{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:JWHVHFJURLXANJJQXEKI7FHBTI","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":"a5b7ab7a14a350d6d7830fb4a2a29af03ef430166fa09b681db584618de648cd","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-05-23T13:28:31Z","title_canon_sha256":"4a64206c22f0b79ce985293c0517b1516efa066ba87110d777e14000d799dd8e"},"schema_version":"1.0","source":{"id":"1505.06327","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.06327","created_at":"2026-05-18T01:04:14Z"},{"alias_kind":"arxiv_version","alias_value":"1505.06327v1","created_at":"2026-05-18T01:04:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.06327","created_at":"2026-05-18T01:04:14Z"},{"alias_kind":"pith_short_12","alias_value":"JWHVHFJURLXA","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JWHVHFJURLXANJJQ","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JWHVHFJU","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:bdc36122c281cc1b711569c30b99ad6d16fa65bcae33229966fd36a529c391c1","target":"graph","created_at":"2026-05-18T01:04:14Z","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 Ginzburg-Landau equations in the presence of large electric currents, that are smaller than the critical current where the normal state losses its stability. For steady-state solutions in the large $\\kappa$ limit, we prove that the superconductivity order parameter is exponentially small in a significant part of the domain, and small in the rest of it. Similar results are obtained for the time-dependent problem, in continuation of the paper by the two first authors [3]. We conclude by obtaining some weaker results, albeit similar, for steady-state solutions in the large domain lim","authors_text":"Bernard Helffer, Xing-Bin Pan, Yaniv Almog","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-05-23T13:28:31Z","title":"Mixed normal-superconducting states in the presence of strong electric currents"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.06327","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:a498f28c268d33da52b95f785db085af79c1b85e14fd77c9438b3f44efcf49d7","target":"record","created_at":"2026-05-18T01:04:14Z","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":"a5b7ab7a14a350d6d7830fb4a2a29af03ef430166fa09b681db584618de648cd","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-05-23T13:28:31Z","title_canon_sha256":"4a64206c22f0b79ce985293c0517b1516efa066ba87110d777e14000d799dd8e"},"schema_version":"1.0","source":{"id":"1505.06327","kind":"arxiv","version":1}},"canonical_sha256":"4d8f5395348aee06a530b9148f94e19a340791e08ee2047ad5cffc630afad0a5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4d8f5395348aee06a530b9148f94e19a340791e08ee2047ad5cffc630afad0a5","first_computed_at":"2026-05-18T01:04:14.658689Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:14.658689Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PRUApnPuY8V1L0mxXT9IRAwx7P045VqeuVogE+2Pn5GNW24jHexJS6X9/EGo2VGp2wUwjujXq/8w7T8laeqAAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:14.659137Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.06327","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a498f28c268d33da52b95f785db085af79c1b85e14fd77c9438b3f44efcf49d7","sha256:bdc36122c281cc1b711569c30b99ad6d16fa65bcae33229966fd36a529c391c1"],"state_sha256":"353632ff382a2338cb036094957255b43b4e15898d53d6c0722d06334831a295"}