{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:CRGWYH5TT5LGZK5QH5W7VXMEE4","short_pith_number":"pith:CRGWYH5T","canonical_record":{"source":{"id":"2505.12276","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2025-05-18T07:28:10Z","cross_cats_sorted":[],"title_canon_sha256":"f5e70c9ce4eb3b85418a1e8832a48e85897de2a75a82f69bde474dc9659c0c51","abstract_canon_sha256":"98f0d1a4e56fe95c4195c8e8246c54d7a56deb033685594dd0f3115d8d2b999f"},"schema_version":"1.0"},"canonical_sha256":"144d6c1fb39f566cabb03f6dfadd84270ddbb880dca89061f98f71c913ee7f49","source":{"kind":"arxiv","id":"2505.12276","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.12276","created_at":"2026-07-05T11:05:01Z"},{"alias_kind":"arxiv_version","alias_value":"2505.12276v1","created_at":"2026-07-05T11:05:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.12276","created_at":"2026-07-05T11:05:01Z"},{"alias_kind":"pith_short_12","alias_value":"CRGWYH5TT5LG","created_at":"2026-07-05T11:05:01Z"},{"alias_kind":"pith_short_16","alias_value":"CRGWYH5TT5LGZK5Q","created_at":"2026-07-05T11:05:01Z"},{"alias_kind":"pith_short_8","alias_value":"CRGWYH5T","created_at":"2026-07-05T11:05:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:CRGWYH5TT5LGZK5QH5W7VXMEE4","target":"record","payload":{"canonical_record":{"source":{"id":"2505.12276","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2025-05-18T07:28:10Z","cross_cats_sorted":[],"title_canon_sha256":"f5e70c9ce4eb3b85418a1e8832a48e85897de2a75a82f69bde474dc9659c0c51","abstract_canon_sha256":"98f0d1a4e56fe95c4195c8e8246c54d7a56deb033685594dd0f3115d8d2b999f"},"schema_version":"1.0"},"canonical_sha256":"144d6c1fb39f566cabb03f6dfadd84270ddbb880dca89061f98f71c913ee7f49","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:05:01.385750Z","signature_b64":"Ty2ud2KttGm8AoYKL7B/ldt6KNJTBIkplvb9pjkJCNmYavwAIgDbxqe12j/udCi5L4irzbXToCnhTEuFenLYAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"144d6c1fb39f566cabb03f6dfadd84270ddbb880dca89061f98f71c913ee7f49","last_reissued_at":"2026-07-05T11:05:01.385241Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:05:01.385241Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2505.12276","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":"2026-07-05T11:05:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bi/8+UEUGGLRYvs9ezWwXUxzZ0am+0PEUHY8lKdIDogwfOiKnL3fSL7lSrvMfLjPpGRLzPAEPS7Uo26b/Ps8Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T17:29:57.931514Z"},"content_sha256":"0813d6763d2a026816e3e6e376768da88cf0bfa74d20a53a609178cb44f2afe6","schema_version":"1.0","event_id":"sha256:0813d6763d2a026816e3e6e376768da88cf0bfa74d20a53a609178cb44f2afe6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:CRGWYH5TT5LGZK5QH5W7VXMEE4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Community detection of hypergraphs by Ricci flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.SI","authors_text":"Jicheng Ma, Liang Zhao, Yulu Tian, Yunyan Yang","submitted_at":"2025-05-18T07:28:10Z","abstract_excerpt":"Community detection in hypergraphs is both instrumental for functional module identification and intricate due to higher-order interactions among nodes. We define a hypergraph Ricci flow that directly operates on higher-order interactions of hypergraphs and prove long-time existence of the flow. Building on this theoretical foundation, we develop HyperRCD-a Ricci-flow-based community detection approach that deforms hyperedge weights through curvature-driven evolution, which provides an effective mathematical representation of higher-order interactions mediated by weighted hyperedges between no"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.12276","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/2505.12276/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":"2026-07-05T11:05:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Jdd+SX1WAavq8g0i/mL8IHfyVheCp/7rTGfwmm9BKFN0Cs4aUNcFkyAVahBc9OmgmnpdC433oXxciAwOW1IzCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T17:29:57.932439Z"},"content_sha256":"79f7591f2dac5e2003695e4d7045a89721ba2c51fd5aef2c2d0aaea54a4256b3","schema_version":"1.0","event_id":"sha256:79f7591f2dac5e2003695e4d7045a89721ba2c51fd5aef2c2d0aaea54a4256b3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CRGWYH5TT5LGZK5QH5W7VXMEE4/bundle.json","state_url":"https