{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:3BO3DP4WSDAGKH337FSTVJA33S","short_pith_number":"pith:3BO3DP4W","schema_version":"1.0","canonical_sha256":"d85db1bf9690c0651f7bf9653aa41bdcb442ae4a0a417d6709d91ad17fa8a498","source":{"kind":"arxiv","id":"2506.05971","version":1},"attestation_state":"computed","paper":{"title":"On Measuring Long-Range Interactions in Graph Neural Networks","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"cs.LG","authors_text":"Benjamin Gutteridge, Jacob Bamberger, Michael M. Bronstein, Scott le Roux, Xiaowen Dong","submitted_at":"2025-06-06T10:48:30Z","abstract_excerpt":"Long-range graph tasks -- those dependent on interactions between distant nodes -- are an open problem in graph neural network research. Real-world benchmark tasks, especially the Long Range Graph Benchmark, have become popular for validating the long-range capability of proposed architectures. However, this is an empirical approach that lacks both robustness and theoretical underpinning; a more principled characterization of the long-range problem is required. To bridge this gap, we formalize long-range interactions in graph tasks, introduce a range measure for operators on graphs, and valida"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2506.05971","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-06-06T10:48:30Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"abc363c20ba2ea9aeab93f5fb6d96019ef23ae12d2eb8c8a14500a1bafe5c02e","abstract_canon_sha256":"f66b93d35f15e5ceea6c1b35877915d5d54080a6f2ec4f1537fbbcbbc64f6033"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:17:14.030182Z","signature_b64":"ayM6vFN7N1QzZy/YfgvPDQcr2buPqQgQ7Bc8FSc0lk8++OOYxXv9rvhNkqLAK+uNhcQSc88qKZ0jIYZODjaBDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d85db1bf9690c0651f7bf9653aa41bdcb442ae4a0a417d6709d91ad17fa8a498","last_reissued_at":"2026-07-05T11:17:14.029671Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:17:14.029671Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Measuring Long-Range Interactions in Graph Neural Networks","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"cs.LG","authors_text":"Benjamin Gutteridge, Jacob Bamberger, Michael M. Bronstein, Scott le Roux, Xiaowen Dong","submitted_at":"2025-06-06T10:48:30Z","abstract_excerpt":"Long-range graph tasks -- those dependent on interactions between distant nodes -- are an open problem in graph neural network research. Real-world benchmark tasks, especially the Long Range Graph Benchmark, have become popular for validating the long-range capability of proposed architectures. However, this is an empirical approach that lacks both robustness and theoretical underpinning; a more principled characterization of the long-range problem is required. To bridge this gap, we formalize long-range interactions in graph tasks, introduce a range measure for operators on graphs, and valida"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.05971","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/2506.05971/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2506.05971","created_at":"2026-07-05T11:17:14.029735+00:00"},{"alias_kind":"arxiv_version","alias_value":"2506.05971v1","created_at":"2026-07-05T11:17:14.029735+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.05971","created_at":"2026-07-05T11:17:14.029735+00:00"},{"alias_kind":"pith_short_12","alias_value":"3BO3DP4WSDAG","created_at":"2026-07-05T11:17:14.029735+00:00"},{"alias_kind":"pith_short_16","alias_value":"3BO3DP4WSDAGKH33","created_at":"2026-07-05T11:17:14.029735+00:00"},{"alias_kind":"pith_short_8","alias_value":"3BO3DP4W","created_at":"2026-07-05T11:17:14.029735+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":3,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2607.05257","citing_title":"GeoFlow: Geo-Aware Modeling of Inter-Area Relationships in Origin-Destination Flow Prediction and Generation","ref_index":35,"is_internal_anchor":true},{"citing_arxiv_id":"2606.21333","citing_title":"Ramanujan Graph Rewiring with Non Negative Resistance Curvature","ref_index":8,"is_internal_anchor":false},{"citing_arxiv_id":"2606.07327","citing_title":"Six Open Questions in Machine-Learned Interatomic Potential Foundation Models","ref_index":107,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/3BO3DP4WSDAGKH337FSTVJA33S","json":"https://pith.science/pith/3BO3DP4WSDAGKH337FSTVJA33S.json","graph_json":"https://pith.science/api/pith-number/3BO3DP4WSDAGKH337FSTVJA33S/graph.json","events_json":"https://pith.science/api/pith-number/3BO3DP4WSDAGKH337FSTVJA33S/events.json","paper":"https://pith.science/paper/3BO3DP4W"},"agent_actions":{"view_html":"https://pith.science/pith/3BO3DP4WSDAGKH337FSTVJA33S","download_json":"https://pith.science/pith/3BO3DP4WSDAGKH337FSTVJA33S.json","view_paper":"https://pith.science/paper/3BO3DP4W","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2506.05971&json=true","fetch_graph":"https://pith.science/api/pith-number/3BO3DP4WSDAGKH337FSTVJA33S/graph.json","fetch_events":"https://pith.science/api/pith-number/3BO3DP4WSDAGKH337FSTVJA33S/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3BO3DP4WSDAGKH337FSTVJA33S/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3BO3DP4WSDAGKH337FSTVJA33S/action/storage_attestation","attest_author":"https://pith.science/pith/3BO3DP4WSDAGKH337FSTVJA33S/action/author_attestation","sign_citation":"https://pith.science/pith/3BO3DP4WSDAGKH337FSTVJA33S/action/citation_signature","submit_replication":"https://pith.science/pith/3BO3DP4WSDAGKH337FSTVJA33S/action/replication_record"}},"created_at":"2026-07-05T11:17:14.029735+00:00","updated_at":"2026-07-05T11:17:14.029735+00:00"}