{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:2F2PTLOVS6CUSLLFAYPHHGDUIN","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":"2ec3b512893bf86de0c7f31ee01d797772aba4b095f8df0f511c3a3ce3f37508","cross_cats_sorted":["cs.AI"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-12-15T06:52:40Z","title_canon_sha256":"ea38dc72721be7fb4140b98390f0307b1e4b5bf14d633434bf8bc6a7673eeae6"},"schema_version":"1.0","source":{"id":"2412.11085","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.11085","created_at":"2026-07-05T09:49:27Z"},{"alias_kind":"arxiv_version","alias_value":"2412.11085v1","created_at":"2026-07-05T09:49:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.11085","created_at":"2026-07-05T09:49:27Z"},{"alias_kind":"pith_short_12","alias_value":"2F2PTLOVS6CU","created_at":"2026-07-05T09:49:27Z"},{"alias_kind":"pith_short_16","alias_value":"2F2PTLOVS6CUSLLF","created_at":"2026-07-05T09:49:27Z"},{"alias_kind":"pith_short_8","alias_value":"2F2PTLOV","created_at":"2026-07-05T09:49:27Z"}],"graph_snapshots":[{"event_id":"sha256:77d5031ecdac467dbe78e60039aa2496e49f6a9379f767668a9f63a2f21d23a9","target":"graph","created_at":"2026-07-05T09:49:27Z","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/2412.11085/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Real-world graphs have inherently complex and diverse topological patterns, known as topological heterogeneity. Most existing works learn graph representation in a single constant curvature space that is insufficient to match the complex geometric shapes, resulting in low-quality embeddings with high distortion. This also constitutes a critical challenge for graph foundation models, which are expected to uniformly handle a wide variety of diverse graph data. Recent studies have indicated that product manifold gains the possibility to address topological heterogeneity. However, the product mani","authors_text":"Haonan Yuan, Jianxin Li, Min Zhou, Qingyun Sun, Xingcheng Fu, Yisen Gao, Zihao Guo","cross_cats":["cs.AI"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-12-15T06:52:40Z","title":"GraphMoRE: Mitigating Topological Heterogeneity via Mixture of Riemannian Experts"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.11085","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":"sha256:3df4a99ccafee20bfee5bc73ddbf7ef6a9e4412bbd4c10cc09e63c063c4d29ea","target":"record","created_at":"2026-07-05T09:49:27Z","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":"2ec3b512893bf86de0c7f31ee01d797772aba4b095f8df0f511c3a3ce3f37508","cross_cats_sorted":["cs.AI"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-12-15T06:52:40Z","title_canon_sha256":"ea38dc72721be7fb4140b98390f0307b1e4b5bf14d633434bf8bc6a7673eeae6"},"schema_version":"1.0","source":{"id":"2412.11085","kind":"arxiv","version":1}},"canonical_sha256":"d174f9add59785492d65061e739874434de0186bda8ba68c07299777052c29f6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d174f9add59785492d65061e739874434de0186bda8ba68c07299777052c29f6","first_computed_at":"2026-07-05T09:49:27.330576Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:49:27.330576Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YKYo8fB+mC/xvJvT0yUQ5MJdSmCClpvQtuihgXZwsRY9Hb8qb9I68K02KBarGtJVt4fVb+ZaJ/LXGVNh7rG8AA==","signature_status":"signed_v1","signed_at":"2026-07-05T09:49:27.331048Z","signed_message":"canonical_sha256_bytes"},"source_id":"2412.11085","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3df4a99ccafee20bfee5bc73ddbf7ef6a9e4412bbd4c10cc09e63c063c4d29ea","sha256:77d5031ecdac467dbe78e60039aa2496e49f6a9379f767668a9f63a2f21d23a9"],"state_sha256":"f4cf3b847dacaf8523b1745fc3555abc3066a80d6b10fde3f0d74e771539eaa8"}