{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:7ZSBEBWFZPCICXHLZOKFNOQGLU","short_pith_number":"pith:7ZSBEBWF","canonical_record":{"source":{"id":"2406.03164","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2024-06-05T11:56:54Z","cross_cats_sorted":[],"title_canon_sha256":"67eb6c05e20000ad08d3bd75478dd8683ed9c4212fcfc0c161d0a45eca4e2d32","abstract_canon_sha256":"3230d38a19be1ba7f9ad7f8a4e7c6d24a80400d7db348c490184841007eb5e0c"},"schema_version":"1.0"},"canonical_sha256":"fe641206c5cbc4815cebcb9456ba065d3943a3a7a2bbda2ef86a786683774e99","source":{"kind":"arxiv","id":"2406.03164","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2406.03164","created_at":"2026-07-05T08:27:52Z"},{"alias_kind":"arxiv_version","alias_value":"2406.03164v1","created_at":"2026-07-05T08:27:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.03164","created_at":"2026-07-05T08:27:52Z"},{"alias_kind":"pith_short_12","alias_value":"7ZSBEBWFZPCI","created_at":"2026-07-05T08:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"7ZSBEBWFZPCICXHL","created_at":"2026-07-05T08:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"7ZSBEBWF","created_at":"2026-07-05T08:27:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:7ZSBEBWFZPCICXHLZOKFNOQGLU","target":"record","payload":{"canonical_record":{"source":{"id":"2406.03164","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2024-06-05T11:56:54Z","cross_cats_sorted":[],"title_canon_sha256":"67eb6c05e20000ad08d3bd75478dd8683ed9c4212fcfc0c161d0a45eca4e2d32","abstract_canon_sha256":"3230d38a19be1ba7f9ad7f8a4e7c6d24a80400d7db348c490184841007eb5e0c"},"schema_version":"1.0"},"canonical_sha256":"fe641206c5cbc4815cebcb9456ba065d3943a3a7a2bbda2ef86a786683774e99","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:27:52.259344Z","signature_b64":"SkwWAyIjHM18Nba0h13UX6cQDD2Hefk86BKV27b/Lk1u/LB1hTX956OE996PhE96o3sc2ewNDf0kyd/WbaxnBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fe641206c5cbc4815cebcb9456ba065d3943a3a7a2bbda2ef86a786683774e99","last_reissued_at":"2026-07-05T08:27:52.258880Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:27:52.258880Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2406.03164","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":"2026-07-05T08:27:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cKiqIB6QP8n5S/tuC6bpV5rXYIYGX1aceEYmyxpB1wyVqA0tXXSwxsPTf4Z8YeVGce5S1FWPZSRMq8PXMUi5Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T07:44:54.022711Z"},"content_sha256":"c09a438983346dc1ec98f4c388b409d8d214c8831bb970767fa0ddd13915b74c","schema_version":"1.0","event_id":"sha256:c09a438983346dc1ec98f4c388b409d8d214c8831bb970767fa0ddd13915b74c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:7ZSBEBWFZPCICXHLZOKFNOQGLU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Topological Neural Networks go Persistent, Equivariant, and Continuous","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Amauri H Souza, Vikas Garg, Yogesh Verma","submitted_at":"2024-06-05T11:56:54Z","abstract_excerpt":"Topological Neural Networks (TNNs) incorporate higher-order relational information beyond pairwise interactions, enabling richer representations than Graph Neural Networks (GNNs). Concurrently, topological descriptors based on persistent homology (PH) are being increasingly employed to augment the GNNs. We investigate the benefits of integrating these two paradigms. Specifically, we introduce TopNets as a broad framework that subsumes and unifies various methods in the intersection of GNNs/TNNs and PH such as (generalizations of) RePHINE and TOGL. TopNets can also be readily adapted to handle "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.03164","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/2406.03164/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":"2026-07-05T08:27:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z9w1zEHfeD1Ess6cUa+pXdryN6K7WaJe6dv3XeHAAd37wq8zp8qOuI5cm2C1He2XKWDXDJVEFj0/pSn2zpH5Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T07:44:54.023209Z"},"content_sha256":"3e8d95fb2df4558e4addaaea3d47ed7c47c3d0bb91fb8410a8053fb635b273f9","schema_version":"1.0","event_id":"sha256:3e8d95fb2df4558e4addaaea3d47ed7c47c3d0bb91fb8410a8053fb635b273f9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7ZSBEBWFZPCICXHLZOKFNOQGLU/bundle.json","state_url":"https://pith.science/