{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:T4ZW52N22QLWHUA572TY6ZBOZ6","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":"746541a34f3d5b681f6c45f891f1718de5c72820a0775d41befbf3b702cf0d0b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-09-30T16:04:51Z","title_canon_sha256":"f1cf8409fcff820c1bebb8ade5162133138bf33f03539eb0a61e4696d03ddc0f"},"schema_version":"1.0","source":{"id":"1309.7903","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.7903","created_at":"2026-05-18T03:11:47Z"},{"alias_kind":"arxiv_version","alias_value":"1309.7903v1","created_at":"2026-05-18T03:11:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.7903","created_at":"2026-05-18T03:11:47Z"},{"alias_kind":"pith_short_12","alias_value":"T4ZW52N22QLW","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"T4ZW52N22QLWHUA5","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"T4ZW52N2","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:a8d5e205b55469eaf54e8c298e3974a73923585970ef34c008dd623853d7aedc","target":"graph","created_at":"2026-05-18T03:11:47Z","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"},"paper":{"abstract_excerpt":"Intersection growth concerns the asymptotic behavior of the index of the intersection of all subgroups of a group that have index at most n. In this note we show that the intersection growth of some groups may not be a nicely behaved function by showing the following seemingly contradictory results: (a) for any group G the intersection growth function i_G(n) is super linear infinitely often; and (b) for any increasing function f there exists a group G such that i_G below f infinitely often.","authors_text":"Francesco Matucci, Martin Kassabov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-09-30T16:04:51Z","title":"On groups with slow intersection growth"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.7903","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":"sha256:9525e04e72feed65b51b2ec4d3cd9cd60e0d3d0f806be13380c999f6f7b90462","target":"record","created_at":"2026-05-18T03:11:47Z","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":"746541a34f3d5b681f6c45f891f1718de5c72820a0775d41befbf3b702cf0d0b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-09-30T16:04:51Z","title_canon_sha256":"f1cf8409fcff820c1bebb8ade5162133138bf33f03539eb0a61e4696d03ddc0f"},"schema_version":"1.0","source":{"id":"1309.7903","kind":"arxiv","version":1}},"canonical_sha256":"9f336ee9bad41763d01dfea78f642ecf8f506f3521c6230c7e85217b2d988144","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9f336ee9bad41763d01dfea78f642ecf8f506f3521c6230c7e85217b2d988144","first_computed_at":"2026-05-18T03:11:47.867608Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:11:47.867608Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RsMO1gtnmoC/iHxvHm/W1k93FgT1OmiN0o/yaV6xsOuBHcz5dijyvraQH7pfROZvYe/aKL2gnYLgay4HEEePBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:11:47.868366Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.7903","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9525e04e72feed65b51b2ec4d3cd9cd60e0d3d0f806be13380c999f6f7b90462","sha256:a8d5e205b55469eaf54e8c298e3974a73923585970ef34c008dd623853d7aedc"],"state_sha256":"1c5c308ff131a5588780fc496eb534820891ac55d778207301b8732fa82a9082"}