{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:ZQVNMKI4NSSRDJ4B3WSFQ2G2LF","short_pith_number":"pith:ZQVNMKI4","canonical_record":{"source":{"id":"1907.00481","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-06-30T22:08:16Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"5b389980814dc9d98e6270b214b9d6035d2d24f5c3a240b7a619cd99206f2803","abstract_canon_sha256":"b50c614db414556b4dc5ed83e81496dac3e464af0ec2d97516a696e3ef5ff7b8"},"schema_version":"1.0"},"canonical_sha256":"cc2ad6291c6ca511a781dda45868da5974e4b12983b34119f4dea2a4ffab8a98","source":{"kind":"arxiv","id":"1907.00481","version":6},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.00481","created_at":"2026-07-05T02:02:50Z"},{"alias_kind":"arxiv_version","alias_value":"1907.00481v6","created_at":"2026-07-05T02:02:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.00481","created_at":"2026-07-05T02:02:50Z"},{"alias_kind":"pith_short_12","alias_value":"ZQVNMKI4NSSR","created_at":"2026-07-05T02:02:50Z"},{"alias_kind":"pith_short_16","alias_value":"ZQVNMKI4NSSRDJ4B","created_at":"2026-07-05T02:02:50Z"},{"alias_kind":"pith_short_8","alias_value":"ZQVNMKI4","created_at":"2026-07-05T02:02:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:ZQVNMKI4NSSRDJ4B3WSFQ2G2LF","target":"record","payload":{"canonical_record":{"source":{"id":"1907.00481","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-06-30T22:08:16Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"5b389980814dc9d98e6270b214b9d6035d2d24f5c3a240b7a619cd99206f2803","abstract_canon_sha256":"b50c614db414556b4dc5ed83e81496dac3e464af0ec2d97516a696e3ef5ff7b8"},"schema_version":"1.0"},"canonical_sha256":"cc2ad6291c6ca511a781dda45868da5974e4b12983b34119f4dea2a4ffab8a98","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:02:50.661989Z","signature_b64":"Tq+B3j1xudueS8VoldI0+c9UjnVgRZGYHVYIxpNL7bhgWFNFTGIZWoXHzx5cygFZUCNBPlP5asTln7qz/wkXDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cc2ad6291c6ca511a781dda45868da5974e4b12983b34119f4dea2a4ffab8a98","last_reissued_at":"2026-07-05T02:02:50.661426Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:02:50.661426Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1907.00481","source_version":6,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T02:02:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u1yKDEGO1YBPz6gyF23beaSy9PQ0H3rNZdEbhdZxmnqCo00g4v9HlcK8xRhHk9+LbBatbrMNJWFV6Xvu7eOYBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T05:13:04.775661Z"},"content_sha256":"fabed8e6f692991a27c3832bc0e094f2901ab3ac46fcd8f2c5da291cbc5e8c00","schema_version":"1.0","event_id":"sha256:fabed8e6f692991a27c3832bc0e094f2901ab3ac46fcd8f2c5da291cbc5e8c00"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:ZQVNMKI4NSSRDJ4B3WSFQ2G2LF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spectral Clustering with Graph Neural Networks for Graph Pooling","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Cesare Alippi, Daniele Grattarola, Filippo Maria Bianchi","submitted_at":"2019-06-30T22:08:16Z","abstract_excerpt":"Spectral clustering (SC) is a popular clustering technique to find strongly connected communities on a graph. SC can be used in Graph Neural Networks (GNNs) to implement pooling operations that aggregate nodes belonging to the same cluster. However, the eigendecomposition of the Laplacian is expensive and, since clustering results are graph-specific, pooling methods based on SC must perform a new optimization for each new sample. In this paper, we propose a graph clustering approach that addresses these limitations of SC. We formulate a continuous relaxation of the normalized minCUT problem an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.00481","kind":"arxiv","version":6},"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/1907.00481/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":"2026-07-05T02:02:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TKZzC5ieBSKE9C9BZX+3WEnkPzQHJ9+hJEBvr56PvRReX0oyPMOC/dGpdeQCe8rhFG0tFOE0PNhg6coeEGXeBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T05:13:04.776215Z"},"content_sha256":"48a890c6e4a8d070cbf681ded5bcf8cab683a8910c5aeedaab510125ad871cf8","schema_version":"1.0","event_id":"sha256:48a890c6e4a8d070cbf681ded5bcf8cab683a8910c5aeedaab510125ad871cf8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZQVNMKI4NSSRDJ4B3WSFQ2G2LF/bundle.json","state_url":"https://