{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:EKT7TBTNBXPHSBPEW5HZ354XGO","short_pith_number":"pith:EKT7TBTN","canonical_record":{"source":{"id":"1305.5643","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.supr-con","submitted_at":"2013-05-24T08:03:53Z","cross_cats_sorted":[],"title_canon_sha256":"80807709757d44f5f087dd93c00291ca2955e344a4bce963f331baea11997f25","abstract_canon_sha256":"c5df5b234c6703074db8af1550740b73c5edabd7c6d40742e89bee87a3f62593"},"schema_version":"1.0"},"canonical_sha256":"22a7f9866d0dde7905e4b74f9df79733880d3c998399ffebbe2ddea3084cde81","source":{"kind":"arxiv","id":"1305.5643","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.5643","created_at":"2026-05-18T03:19:58Z"},{"alias_kind":"arxiv_version","alias_value":"1305.5643v2","created_at":"2026-05-18T03:19:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.5643","created_at":"2026-05-18T03:19:58Z"},{"alias_kind":"pith_short_12","alias_value":"EKT7TBTNBXPH","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"EKT7TBTNBXPHSBPE","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"EKT7TBTN","created_at":"2026-05-18T12:27:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:EKT7TBTNBXPHSBPEW5HZ354XGO","target":"record","payload":{"canonical_record":{"source":{"id":"1305.5643","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.supr-con","submitted_at":"2013-05-24T08:03:53Z","cross_cats_sorted":[],"title_canon_sha256":"80807709757d44f5f087dd93c00291ca2955e344a4bce963f331baea11997f25","abstract_canon_sha256":"c5df5b234c6703074db8af1550740b73c5edabd7c6d40742e89bee87a3f62593"},"schema_version":"1.0"},"canonical_sha256":"22a7f9866d0dde7905e4b74f9df79733880d3c998399ffebbe2ddea3084cde81","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:19:58.746699Z","signature_b64":"pM2sGYqux70FOu5HPd3I1p/0drg8grXjRhokrrAY11fg/TuRSWta2wKFXRELzETg0uXIYqeJ5+13DYPPBzOVAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"22a7f9866d0dde7905e4b74f9df79733880d3c998399ffebbe2ddea3084cde81","last_reissued_at":"2026-05-18T03:19:58.745924Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:19:58.745924Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1305.5643","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:19:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Bi/nIiMu1RqfDied/GxNdyq2RgALy/qx65ahvIYLKlU8OzzYZWpxhlhciaRyknooaAcHcOpp53fgF/SBGTWPDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T19:05:35.402082Z"},"content_sha256":"154cf07c2c464911df6758f365006639a71f7fb6ff5ad7fdc006f3c631aa5d42","schema_version":"1.0","event_id":"sha256:154cf07c2c464911df6758f365006639a71f7fb6ff5ad7fdc006f3c631aa5d42"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:EKT7TBTNBXPHSBPEW5HZ354XGO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The critical state in thin superconductors as a mixed boundary value problem: analysis and solution by means of the Erd\\'elyi-Kober operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.supr-con","authors_text":"Francesco Grilli, Roberto Brambilla","submitted_at":"2013-05-24T08:03:53Z","abstract_excerpt":"With this paper we provide an effective method to solve a large class of problems related to the electromagnetic behavior of thin superconductors. Here all the problems are reduced to finding the weight functions for the Green integrals that represent the magnetic field components; these latter must satisfy the mixed boundary value conditions that naturally arise from the critical state assumptions. The use of the Erd\\'elyi-Kober operators and of the Hankel transforms (and mostly the employment of their composition properties) is the keystone to unify the method toward the solution. In fact, t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.5643","kind":"arxiv","version":2},"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":"2026-05-18T03:19:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NXWG/iOtShyr0zALWGfXesDbQXL3iifBsP/vpE35Kr9/BmuMQQtd2U49tYj6Spuo/iCV999W9w1zczssbZKJDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T19:05:35.402445Z"},"content_sha256":"f3d61bb5e88cfbb029d27f7fd2179cc7b3d34227f65d0afd52391a75439460e3","schema_version":"1.0","event_id":"sha256:f3d61bb5e88cfbb029d27f7fd2179cc7b3d34227f65d0afd52391a75439460e3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EKT7TBTNBXPHSBPEW5HZ354XGO/bundle.json","state_url":"https://pith.science