{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:MAIGHXRXAMWL35APTWIQSPZZOJ","short_pith_number":"pith:MAIGHXRX","canonical_record":{"source":{"id":"2106.06666","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2021-06-12T02:07:07Z","cross_cats_sorted":[],"title_canon_sha256":"483dc5ab927f746d142a533d583d66fab178830ba53a4d4fb1a530fd4665b513","abstract_canon_sha256":"07ed6bdd7286daa01f046c0d2c4878961e1f3ecd56e99e9a0fe76a0173e5e41c"},"schema_version":"1.0"},"canonical_sha256":"601063de37032cbdf40f9d91093f39725408944a8ec09cf357c36cbf36bcc03e","source":{"kind":"arxiv","id":"2106.06666","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2106.06666","created_at":"2026-07-05T04:14:37Z"},{"alias_kind":"arxiv_version","alias_value":"2106.06666v3","created_at":"2026-07-05T04:14:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2106.06666","created_at":"2026-07-05T04:14:37Z"},{"alias_kind":"pith_short_12","alias_value":"MAIGHXRXAMWL","created_at":"2026-07-05T04:14:37Z"},{"alias_kind":"pith_short_16","alias_value":"MAIGHXRXAMWL35AP","created_at":"2026-07-05T04:14:37Z"},{"alias_kind":"pith_short_8","alias_value":"MAIGHXRX","created_at":"2026-07-05T04:14:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:MAIGHXRXAMWL35APTWIQSPZZOJ","target":"record","payload":{"canonical_record":{"source":{"id":"2106.06666","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2021-06-12T02:07:07Z","cross_cats_sorted":[],"title_canon_sha256":"483dc5ab927f746d142a533d583d66fab178830ba53a4d4fb1a530fd4665b513","abstract_canon_sha256":"07ed6bdd7286daa01f046c0d2c4878961e1f3ecd56e99e9a0fe76a0173e5e41c"},"schema_version":"1.0"},"canonical_sha256":"601063de37032cbdf40f9d91093f39725408944a8ec09cf357c36cbf36bcc03e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:14:37.668096Z","signature_b64":"YnyWHw9cEADgWEZ82pJeiSV5UYYnc18bNnO91iOz7tJkL8oa8KdeJDX7AHfgR6dlFF40JM8IbfRyvGLtaaxgBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"601063de37032cbdf40f9d91093f39725408944a8ec09cf357c36cbf36bcc03e","last_reissued_at":"2026-07-05T04:14:37.667728Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:14:37.667728Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2106.06666","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:14:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oJ3vUV1bBamvGXcFnaKgGHWNJPxc9TUhE2G+nj6S6J943zend0fXi8QtOgUl14Z9MN3sXBMUlKtEO+hUFH6kCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T09:03:39.531451Z"},"content_sha256":"ab72dbe8a73fba75e8d1fb0f4bdae46d3309bf1f397fd52042a04e6e6cf2a35f","schema_version":"1.0","event_id":"sha256:ab72dbe8a73fba75e8d1fb0f4bdae46d3309bf1f397fd52042a04e6e6cf2a35f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:MAIGHXRXAMWL35APTWIQSPZZOJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Learnable Hypergraph Laplacian for Hypergraph Learning","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Jiying Zhang, Runiu Lu, Shu-Tao Xia, Xi Xiao, Yuzhao Chen","submitted_at":"2021-06-12T02:07:07Z","abstract_excerpt":"Hypergraph Convolutional Neural Networks (HGCNNs) have demonstrated their potential in modeling high-order relations preserved in graph-structured data. However, most existing convolution filters are localized and determined by the pre-defined initial hypergraph topology, neglecting to explore implicit and long-range relations in real-world data. In this paper, we propose the first learning-based method tailored for constructing adaptive hypergraph structure, termed HypERgrAph Laplacian aDaptor (HERALD), which serves as a generic plug-and-play module for improving the representational power of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.06666","kind":"arxiv","version":3},"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/2106.06666/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":"2026-07-05T04:14:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ryV7N3+veqXx2s9CffgG8ECQU9yXGfTS8VEvfY6yzwQKWs3bXRXZlbWsvzNle9oZRYd+u6ebSpCWRq+e/g1DCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T09:03:39.532861Z"},"content_sha256":"87c80f7b97784f429f41a6595dd40bdec5fc8c1d5b8dff1c6ca2fe524afe1ab8","schema_version":"1.0","event_id":"sha256:87c80f7b97784f429f41a6595dd40bdec5fc8c1d5b8dff1c6ca2fe524afe1ab8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MAIGHXRXAMWL35APTWIQSPZZOJ/bundle.json","state_url":"https://pith.science/pith/MAIGHXRXAMWL35APTWIQSPZZOJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MAIGHXRXAMWL35APTWIQSPZZOJ/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":"2026-08-14T09:03:39Z","links":{"resolver":"https://pith.science/pith/MAIGHXRXAMWL35APTWIQSPZZOJ","bundle":"https://pith.science/pith/MAIGHXRXAMWL35APTWIQSPZZOJ/bundle.json","state":"https://pith.science/pith/MAIGHXRXAMWL35APTWIQSPZZOJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MAIGHXRXAMWL35APTWIQSPZZOJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:MAIGHXRXAMWL35APTWIQSPZZOJ","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":"07ed6bdd7286daa01f046c0d2c4878961e1f3ecd56e99e9a0fe76a0173e5e41c","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2021-06-12T02:07:07Z","title_canon_sha256":"483dc5ab927f746d142a533d583d66fab178830ba53a4d4fb1a530fd4665b513"},"schema_version":"1.0","source":{"id":"2106.06666","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2106.06666","created_at":"2026-07-05T04:14:37Z"},{"alias_kind":"arxiv_version","alias_value":"2106.06666v3","created_at":"2026-07-05T04:14:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2106.06666","created_at":"2026-07-05T04:14:37Z"},{"alias_kind":"pith_short_12","alias_value":"MAIGHXRXAMWL","created_at":"2026-07-05T04:14:37Z"},{"alias_kind":"pith_short_16","alias_value":"MAIGHXRXAMWL35AP","created_at":"2026-07-05T04:14:37Z"},{"alias_kind":"pith_short_8","alias_value":"MAIGHXRX","created_at":"2026-07-05T04:14:37Z"}],"graph_snapshots":[{"event_id":"sha256:87c80f7b97784f429f41a6595dd40bdec5fc8c1d5b8dff1c6ca2fe524afe1ab8","target":"graph","created_at":"2026-07-05T04:14:37Z","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/2106.06666/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Hypergraph Convolutional Neural Networks (HGCNNs) have demonstrated their potential in modeling high-order relations preserved in graph-structured data. However, most existing convolution filters are localized and determined by the pre-defined initial hypergraph topology, neglecting to explore implicit and long-range relations in real-world data. In this paper, we propose the first learning-based method tailored for constructing adaptive hypergraph structure, termed HypERgrAph Laplacian aDaptor (HERALD), which serves as a generic plug-and-play module for improving the representational power of","authors_text":"Jiying Zhang, Runiu Lu, Shu-Tao Xia, Xi Xiao, Yuzhao Chen","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2021-06-12T02:07:07Z","title":"Learnable Hypergraph Laplacian for Hypergraph Learning"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.06666","kind":"arxiv","version":3},"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:ab72dbe8a73fba75e8d1fb0f4bdae46d3309bf1f397fd52042a04e6e6cf2a35f","target":"record","created_at":"2026-07-05T04:14:37Z","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":"07ed6bdd7286daa01f046c0d2c4878961e1f3ecd56e99e9a0fe76a0173e5e41c","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2021-06-12T02:07:07Z","title_canon_sha256":"483dc5ab927f746d142a533d583d66fab178830ba53a4d4fb1a530fd4665b513"},"schema_version":"1.0","source":{"id":"2106.06666","kind":"arxiv","version":3}},"canonical_sha256":"601063de37032cbdf40f9d91093f39725408944a8ec09cf357c36cbf36bcc03e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"601063de37032cbdf40f9d91093f39725408944a8ec09cf357c36cbf36bcc03e","first_computed_at":"2026-07-05T04:14:37.667728Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:14:37.667728Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YnyWHw9cEADgWEZ82pJeiSV5UYYnc18bNnO91iOz7tJkL8oa8KdeJDX7AHfgR6dlFF40JM8IbfRyvGLtaaxgBA==","signature_status":"signed_v1","signed_at":"2026-07-05T04:14:37.668096Z","signed_message":"canonical_sha256_bytes"},"source_id":"2106.06666","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ab72dbe8a73fba75e8d1fb0f4bdae46d3309bf1f397fd52042a04e6e6cf2a35f","sha256:87c80f7b97784f429f41a6595dd40bdec5fc8c1d5b8dff1c6ca2fe524afe1ab8"],"state_sha256":"c145160b76e9eb1fd98b58c5283156f9373297a7897a8b9f8203f91c3ac6d8a7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T6SwZz08iRUnt+1UJmfvSnjF6Z8DMIFdD6owKLWOJm9zKOe84SwUY6Vn42s6bRJVQ5laY9P3g0HdpIYtODPLDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T09:03:39.538497Z","bundle_sha256":"7bc7209743b9ee7d7184176df2332d5b5af7dc98db1e99170e927f5ad2b2ad71"}}