pith.science/pith/ZQVNMKI4NSSRDJ4B3WSFQ2G2LF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZQVNMKI4NSSRDJ4B3WSFQ2G2LF/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":"2026-08-11T05:13:04Z","links":{"resolver":"https://pith.science/pith/ZQVNMKI4NSSRDJ4B3WSFQ2G2LF","bundle":"https://pith.science/pith/ZQVNMKI4NSSRDJ4B3WSFQ2G2LF/bundle.json","state":"https://pith.science/pith/ZQVNMKI4NSSRDJ4B3WSFQ2G2LF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZQVNMKI4NSSRDJ4B3WSFQ2G2LF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:ZQVNMKI4NSSRDJ4B3WSFQ2G2LF","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":"b50c614db414556b4dc5ed83e81496dac3e464af0ec2d97516a696e3ef5ff7b8","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-06-30T22:08:16Z","title_canon_sha256":"5b389980814dc9d98e6270b214b9d6035d2d24f5c3a240b7a619cd99206f2803"},"schema_version":"1.0","source":{"id":"1907.00481","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.00481","created_at":"2026-07-05T02:02:50Z"},{"alias_kind":"arxiv_version","alias_value":"1907.00481v6","created_at":"2026-07-05T02:02:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.00481","created_at":"2026-07-05T02:02:50Z"},{"alias_kind":"pith_short_12","alias_value":"ZQVNMKI4NSSR","created_at":"2026-07-05T02:02:50Z"},{"alias_kind":"pith_short_16","alias_value":"ZQVNMKI4NSSRDJ4B","created_at":"2026-07-05T02:02:50Z"},{"alias_kind":"pith_short_8","alias_value":"ZQVNMKI4","created_at":"2026-07-05T02:02:50Z"}],"graph_snapshots":[{"event_id":"sha256:48a890c6e4a8d070cbf681ded5bcf8cab683a8910c5aeedaab510125ad871cf8","target":"graph","created_at":"2026-07-05T02:02:50Z","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/1907.00481/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Spectral clustering (SC) is a popular clustering technique to find strongly connected communities on a graph. SC can be used in Graph Neural Networks (GNNs) to implement pooling operations that aggregate nodes belonging to the same cluster. However, the eigendecomposition of the Laplacian is expensive and, since clustering results are graph-specific, pooling methods based on SC must perform a new optimization for each new sample. In this paper, we propose a graph clustering approach that addresses these limitations of SC. We formulate a continuous relaxation of the normalized minCUT problem an","authors_text":"Cesare Alippi, Daniele Grattarola, Filippo Maria Bianchi","cross_cats":["stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-06-30T22:08:16Z","title":"Spectral Clustering with Graph Neural Networks for Graph Pooling"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.00481","kind":"arxiv","version":6},"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:fabed8e6f692991a27c3832bc0e094f2901ab3ac46fcd8f2c5da291cbc5e8c00","target":"record","created_at":"2026-07-05T02:02:50Z","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":"b50c614db414556b4dc5ed83e81496dac3e464af0ec2d97516a696e3ef5ff7b8","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-06-30T22:08:16Z","title_canon_sha256":"5b389980814dc9d98e6270b214b9d6035d2d24f5c3a240b7a619cd99206f2803"},"schema_version":"1.0","source":{"id":"1907.00481","kind":"arxiv","version":6}},"canonical_sha256":"cc2ad6291c6ca511a781dda45868da5974e4b12983b34119f4dea2a4ffab8a98","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cc2ad6291c6ca511a781dda45868da5974e4b12983b34119f4dea2a4ffab8a98","first_computed_at":"2026-07-05T02:02:50.661426Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:02:50.661426Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Tq+B3j1xudueS8VoldI0+c9UjnVgRZGYHVYIxpNL7bhgWFNFTGIZWoXHzx5cygFZUCNBPlP5asTln7qz/wkXDA==","signature_status":"signed_v1","signed_at":"2026-07-05T02:02:50.661989Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.00481","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fabed8e6f692991a27c3832bc0e094f2901ab3ac46fcd8f2c5da291cbc5e8c00","sha256:48a890c6e4a8d070cbf681ded5bcf8cab683a8910c5aeedaab510125ad871cf8"],"state_sha256":"e923bc2d96cedb7940f9ad23b23e794490b4acbee0bb3a71b1fbd28db3beb64f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sI0rhm6oXN7J7Wcp4b5cIc0Q4G3R4YbtAwNN48MnIv8b3muCZRy24P1J0dbKkUezHLJedB6DwVJOfBOiqgucDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T05:13:04.780224Z","bundle_sha256":"dc69d5eb319a800e4f04cb314d2613bff0474632527c5ceaa58967209e436685"}}