{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:3ILDD7UFOZFTXU6QYJE3VL5L5U","short_pith_number":"pith:3ILDD7UF","canonical_record":{"source":{"id":"2403.09949","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-03-15T01:21:11Z","cross_cats_sorted":[],"title_canon_sha256":"9633002c6d26bd44f80b809ad9b8ee9d7e1d21a8cadd2dcdda25b943a1162d6a","abstract_canon_sha256":"86ed7cb195e12e56de20aa1b28c02cb75eb58e30c9639262495471538232ef1a"},"schema_version":"1.0"},"canonical_sha256":"da1631fe85764b3bd3d0c249baafabed1376415337b451adce874d7e7815b508","source":{"kind":"arxiv","id":"2403.09949","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2403.09949","created_at":"2026-07-05T07:56:27Z"},{"alias_kind":"arxiv_version","alias_value":"2403.09949v1","created_at":"2026-07-05T07:56:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.09949","created_at":"2026-07-05T07:56:27Z"},{"alias_kind":"pith_short_12","alias_value":"3ILDD7UFOZFT","created_at":"2026-07-05T07:56:27Z"},{"alias_kind":"pith_short_16","alias_value":"3ILDD7UFOZFTXU6Q","created_at":"2026-07-05T07:56:27Z"},{"alias_kind":"pith_short_8","alias_value":"3ILDD7UF","created_at":"2026-07-05T07:56:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:3ILDD7UFOZFTXU6QYJE3VL5L5U","target":"record","payload":{"canonical_record":{"source":{"id":"2403.09949","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-03-15T01:21:11Z","cross_cats_sorted":[],"title_canon_sha256":"9633002c6d26bd44f80b809ad9b8ee9d7e1d21a8cadd2dcdda25b943a1162d6a","abstract_canon_sha256":"86ed7cb195e12e56de20aa1b28c02cb75eb58e30c9639262495471538232ef1a"},"schema_version":"1.0"},"canonical_sha256":"da1631fe85764b3bd3d0c249baafabed1376415337b451adce874d7e7815b508","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:56:27.678529Z","signature_b64":"DcjuPCguwXHC7afctKaYobskMbKO/kmy6tbmSAWZtOkqDNksy+A2JpD7rhO9D9OBkbQVVHxQ89OmelIHR76EBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"da1631fe85764b3bd3d0c249baafabed1376415337b451adce874d7e7815b508","last_reissued_at":"2026-07-05T07:56:27.676987Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:56:27.676987Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2403.09949","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":"2026-07-05T07:56:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"baF88uzTP2abWaEhyHu2FuzP6Rq33VR6rp8ymAhIROqhKMWC/qVNSMW/WyLgMhfrCVtBh1cdqzV39SHnldNtDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T13:43:51.257030Z"},"content_sha256":"ac9a55bc63ef6b54476394d1973a2e58b28bc1c13351ea33b5402ddd235e0338","schema_version":"1.0","event_id":"sha256:ac9a55bc63ef6b54476394d1973a2e58b28bc1c13351ea33b5402ddd235e0338"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:3ILDD7UFOZFTXU6QYJE3VL5L5U","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A priori $L^\\infty-$bound for Ginzburg-Landau energy minimizers with divergence penalization","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Andrew Colinet, Dominik Stantejsky, Lia Bronsard","submitted_at":"2024-03-15T01:21:11Z","abstract_excerpt":"We consider minimizers $u_\\varepsilon$ of the Ginzburg-Landau energy with quadratic divergence penalization on a simply-connected two-dimensional domain $\\Omega$. On the boundary, strong tangential anchoring is imposed. We prove that minimizers satisfy a $L^\\infty$-bound uniform in $\\varepsilon$ when $\\Omega$ has $C^{2,1}-$boundary and that the Lipschitz constant blows up like $\\varepsilon^{-1}$ when $\\Omega$ has $C^{3,1}-$boundary. Our theorem extends to $W^{2,p}-$regularity result for our elliptic system with mixed Dirichlet-Neumann boundary condition."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.09949","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2403.09949/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T07:56:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+CkG+xf3fv51ASxZN0TJmL/ZoioL9MCo6LvVSvWAgQ+gcIEbNVaCxGT8H0rNAZ4rNOpGWgDhxO7gBi3Wtc5QAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T13:43:51.257416Z"},"content_sha256":"732670900f38df7e691df7b89f5911fb74157ff7c1d354448e20a470cd6bd589","schema_version":"1.0","event_id":"sha256:732670900f38df7e691df7b89f5911fb74157ff7c1d354448e20a470cd6bd589"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3ILDD7UFOZFTXU6QYJE3VL5L5U/bundle.json","state_url":"https://pith.science