{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:WMKX3HA7ILEJWTXOFJPRXQ7NGK","short_pith_number":"pith:WMKX3HA7","canonical_record":{"source":{"id":"1701.03697","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-01-13T15:09:41Z","cross_cats_sorted":[],"title_canon_sha256":"a96fe3d57503217043174403cab9081e39e6da542fe5991f705a240564080096","abstract_canon_sha256":"e7b9c3f38e04f6b118ee030013d92d4f962e53b21a60a95708f71d16d653ad98"},"schema_version":"1.0"},"canonical_sha256":"b3157d9c1f42c89b4eee2a5f1bc3ed32832579725955d82d6c48534c3dde427e","source":{"kind":"arxiv","id":"1701.03697","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.03697","created_at":"2026-05-18T00:47:56Z"},{"alias_kind":"arxiv_version","alias_value":"1701.03697v2","created_at":"2026-05-18T00:47:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.03697","created_at":"2026-05-18T00:47:56Z"},{"alias_kind":"pith_short_12","alias_value":"WMKX3HA7ILEJ","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"WMKX3HA7ILEJWTXO","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"WMKX3HA7","created_at":"2026-05-18T12:31:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:WMKX3HA7ILEJWTXOFJPRXQ7NGK","target":"record","payload":{"canonical_record":{"source":{"id":"1701.03697","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-01-13T15:09:41Z","cross_cats_sorted":[],"title_canon_sha256":"a96fe3d57503217043174403cab9081e39e6da542fe5991f705a240564080096","abstract_canon_sha256":"e7b9c3f38e04f6b118ee030013d92d4f962e53b21a60a95708f71d16d653ad98"},"schema_version":"1.0"},"canonical_sha256":"b3157d9c1f42c89b4eee2a5f1bc3ed32832579725955d82d6c48534c3dde427e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:47:56.532363Z","signature_b64":"cDDkLBMPUvIGaNoU/WsrkDOtYksP3qpcPHl6gIvi9fLehRb5oIpOgNSBe4QgbalX9Z+L+ROblWjy53fGzd/rAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b3157d9c1f42c89b4eee2a5f1bc3ed32832579725955d82d6c48534c3dde427e","last_reissued_at":"2026-05-18T00:47:56.531850Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:47:56.531850Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.03697","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":"2026-05-18T00:47:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S8LNzBYJM7aqP0JigXHT+KhKHhCTiBPLuQK3X3TnmfQ33Qul8Sz1nQsYkIT48iRLYwl5STou2kHlAN13ip+IBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T21:16:15.357880Z"},"content_sha256":"aef69b39c8e75ab39fbd397cf0d6f722596717ceea8eb60c12d3d1b165a105e1","schema_version":"1.0","event_id":"sha256:aef69b39c8e75ab39fbd397cf0d6f722596717ceea8eb60c12d3d1b165a105e1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:WMKX3HA7ILEJWTXOFJPRXQ7NGK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Ginzburg -Landau energy with a magnetic field vanishing along a curve","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ayman Kachmar, Marwa Nasrallah","submitted_at":"2017-01-13T15:09:41Z","abstract_excerpt":"The energy of a type II superconductor placed in a strong non-uniform, smooth and signed magnetic field is displayed via a universal characteristic function defined by means of a simplified two dimensional Ginzburg-Landau functional. We study the asymptotic behavior of this functional in a specific asymptotic regime, thereby linking it to a one dimensional functional, using methods developed by Almog-Helffer and Fournais-Helffer devoted to the analysis of surface superconductivity in the presence of a uniform magnetic field. As a result, we obtain an asymptotic formula reminiscent of the one f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.03697","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":"2026-05-18T00:47:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LCCZ/nuaOS0pxir91xXR2aLF3Oc/LiFg9RNhpWR3izXtn0z6zFT9IzN4WKxs6Z7Fl8gatjOTocgIZon6Pw7yCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T21:16:15.358532Z"},"content_sha256":"f5d592b04620864ec4cce4a9713e3ff28bae5389028af889d39442d7504b0186","schema_version":"1.0","event_id":"sha256:f5d592b04620864ec4cce4a9713e3ff28bae5389028af889d39442d7504b0186"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WMKX3HA7ILEJWTXOFJPRXQ7NGK/bundle.json","state_url":"https://pith.science