{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:5DCRAMDW47VHASQRSAYVGYT5SW","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":"e777b8482be115d70ae9cc9b586e0c9d33826319e0ba9151dd7e777a303c8e14","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-09-28T19:37:28Z","title_canon_sha256":"a9970074d68bb845fb869f39353d88337d619434bc619f29a4bb94ccd51d3050"},"schema_version":"1.0","source":{"id":"1109.6309","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.6309","created_at":"2026-05-18T04:05:27Z"},{"alias_kind":"arxiv_version","alias_value":"1109.6309v2","created_at":"2026-05-18T04:05:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.6309","created_at":"2026-05-18T04:05:27Z"},{"alias_kind":"pith_short_12","alias_value":"5DCRAMDW47VH","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"5DCRAMDW47VHASQR","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"5DCRAMDW","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:82bd9ce1d33af8de8fa1fe94edfd2cbdd14be3602cba06563ba9b8986d12366c","target":"graph","created_at":"2026-05-18T04:05:27Z","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"},"paper":{"abstract_excerpt":"We introduce a combinatorial property for finitely generated groups called stackable that implies the existence of an inductive procedure for constructing van Kampen diagrams with respect to a canonical finite presentation. We also define algorithmically stackable groups, for which this procedure is an effective algorithm. This property gives a common model for algorithms arising from both rewriting systems and almost convexity for groups.\n  We also introduce a new pair of asymptotic invariants that are filling inequalities refining the notions of intrinsic and extrinsic diameter inequalities ","authors_text":"Mark Brittenham, Susan Hermiller","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-09-28T19:37:28Z","title":"Stackable groups, tame filling invariants, and algorithmic properties of groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.6309","kind":"arxiv","version":2},"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:fcae480f3b76d62d7a9efe8c55129b8e0693d89dc8207f02a6d61fe1c37e49ef","target":"record","created_at":"2026-05-18T04:05:27Z","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":"e777b8482be115d70ae9cc9b586e0c9d33826319e0ba9151dd7e777a303c8e14","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-09-28T19:37:28Z","title_canon_sha256":"a9970074d68bb845fb869f39353d88337d619434bc619f29a4bb94ccd51d3050"},"schema_version":"1.0","source":{"id":"1109.6309","kind":"arxiv","version":2}},"canonical_sha256":"e8c5103076e7ea704a11903153627d95bdd3eb0bd1b0ec6a88069d63ceb5e677","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e8c5103076e7ea704a11903153627d95bdd3eb0bd1b0ec6a88069d63ceb5e677","first_computed_at":"2026-05-18T04:05:27.007509Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:05:27.007509Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IZe0805lPlPx7jUrAahNzkLC1S8m9A2f3p19NtX8X5dIFr+3e7tDHg2fWX5fL5CZf7WjF14iTSi+/oke1YkHAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:05:27.008505Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.6309","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fcae480f3b76d62d7a9efe8c55129b8e0693d89dc8207f02a6d61fe1c37e49ef","sha256:82bd9ce1d33af8de8fa1fe94edfd2cbdd14be3602cba06563ba9b8986d12366c"],"state_sha256":"f4ec3d40be97d413bf420ba8d2fe567476a1b04c0b5e3b59933c9ced048e6a93"}