{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:T56SPUJPYZ7B75XAEORXU2SZBK","short_pith_number":"pith:T56SPUJP","canonical_record":{"source":{"id":"2106.12162","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2021-06-23T05:06:59Z","cross_cats_sorted":["cs.SI"],"title_canon_sha256":"70c45433922b6d07d7e9ffcc6812305be4034682bf1c721492dc661751358f2c","abstract_canon_sha256":"0a5cfa2f499afc34146eacbe7ec23984ef2ac493e39df99511c5f43e9dcca858"},"schema_version":"1.0"},"canonical_sha256":"9f7d27d12fc67e1ff6e023a37a6a590aa4b713fe4da0a5e6beb7660306fe601e","source":{"kind":"arxiv","id":"2106.12162","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2106.12162","created_at":"2026-07-05T06:11:53Z"},{"alias_kind":"arxiv_version","alias_value":"2106.12162v2","created_at":"2026-07-05T06:11:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2106.12162","created_at":"2026-07-05T06:11:53Z"},{"alias_kind":"pith_short_12","alias_value":"T56SPUJPYZ7B","created_at":"2026-07-05T06:11:53Z"},{"alias_kind":"pith_short_16","alias_value":"T56SPUJPYZ7B75XA","created_at":"2026-07-05T06:11:53Z"},{"alias_kind":"pith_short_8","alias_value":"T56SPUJP","created_at":"2026-07-05T06:11:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:T56SPUJPYZ7B75XAEORXU2SZBK","target":"record","payload":{"canonical_record":{"source":{"id":"2106.12162","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2021-06-23T05:06:59Z","cross_cats_sorted":["cs.SI"],"title_canon_sha256":"70c45433922b6d07d7e9ffcc6812305be4034682bf1c721492dc661751358f2c","abstract_canon_sha256":"0a5cfa2f499afc34146eacbe7ec23984ef2ac493e39df99511c5f43e9dcca858"},"schema_version":"1.0"},"canonical_sha256":"9f7d27d12fc67e1ff6e023a37a6a590aa4b713fe4da0a5e6beb7660306fe601e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:11:53.510123Z","signature_b64":"77UKgRAXeSI/7xbdPOr3EJojG1tks1Ex4D7VzesFpi0zE+Zwud3295YvRYGF9JFy0cvkr864YH14PHp91G05CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9f7d27d12fc67e1ff6e023a37a6a590aa4b713fe4da0a5e6beb7660306fe601e","last_reissued_at":"2026-07-05T06:11:53.509705Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:11:53.509705Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2106.12162","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":"2026-07-05T06:11:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hXZopRzup6IUNlyGUaohsm1tEdeFa37oaQ0sGMsG0VB8IIUOKPNgbxUuepuhS4s39NqhHktPJwYs/+cY8FguBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T06:45:19.733785Z"},"content_sha256":"e784b91a31bbeaa231e0b173826c1b1d8f064c2112d354f09856305e798b3d62","schema_version":"1.0","event_id":"sha256:e784b91a31bbeaa231e0b173826c1b1d8f064c2112d354f09856305e798b3d62"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:T56SPUJPYZ7B75XAEORXU2SZBK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Randomizing hypergraphs preserving degree correlation and local clustering","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SI"],"primary_cat":"physics.soc-ph","authors_text":"Kazuki Nakajima, Kazuyuki Shudo, Naoki Masuda","submitted_at":"2021-06-23T05:06:59Z","abstract_excerpt":"Many complex systems involve direct interactions among more than two entities and can be represented by hypergraphs, in which hyperedges encode higher-order interactions among an arbitrary number of nodes. To analyze structures and dynamics of given hypergraphs, a solid practice is to compare them with those for randomized hypergraphs that preserve some specific properties of the original hypergraphs. In the present study, we propose a family of such reference models for hypergraphs, called the hyper dK-series, by extending the so-called dK-series for dyadic networks to the case of hypergraphs"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.12162","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2106.12162/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":"2026-07-05T06:11:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vCnTy7f48phCAPNd4P9nhAlmCRfcwqXCtT37lbmy1nc/N9b721rGHXdlUc4wqKbFqSa6IWTkWdBjuinHwoHrCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T06:45:19.734362Z"},"content_sha256":"c3fc9ef54015bbef6729e6b3b91289f1baecdce5d86ff7a3ad70bc52c4694810","schema_version":"1.0","event_id":"sha256:c3fc9ef54015bbef6729e6b3b91289f1baecdce5d86ff7a3ad70bc52c4694810"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T56SPUJPYZ7B75XAEORXU2SZBK/bundle.json","state_url":"https://pith.science/pith/T56SPUJPYZ7B75XAEORXU2SZBK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T56SPUJPYZ7B75XAEORXU2SZBK/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":"2026-08-22T06:45:19Z","links":{"resolver":"https://pith.science/pith/T56SPUJPYZ7B75XAEORXU2SZBK","bundle":"https://pith.science/pith/T56SPUJPYZ7B75XAEORXU2SZBK/bundle.json","state":"https://pith.science/pith/T56SPUJPYZ7B75XAEORXU2SZBK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T56SPUJPYZ7B75XAEORXU2SZBK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:T56SPUJPYZ7B75XAEORXU2SZBK","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":"0a5cfa2f499afc34146eacbe7ec23984ef2ac493e39df99511c5f43e9dcca858","cross_cats_sorted":["cs.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2021-06-23T05:06:59Z","title_canon_sha256":"70c45433922b6d07d7e9ffcc6812305be4034682bf1c721492dc661751358f2c"},"schema_version":"1.0","source":{"id":"2106.12162","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2106.12162","created_at":"2026-07-05T06:11:53Z"},{"alias_kind":"arxiv_version","alias_value":"2106.12162v2","created_at":"2026-07-05T06:11:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2106.12162","created_at":"2026-07-05T06:11:53Z"},{"alias_kind":"pith_short_12","alias_value":"T56SPUJPYZ7B","created_at":"2026-07-05T06:11:53Z"},{"alias_kind":"pith_short_16","alias_value":"T56SPUJPYZ7B75XA","created_at":"2026-07-05T06:11:53Z"},{"alias_kind":"pith_short_8","alias_value":"T56SPUJP","created_at":"2026-07-05T06:11:53Z"}],"graph_snapshots":[{"event_id":"sha256:c3fc9ef54015bbef6729e6b3b91289f1baecdce5d86ff7a3ad70bc52c4694810","target":"graph","created_at":"2026-07-05T06:11:53Z","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/2106.12162/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Many complex systems involve direct interactions among more than two entities and can be represented by hypergraphs, in which hyperedges encode higher-order interactions among an arbitrary number of nodes. To analyze structures and dynamics of given hypergraphs, a solid practice is to compare them with those for randomized hypergraphs that preserve some specific properties of the original hypergraphs. In the present study, we propose a family of such reference models for hypergraphs, called the hyper dK-series, by extending the so-called dK-series for dyadic networks to the case of hypergraphs","authors_text":"Kazuki Nakajima, Kazuyuki Shudo, Naoki Masuda","cross_cats":["cs.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2021-06-23T05:06:59Z","title":"Randomizing hypergraphs preserving degree correlation and local clustering"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.12162","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:e784b91a31bbeaa231e0b173826c1b1d8f064c2112d354f09856305e798b3d62","target":"record","created_at":"2026-07-05T06:11:53Z","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":"0a5cfa2f499afc34146eacbe7ec23984ef2ac493e39df99511c5f43e9dcca858","cross_cats_sorted":["cs.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2021-06-23T05:06:59Z","title_canon_sha256":"70c45433922b6d07d7e9ffcc6812305be4034682bf1c721492dc661751358f2c"},"schema_version":"1.0","source":{"id":"2106.12162","kind":"arxiv","version":2}},"canonical_sha256":"9f7d27d12fc67e1ff6e023a37a6a590aa4b713fe4da0a5e6beb7660306fe601e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9f7d27d12fc67e1ff6e023a37a6a590aa4b713fe4da0a5e6beb7660306fe601e","first_computed_at":"2026-07-05T06:11:53.509705Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:11:53.509705Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"77UKgRAXeSI/7xbdPOr3EJojG1tks1Ex4D7VzesFpi0zE+Zwud3295YvRYGF9JFy0cvkr864YH14PHp91G05CQ==","signature_status":"signed_v1","signed_at":"2026-07-05T06:11:53.510123Z","signed_message":"canonical_sha256_bytes"},"source_id":"2106.12162","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e784b91a31bbeaa231e0b173826c1b1d8f064c2112d354f09856305e798b3d62","sha256:c3fc9ef54015bbef6729e6b3b91289f1baecdce5d86ff7a3ad70bc52c4694810"],"state_sha256":"c7459c6d7a3124b6fddc33a31760d3ac9e01c080ce0772ce247a1ff7037ea563"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"R6wmTvYP/oHdPiby/Wp4ivrZY8Jw6c0u0atEhzBAkvAKkzAOcm4UP6RCJvH399M8MwFTGwRPzCAwwFyXUVROBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-22T06:45:19.738216Z","bundle_sha256":"40014095d24191b8a25be1693993e5deaaef6be949240953bff1281f7e555857"}}