{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:FQDW2PAPCMHP6RHI7S4UPYCSRK","short_pith_number":"pith:FQDW2PAP","schema_version":"1.0","canonical_sha256":"2c076d3c0f130eff44e8fcb947e0528aaff69ee2d232992536284be01467d81b","source":{"kind":"arxiv","id":"2607.02102","version":1},"attestation_state":"computed","paper":{"title":"From Finite Cayley Graphs to Growth of Infinite Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Tal Weissblat","submitted_at":"2026-07-02T12:37:21Z","abstract_excerpt":"Graph neural networks (GNNs) have recently been shown to learn algebraic properties of finite groups from their Cayley graphs [1,2]. In this work, we investigate whether such models generalize to infinite finitely generated groups. Motivated by Gromov's theorem [3], a GNN is trained and validated exclusively on finite complete and truncated Cayley graphs, and then evaluated, without retraining, on truncated Cayley graphs of unseen infinite groups. The evaluation includes free abelian groups of various ranks, the discrete Heisenberg group, the infinite dihedral group, free groups, and direct pr"},"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":"2607.02102","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2026-07-02T12:37:21Z","cross_cats_sorted":[],"title_canon_sha256":"a9376e6b615234e4455a674084b3d135d47154841e27568832fd2ac44eb57d51","abstract_canon_sha256":"a5bdf2a0e7f8cfc3e9ca107b868cdc2bdad922afe3cdbfa5996731c3f2661635"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-03T01:17:42.305980Z","signature_b64":"6PdmHOABlQY1rzveNas4JYUDYQBLC6kAWZ/LGtzztqHAbtbs10w/zP6S94CgVOLZ/ebtooHSYHoiz0S8vMm2Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2c076d3c0f130eff44e8fcb947e0528aaff69ee2d232992536284be01467d81b","last_reissued_at":"2026-07-03T01:17:42.305591Z","signature_status":"signed_v1","first_computed_at":"2026-07-03T01:17:42.305591Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"From Finite Cayley Graphs to Growth of Infinite Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Tal Weissblat","submitted_at":"2026-07-02T12:37:21Z","abstract_excerpt":"Graph neural networks (GNNs) have recently been shown to learn algebraic properties of finite groups from their Cayley graphs [1,2]. In this work, we investigate whether such models generalize to infinite finitely generated groups. Motivated by Gromov's theorem [3], a GNN is trained and validated exclusively on finite complete and truncated Cayley graphs, and then evaluated, without retraining, on truncated Cayley graphs of unseen infinite groups. The evaluation includes free abelian groups of various ranks, the discrete Heisenberg group, the infinite dihedral group, free groups, and direct pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.02102","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/2607.02102/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":"2607.02102","created_at":"2026-07-03T01:17:42.305650+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.02102v1","created_at":"2026-07-03T01:17:42.305650+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.02102","created_at":"2026-07-03T01:17:42.305650+00:00"},{"alias_kind":"pith_short_12","alias_value":"FQDW2PAPCMHP","created_at":"2026-07-03T01:17:42.305650+00:00"},{"alias_kind":"pith_short_16","alias_value":"FQDW2PAPCMHP6RHI","created_at":"2026-07-03T01:17:42.305650+00:00"},{"alias_kind":"pith_short_8","alias_value":"FQDW2PAP","created_at":"2026-07-03T01:17:42.305650+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/FQDW2PAPCMHP6RHI7S4UPYCSRK","json":"https://pith.science/pith/FQDW2PAPCMHP6RHI7S4UPYCSRK.json","graph_json":"https://pith.science/api/pith-number/FQDW2PAPCMHP6RHI7S4UPYCSRK/graph.json","events_json":"https://pith.science/api/pith-number/FQDW2PAPCMHP6RHI7S4UPYCSRK/events.json","paper":"https://pith.science/paper/FQDW2PAP"},"agent_actions":{"view_html":"https://pith.science/pith/FQDW2PAPCMHP6RHI7S4UPYCSRK","download_json":"https://pith.science/pith/FQDW2PAPCMHP6RHI7S4UPYCSRK.json","view_paper":"https://pith.science/paper/FQDW2PAP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.02102&json=true","fetch_graph":"https://pith.science/api/pith-number/FQDW2PAPCMHP6RHI7S4UPYCSRK/graph.json","fetch_events":"https://pith.science/api/pith-number/FQDW2PAPCMHP6RHI7S4UPYCSRK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FQDW2PAPCMHP6RHI7S4UPYCSRK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FQDW2PAPCMHP6RHI7S4UPYCSRK/action/storage_attestation","attest_author":"https://pith.science/pith/FQDW2PAPCMHP6RHI7S4UPYCSRK/action/author_attestation","sign_citation":"https://pith.science/pith/FQDW2PAPCMHP6RHI7S4UPYCSRK/action/citation_signature","submit_replication":"https://pith.science/pith/FQDW2PAPCMHP6RHI7S4UPYCSRK/action/replication_record"}},"created_at":"2026-07-03T01:17:42.305650+00:00","updated_at":"2026-07-03T01:17:42.305650+00:00"}