{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:3TAVJBS2AICS5XZJPVBST4YGTO","short_pith_number":"pith:3TAVJBS2","canonical_record":{"source":{"id":"1110.5987","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-10-27T05:36:15Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"b0b53a7a529d4c8dd958144e7bf48e736f9948579db8117ac13f8ae14170ef80","abstract_canon_sha256":"5ea8c154f3e845aac87caf797e52e9f35e4dbf08f161289451edb47285b680b7"},"schema_version":"1.0"},"canonical_sha256":"dcc154865a02052edf297d4329f3069b9e372fdc195ae3f530d61d83d784e80a","source":{"kind":"arxiv","id":"1110.5987","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.5987","created_at":"2026-05-18T04:10:09Z"},{"alias_kind":"arxiv_version","alias_value":"1110.5987v1","created_at":"2026-05-18T04:10:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.5987","created_at":"2026-05-18T04:10:09Z"},{"alias_kind":"pith_short_12","alias_value":"3TAVJBS2AICS","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"3TAVJBS2AICS5XZJ","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"3TAVJBS2","created_at":"2026-05-18T12:26:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:3TAVJBS2AICS5XZJPVBST4YGTO","target":"record","payload":{"canonical_record":{"source":{"id":"1110.5987","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-10-27T05:36:15Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"b0b53a7a529d4c8dd958144e7bf48e736f9948579db8117ac13f8ae14170ef80","abstract_canon_sha256":"5ea8c154f3e845aac87caf797e52e9f35e4dbf08f161289451edb47285b680b7"},"schema_version":"1.0"},"canonical_sha256":"dcc154865a02052edf297d4329f3069b9e372fdc195ae3f530d61d83d784e80a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:10:09.998517Z","signature_b64":"8gZAKBz9mgBlInPbIAG+poA4gPNyxM2TXlwuzzgGG+lgomuZ1qMUkZD85qF/3RDhk91vbZjDQvND1hsdQFfkAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dcc154865a02052edf297d4329f3069b9e372fdc195ae3f530d61d83d784e80a","last_reissued_at":"2026-05-18T04:10:09.997862Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:10:09.997862Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1110.5987","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:10:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JhPwgkA6vUrohppVW7HC4Xx0i6LoFTv0D7qDwCi4fM/MlmUs3NCga7rxY8Ywxvbdu0zAzd3+3ZJtDa50VfwtBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T02:44:24.483542Z"},"content_sha256":"345f0f507050ae33559bc6fb08da94ad618aec603d2e5c5c8a41a65de3e074ea","schema_version":"1.0","event_id":"sha256:345f0f507050ae33559bc6fb08da94ad618aec603d2e5c5c8a41a65de3e074ea"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:3TAVJBS2AICS5XZJPVBST4YGTO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Abrikosov Vortex Lattices at Weak Magnetic Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"I. M. Sigal, T. Tzaneteas","submitted_at":"2011-10-27T05:36:15Z","abstract_excerpt":"We prove existence of Abrikosov vortex lattice solutions of the Ginzburg-Landau equations in two dimensions, for magnetic fields larger than but close to the first critical magnetic field."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.5987","kind":"arxiv","version":1},"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":"2026-05-18T04:10:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tByyifWhYJGgBjb993MkZhDHeSGed3JrEPRC2HQWJiCSVltwBYuaC1ooZVQo0t8JJs/ZYTHlpitJ1ttbkDb5BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T02:44:24.483887Z"},"content_sha256":"9375b3df67bedb1ebd393a0362d3b2c4714545ff8c0f7e82f88989aa571d7e90","schema_version":"1.0","event_id":"sha256:9375b3df67bedb1ebd393a0362d3b2c4714545ff8c0f7e82f88989aa571d7e90"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3TAVJBS2AICS5XZJPVBST4YGTO/bundle.json","state_url":"https://pith.science/pith/3TAVJBS2AICS5XZJPVBST4YGTO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3TAVJBS2AICS5XZJPVBST4YGTO/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":"2026-05-20T02:44:24Z","links":{"resolver":"https://pith.science/pith/3TAVJBS2AICS5XZJPVBST4YGTO","bundle":"https://pith.science/pith/3TAVJBS2AICS5XZJPVBST4YGTO/bundle.json","state":"https://pith.science/pith/3TAVJBS2AICS5XZJPVBST4YGTO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3TAVJBS2AICS5XZJPVBST4YGTO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:3TAVJBS2AICS5XZJPVBST4YGTO","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":"5ea8c154f3e845aac87caf797e52e9f35e4dbf08f161289451edb47285b680b7","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-10-27T05:36:15Z","title_canon_sha256":"b0b53a7a529d4c8dd958144e7bf48e736f9948579db8117ac13f8ae14170ef80"},"schema_version":"1.0","source":{"id":"1110.5987","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.5987","created_at":"2026-05-18T04:10:09Z"},{"alias_kind":"arxiv_version","alias_value":"1110.5987v1","created_at":"2026-05-18T04:10:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.5987","created_at":"2026-05-18T04:10:09Z"},{"alias_kind":"pith_short_12","alias_value":"3TAVJBS2AICS","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"3TAVJBS2AICS5XZJ","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"3TAVJBS2","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:9375b3df67bedb1ebd393a0362d3b2c4714545ff8c0f7e82f88989aa571d7e90","target":"graph","created_at":"2026-05-18T04:10:09Z","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 prove existence of Abrikosov vortex lattice solutions of the Ginzburg-Landau equations in two dimensions, for magnetic fields larger than but close to the first critical magnetic field.","authors_text":"I. M. Sigal, T. Tzaneteas","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-10-27T05:36:15Z","title":"Abrikosov Vortex Lattices at Weak Magnetic Fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.5987","kind":"arxiv","version":1},"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":"sha256:345f0f507050ae33559bc6fb08da94ad618aec603d2e5c5c8a41a65de3e074ea","target":"record","created_at":"2026-05-18T04:10:09Z","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":"5ea8c154f3e845aac87caf797e52e9f35e4dbf08f161289451edb47285b680b7","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-10-27T05:36:15Z","title_canon_sha256":"b0b53a7a529d4c8dd958144e7bf48e736f9948579db8117ac13f8ae14170ef80"},"schema_version":"1.0","source":{"id":"1110.5987","kind":"arxiv","version":1}},"canonical_sha256":"dcc154865a02052edf297d4329f3069b9e372fdc195ae3f530d61d83d784e80a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dcc154865a02052edf297d4329f3069b9e372fdc195ae3f530d61d83d784e80a","first_computed_at":"2026-05-18T04:10:09.997862Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:10:09.997862Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8gZAKBz9mgBlInPbIAG+poA4gPNyxM2TXlwuzzgGG+lgomuZ1qMUkZD85qF/3RDhk91vbZjDQvND1hsdQFfkAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:10:09.998517Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.5987","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:345f0f507050ae33559bc6fb08da94ad618aec603d2e5c5c8a41a65de3e074ea","sha256:9375b3df67bedb1ebd393a0362d3b2c4714545ff8c0f7e82f88989aa571d7e90"],"state_sha256":"4ef97836a7c08ab5936a4f033613e84ea145fe2cd598a90183b381622fdc243f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xcIZJZbK3DE8PgcXPsSIYVbAfy7snA0KisM2836n7SjTgHXKOGz/qXVZEoU4YJlQYbJcAC3dM3sX/4H6pIeOBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-20T02:44:24.485816Z","bundle_sha256":"ffbeb09495abda6a89e6b59d7e551cad3e307d40ddd10c65db2fa5679459d08b"}}