{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:AMC4XOFTCO46VXMD3SRESUZTJO","short_pith_number":"pith:AMC4XOFT","canonical_record":{"source":{"id":"1606.07834","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-06-24T20:41:21Z","cross_cats_sorted":["hep-th","math.MP"],"title_canon_sha256":"20a99ade0fc341084d740bf1f5ad8d114f856a806cc47e94ebea9b17596f7681","abstract_canon_sha256":"48bb7466933f734614277fd9b556db890dfa9fb32777bd7ba4763a7a8e01e447"},"schema_version":"1.0"},"canonical_sha256":"0305cbb8b313b9eadd83dca24953334bace958e8d3b771119bb63e4ab0c81b08","source":{"kind":"arxiv","id":"1606.07834","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.07834","created_at":"2026-05-18T01:02:30Z"},{"alias_kind":"arxiv_version","alias_value":"1606.07834v1","created_at":"2026-05-18T01:02:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.07834","created_at":"2026-05-18T01:02:30Z"},{"alias_kind":"pith_short_12","alias_value":"AMC4XOFTCO46","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"AMC4XOFTCO46VXMD","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"AMC4XOFT","created_at":"2026-05-18T12:30:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:AMC4XOFTCO46VXMD3SRESUZTJO","target":"record","payload":{"canonical_record":{"source":{"id":"1606.07834","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-06-24T20:41:21Z","cross_cats_sorted":["hep-th","math.MP"],"title_canon_sha256":"20a99ade0fc341084d740bf1f5ad8d114f856a806cc47e94ebea9b17596f7681","abstract_canon_sha256":"48bb7466933f734614277fd9b556db890dfa9fb32777bd7ba4763a7a8e01e447"},"schema_version":"1.0"},"canonical_sha256":"0305cbb8b313b9eadd83dca24953334bace958e8d3b771119bb63e4ab0c81b08","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:02:30.499715Z","signature_b64":"akWbSQUG86wPwTfx4Idw3QweMLW8Jtoz9BvwgFnYrmqPPKs2VKYFzTG2ncfOlv2v9DdyYCKGYPf+7nqmcgInAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0305cbb8b313b9eadd83dca24953334bace958e8d3b771119bb63e4ab0c81b08","last_reissued_at":"2026-05-18T01:02:30.499094Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:02:30.499094Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1606.07834","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":"2026-05-18T01:02:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H58S8oqCr4fRfvmx+IG/Crhbj6QUPl0b6q3C3Q4EvZgLFbtmt0c2IROz1mcITgae3V9zWrBdpXfSq6rGcCyIDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T18:12:02.008212Z"},"content_sha256":"cbf0939f33188d000be039d7654b709bf4e6352ebd42f6cc319ca48798a335a2","schema_version":"1.0","event_id":"sha256:cbf0939f33188d000be039d7654b709bf4e6352ebd42f6cc319ca48798a335a2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:AMC4XOFTCO46VXMD3SRESUZTJO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Zeta Functions of the Dirac Operator on Quantum Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.MP"],"primary_cat":"math-ph","authors_text":"J. M. Harrison, K. Kirsten, T. Weyand","submitted_at":"2016-06-24T20:41:21Z","abstract_excerpt":"We construct spectral zeta functions for the Dirac operator on metric graphs. We start with the case of a rose graph, a graph with a single vertex where every edge is a loop. The technique is then developed to cover any finite graph with general energy independent matching conditions at the vertices. The regularized spectral determinant of the Dirac operator is also obtained as the derivative of the zeta function at a special value. In each case the zeta function is formulated using a contour integral method, which extends results obtained for Laplace and Schrodinger operators on graphs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.07834","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":"2026-05-18T01:02:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UKoDsWwsBCucv/Jek+aWanIQx0truXH5wTC4jjBAtWQNYl/vVk7ZS2Jdyu2SMhrg1z4Vcih41mEe48j4PfiDBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T18:12:02.008908Z"},"content_sha256":"d9f71b636c4da46a2a1746ca01d00fb8168fb6c69868795f9a02653e35c61b88","schema_version":"1.0","event_id":"sha256:d9f71b636c4da46a2a1746ca01d00fb8168fb6c69868795f9a02653e35c61b88"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AMC4XOFTCO46VXMD3SRESUZTJO/bundle.json","state_url":"https://pith