/pith/3ILDD7UFOZFTXU6QYJE3VL5L5U/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3ILDD7UFOZFTXU6QYJE3VL5L5U/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":"2026-07-07T13:43:51Z","links":{"resolver":"https://pith.science/pith/3ILDD7UFOZFTXU6QYJE3VL5L5U","bundle":"https://pith.science/pith/3ILDD7UFOZFTXU6QYJE3VL5L5U/bundle.json","state":"https://pith.science/pith/3ILDD7UFOZFTXU6QYJE3VL5L5U/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3ILDD7UFOZFTXU6QYJE3VL5L5U/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:3ILDD7UFOZFTXU6QYJE3VL5L5U","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":"86ed7cb195e12e56de20aa1b28c02cb75eb58e30c9639262495471538232ef1a","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-03-15T01:21:11Z","title_canon_sha256":"9633002c6d26bd44f80b809ad9b8ee9d7e1d21a8cadd2dcdda25b943a1162d6a"},"schema_version":"1.0","source":{"id":"2403.09949","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2403.09949","created_at":"2026-07-05T07:56:27Z"},{"alias_kind":"arxiv_version","alias_value":"2403.09949v1","created_at":"2026-07-05T07:56:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.09949","created_at":"2026-07-05T07:56:27Z"},{"alias_kind":"pith_short_12","alias_value":"3ILDD7UFOZFT","created_at":"2026-07-05T07:56:27Z"},{"alias_kind":"pith_short_16","alias_value":"3ILDD7UFOZFTXU6Q","created_at":"2026-07-05T07:56:27Z"},{"alias_kind":"pith_short_8","alias_value":"3ILDD7UF","created_at":"2026-07-05T07:56:27Z"}],"graph_snapshots":[{"event_id":"sha256:732670900f38df7e691df7b89f5911fb74157ff7c1d354448e20a470cd6bd589","target":"graph","created_at":"2026-07-05T07:56:27Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2403.09949/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider minimizers $u_\\varepsilon$ of the Ginzburg-Landau energy with quadratic divergence penalization on a simply-connected two-dimensional domain $\\Omega$. On the boundary, strong tangential anchoring is imposed. We prove that minimizers satisfy a $L^\\infty$-bound uniform in $\\varepsilon$ when $\\Omega$ has $C^{2,1}-$boundary and that the Lipschitz constant blows up like $\\varepsilon^{-1}$ when $\\Omega$ has $C^{3,1}-$boundary. Our theorem extends to $W^{2,p}-$regularity result for our elliptic system with mixed Dirichlet-Neumann boundary condition.","authors_text":"Andrew Colinet, Dominik Stantejsky, Lia Bronsard","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-03-15T01:21:11Z","title":"A priori $L^\\infty-$bound for Ginzburg-Landau energy minimizers with divergence penalization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.09949","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:ac9a55bc63ef6b54476394d1973a2e58b28bc1c13351ea33b5402ddd235e0338","target":"record","created_at":"2026-07-05T07:56:27Z","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":"86ed7cb195e12e56de20aa1b28c02cb75eb58e30c9639262495471538232ef1a","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-03-15T01:21:11Z","title_canon_sha256":"9633002c6d26bd44f80b809ad9b8ee9d7e1d21a8cadd2dcdda25b943a1162d6a"},"schema_version":"1.0","source":{"id":"2403.09949","kind":"arxiv","version":1}},"canonical_sha256":"da1631fe85764b3bd3d0c249baafabed1376415337b451adce874d7e7815b508","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"da1631fe85764b3bd3d0c249baafabed1376415337b451adce874d7e7815b508","first_computed_at":"2026-07-05T07:56:27.676987Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:56:27.676987Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DcjuPCguwXHC7afctKaYobskMbKO/kmy6tbmSAWZtOkqDNksy+A2JpD7rhO9D9OBkbQVVHxQ89OmelIHR76EBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T07:56:27.678529Z","signed_message":"canonical_sha256_bytes"},"source_id":"2403.09949","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ac9a55bc63ef6b54476394d1973a2e58b28bc1c13351ea33b5402ddd235e0338","sha256:732670900f38df7e691df7b89f5911fb74157ff7c1d354448e20a470cd6bd589"],"state_sha256":"bf69f478bdaccf10b81134ae4fd20b01a1495ac7e44668320eb906cf63e671de"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gYnbQ97bxeAsnpIlyhdSsHW+NDt2Xcr8MBu98fsKwLzc/DHEohUmI7R4FAl0OmrsIoGbskOfC3hCugQPxoc/CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T13:43:51.259376Z","bundle_sha256":"12286cf9ee8e8b83700cb0277b04d5f7d907b81ce3f3b205ac907d75ca5d93cd"}}