{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:IOIMDLOG3XNYTLPS7RN4JO6V4C","short_pith_number":"pith:IOIMDLOG","canonical_record":{"source":{"id":"2507.13664","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.HO","submitted_at":"2025-07-18T05:19:38Z","cross_cats_sorted":["math.CO","math.SP"],"title_canon_sha256":"fbc900dc9d50b42462c5d08c66c47e607bad5de72c570e5d8707bade91cfec3d","abstract_canon_sha256":"9b5531598f0de01c08d070c37c8510821122037d68bb3de93494c7c7367a0c42"},"schema_version":"1.0"},"canonical_sha256":"4390c1adc6dddb89adf2fc5bc4bbd5e08f2270e4695d7dba891d1bb9b79ebd4c","source":{"kind":"arxiv","id":"2507.13664","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.13664","created_at":"2026-07-05T11:39:20Z"},{"alias_kind":"arxiv_version","alias_value":"2507.13664v1","created_at":"2026-07-05T11:39:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.13664","created_at":"2026-07-05T11:39:20Z"},{"alias_kind":"pith_short_12","alias_value":"IOIMDLOG3XNY","created_at":"2026-07-05T11:39:20Z"},{"alias_kind":"pith_short_16","alias_value":"IOIMDLOG3XNYTLPS","created_at":"2026-07-05T11:39:20Z"},{"alias_kind":"pith_short_8","alias_value":"IOIMDLOG","created_at":"2026-07-05T11:39:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:IOIMDLOG3XNYTLPS7RN4JO6V4C","target":"record","payload":{"canonical_record":{"source":{"id":"2507.13664","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.HO","submitted_at":"2025-07-18T05:19:38Z","cross_cats_sorted":["math.CO","math.SP"],"title_canon_sha256":"fbc900dc9d50b42462c5d08c66c47e607bad5de72c570e5d8707bade91cfec3d","abstract_canon_sha256":"9b5531598f0de01c08d070c37c8510821122037d68bb3de93494c7c7367a0c42"},"schema_version":"1.0"},"canonical_sha256":"4390c1adc6dddb89adf2fc5bc4bbd5e08f2270e4695d7dba891d1bb9b79ebd4c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:39:20.916358Z","signature_b64":"WJhVbwHCgwF93v2PF9Vh2ud/nIDihsTBB1mv4SU3yLEKXXHeUFzTfZahYS8Zrq4oGvyA7WF6bN+hRV+lN38xBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4390c1adc6dddb89adf2fc5bc4bbd5e08f2270e4695d7dba891d1bb9b79ebd4c","last_reissued_at":"2026-07-05T11:39:20.915935Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:39:20.915935Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2507.13664","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":"2026-07-05T11:39:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e8Q3/JWbXK/gW97K4yu60lUgdNQk/2u6otvo1J73EEJsg8SAzT2b2U30xm/avJF+XAjL5jpRGB+2wVGrNiUDDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T14:48:50.414453Z"},"content_sha256":"b6f484ba06538f1a64edb96ed36537886b9ae8601c04d630f4df422b4c48e03d","schema_version":"1.0","event_id":"sha256:b6f484ba06538f1a64edb96ed36537886b9ae8601c04d630f4df422b4c48e03d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:IOIMDLOG3XNYTLPS7RN4JO6V4C","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spectral Theory of Hypergraphs: A Survey","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO","math.SP"],"primary_cat":"math.HO","authors_text":"K Arathi Bhat, Shashwath S Shetty","submitted_at":"2025-07-18T05:19:38Z","abstract_excerpt":"Hypergraphs require higher-dimensional representations, which makes it more difficult to compute and interpret their spectral properties. This survey article uses the framework of hypermatrices to give an in-depth overview of the spectral theory of hypergraphs. Our focus in this article relies on the theoretical aspects of hypergraphs that help to ease the computational methods. Spectral theory hypergraphs, one of the most advanced fields of study, are constantly finding novel applications in various domains such as theoretical computer science, quantum physics, and theoretical chemistry, amon"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.13664","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.13664/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T11:39:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VlvKGb9rm2aqb+Xiug4svwgpjggOAtD/TutvQIUEpVW0m4mu2crA+Ia+jTarSM+eJOT/EhTTXeh7nwRceRC8Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T14:48:50.414946Z"},"content_sha256":"a6ab8953fb3f732052d4b75e565e5eb6c7011d602a6cafe2cee39bcdc4924739","schema_version":"1.0","event_id":"sha256:a6ab8953fb3f732052d4b75e565e5eb6c7011d602a6cafe2cee39bcdc4924739"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IOIMDLOG3XNYTLPS7RN4JO6V4C/bundle.json","state_url":"https://pith.science/pith/IOIMDLOG3XNYTLPS7RN4JO6V4C/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IOIMDLOG3XNYTLPS7RN4JO6V4C/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":"2026-08-08T14:48:50Z","links":{"resolver":"https://pith.science/pith/IOIMDLOG3XNYTLPS7RN4JO6V4C","bundle":"https://pith.science/pith/IOIMDLOG3XNYTLPS7RN4JO6V4C/bundle.json","state":"https://pith.science/pith/IOIMDLOG3XNYTLPS7RN4JO6V4C/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IOIMDLOG3XNYTLPS7RN4JO6V4C/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:IOIMDLOG3XNYTLPS7RN4JO6V4C","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":"9b5531598f0de01c08d070c37c8510821122037d68bb3de93494c7c7367a0c42","cross_cats_sorted":["math.CO","math.SP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.HO","submitted_at":"2025-07-18T05:19:38Z","title_canon_sha256":"fbc900dc9d50b42462c5d08c66c47e607bad5de72c570e5d8707bade91cfec3d"},"schema_version":"1.0","source":{"id":"2507.13664","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.13664","created_at":"2026-07-05T11:39:20Z"},{"alias_kind":"arxiv_version","alias_value":"2507.13664v1","created_at":"2026-07-05T11:39:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.13664","created_at":"2026-07-05T11:39:20Z"},{"alias_kind":"pith_short_12","alias_value":"IOIMDLOG3XNY","created_at":"2026-07-05T11:39:20Z"},{"alias_kind":"pith_short_16","alias_value":"IOIMDLOG3XNYTLPS","created_at":"2026-07-05T11:39:20Z"},{"alias_kind":"pith_short_8","alias_value":"IOIMDLOG","created_at":"2026-07-05T11:39:20Z"}],"graph_snapshots":[{"event_id":"sha256:a6ab8953fb3f732052d4b75e565e5eb6c7011d602a6cafe2cee39bcdc4924739","target":"graph","created_at":"2026-07-05T11:39:20Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2507.13664/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Hypergraphs require higher-dimensional representations, which makes it more difficult to compute and interpret their spectral properties. This survey article uses the framework of hypermatrices to give an in-depth overview of the spectral theory of hypergraphs. Our focus in this article relies on the theoretical aspects of hypergraphs that help to ease the computational methods. Spectral theory hypergraphs, one of the most advanced fields of study, are constantly finding novel applications in various domains such as theoretical computer science, quantum physics, and theoretical chemistry, amon","authors_text":"K Arathi Bhat, Shashwath S Shetty","cross_cats":["math.CO","math.SP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.HO","submitted_at":"2025-07-18T05:19:38Z","title":"Spectral Theory of Hypergraphs: A Survey"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.13664","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:b6f484ba06538f1a64edb96ed36537886b9ae8601c04d630f4df422b4c48e03d","target":"record","created_at":"2026-07-05T11:39:20Z","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":"9b5531598f0de01c08d070c37c8510821122037d68bb3de93494c7c7367a0c42","cross_cats_sorted":["math.CO","math.SP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.HO","submitted_at":"2025-07-18T05:19:38Z","title_canon_sha256":"fbc900dc9d50b42462c5d08c66c47e607bad5de72c570e5d8707bade91cfec3d"},"schema_version":"1.0","source":{"id":"2507.13664","kind":"arxiv","version":1}},"canonical_sha256":"4390c1adc6dddb89adf2fc5bc4bbd5e08f2270e4695d7dba891d1bb9b79ebd4c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4390c1adc6dddb89adf2fc5bc4bbd5e08f2270e4695d7dba891d1bb9b79ebd4c","first_computed_at":"2026-07-05T11:39:20.915935Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:39:20.915935Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WJhVbwHCgwF93v2PF9Vh2ud/nIDihsTBB1mv4SU3yLEKXXHeUFzTfZahYS8Zrq4oGvyA7WF6bN+hRV+lN38xBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:39:20.916358Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.13664","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b6f484ba06538f1a64edb96ed36537886b9ae8601c04d630f4df422b4c48e03d","sha256:a6ab8953fb3f732052d4b75e565e5eb6c7011d602a6cafe2cee39bcdc4924739"],"state_sha256":"cfeaa8ee868ffd9e424a119344015594cc12a305082bad03f27877da6495b23c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/ro1RXvVuSkn5+QCb9xfofXdHAdR4aHaw/E254huBU1PAHcrmn4oxkp6MuDZlA2O8SUtAy8pcjv0IYh6WycxCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T14:48:50.419708Z","bundle_sha256":"9119654f3512024b00d108a80e44bd0e03244c597da8099043076df8fb10472d"}}