pith/7ZSBEBWFZPCICXHLZOKFNOQGLU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7ZSBEBWFZPCICXHLZOKFNOQGLU/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":"2026-08-09T07:44:54Z","links":{"resolver":"https://pith.science/pith/7ZSBEBWFZPCICXHLZOKFNOQGLU","bundle":"https://pith.science/pith/7ZSBEBWFZPCICXHLZOKFNOQGLU/bundle.json","state":"https://pith.science/pith/7ZSBEBWFZPCICXHLZOKFNOQGLU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7ZSBEBWFZPCICXHLZOKFNOQGLU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:7ZSBEBWFZPCICXHLZOKFNOQGLU","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":"3230d38a19be1ba7f9ad7f8a4e7c6d24a80400d7db348c490184841007eb5e0c","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2024-06-05T11:56:54Z","title_canon_sha256":"67eb6c05e20000ad08d3bd75478dd8683ed9c4212fcfc0c161d0a45eca4e2d32"},"schema_version":"1.0","source":{"id":"2406.03164","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2406.03164","created_at":"2026-07-05T08:27:52Z"},{"alias_kind":"arxiv_version","alias_value":"2406.03164v1","created_at":"2026-07-05T08:27:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.03164","created_at":"2026-07-05T08:27:52Z"},{"alias_kind":"pith_short_12","alias_value":"7ZSBEBWFZPCI","created_at":"2026-07-05T08:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"7ZSBEBWFZPCICXHL","created_at":"2026-07-05T08:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"7ZSBEBWF","created_at":"2026-07-05T08:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:3e8d95fb2df4558e4addaaea3d47ed7c47c3d0bb91fb8410a8053fb635b273f9","target":"graph","created_at":"2026-07-05T08:27:52Z","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/2406.03164/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Topological Neural Networks (TNNs) incorporate higher-order relational information beyond pairwise interactions, enabling richer representations than Graph Neural Networks (GNNs). Concurrently, topological descriptors based on persistent homology (PH) are being increasingly employed to augment the GNNs. We investigate the benefits of integrating these two paradigms. Specifically, we introduce TopNets as a broad framework that subsumes and unifies various methods in the intersection of GNNs/TNNs and PH such as (generalizations of) RePHINE and TOGL. TopNets can also be readily adapted to handle ","authors_text":"Amauri H Souza, Vikas Garg, Yogesh Verma","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2024-06-05T11:56:54Z","title":"Topological Neural Networks go Persistent, Equivariant, and Continuous"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.03164","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:c09a438983346dc1ec98f4c388b409d8d214c8831bb970767fa0ddd13915b74c","target":"record","created_at":"2026-07-05T08:27:52Z","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":"3230d38a19be1ba7f9ad7f8a4e7c6d24a80400d7db348c490184841007eb5e0c","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2024-06-05T11:56:54Z","title_canon_sha256":"67eb6c05e20000ad08d3bd75478dd8683ed9c4212fcfc0c161d0a45eca4e2d32"},"schema_version":"1.0","source":{"id":"2406.03164","kind":"arxiv","version":1}},"canonical_sha256":"fe641206c5cbc4815cebcb9456ba065d3943a3a7a2bbda2ef86a786683774e99","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fe641206c5cbc4815cebcb9456ba065d3943a3a7a2bbda2ef86a786683774e99","first_computed_at":"2026-07-05T08:27:52.258880Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:27:52.258880Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SkwWAyIjHM18Nba0h13UX6cQDD2Hefk86BKV27b/Lk1u/LB1hTX956OE996PhE96o3sc2ewNDf0kyd/WbaxnBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T08:27:52.259344Z","signed_message":"canonical_sha256_bytes"},"source_id":"2406.03164","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c09a438983346dc1ec98f4c388b409d8d214c8831bb970767fa0ddd13915b74c","sha256:3e8d95fb2df4558e4addaaea3d47ed7c47c3d0bb91fb8410a8053fb635b273f9"],"state_sha256":"16b2187ed359ec92e31ba4dcb7d1658276b932911bbf9a7883dd04a121b2ee3a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fDb44KWNI4Y4EDvUukBYJsjMg1YTHrBGCrRK8kGX1qZgwZWkwz+OVAXn6da7UdSmb9+ZQLMJNd2PJkZOVL5nBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T07:44:54.027525Z","bundle_sha256":"ffb1e30d2c82cac2a90c7572d8d56a3b047cebd55a28e9a51e01e2c5dcd5a0d4"}}