{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:D4ZEG67EI22ZLOPQNGTDA7CR3T","short_pith_number":"pith:D4ZEG67E","canonical_record":{"source":{"id":"1009.1600","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-09-08T18:02:59Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"1f9e01ec66f0f8bf0f2f36f8f50e9962cb1201ed7654e2f5b4355e0478617da4","abstract_canon_sha256":"44d20b904c01f6e279527e56dc91141c5507fc26fbdec4f185bb5ee697e4bad9"},"schema_version":"1.0"},"canonical_sha256":"1f32437be446b595b9f069a6307c51dcd8e6f088e645293e6fe23bba9fac502a","source":{"kind":"arxiv","id":"1009.1600","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.1600","created_at":"2026-05-18T04:41:14Z"},{"alias_kind":"arxiv_version","alias_value":"1009.1600v1","created_at":"2026-05-18T04:41:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.1600","created_at":"2026-05-18T04:41:14Z"},{"alias_kind":"pith_short_12","alias_value":"D4ZEG67EI22Z","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"D4ZEG67EI22ZLOPQ","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"D4ZEG67E","created_at":"2026-05-18T12:26:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:D4ZEG67EI22ZLOPQNGTDA7CR3T","target":"record","payload":{"canonical_record":{"source":{"id":"1009.1600","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-09-08T18:02:59Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"1f9e01ec66f0f8bf0f2f36f8f50e9962cb1201ed7654e2f5b4355e0478617da4","abstract_canon_sha256":"44d20b904c01f6e279527e56dc91141c5507fc26fbdec4f185bb5ee697e4bad9"},"schema_version":"1.0"},"canonical_sha256":"1f32437be446b595b9f069a6307c51dcd8e6f088e645293e6fe23bba9fac502a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:41:14.424509Z","signature_b64":"hYYmMFwlHubyG0jg0lLfk9lRLlr0QZkrWYTzW2b3LiffSmv7mbDSu7k/XWph9Ve22Vd2EtB2324senuatVV1BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1f32437be446b595b9f069a6307c51dcd8e6f088e645293e6fe23bba9fac502a","last_reissued_at":"2026-05-18T04:41:14.424001Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:41:14.424001Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1009.1600","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":"2026-05-18T04:41:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qusWL4VScqseAntTyEaFjeGtizIl3D5MrI4G7ICUNqvM60OR/NgGPQbEum9e+gGrE1gLodP3N17PHngwv7bZAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T23:36:43.022562Z"},"content_sha256":"557b8b0cf164a3d383c14b51faa821d0940afa10a5b43b90f9fbbbba4cd89cba","schema_version":"1.0","event_id":"sha256:557b8b0cf164a3d383c14b51faa821d0940afa10a5b43b90f9fbbbba4cd89cba"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:D4ZEG67EI22ZLOPQNGTDA7CR3T","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Minimizers of the Lawrence-Doniach Functional with Oblique Magnetic Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"\\'Etienne Sandier, Lia Bronsard, Stan Alama","submitted_at":"2010-09-08T18:02:59Z","abstract_excerpt":"We study minimizers of the Lawrence--Doniach energy, which describes equilibrium states of superconductors with layered structure, assuming Floquet-periodic boundary conditions. Specifically, we consider the effect of a constant magnetic field applied obliquely to the superconducting planes in the limit as both the layer spacing $s\\to 0$ and the Ginzburg--Landau parameter $\\kappa=\\eps^{-1}\\to\\infty$, under the hypotheses that $s=\\eps^\\alpha$ with $0<\\alpha<1$. By deriving sharp matching upper and lower bounds on the energy of minimizers, we determine the lower critical field and the orientatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.1600","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":"2026-05-18T04:41:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Bv9Beif//3Azm4+pnK1+WZmIVSsVIREIOGojbYaX5cE+Pf7WHw42wQvXIwvyxcLR9Whlh7IxYW+mep57kl8eBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T23:36:43.022907Z"},"content_sha256":"ba67850d5b76e261f42c0cd7dc0c93487361aaa307885c9f56850a02e778b831","schema_version":"1.0","event_id":"sha256:ba67850d5b76e261f42c0cd7dc0c93487361aaa307885c9f56850a02e778b831"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D4ZEG67EI22ZLOPQNGTDA7CR3T/bundle.json","state_url