{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:SIOS5LF57OI6AD2AH3NJJW3B7S","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":"28f9fb15f94a4192fdf85cfa3981a92f3d651303fd503defe2dd725f02f89be3","cross_cats_sorted":["math.AP","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-12-11T10:09:45Z","title_canon_sha256":"fdcf9b883a2d8f3fc2543af8b87a9e1b5674d7f827e7a57d8341660da459da4d"},"schema_version":"1.0","source":{"id":"1512.03573","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.03573","created_at":"2026-05-18T01:24:32Z"},{"alias_kind":"arxiv_version","alias_value":"1512.03573v1","created_at":"2026-05-18T01:24:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.03573","created_at":"2026-05-18T01:24:32Z"},{"alias_kind":"pith_short_12","alias_value":"SIOS5LF57OI6","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"SIOS5LF57OI6AD2A","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"SIOS5LF5","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:e8a13e6a86eb016f929fbcff8e60d0d1a16f48dbd3d41e8983807e2859faa16b","target":"graph","created_at":"2026-05-18T01:24:32Z","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":"Given a bounded smooth domain $\\Omega\\subset\\mathbb{R}^3$, we explore the relation between couplings of the free Dirac operator $-i\\alpha\\cdot\\nabla+m\\beta$ with pure electrostatic shell potentials $\\lambda\\delta_{\\partial\\Omega}$ ($\\lambda\\in\\mathbb{R}$) and some perturbations of those potentials given by the normal vector field $N$ on the shell $\\partial\\Omega$, namely $\\{\\lambda_e+\\lambda_n(\\alpha\\cdot N)\\}\\delta_{\\partial\\Omega}$ ($\\lambda_e$, $\\lambda_n\\in\\mathbb{R}$). Under the appropiate change of parameters, the couplings with perturbed and unperturbed electrostatic shell potentials yi","authors_text":"Albert Mas","cross_cats":["math.AP","math.MP","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-12-11T10:09:45Z","title":"Dirac operators, shell interactions and discontinuous gauge functions across the boundary"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.03573","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":"sha256:446cd8a6dc2a313b1bfc70d089c68fe67ef1e0b87dd284fceba4f61d3cdd0c7f","target":"record","created_at":"2026-05-18T01:24:32Z","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":"28f9fb15f94a4192fdf85cfa3981a92f3d651303fd503defe2dd725f02f89be3","cross_cats_sorted":["math.AP","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-12-11T10:09:45Z","title_canon_sha256":"fdcf9b883a2d8f3fc2543af8b87a9e1b5674d7f827e7a57d8341660da459da4d"},"schema_version":"1.0","source":{"id":"1512.03573","kind":"arxiv","version":1}},"canonical_sha256":"921d2eacbdfb91e00f403eda94db61fca2813369663da0314f8bf2f1d499b303","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"921d2eacbdfb91e00f403eda94db61fca2813369663da0314f8bf2f1d499b303","first_computed_at":"2026-05-18T01:24:32.039870Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:24:32.039870Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2v7PXpXmN75QqO3ox51oxbwcWXCOTpUK751oIv54R2Y2BjQ4XTP4idewGojVKFC1HTsyjxftjkZsV2cvf6sZAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:24:32.040411Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.03573","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:446cd8a6dc2a313b1bfc70d089c68fe67ef1e0b87dd284fceba4f61d3cdd0c7f","sha256:e8a13e6a86eb016f929fbcff8e60d0d1a16f48dbd3d41e8983807e2859faa16b"],"state_sha256":"25cb6115c98e7eeef1c0b54c45d60555d956924e301455c683197f9c4478ed61"}