/pith/WMKX3HA7ILEJWTXOFJPRXQ7NGK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WMKX3HA7ILEJWTXOFJPRXQ7NGK/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":"2026-05-26T21:16:15Z","links":{"resolver":"https://pith.science/pith/WMKX3HA7ILEJWTXOFJPRXQ7NGK","bundle":"https://pith.science/pith/WMKX3HA7ILEJWTXOFJPRXQ7NGK/bundle.json","state":"https://pith.science/pith/WMKX3HA7ILEJWTXOFJPRXQ7NGK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WMKX3HA7ILEJWTXOFJPRXQ7NGK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:WMKX3HA7ILEJWTXOFJPRXQ7NGK","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":"e7b9c3f38e04f6b118ee030013d92d4f962e53b21a60a95708f71d16d653ad98","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-01-13T15:09:41Z","title_canon_sha256":"a96fe3d57503217043174403cab9081e39e6da542fe5991f705a240564080096"},"schema_version":"1.0","source":{"id":"1701.03697","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.03697","created_at":"2026-05-18T00:47:56Z"},{"alias_kind":"arxiv_version","alias_value":"1701.03697v2","created_at":"2026-05-18T00:47:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.03697","created_at":"2026-05-18T00:47:56Z"},{"alias_kind":"pith_short_12","alias_value":"WMKX3HA7ILEJ","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"WMKX3HA7ILEJWTXO","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"WMKX3HA7","created_at":"2026-05-18T12:31:53Z"}],"graph_snapshots":[{"event_id":"sha256:f5d592b04620864ec4cce4a9713e3ff28bae5389028af889d39442d7504b0186","target":"graph","created_at":"2026-05-18T00:47:56Z","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":"The energy of a type II superconductor placed in a strong non-uniform, smooth and signed magnetic field is displayed via a universal characteristic function defined by means of a simplified two dimensional Ginzburg-Landau functional. We study the asymptotic behavior of this functional in a specific asymptotic regime, thereby linking it to a one dimensional functional, using methods developed by Almog-Helffer and Fournais-Helffer devoted to the analysis of surface superconductivity in the presence of a uniform magnetic field. As a result, we obtain an asymptotic formula reminiscent of the one f","authors_text":"Ayman Kachmar, Marwa Nasrallah","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-01-13T15:09:41Z","title":"On the Ginzburg -Landau energy with a magnetic field vanishing along a curve"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.03697","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:aef69b39c8e75ab39fbd397cf0d6f722596717ceea8eb60c12d3d1b165a105e1","target":"record","created_at":"2026-05-18T00:47:56Z","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":"e7b9c3f38e04f6b118ee030013d92d4f962e53b21a60a95708f71d16d653ad98","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-01-13T15:09:41Z","title_canon_sha256":"a96fe3d57503217043174403cab9081e39e6da542fe5991f705a240564080096"},"schema_version":"1.0","source":{"id":"1701.03697","kind":"arxiv","version":2}},"canonical_sha256":"b3157d9c1f42c89b4eee2a5f1bc3ed32832579725955d82d6c48534c3dde427e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b3157d9c1f42c89b4eee2a5f1bc3ed32832579725955d82d6c48534c3dde427e","first_computed_at":"2026-05-18T00:47:56.531850Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:47:56.531850Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cDDkLBMPUvIGaNoU/WsrkDOtYksP3qpcPHl6gIvi9fLehRb5oIpOgNSBe4QgbalX9Z+L+ROblWjy53fGzd/rAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:47:56.532363Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.03697","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aef69b39c8e75ab39fbd397cf0d6f722596717ceea8eb60c12d3d1b165a105e1","sha256:f5d592b04620864ec4cce4a9713e3ff28bae5389028af889d39442d7504b0186"],"state_sha256":"5b2586fc4a780804205d86ef21acfc1cdca4de2afd37b093eeff528e6a943ad8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+EE+xTOuXcZVAnacOWoTLH1Yhx4zZRcWgcIosdq8kraJFyHr4aWgEM/1b66za/r81Hdy2bGOAjim8I+aV/vqAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T21:16:15.361844Z","bundle_sha256":"c6989b879c29dbdee5d51a60816d240efe2c8f9740dcd6922f88de44d357974d"}}