/pith/EKT7TBTNBXPHSBPEW5HZ354XGO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EKT7TBTNBXPHSBPEW5HZ354XGO/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":"2026-06-03T19:05:35Z","links":{"resolver":"https://pith.science/pith/EKT7TBTNBXPHSBPEW5HZ354XGO","bundle":"https://pith.science/pith/EKT7TBTNBXPHSBPEW5HZ354XGO/bundle.json","state":"https://pith.science/pith/EKT7TBTNBXPHSBPEW5HZ354XGO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EKT7TBTNBXPHSBPEW5HZ354XGO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:EKT7TBTNBXPHSBPEW5HZ354XGO","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":"c5df5b234c6703074db8af1550740b73c5edabd7c6d40742e89bee87a3f62593","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.supr-con","submitted_at":"2013-05-24T08:03:53Z","title_canon_sha256":"80807709757d44f5f087dd93c00291ca2955e344a4bce963f331baea11997f25"},"schema_version":"1.0","source":{"id":"1305.5643","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.5643","created_at":"2026-05-18T03:19:58Z"},{"alias_kind":"arxiv_version","alias_value":"1305.5643v2","created_at":"2026-05-18T03:19:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.5643","created_at":"2026-05-18T03:19:58Z"},{"alias_kind":"pith_short_12","alias_value":"EKT7TBTNBXPH","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"EKT7TBTNBXPHSBPE","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"EKT7TBTN","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:f3d61bb5e88cfbb029d27f7fd2179cc7b3d34227f65d0afd52391a75439460e3","target":"graph","created_at":"2026-05-18T03:19:58Z","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":"With this paper we provide an effective method to solve a large class of problems related to the electromagnetic behavior of thin superconductors. Here all the problems are reduced to finding the weight functions for the Green integrals that represent the magnetic field components; these latter must satisfy the mixed boundary value conditions that naturally arise from the critical state assumptions. The use of the Erd\\'elyi-Kober operators and of the Hankel transforms (and mostly the employment of their composition properties) is the keystone to unify the method toward the solution. In fact, t","authors_text":"Francesco Grilli, Roberto Brambilla","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.supr-con","submitted_at":"2013-05-24T08:03:53Z","title":"The critical state in thin superconductors as a mixed boundary value problem: analysis and solution by means of the Erd\\'elyi-Kober operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.5643","kind":"arxiv","version":2},"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":"sha256:154cf07c2c464911df6758f365006639a71f7fb6ff5ad7fdc006f3c631aa5d42","target":"record","created_at":"2026-05-18T03:19:58Z","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":"c5df5b234c6703074db8af1550740b73c5edabd7c6d40742e89bee87a3f62593","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.supr-con","submitted_at":"2013-05-24T08:03:53Z","title_canon_sha256":"80807709757d44f5f087dd93c00291ca2955e344a4bce963f331baea11997f25"},"schema_version":"1.0","source":{"id":"1305.5643","kind":"arxiv","version":2}},"canonical_sha256":"22a7f9866d0dde7905e4b74f9df79733880d3c998399ffebbe2ddea3084cde81","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"22a7f9866d0dde7905e4b74f9df79733880d3c998399ffebbe2ddea3084cde81","first_computed_at":"2026-05-18T03:19:58.745924Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:19:58.745924Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pM2sGYqux70FOu5HPd3I1p/0drg8grXjRhokrrAY11fg/TuRSWta2wKFXRELzETg0uXIYqeJ5+13DYPPBzOVAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:19:58.746699Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.5643","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:154cf07c2c464911df6758f365006639a71f7fb6ff5ad7fdc006f3c631aa5d42","sha256:f3d61bb5e88cfbb029d27f7fd2179cc7b3d34227f65d0afd52391a75439460e3"],"state_sha256":"a25b4e4a821806ca814c39853833b426291ca8b56d403af0793272c7c4414cb2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WSCLhmGLnnFcCNjtPpJZjNiLD0HW3pPADkcjF4SzNCb9GZesGZ+d1kSFK4wMavyXS/waaEqOKzesJcWX+xAFAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T19:05:35.404409Z","bundle_sha256":"f06051a8feba620a14a39ffe0a71f3aba9288815429e32f669dd8de115225dba"}}