{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:VBPU67727S3RGKHIK2CY3WMKBE","short_pith_number":"pith:VBPU6772","canonical_record":{"source":{"id":"2111.07669","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2021-11-15T10:52:37Z","cross_cats_sorted":[],"title_canon_sha256":"b14c5fc0b7654ee384384489a1dfb8bea36bcdec62e968febd55beffd2b2c7ea","abstract_canon_sha256":"4c8b322e67c3711f1d64251f62b26b79c975d50cca39fb4be63dbf351967d055"},"schema_version":"1.0"},"canonical_sha256":"a85f4f7ffafcb71328e856858dd98a090670a7270be8fa451bfe27522e1bce08","source":{"kind":"arxiv","id":"2111.07669","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2111.07669","created_at":"2026-07-05T03:31:42Z"},{"alias_kind":"arxiv_version","alias_value":"2111.07669v1","created_at":"2026-07-05T03:31:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2111.07669","created_at":"2026-07-05T03:31:42Z"},{"alias_kind":"pith_short_12","alias_value":"VBPU67727S3R","created_at":"2026-07-05T03:31:42Z"},{"alias_kind":"pith_short_16","alias_value":"VBPU67727S3RGKHI","created_at":"2026-07-05T03:31:42Z"},{"alias_kind":"pith_short_8","alias_value":"VBPU6772","created_at":"2026-07-05T03:31:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:VBPU67727S3RGKHIK2CY3WMKBE","target":"record","payload":{"canonical_record":{"source":{"id":"2111.07669","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2021-11-15T10:52:37Z","cross_cats_sorted":[],"title_canon_sha256":"b14c5fc0b7654ee384384489a1dfb8bea36bcdec62e968febd55beffd2b2c7ea","abstract_canon_sha256":"4c8b322e67c3711f1d64251f62b26b79c975d50cca39fb4be63dbf351967d055"},"schema_version":"1.0"},"canonical_sha256":"a85f4f7ffafcb71328e856858dd98a090670a7270be8fa451bfe27522e1bce08","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:31:42.749180Z","signature_b64":"pbXmUcqoAeZ5dCUjhFyrkAwSrpPwBfoL3TV9r56+gs6QZcnfxxqSYNt8TwhhPl+9h3d0aVm3q2wnqt1MQ5vbDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a85f4f7ffafcb71328e856858dd98a090670a7270be8fa451bfe27522e1bce08","last_reissued_at":"2026-07-05T03:31:42.748778Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:31:42.748778Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2111.07669","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":"2026-07-05T03:31:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qeyYgsabKDGFJIjxPjOtwIEkdFMD41ddJhkaIAUTn37nKNN3Eet9xRrAd7ke5iFICN1bh1p14Ho+VHZ6gBLyBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T05:46:21.927063Z"},"content_sha256":"ae3b3cbe5539df2a2752fc096d43d471e2a6dc96dd27a454d35b29bda138f81e","schema_version":"1.0","event_id":"sha256:ae3b3cbe5539df2a2752fc096d43d471e2a6dc96dd27a454d35b29bda138f81e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:VBPU67727S3RGKHIK2CY3WMKBE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Local minimality of $\\mathbb{R}^N$-valued and $\\mathbb{S}^N$-valued Ginzburg-Landau vortex solutions in the unit ball $B^N$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Luc Nguyen, Radu Ignat","submitted_at":"2021-11-15T10:52:37Z","abstract_excerpt":"We study the existence, uniqueness and minimality of critical points of the form $m_{\\varepsilon,\\eta}(x) = (f_{\\varepsilon,\\eta}(|x|)\\frac{x}{|x|}, g_{\\varepsilon,\\eta}(|x|))$ of the functional \\[ E_{\\varepsilon,\\eta}[m] = \\int_{B^N} \\Big[\\frac{1}{2} |\\nabla m|^2 + \\frac{1}{2\\varepsilon^2} (1 - |m|^2)^2 + \\frac{1}{2\\eta^2} m_{N+1}^2\\Big]\\,dx \\] for $m=(m_1, \\dots, m_N, m_{N+1}) \\in H^1(B^N,\\mathbb{R}^{N+1})$ with $m(x) = (x,0)$ on $\\partial B^N$. We establish a necessary and sufficient condition on the dimension $N$ and the parameters $\\varepsilon$ and $\\eta$ for the existence of an escaping "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2111.07669","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/2111.07669/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":"2026-07-05T03:31:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rqAUuCjZdUGoqY8K8syIZt49Zf+3RhYwyAVfY2kB2iRJw5UNId75ekezzFqZECtTZPrFCQYLKw184tjslexjDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T05:46:21.927715Z"},"content_sha256":"fd0a332ffea3401526942211f9b45e36da049f07505388de2efce9bab81409c4","schema_version":"1.0","event_id":"sha256:fd0a332ffea3401526942211f9b45e36da049f07505388de2efce9bab81409c4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VBPU67727S3RGKHIK2CY3WMKBE/bundle.json","state_url":"https://pith.science