{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:NRYN7FMEH3GZCE3IOWIGMYPJOJ","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":"81c7ed0cd9f388954e8188aca938590b9a30882867ae43dcb5c0e1f5632cf6da","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-05-05T13:52:19Z","title_canon_sha256":"80262fd5f3e3c5da5a7f9b95aff0214b18b3079c190367b3c5d75efc7043993e"},"schema_version":"1.0","source":{"id":"1205.1137","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.1137","created_at":"2026-05-18T03:13:23Z"},{"alias_kind":"arxiv_version","alias_value":"1205.1137v1","created_at":"2026-05-18T03:13:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.1137","created_at":"2026-05-18T03:13:23Z"},{"alias_kind":"pith_short_12","alias_value":"NRYN7FMEH3GZ","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"NRYN7FMEH3GZCE3I","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"NRYN7FME","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:da7aa472e871c3fefdd5f53a64b8d6492e23691d9bbb446c2e582041eed18f70","target":"graph","created_at":"2026-05-18T03:13:23Z","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 generalize and strengthen the theorem of Gromov that every compact Riemannian manifold of diameter at most D has a set of generators g_1,...,g_k of length at most 2D and relators of the form g_ig_m = g_j . In particular, we obtain an explicit bound for the number k of generators in terms of the number \"short loops\" at every point and the number of balls required to cover a given semilocally simply connected geodesic space. As a consequence we obtain a fundamental group finiteness theorem (new even for Riemannian manifolds) that implies the fundamental group finiteness theorems of Anderson a","authors_text":"Conrad Plaut, Jay Wilkins","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-05-05T13:52:19Z","title":"Discrete homotopies and the fundamental group"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.1137","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:a3c63583260b804d1895c08b20645be8787b2450cb46b8a8e3870ffaf76f2bcf","target":"record","created_at":"2026-05-18T03:13:23Z","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":"81c7ed0cd9f388954e8188aca938590b9a30882867ae43dcb5c0e1f5632cf6da","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-05-05T13:52:19Z","title_canon_sha256":"80262fd5f3e3c5da5a7f9b95aff0214b18b3079c190367b3c5d75efc7043993e"},"schema_version":"1.0","source":{"id":"1205.1137","kind":"arxiv","version":1}},"canonical_sha256":"6c70df95843ecd91136875906661e97253074a5117f2458ef905ca551c38e9be","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6c70df95843ecd91136875906661e97253074a5117f2458ef905ca551c38e9be","first_computed_at":"2026-05-18T03:13:23.723731Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:13:23.723731Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nVG9beRyrelFo5fz/bFkSQp0XodZbo3N08HYEn2Hd8c7j0rdas9pgrHWWUVpqzyWroadrZQ+Af7NlZncwUgxAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:13:23.724488Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.1137","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a3c63583260b804d1895c08b20645be8787b2450cb46b8a8e3870ffaf76f2bcf","sha256:da7aa472e871c3fefdd5f53a64b8d6492e23691d9bbb446c2e582041eed18f70"],"state_sha256":"53835b0400cbc98345b9ec1220b6f890f7bad5f1e06b4afac673acb8270b9e02"}