{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:HT5GCDMD5PGB4KPHCT6HZ6NWMO","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":"19581c65f44be8b71a0663ffa64f8742edbafb51b35a5b89cea188a706530077","cross_cats_sorted":["hep-th","math.CO","math.MP","quant-ph"],"license":"","primary_cat":"math-ph","submitted_at":"2004-10-28T09:42:19Z","title_canon_sha256":"af740cb4d60a2274f821fb2d0358b9f4804ca420b97c13a7d9a3897ad828e77c"},"schema_version":"1.0","source":{"id":"math-ph/0410059","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0410059","created_at":"2026-05-18T04:17:54Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0410059v2","created_at":"2026-05-18T04:17:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0410059","created_at":"2026-05-18T04:17:54Z"},{"alias_kind":"pith_short_12","alias_value":"HT5GCDMD5PGB","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"HT5GCDMD5PGB4KPH","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"HT5GCDMD","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:61ba0e33df56ddef52248297bfe8ac9c04f4c4a6e0ce2dabbcfb71ff991ad979","target":"graph","created_at":"2026-05-18T04:17:54Z","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 show that graphs, networks and other related discrete model systems carry a natural supersymmetric structure, which, apart from its conceptual importance as to possible physical applications, allows to derive a series of spectral properties for a class of graph operators which typically encode relevant graph characteristics.","authors_text":"Manfred Requardt","cross_cats":["hep-th","math.CO","math.MP","quant-ph"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"2004-10-28T09:42:19Z","title":"Supersymmetry on Graphs and Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0410059","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":"sha256:3872c1b69b312aeabf8175d6ae70aee27203d5fa54110392b78ee5c3f0319358","target":"record","created_at":"2026-05-18T04:17:54Z","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":"19581c65f44be8b71a0663ffa64f8742edbafb51b35a5b89cea188a706530077","cross_cats_sorted":["hep-th","math.CO","math.MP","quant-ph"],"license":"","primary_cat":"math-ph","submitted_at":"2004-10-28T09:42:19Z","title_canon_sha256":"af740cb4d60a2274f821fb2d0358b9f4804ca420b97c13a7d9a3897ad828e77c"},"schema_version":"1.0","source":{"id":"math-ph/0410059","kind":"arxiv","version":2}},"canonical_sha256":"3cfa610d83ebcc1e29e714fc7cf9b663b33ab1ffcd695e2995635b6e895c1777","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3cfa610d83ebcc1e29e714fc7cf9b663b33ab1ffcd695e2995635b6e895c1777","first_computed_at":"2026-05-18T04:17:54.572328Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:17:54.572328Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"M7CiA82ykV+so9mGvL1OBtZ1WyhAFTT3edpJ13mx8KLexXYAqhENo8Is1hyMQahfOb5Ghfy6zCn83fcjQa7HBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:17:54.572888Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/0410059","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3872c1b69b312aeabf8175d6ae70aee27203d5fa54110392b78ee5c3f0319358","sha256:61ba0e33df56ddef52248297bfe8ac9c04f4c4a6e0ce2dabbcfb71ff991ad979"],"state_sha256":"ee8b73fd9e1fc5059376d5154bb94f1fdbf2e88cf47a740cb7f554c8b678d59d"}