{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:7UWIDGXITZ6W4ZSAZY4CUFS4XH","short_pith_number":"pith:7UWIDGXI","canonical_record":{"source":{"id":"1309.6080","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2013-09-24T08:34:44Z","cross_cats_sorted":[],"title_canon_sha256":"e7413139e7d5f5b1e4c07a6f85e9904a166adffa6ab88cc858334e2f150c3518","abstract_canon_sha256":"5834c8b429c2a32f75cb96bf402b8cd86ce521248a3e07dcc7089a3647625cc5"},"schema_version":"1.0"},"canonical_sha256":"fd2c819ae89e7d6e6640ce382a165cb9e256b4cfc296b9ba4655ff81ea780583","source":{"kind":"arxiv","id":"1309.6080","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.6080","created_at":"2026-05-18T03:12:24Z"},{"alias_kind":"arxiv_version","alias_value":"1309.6080v1","created_at":"2026-05-18T03:12:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.6080","created_at":"2026-05-18T03:12:24Z"},{"alias_kind":"pith_short_12","alias_value":"7UWIDGXITZ6W","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"7UWIDGXITZ6W4ZSA","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"7UWIDGXI","created_at":"2026-05-18T12:27:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:7UWIDGXITZ6W4ZSAZY4CUFS4XH","target":"record","payload":{"canonical_record":{"source":{"id":"1309.6080","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2013-09-24T08:34:44Z","cross_cats_sorted":[],"title_canon_sha256":"e7413139e7d5f5b1e4c07a6f85e9904a166adffa6ab88cc858334e2f150c3518","abstract_canon_sha256":"5834c8b429c2a32f75cb96bf402b8cd86ce521248a3e07dcc7089a3647625cc5"},"schema_version":"1.0"},"canonical_sha256":"fd2c819ae89e7d6e6640ce382a165cb9e256b4cfc296b9ba4655ff81ea780583","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:12:24.043532Z","signature_b64":"bl3R3KDeiamTgsbl7HBfxzlgKmvYfSwZDlTDrxU36+VRcJYD46MoIW6ZB/O8EncplSUzOIMfDN/jGOwXXlmeDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fd2c819ae89e7d6e6640ce382a165cb9e256b4cfc296b9ba4655ff81ea780583","last_reissued_at":"2026-05-18T03:12:24.042743Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:12:24.042743Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.6080","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":"2026-05-18T03:12:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8odliEW+Q1nPVV6LrUb021xR3qFOrUgp4jEBqpBLb+tmf1ur505irZAzLgEQ2Win3v6KfWx4S83O0E1UvnjPCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T17:11:08.718455Z"},"content_sha256":"e284f7fb78d998683ecfe9253473509bb2623472ed9842e6b142f3b3813c9dff","schema_version":"1.0","event_id":"sha256:e284f7fb78d998683ecfe9253473509bb2623472ed9842e6b142f3b3813c9dff"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:7UWIDGXITZ6W4ZSAZY4CUFS4XH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the lowest energy of a 3D magnetic hamiltonian with axisymmetric potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Nicolas Popoff","submitted_at":"2013-09-24T08:34:44Z","abstract_excerpt":"We study the bottom of the spectrum of a magnetic hamiltonian with axisymmetrical potential in R3. The associated magnetic field is planar, unitary and non-constant. The problem reduces to a 1D-family of singular Sturm-Liouville operators on the half-line. We study to associated band functions and we compare it to the \"de Gennes\" operators arising in the study of a 2D-hamiltonian with monodimensional, odd and discontinuous magnetic field. We show in particular that the lowest energy is higher in dimension 3."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.6080","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":"2026-05-18T03:12:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1+72o+UUWv/YQ4/2ueELf5w5iNlJKYrDFN9RgolR80G0Hw89BEFfvOax8OmOxbCEmLII/nci41JVTsYMdv7jBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T17:11:08.718819Z"},"content_sha256":"8e91f3727d69bd541c544dbfee8f30accb364f0b502921ed50c712eeeb8c5512","schema_version":"1.0","event_id":"sha256:8e91f3727d69bd541c544dbfee8f30accb364f0b502921ed50c712eeeb8c5512"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7UWIDGXITZ6W4ZSAZY4CUFS4XH/bundle.json","state_url":