{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:YBJAKX5XQYFENIIFEBR4C7QBUH","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":"13cb29d5bb220d67366130c73c0ad109bdf7f916095f33c4596aa1ffe40d8e67","cross_cats_sorted":["cs.SI","stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-07-24T15:07:37Z","title_canon_sha256":"c954edbe63838a8044101051c4379036460d70cd5c3efe98e20beb98b321e8a8"},"schema_version":"1.0","source":{"id":"2607.22381","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.22381","created_at":"2026-07-27T01:21:17Z"},{"alias_kind":"arxiv_version","alias_value":"2607.22381v1","created_at":"2026-07-27T01:21:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.22381","created_at":"2026-07-27T01:21:17Z"},{"alias_kind":"pith_short_12","alias_value":"YBJAKX5XQYFE","created_at":"2026-07-27T01:21:17Z"},{"alias_kind":"pith_short_16","alias_value":"YBJAKX5XQYFENIIF","created_at":"2026-07-27T01:21:17Z"},{"alias_kind":"pith_short_8","alias_value":"YBJAKX5X","created_at":"2026-07-27T01:21:17Z"}],"graph_snapshots":[{"event_id":"sha256:4b229b00f51c6ce4dbc8cc0d60c224a36462d313bdf62b93465d25e8623e2aae","target":"graph","created_at":"2026-07-27T01:21:17Z","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/2607.22381/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Curvature notions on graphs, particularly Ollivier-Ricci and Forman, have emerged as powerful tools for addressing fundamental issues in Graph Neural Networks (GNNs) such as oversmoothing and oversquashing, but rely almost exclusively on local edge-level comparisons and therefore fail to certify how information actually propagates over long distances. We introduce Entropic Curvature, a global, transport-based curvature obtained by extending the Lott-Sturm-Villani framework to graphs through the displacement convexity of entropy along Wasserstein geodesics. We define a tractable Weak Entropic C","authors_text":"Rachid Caich, Yassine Abbahaddou","cross_cats":["cs.SI","stat.ML"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-07-24T15:07:37Z","title":"Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.22381","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":"sha256:1a26766f3d63c9c035bb94fed13988c3e35d18db466f1b2b14a26c4d4eca9e4c","target":"record","created_at":"2026-07-27T01:21:17Z","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":"13cb29d5bb220d67366130c73c0ad109bdf7f916095f33c4596aa1ffe40d8e67","cross_cats_sorted":["cs.SI","stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-07-24T15:07:37Z","title_canon_sha256":"c954edbe63838a8044101051c4379036460d70cd5c3efe98e20beb98b321e8a8"},"schema_version":"1.0","source":{"id":"2607.22381","kind":"arxiv","version":1}},"canonical_sha256":"c052055fb7860a46a1052063c17e01a1d09d6a612bfbf2ef59d4f23e29967ef6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c052055fb7860a46a1052063c17e01a1d09d6a612bfbf2ef59d4f23e29967ef6","first_computed_at":"2026-07-27T01:21:17.576289Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-27T01:21:17.576289Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tl3kb6sO6Yp8lXCvs87bUP8HBumbgMvi/sBS29BhASyZsGDG4wbtVKTA+LQXH8OIrH4iJezzKsRr8wMvUHCXAw==","signature_status":"signed_v1","signed_at":"2026-07-27T01:21:17.577150Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.22381","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1a26766f3d63c9c035bb94fed13988c3e35d18db466f1b2b14a26c4d4eca9e4c","sha256:4b229b00f51c6ce4dbc8cc0d60c224a36462d313bdf62b93465d25e8623e2aae"],"state_sha256":"fd5b66c3ae77529c5788cdae2d0a7c4be0cf91d78273ee5356d1f8ac23b6a696"}