36e79347fcb08eb6d40355cb1c8fc05124e003342e95fe43c15bcd925f7"},"schema_version":"1.0"},"canonical_sha256":"548b8fda6fb645129f3c0c521c329b4cd6be2bdb1f1cfa5ab3690ccbcbaac5b9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:20:45.576501Z","signature_b64":"LiyZtydKGQAMOBv+cW92xQRSXDhtNKbFD6mefIc+qqOuBX0eICwW8Ejb3PJYvuTWRomKQPVupEC3Z5bHr9RvCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"548b8fda6fb645129f3c0c521c329b4cd6be2bdb1f1cfa5ab3690ccbcbaac5b9","last_reissued_at":"2026-05-18T03:20:45.575896Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:20:45.575896Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1110.1423","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":"2026-05-18T03:20:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"463/f9tQy8EjMmvgXRASac1ML+7zkqkpNvdV9ty8LhhETCDnbOg/yBqTFakwPx8DDMULzyCljcOp/zTp1lZCAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T02:40:10.034753Z"},"content_sha256":"6dd0bd258d657b0ff5b4b4503d11cbf3296daaa247df404ef416b107f9218bc6","schema_version":"1.0","event_id":"sha256:6dd0bd258d657b0ff5b4b4503d11cbf3296daaa247df404ef416b107f9218bc6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:KSFY7WTPWZCRFHZ4BRJBYMU3JT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Sharp Existence Theorem for Vortices in the Theory of Branes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Xiaosen Han","submitted_at":"2011-10-07T02:21:04Z","abstract_excerpt":"We investigate the BPS equations arising from the theory of multi-intersection of D-branes. By using the direct minimization method, we establish sharp existence and uniqueness theorems for multiple vortex solutions of the BPS equations over a doubly periodic domain and over the full plane, respectively. In particular, we obtain an explicit necessary and sufficient condition for the existence of a unique solution for the doubly periodic domain case."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.1423","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":"2026-05-18T03:20:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"leqJL0X75j+2KJsnrRfshz1o6pcjr2WxbkaxPb53JNgJwKq0nxPN4GfQITeE21zq5q3vVxtJvRzwtISWCMhrCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T02:40:10.035090Z"},"content_sha256":"9a436678ccf6bdcb43da1a28b2ae2ee39c2327510c60581cc0f5adf0ae699b9d","schema_version":"1.0","event_id":"sha256:9a436678ccf6bdcb43da1a28b2ae2ee39c2327510c60581cc0f5adf0ae699b9d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KSFY7WTPWZCRFHZ4BRJBYMU3JT/bundle.json","state_url":"https://pith.science/pith/KSFY7WTPWZCRFHZ4BRJBYMU3JT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KSFY7WTPWZCRFHZ4BRJBYMU3JT/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":"2026-06-03T02:40:10Z","links":{"resolver":"https://pith.science/pith/KSFY7WTPWZCRFHZ4BRJBYMU3JT","bundle":"https://pith.science/pith/KSFY7WTPWZCRFHZ4BRJBYMU3JT/bundle.json","state":"https://pith.science/pith/KSFY7WTPWZCRFHZ4BRJBYMU3JT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KSFY7WTPWZCRFHZ4BRJBYMU3JT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:KSFY7WTPWZCRFHZ4BRJBYMU3JT","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":"bf43e36e79347fcb08eb6d40355cb1c8fc05124e003342e95fe43c15bcd925f7","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-10-07T02:21:04Z","title_canon_sha256":"115f0331cb313f660cf661bdea9742987e047875ae9b244a18f49f6874b36008"},"schema_version":"1.0","source":{"id":"1110.1423","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.1423","created_at":"2026-05-18T03:20:45Z"},{"alias_kind":"arxiv_version","alias_value":"1110.1423v2","created_at":"2026-05-18T03:20:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.1423","created_at":"2026-05-18T03:20:45Z"},{"alias_kind":"pith_short_12","alias_value":"KSFY7WTPWZCR","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"KSFY7WTPWZCRFHZ4","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"KSFY7WTP","created_at":"2026-05-18T12:26:34Z"}],"graph_snapshots":[{"event_id":"sha256:9a436678ccf6bdcb43da1a28b2ae2ee39c2327510c60581cc0f5adf0ae699b9d","target":"graph","created_at":"2026-05-18T03:20:45Z","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 investigate the BPS equations arising from the theory of multi-intersection of D-branes. By using the direct minimization method, we establish sharp existence and uniqueness theorems for multiple vortex solutions of the BPS equations over a doubly periodic domain and over the full plane, respectively. In particular, we obtain an explicit necessary and sufficient condition for the existence of a unique solution for the doubly periodic domain case.","authors_text":"Xiaosen Han","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-10-07T02:21:04Z","title":"A Sharp Existence Theorem for Vortices in the Theory of Branes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.1423","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":"sha256:6dd0bd258d657b0ff5b4b4503d11cbf3296daaa247df404ef416b107f9218bc6","target":"record","created_at":"2026-05-18T03:20:45Z","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":"bf43e36e79347fcb08eb6d40355cb1c8fc05124e003342e95fe43c15bcd925f7","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-10-07T02:21:04Z","title_canon_sha256":"115f0331cb313f660cf661bdea9742987e047875ae9b244a18f49f6874b36008"},"schema_version":"1.0","source":{"id":"1110.1423","kind":"arxiv","version":2}},"canonical_sha256":"548b8fda6fb645129f3c0c521c329b4cd6be2bdb1f1cfa5ab3690ccbcbaac5b9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"548b8fda6fb645129f3c0c521c329b4cd6be2bdb1f1cfa5ab3690ccbcbaac5b9","first_computed_at":"2026-05-18T03:20:45.575896Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:20:45.575896Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LiyZtydKGQAMOBv+cW92xQRSXDhtNKbFD6mefIc+qqOuBX0eICwW8Ejb3PJYvuTWRomKQPVupEC3Z5bHr9RvCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:20:45.576501Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.1423","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6dd0bd258d657b0ff5b4b4503d11cbf3296daaa247df404ef416b107f9218bc6","sha256:9a436678ccf6bdcb43da1a28b2ae2ee39c2327510c60581cc0f5adf0ae699b9d"],"state_sha256":"a412f2e09acd6d9f1c59638724d6d15d81bba31727d7d0c6a11142b58da2863c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ktqa4iYKo/XYNe1m93e1Q2fcRcGwUhwJTz46XLeCGjAoNq/Z+NrAOS3/8+XyNEXXXT4xOKpQ40pCXzYETuqlDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T02:40:10.037048Z","bundle_sha256":"e5406e8fddc5ab55c2bcdf5f9a6ee85c412a50b9dde8789c702c777f484463a1"}}