"https://pith.science/pith/7UWIDGXITZ6W4ZSAZY4CUFS4XH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7UWIDGXITZ6W4ZSAZY4CUFS4XH/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":"2026-06-23T17:11:08Z","links":{"resolver":"https://pith.science/pith/7UWIDGXITZ6W4ZSAZY4CUFS4XH","bundle":"https://pith.science/pith/7UWIDGXITZ6W4ZSAZY4CUFS4XH/bundle.json","state":"https://pith.science/pith/7UWIDGXITZ6W4ZSAZY4CUFS4XH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7UWIDGXITZ6W4ZSAZY4CUFS4XH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:7UWIDGXITZ6W4ZSAZY4CUFS4XH","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":"5834c8b429c2a32f75cb96bf402b8cd86ce521248a3e07dcc7089a3647625cc5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2013-09-24T08:34:44Z","title_canon_sha256":"e7413139e7d5f5b1e4c07a6f85e9904a166adffa6ab88cc858334e2f150c3518"},"schema_version":"1.0","source":{"id":"1309.6080","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.6080","created_at":"2026-05-18T03:12:24Z"},{"alias_kind":"arxiv_version","alias_value":"1309.6080v1","created_at":"2026-05-18T03:12:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.6080","created_at":"2026-05-18T03:12:24Z"},{"alias_kind":"pith_short_12","alias_value":"7UWIDGXITZ6W","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"7UWIDGXITZ6W4ZSA","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"7UWIDGXI","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:8e91f3727d69bd541c544dbfee8f30accb364f0b502921ed50c712eeeb8c5512","target":"graph","created_at":"2026-05-18T03:12:24Z","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 bottom of the spectrum of a magnetic hamiltonian with axisymmetrical potential in R3. The associated magnetic field is planar, unitary and non-constant. The problem reduces to a 1D-family of singular Sturm-Liouville operators on the half-line. We study to associated band functions and we compare it to the \"de Gennes\" operators arising in the study of a 2D-hamiltonian with monodimensional, odd and discontinuous magnetic field. We show in particular that the lowest energy is higher in dimension 3.","authors_text":"Nicolas Popoff","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2013-09-24T08:34:44Z","title":"On the lowest energy of a 3D magnetic hamiltonian with axisymmetric potential"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.6080","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:e284f7fb78d998683ecfe9253473509bb2623472ed9842e6b142f3b3813c9dff","target":"record","created_at":"2026-05-18T03:12:24Z","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":"5834c8b429c2a32f75cb96bf402b8cd86ce521248a3e07dcc7089a3647625cc5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2013-09-24T08:34:44Z","title_canon_sha256":"e7413139e7d5f5b1e4c07a6f85e9904a166adffa6ab88cc858334e2f150c3518"},"schema_version":"1.0","source":{"id":"1309.6080","kind":"arxiv","version":1}},"canonical_sha256":"fd2c819ae89e7d6e6640ce382a165cb9e256b4cfc296b9ba4655ff81ea780583","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fd2c819ae89e7d6e6640ce382a165cb9e256b4cfc296b9ba4655ff81ea780583","first_computed_at":"2026-05-18T03:12:24.042743Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:12:24.042743Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bl3R3KDeiamTgsbl7HBfxzlgKmvYfSwZDlTDrxU36+VRcJYD46MoIW6ZB/O8EncplSUzOIMfDN/jGOwXXlmeDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:12:24.043532Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.6080","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e284f7fb78d998683ecfe9253473509bb2623472ed9842e6b142f3b3813c9dff","sha256:8e91f3727d69bd541c544dbfee8f30accb364f0b502921ed50c712eeeb8c5512"],"state_sha256":"e582654f6115ba5d70df7319e0766ca1201fe1d3895e9da516ef0f5f02674a9c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LFht4r+LZ3ZqUTTvaewzAJwK3vrnItE81C4iUQDRibqbjzU8TJR3X4ECP8IvOPRaWOU7p4fkJZgcFNoj8R2FAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T17:11:08.720701Z","bundle_sha256":"dfd65dcc2e1c12646a997730a559e388d4c10589f9e4020a5b99ddd947b7b8ff"}}