":"https://pith.science/pith/D4ZEG67EI22ZLOPQNGTDA7CR3T/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D4ZEG67EI22ZLOPQNGTDA7CR3T/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":"2026-06-02T23:36:43Z","links":{"resolver":"https://pith.science/pith/D4ZEG67EI22ZLOPQNGTDA7CR3T","bundle":"https://pith.science/pith/D4ZEG67EI22ZLOPQNGTDA7CR3T/bundle.json","state":"https://pith.science/pith/D4ZEG67EI22ZLOPQNGTDA7CR3T/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D4ZEG67EI22ZLOPQNGTDA7CR3T/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:D4ZEG67EI22ZLOPQNGTDA7CR3T","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":"44d20b904c01f6e279527e56dc91141c5507fc26fbdec4f185bb5ee697e4bad9","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-09-08T18:02:59Z","title_canon_sha256":"1f9e01ec66f0f8bf0f2f36f8f50e9962cb1201ed7654e2f5b4355e0478617da4"},"schema_version":"1.0","source":{"id":"1009.1600","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.1600","created_at":"2026-05-18T04:41:14Z"},{"alias_kind":"arxiv_version","alias_value":"1009.1600v1","created_at":"2026-05-18T04:41:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.1600","created_at":"2026-05-18T04:41:14Z"},{"alias_kind":"pith_short_12","alias_value":"D4ZEG67EI22Z","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"D4ZEG67EI22ZLOPQ","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"D4ZEG67E","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:ba67850d5b76e261f42c0cd7dc0c93487361aaa307885c9f56850a02e778b831","target":"graph","created_at":"2026-05-18T04:41:14Z","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 minimizers of the Lawrence--Doniach energy, which describes equilibrium states of superconductors with layered structure, assuming Floquet-periodic boundary conditions. Specifically, we consider the effect of a constant magnetic field applied obliquely to the superconducting planes in the limit as both the layer spacing $s\\to 0$ and the Ginzburg--Landau parameter $\\kappa=\\eps^{-1}\\to\\infty$, under the hypotheses that $s=\\eps^\\alpha$ with $0<\\alpha<1$. By deriving sharp matching upper and lower bounds on the energy of minimizers, we determine the lower critical field and the orientatio","authors_text":"\\'Etienne Sandier, Lia Bronsard, Stan Alama","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-09-08T18:02:59Z","title":"Minimizers of the Lawrence-Doniach Functional with Oblique Magnetic Fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.1600","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":"sha256:557b8b0cf164a3d383c14b51faa821d0940afa10a5b43b90f9fbbbba4cd89cba","target":"record","created_at":"2026-05-18T04:41:14Z","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":"44d20b904c01f6e279527e56dc91141c5507fc26fbdec4f185bb5ee697e4bad9","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-09-08T18:02:59Z","title_canon_sha256":"1f9e01ec66f0f8bf0f2f36f8f50e9962cb1201ed7654e2f5b4355e0478617da4"},"schema_version":"1.0","source":{"id":"1009.1600","kind":"arxiv","version":1}},"canonical_sha256":"1f32437be446b595b9f069a6307c51dcd8e6f088e645293e6fe23bba9fac502a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1f32437be446b595b9f069a6307c51dcd8e6f088e645293e6fe23bba9fac502a","first_computed_at":"2026-05-18T04:41:14.424001Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:41:14.424001Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hYYmMFwlHubyG0jg0lLfk9lRLlr0QZkrWYTzW2b3LiffSmv7mbDSu7k/XWph9Ve22Vd2EtB2324senuatVV1BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:41:14.424509Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.1600","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:557b8b0cf164a3d383c14b51faa821d0940afa10a5b43b90f9fbbbba4cd89cba","sha256:ba67850d5b76e261f42c0cd7dc0c93487361aaa307885c9f56850a02e778b831"],"state_sha256":"fc4552e81562ba16496e57ebc4775ec9603f536f7268b6f87ce2a1ccf93e8a00"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"adp4qn8FtxUzfC5d9WpeIiwPHkX4mpr+li+tdTrjEx28T3chUiAWjTleyE1L9eaD1HkuFudEOs9cLKrLxoJpCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T23:36:43.025207Z","bundle_sha256":"6348f363495a9e1bcbd4d11be0222a932fecd096b24fe00ab50266340478439d"}}