{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:OM2Q2OIP4CTXBZFF2X7W3PLXZB","short_pith_number":"pith:OM2Q2OIP","canonical_record":{"source":{"id":"0712.0869","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2007-12-06T05:23:34Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"f06c841c2691e6c8b108d4846946204fa44afdfa41155047c809e6fd615e32b7","abstract_canon_sha256":"d99e2f5e322ed9a6a989def7f3b0461a479a01b2fc0163d713ce6ef884e0e704"},"schema_version":"1.0"},"canonical_sha256":"73350d390fe0a770e4a5d5ff6dbd77c8631ffff3c29ce4220b587219f269b315","source":{"kind":"arxiv","id":"0712.0869","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0712.0869","created_at":"2026-05-18T04:34:10Z"},{"alias_kind":"arxiv_version","alias_value":"0712.0869v2","created_at":"2026-05-18T04:34:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0712.0869","created_at":"2026-05-18T04:34:10Z"},{"alias_kind":"pith_short_12","alias_value":"OM2Q2OIP4CTX","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"OM2Q2OIP4CTXBZFF","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"OM2Q2OIP","created_at":"2026-05-18T12:25:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:OM2Q2OIP4CTXBZFF2X7W3PLXZB","target":"record","payload":{"canonical_record":{"source":{"id":"0712.0869","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2007-12-06T05:23:34Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"f06c841c2691e6c8b108d4846946204fa44afdfa41155047c809e6fd615e32b7","abstract_canon_sha256":"d99e2f5e322ed9a6a989def7f3b0461a479a01b2fc0163d713ce6ef884e0e704"},"schema_version":"1.0"},"canonical_sha256":"73350d390fe0a770e4a5d5ff6dbd77c8631ffff3c29ce4220b587219f269b315","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:34:10.266218Z","signature_b64":"LL3d87Sw73HcloUnj9uu1g1J66fr7O03AxpvWEuFCI0B4AYjD9zvEVzkG+r/U5Ll9xsgOUY6gnUe4aovOASXBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"73350d390fe0a770e4a5d5ff6dbd77c8631ffff3c29ce4220b587219f269b315","last_reissued_at":"2026-05-18T04:34:10.265606Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:34:10.265606Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0712.0869","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":"2026-05-18T04:34:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/AvGbCqc8hh5gB2d8eCwQFc+AGvfQiExUy5To87nvURDMXBauUX+dk22CABCdIKgnw6UcyvFBX0n18VKyIBuAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T16:15:13.203735Z"},"content_sha256":"6f45b0ff298e60e164bdce41c6f22acf95dd748adfb02d32de56a173a3f9b38b","schema_version":"1.0","event_id":"sha256:6f45b0ff298e60e164bdce41c6f22acf95dd748adfb02d32de56a173a3f9b38b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:OM2Q2OIP4CTXBZFF2X7W3PLXZB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum graphs with spin Hamiltonians","license":"","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"J. M. Harrison","submitted_at":"2007-12-06T05:23:34Z","abstract_excerpt":"The article surveys quantization schemes for metric graphs with spin. Typically quantum graphs are defined with the Laplace or Schrodinger operator which describe particles whose intrinsic angular momentum (spin) is zero. However, in many applications, for example modeling an electron (which has spin-1/2) on a network of thin wires, it is necessary to consider operators which allow spin-orbit interaction. The article presents a review of quantization schemes for graphs with three such Hamiltonian operators, the Dirac, Pauli and Rashba Hamiltonians. Comparing results for the trace formula, spec"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0712.0869","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":"2026-05-18T04:34:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RnqS1AZIta1h8blqG3f+0ysC/M8z2YRa7Q4OBy5S3fvBM4uoNX6SZ8XuCaypnv38uZXNpwzRODd2MXZT0XsVBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T16:15:13.204378Z"},"content_sha256":"517d5ddfc52dc2020fa3a1b7ecda14167cf38716fa1414dd5d943810ccb39f0f","schema_version":"1.0","event_id":"sha256:517d5ddfc52dc2020fa3a1b7ecda14167cf38716fa1414dd5d943810ccb39f0f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OM2Q2OIP4CTXBZFF2X7W3PLXZB/bundle.json","state_url":"https://pith.science/pith/OM2Q2OIP4CTXBZFF2X7W3PLXZB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OM2Q2OIP4CTXBZFF2X7W3PLXZB/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":"2026-06-07T16:15:13Z","links":{"resolver":"https://pith.science/pith/OM2Q2OIP4CTXBZFF2X7W3PLXZB","bundle":"https://pith.science/pith/OM2Q2OIP4CTXBZFF2X7W3PLXZB/bundle.json","state":"https://pith.science/pith/OM2Q2OIP4CTXBZFF2X7W3PLXZB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OM2Q2OIP4CTXBZFF2X7W3PLXZB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:OM2Q2OIP4CTXBZFF2X7W3PLXZB","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":"d99e2f5e322ed9a6a989def7f3b0461a479a01b2fc0163d713ce6ef884e0e704","cross_cats_sorted":["math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2007-12-06T05:23:34Z","title_canon_sha256":"f06c841c2691e6c8b108d4846946204fa44afdfa41155047c809e6fd615e32b7"},"schema_version":"1.0","source":{"id":"0712.0869","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0712.0869","created_at":"2026-05-18T04:34:10Z"},{"alias_kind":"arxiv_version","alias_value":"0712.0869v2","created_at":"2026-05-18T04:34:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0712.0869","created_at":"2026-05-18T04:34:10Z"},{"alias_kind":"pith_short_12","alias_value":"OM2Q2OIP4CTX","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"OM2Q2OIP4CTXBZFF","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"OM2Q2OIP","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:517d5ddfc52dc2020fa3a1b7ecda14167cf38716fa1414dd5d943810ccb39f0f","target":"graph","created_at":"2026-05-18T04:34:10Z","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":"The article surveys quantization schemes for metric graphs with spin. Typically quantum graphs are defined with the Laplace or Schrodinger operator which describe particles whose intrinsic angular momentum (spin) is zero. However, in many applications, for example modeling an electron (which has spin-1/2) on a network of thin wires, it is necessary to consider operators which allow spin-orbit interaction. The article presents a review of quantization schemes for graphs with three such Hamiltonian operators, the Dirac, Pauli and Rashba Hamiltonians. Comparing results for the trace formula, spec","authors_text":"J. M. Harrison","cross_cats":["math.MP"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"2007-12-06T05:23:34Z","title":"Quantum graphs with spin Hamiltonians"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0712.0869","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":"sha256:6f45b0ff298e60e164bdce41c6f22acf95dd748adfb02d32de56a173a3f9b38b","target":"record","created_at":"2026-05-18T04:34:10Z","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":"d99e2f5e322ed9a6a989def7f3b0461a479a01b2fc0163d713ce6ef884e0e704","cross_cats_sorted":["math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2007-12-06T05:23:34Z","title_canon_sha256":"f06c841c2691e6c8b108d4846946204fa44afdfa41155047c809e6fd615e32b7"},"schema_version":"1.0","source":{"id":"0712.0869","kind":"arxiv","version":2}},"canonical_sha256":"73350d390fe0a770e4a5d5ff6dbd77c8631ffff3c29ce4220b587219f269b315","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"73350d390fe0a770e4a5d5ff6dbd77c8631ffff3c29ce4220b587219f269b315","first_computed_at":"2026-05-18T04:34:10.265606Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:34:10.265606Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LL3d87Sw73HcloUnj9uu1g1J66fr7O03AxpvWEuFCI0B4AYjD9zvEVzkG+r/U5Ll9xsgOUY6gnUe4aovOASXBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:34:10.266218Z","signed_message":"canonical_sha256_bytes"},"source_id":"0712.0869","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6f45b0ff298e60e164bdce41c6f22acf95dd748adfb02d32de56a173a3f9b38b","sha256:517d5ddfc52dc2020fa3a1b7ecda14167cf38716fa1414dd5d943810ccb39f0f"],"state_sha256":"f59e4f1c13df61f020520b6c8cb11c9f4ee2c8b4214bb55f38fa0234bbc52143"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"by/71LOtEul+xZkF+KNkQcFf/AZtI/GYuahtKEoSZwke2vox313P3iBWOwJyw77Sy4/O1QlPFu4aSSZydEP/CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T16:15:13.207784Z","bundle_sha256":"1740deb6b5f94ff718e5866b8beb0c2a1cc404f7e965eb7a2caf269f91bf12fa"}}