{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1995:4S2RZSL3VSX2CBJECJ4Y5IRPOD","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":"658875e65768efd36d76aee9d5c2e27f6934a7e84e4b74f3691255f8410757e6","cross_cats_sorted":["math.DG"],"license":"","primary_cat":"dg-ga","submitted_at":"1995-06-25T14:45:43Z","title_canon_sha256":"b65dc29c7d34f9ccc42c2cce8286192eceba4830673b5ba14ecfc844c5568cb4"},"schema_version":"1.0","source":{"id":"dg-ga/9506010","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"dg-ga/9506010","created_at":"2026-05-18T01:06:48Z"},{"alias_kind":"arxiv_version","alias_value":"dg-ga/9506010v1","created_at":"2026-05-18T01:06:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.dg-ga/9506010","created_at":"2026-05-18T01:06:48Z"},{"alias_kind":"pith_short_12","alias_value":"4S2RZSL3VSX2","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"4S2RZSL3VSX2CBJE","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"4S2RZSL3","created_at":"2026-05-18T12:25:47Z"}],"graph_snapshots":[{"event_id":"sha256:60a9197ba91ea1a603f2dc32e1acaea27dc2138567a267280d63b0461167be2f","target":"graph","created_at":"2026-05-18T01:06:48Z","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":"We address two fundamental and well-known problems of Gromov and Lyndon:\n \\demo{Problem A} (Gromov, see [5]). Consider a category $M_n$ of closed manifolds of dimension $n$ with nonzero-degree ways as morphisms. Study a partial order $M \\ge N \\Leftrightarrow Mor (M, N) \\neq \\phi$. For which $N$ the degrees of maps $f: M \\to N$ are bounded for all $M$?\n \\demo{Problem B} (Lyndon, [12], problem 13). Extend and relate the theories of deficiency, the rate of growth and the Euler-Poincar\\'e characteristic. In particular, what influence does the deficiency have on the structure of an infinite group?","authors_text":"Alexander Reznikov","cross_cats":["math.DG"],"headline":"","license":"","primary_cat":"dg-ga","submitted_at":"1995-06-25T14:45:43Z","title":"Volumes of Discrete Groups and Topological Complexity of Homology Spheres"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"dg-ga/9506010","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":"sha256:7080a0f7c5a529779b0571cb12b9eb9d5c7358fea1f96d934213e555d4e66075","target":"record","created_at":"2026-05-18T01:06:48Z","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":"658875e65768efd36d76aee9d5c2e27f6934a7e84e4b74f3691255f8410757e6","cross_cats_sorted":["math.DG"],"license":"","primary_cat":"dg-ga","submitted_at":"1995-06-25T14:45:43Z","title_canon_sha256":"b65dc29c7d34f9ccc42c2cce8286192eceba4830673b5ba14ecfc844c5568cb4"},"schema_version":"1.0","source":{"id":"dg-ga/9506010","kind":"arxiv","version":1}},"canonical_sha256":"e4b51cc97bacafa1052412798ea22f70f620ce4bf5cd140508b8c8d5578d121b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e4b51cc97bacafa1052412798ea22f70f620ce4bf5cd140508b8c8d5578d121b","first_computed_at":"2026-05-18T01:06:48.634572Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:06:48.634572Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0Miaacl2oCdMnZ93IF0fo9l6nl9GXWQLYEav42WPx6vmlCaPdm9CqKjKvMUDcLozDAw9ssACEKw4bxUEX1O0Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:06:48.635090Z","signed_message":"canonical_sha256_bytes"},"source_id":"dg-ga/9506010","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7080a0f7c5a529779b0571cb12b9eb9d5c7358fea1f96d934213e555d4e66075","sha256:60a9197ba91ea1a603f2dc32e1acaea27dc2138567a267280d63b0461167be2f"],"state_sha256":"173ff4e8a2407244018fe9e3e7e6956624322b7ba0834ce1dc9b3434ada04991"}