/pith/VBPU67727S3RGKHIK2CY3WMKBE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VBPU67727S3RGKHIK2CY3WMKBE/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":"2026-07-07T05:46:21Z","links":{"resolver":"https://pith.science/pith/VBPU67727S3RGKHIK2CY3WMKBE","bundle":"https://pith.science/pith/VBPU67727S3RGKHIK2CY3WMKBE/bundle.json","state":"https://pith.science/pith/VBPU67727S3RGKHIK2CY3WMKBE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VBPU67727S3RGKHIK2CY3WMKBE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:VBPU67727S3RGKHIK2CY3WMKBE","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":"4c8b322e67c3711f1d64251f62b26b79c975d50cca39fb4be63dbf351967d055","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2021-11-15T10:52:37Z","title_canon_sha256":"b14c5fc0b7654ee384384489a1dfb8bea36bcdec62e968febd55beffd2b2c7ea"},"schema_version":"1.0","source":{"id":"2111.07669","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2111.07669","created_at":"2026-07-05T03:31:42Z"},{"alias_kind":"arxiv_version","alias_value":"2111.07669v1","created_at":"2026-07-05T03:31:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2111.07669","created_at":"2026-07-05T03:31:42Z"},{"alias_kind":"pith_short_12","alias_value":"VBPU67727S3R","created_at":"2026-07-05T03:31:42Z"},{"alias_kind":"pith_short_16","alias_value":"VBPU67727S3RGKHI","created_at":"2026-07-05T03:31:42Z"},{"alias_kind":"pith_short_8","alias_value":"VBPU6772","created_at":"2026-07-05T03:31:42Z"}],"graph_snapshots":[{"event_id":"sha256:fd0a332ffea3401526942211f9b45e36da049f07505388de2efce9bab81409c4","target":"graph","created_at":"2026-07-05T03:31:42Z","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/2111.07669/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the existence, uniqueness and minimality of critical points of the form $m_{\\varepsilon,\\eta}(x) = (f_{\\varepsilon,\\eta}(|x|)\\frac{x}{|x|}, g_{\\varepsilon,\\eta}(|x|))$ of the functional \\[ E_{\\varepsilon,\\eta}[m] = \\int_{B^N} \\Big[\\frac{1}{2} |\\nabla m|^2 + \\frac{1}{2\\varepsilon^2} (1 - |m|^2)^2 + \\frac{1}{2\\eta^2} m_{N+1}^2\\Big]\\,dx \\] for $m=(m_1, \\dots, m_N, m_{N+1}) \\in H^1(B^N,\\mathbb{R}^{N+1})$ with $m(x) = (x,0)$ on $\\partial B^N$. We establish a necessary and sufficient condition on the dimension $N$ and the parameters $\\varepsilon$ and $\\eta$ for the existence of an escaping ","authors_text":"Luc Nguyen, Radu Ignat","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2021-11-15T10:52:37Z","title":"Local minimality of $\\mathbb{R}^N$-valued and $\\mathbb{S}^N$-valued Ginzburg-Landau vortex solutions in the unit ball $B^N$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2111.07669","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:ae3b3cbe5539df2a2752fc096d43d471e2a6dc96dd27a454d35b29bda138f81e","target":"record","created_at":"2026-07-05T03:31:42Z","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":"4c8b322e67c3711f1d64251f62b26b79c975d50cca39fb4be63dbf351967d055","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2021-11-15T10:52:37Z","title_canon_sha256":"b14c5fc0b7654ee384384489a1dfb8bea36bcdec62e968febd55beffd2b2c7ea"},"schema_version":"1.0","source":{"id":"2111.07669","kind":"arxiv","version":1}},"canonical_sha256":"a85f4f7ffafcb71328e856858dd98a090670a7270be8fa451bfe27522e1bce08","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a85f4f7ffafcb71328e856858dd98a090670a7270be8fa451bfe27522e1bce08","first_computed_at":"2026-07-05T03:31:42.748778Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:31:42.748778Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pbXmUcqoAeZ5dCUjhFyrkAwSrpPwBfoL3TV9r56+gs6QZcnfxxqSYNt8TwhhPl+9h3d0aVm3q2wnqt1MQ5vbDw==","signature_status":"signed_v1","signed_at":"2026-07-05T03:31:42.749180Z","signed_message":"canonical_sha256_bytes"},"source_id":"2111.07669","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ae3b3cbe5539df2a2752fc096d43d471e2a6dc96dd27a454d35b29bda138f81e","sha256:fd0a332ffea3401526942211f9b45e36da049f07505388de2efce9bab81409c4"],"state_sha256":"ab8376e6fd3b66402b86911037adc6a19ae413952c34316fed4dd9dac88e7446"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RuUCoDQ2TsWA+gxYwy4/MNBE28Ac0ruzSoPX9zRgCFEeS05vbwfk4jV2lRmwBwRVI+8d7ySm8ysnPn6Uqt2YCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T05:46:21.931083Z","bundle_sha256":"ffc97ed5e56a499bd44c4f95c75da60925c26ca81955b9d0e1bba94604d83e29"}}