.science/pith/AMC4XOFTCO46VXMD3SRESUZTJO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AMC4XOFTCO46VXMD3SRESUZTJO/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":"2026-05-31T18:12:02Z","links":{"resolver":"https://pith.science/pith/AMC4XOFTCO46VXMD3SRESUZTJO","bundle":"https://pith.science/pith/AMC4XOFTCO46VXMD3SRESUZTJO/bundle.json","state":"https://pith.science/pith/AMC4XOFTCO46VXMD3SRESUZTJO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AMC4XOFTCO46VXMD3SRESUZTJO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:AMC4XOFTCO46VXMD3SRESUZTJO","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":"48bb7466933f734614277fd9b556db890dfa9fb32777bd7ba4763a7a8e01e447","cross_cats_sorted":["hep-th","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-06-24T20:41:21Z","title_canon_sha256":"20a99ade0fc341084d740bf1f5ad8d114f856a806cc47e94ebea9b17596f7681"},"schema_version":"1.0","source":{"id":"1606.07834","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.07834","created_at":"2026-05-18T01:02:30Z"},{"alias_kind":"arxiv_version","alias_value":"1606.07834v1","created_at":"2026-05-18T01:02:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.07834","created_at":"2026-05-18T01:02:30Z"},{"alias_kind":"pith_short_12","alias_value":"AMC4XOFTCO46","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"AMC4XOFTCO46VXMD","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"AMC4XOFT","created_at":"2026-05-18T12:30:07Z"}],"graph_snapshots":[{"event_id":"sha256:d9f71b636c4da46a2a1746ca01d00fb8168fb6c69868795f9a02653e35c61b88","target":"graph","created_at":"2026-05-18T01:02:30Z","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 construct spectral zeta functions for the Dirac operator on metric graphs. We start with the case of a rose graph, a graph with a single vertex where every edge is a loop. The technique is then developed to cover any finite graph with general energy independent matching conditions at the vertices. The regularized spectral determinant of the Dirac operator is also obtained as the derivative of the zeta function at a special value. In each case the zeta function is formulated using a contour integral method, which extends results obtained for Laplace and Schrodinger operators on graphs.","authors_text":"J. M. Harrison, K. Kirsten, T. Weyand","cross_cats":["hep-th","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-06-24T20:41:21Z","title":"Zeta Functions of the Dirac Operator on Quantum Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.07834","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:cbf0939f33188d000be039d7654b709bf4e6352ebd42f6cc319ca48798a335a2","target":"record","created_at":"2026-05-18T01:02:30Z","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":"48bb7466933f734614277fd9b556db890dfa9fb32777bd7ba4763a7a8e01e447","cross_cats_sorted":["hep-th","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-06-24T20:41:21Z","title_canon_sha256":"20a99ade0fc341084d740bf1f5ad8d114f856a806cc47e94ebea9b17596f7681"},"schema_version":"1.0","source":{"id":"1606.07834","kind":"arxiv","version":1}},"canonical_sha256":"0305cbb8b313b9eadd83dca24953334bace958e8d3b771119bb63e4ab0c81b08","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0305cbb8b313b9eadd83dca24953334bace958e8d3b771119bb63e4ab0c81b08","first_computed_at":"2026-05-18T01:02:30.499094Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:02:30.499094Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"akWbSQUG86wPwTfx4Idw3QweMLW8Jtoz9BvwgFnYrmqPPKs2VKYFzTG2ncfOlv2v9DdyYCKGYPf+7nqmcgInAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:02:30.499715Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.07834","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cbf0939f33188d000be039d7654b709bf4e6352ebd42f6cc319ca48798a335a2","sha256:d9f71b636c4da46a2a1746ca01d00fb8168fb6c69868795f9a02653e35c61b88"],"state_sha256":"f8d565c66560cb89300fc5b2a548747460ab9a78bf4e271bfe50c1bc3d1968ed"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ohCxSRzaDGXtI6pD1bK7fpCkZOs5GeJFnH4WoeKoV7XZbMEu04I2M/eAe5MjIaxHfMkR7dpF74XMQndm0M1/DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T18:12:02.013146Z","bundle_sha256":"c5dfd817007b62ea3599862dd2d6c60189105fc65d29bf8c0d1f856fd5356894"}}