://pith.science/pith/CRGWYH5TT5LGZK5QH5W7VXMEE4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CRGWYH5TT5LGZK5QH5W7VXMEE4/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":"2026-08-16T17:29:57Z","links":{"resolver":"https://pith.science/pith/CRGWYH5TT5LGZK5QH5W7VXMEE4","bundle":"https://pith.science/pith/CRGWYH5TT5LGZK5QH5W7VXMEE4/bundle.json","state":"https://pith.science/pith/CRGWYH5TT5LGZK5QH5W7VXMEE4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CRGWYH5TT5LGZK5QH5W7VXMEE4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:CRGWYH5TT5LGZK5QH5W7VXMEE4","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":"98f0d1a4e56fe95c4195c8e8246c54d7a56deb033685594dd0f3115d8d2b999f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2025-05-18T07:28:10Z","title_canon_sha256":"f5e70c9ce4eb3b85418a1e8832a48e85897de2a75a82f69bde474dc9659c0c51"},"schema_version":"1.0","source":{"id":"2505.12276","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.12276","created_at":"2026-07-05T11:05:01Z"},{"alias_kind":"arxiv_version","alias_value":"2505.12276v1","created_at":"2026-07-05T11:05:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.12276","created_at":"2026-07-05T11:05:01Z"},{"alias_kind":"pith_short_12","alias_value":"CRGWYH5TT5LG","created_at":"2026-07-05T11:05:01Z"},{"alias_kind":"pith_short_16","alias_value":"CRGWYH5TT5LGZK5Q","created_at":"2026-07-05T11:05:01Z"},{"alias_kind":"pith_short_8","alias_value":"CRGWYH5T","created_at":"2026-07-05T11:05:01Z"}],"graph_snapshots":[{"event_id":"sha256:79f7591f2dac5e2003695e4d7045a89721ba2c51fd5aef2c2d0aaea54a4256b3","target":"graph","created_at":"2026-07-05T11:05:01Z","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/2505.12276/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Community detection in hypergraphs is both instrumental for functional module identification and intricate due to higher-order interactions among nodes. We define a hypergraph Ricci flow that directly operates on higher-order interactions of hypergraphs and prove long-time existence of the flow. Building on this theoretical foundation, we develop HyperRCD-a Ricci-flow-based community detection approach that deforms hyperedge weights through curvature-driven evolution, which provides an effective mathematical representation of higher-order interactions mediated by weighted hyperedges between no","authors_text":"Jicheng Ma, Liang Zhao, Yulu Tian, Yunyan Yang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2025-05-18T07:28:10Z","title":"Community detection of hypergraphs by Ricci flow"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.12276","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":"sha256:0813d6763d2a026816e3e6e376768da88cf0bfa74d20a53a609178cb44f2afe6","target":"record","created_at":"2026-07-05T11:05:01Z","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":"98f0d1a4e56fe95c4195c8e8246c54d7a56deb033685594dd0f3115d8d2b999f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2025-05-18T07:28:10Z","title_canon_sha256":"f5e70c9ce4eb3b85418a1e8832a48e85897de2a75a82f69bde474dc9659c0c51"},"schema_version":"1.0","source":{"id":"2505.12276","kind":"arxiv","version":1}},"canonical_sha256":"144d6c1fb39f566cabb03f6dfadd84270ddbb880dca89061f98f71c913ee7f49","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"144d6c1fb39f566cabb03f6dfadd84270ddbb880dca89061f98f71c913ee7f49","first_computed_at":"2026-07-05T11:05:01.385241Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:05:01.385241Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ty2ud2KttGm8AoYKL7B/ldt6KNJTBIkplvb9pjkJCNmYavwAIgDbxqe12j/udCi5L4irzbXToCnhTEuFenLYAw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:05:01.385750Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.12276","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0813d6763d2a026816e3e6e376768da88cf0bfa74d20a53a609178cb44f2afe6","sha256:79f7591f2dac5e2003695e4d7045a89721ba2c51fd5aef2c2d0aaea54a4256b3"],"state_sha256":"9bb11ff63c2f2a1d8df706e03ac438d8eb4fc7d3f2d73f07624e4a8c1e5170be"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x0R9rnqYjkEqvwXRFOzxIDZzNt2WjiwEQPKP83Qaj5aY9ZmuGCrCAetSkAd3DI1j5TXw9jdukDqgEZxnaxc+Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T17:29:57.939255Z","bundle_sha256":"e4e3622699ecca36ae0834b8849cedc6410746ff4df7d10b32532d7cff5bd700"}}