{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:AU26XZG6D2OUCYC3Y2ZNESVC3E","short_pith_number":"pith:AU26XZG6","canonical_record":{"source":{"id":"1410.2342","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-10-09T03:04:25Z","cross_cats_sorted":[],"title_canon_sha256":"cf203c6d1e1dc3884c0986338d41ce592c11583f8a32339235dcbf8936425bda","abstract_canon_sha256":"de28e7fe72686e2bd31dad1c5e92f1b848534f534b46d65ecdd53f920ac773d4"},"schema_version":"1.0"},"canonical_sha256":"0535ebe4de1e9d41605bc6b2d24aa2d93511eb2e5cc7e2701114e265ab96e83f","source":{"kind":"arxiv","id":"1410.2342","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.2342","created_at":"2026-05-18T02:40:46Z"},{"alias_kind":"arxiv_version","alias_value":"1410.2342v1","created_at":"2026-05-18T02:40:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.2342","created_at":"2026-05-18T02:40:46Z"},{"alias_kind":"pith_short_12","alias_value":"AU26XZG6D2OU","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"AU26XZG6D2OUCYC3","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"AU26XZG6","created_at":"2026-05-18T12:28:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:AU26XZG6D2OUCYC3Y2ZNESVC3E","target":"record","payload":{"canonical_record":{"source":{"id":"1410.2342","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-10-09T03:04:25Z","cross_cats_sorted":[],"title_canon_sha256":"cf203c6d1e1dc3884c0986338d41ce592c11583f8a32339235dcbf8936425bda","abstract_canon_sha256":"de28e7fe72686e2bd31dad1c5e92f1b848534f534b46d65ecdd53f920ac773d4"},"schema_version":"1.0"},"canonical_sha256":"0535ebe4de1e9d41605bc6b2d24aa2d93511eb2e5cc7e2701114e265ab96e83f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:40:46.629895Z","signature_b64":"p9RpZrYjYJTUhDra0fVftFNHf9h8W3Jh9zZA/KBRdIJ9jJ0NKJSIU9G1hlZRpr4blZpekfS3HBpjJ2CixjUFBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0535ebe4de1e9d41605bc6b2d24aa2d93511eb2e5cc7e2701114e265ab96e83f","last_reissued_at":"2026-05-18T02:40:46.629398Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:40:46.629398Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1410.2342","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:40:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JTjU0xFcRpI5MFA6YXyG6YNBWMjI7bd/MFYuSZtR7XUiiXO034eZkKfpzcBYxrD9tLoBmObGTQd/GVqzd93XAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T21:28:30.535950Z"},"content_sha256":"667adb8fe30c9905d7dfb0d477e22f39d4436358d04c6e700d2d661ed0441283","schema_version":"1.0","event_id":"sha256:667adb8fe30c9905d7dfb0d477e22f39d4436358d04c6e700d2d661ed0441283"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:AU26XZG6D2OUCYC3Y2ZNESVC3E","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A uniform model for almost convexity and rewriting systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Mark Brittenham, Susan Hermiller","submitted_at":"2014-10-09T03:04:25Z","abstract_excerpt":"We introduce a topological property for finitely generated groups called stackable that implies the existence of an inductive procedure for constructing van Kampen diagrams with respect to a particular finite presentation. We also define algorithmically stackable groups, for which this procedure is an algorithm. This property gives a common model for algorithms arising from both rewriting systems and almost convexity for groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.2342","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":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:40:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eFQzgwlP8BUJCWhmOvg4T8C21TNqjQmZRYG1vmz1WIAdWJ75Xbs9YphGfcBagJlCHi3DOWG/rlLaPV8XTE7zBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T21:28:30.536380Z"},"content_sha256":"aa6735cc1c8c7c04c457618af30bbb9781fd6f64c8a78a6057fdeb12cc6b7fb0","schema_version":"1.0","event_id":"sha256:aa6735cc1c8c7c04c457618af30bbb9781fd6f64c8a78a6057fdeb12cc6b7fb0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AU26XZG6D2OUCYC3Y2ZNESVC3E/bundle.json","state_url":"https://pith.science/pith/AU26XZG6D2OUCYC3Y2ZNESVC3E/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AU26XZG6D2OUCYC3Y2ZNESVC3E/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-05T21:28:30Z","links":{"resolver":"https://pith.science/pith/AU26XZG6D2OUCYC3Y2ZNESVC3E","bundle":"https://pith.science/pith/AU26XZG6D2OUCYC3Y2ZNESVC3E/bundle.json","state":"https://pith.science/pith/AU26XZG6D2OUCYC3Y2ZNESVC3E/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AU26XZG6D2OUCYC3Y2ZNESVC3E/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:AU26XZG6D2OUCYC3Y2ZNESVC3E","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":"de28e7fe72686e2bd31dad1c5e92f1b848534f534b46d65ecdd53f920ac773d4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-10-09T03:04:25Z","title_canon_sha256":"cf203c6d1e1dc3884c0986338d41ce592c11583f8a32339235dcbf8936425bda"},"schema_version":"1.0","source":{"id":"1410.2342","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.2342","created_at":"2026-05-18T02:40:46Z"},{"alias_kind":"arxiv_version","alias_value":"1410.2342v1","created_at":"2026-05-18T02:40:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.2342","created_at":"2026-05-18T02:40:46Z"},{"alias_kind":"pith_short_12","alias_value":"AU26XZG6D2OU","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"AU26XZG6D2OUCYC3","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"AU26XZG6","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:aa6735cc1c8c7c04c457618af30bbb9781fd6f64c8a78a6057fdeb12cc6b7fb0","target":"graph","created_at":"2026-05-18T02:40:46Z","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 topological property for finitely generated groups called stackable that implies the existence of an inductive procedure for constructing van Kampen diagrams with respect to a particular finite presentation. We also define algorithmically stackable groups, for which this procedure is an algorithm. This property gives a common model for algorithms arising from both rewriting systems and almost convexity for groups.","authors_text":"Mark Brittenham, Susan Hermiller","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-10-09T03:04:25Z","title":"A uniform model for almost convexity and rewriting systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.2342","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":"sha256:667adb8fe30c9905d7dfb0d477e22f39d4436358d04c6e700d2d661ed0441283","target":"record","created_at":"2026-05-18T02:40:46Z","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":"de28e7fe72686e2bd31dad1c5e92f1b848534f534b46d65ecdd53f920ac773d4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-10-09T03:04:25Z","title_canon_sha256":"cf203c6d1e1dc3884c0986338d41ce592c11583f8a32339235dcbf8936425bda"},"schema_version":"1.0","source":{"id":"1410.2342","kind":"arxiv","version":1}},"canonical_sha256":"0535ebe4de1e9d41605bc6b2d24aa2d93511eb2e5cc7e2701114e265ab96e83f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0535ebe4de1e9d41605bc6b2d24aa2d93511eb2e5cc7e2701114e265ab96e83f","first_computed_at":"2026-05-18T02:40:46.629398Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:40:46.629398Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"p9RpZrYjYJTUhDra0fVftFNHf9h8W3Jh9zZA/KBRdIJ9jJ0NKJSIU9G1hlZRpr4blZpekfS3HBpjJ2CixjUFBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:40:46.629895Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.2342","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:667adb8fe30c9905d7dfb0d477e22f39d4436358d04c6e700d2d661ed0441283","sha256:aa6735cc1c8c7c04c457618af30bbb9781fd6f64c8a78a6057fdeb12cc6b7fb0"],"state_sha256":"dffefbb609b7c2262b2abac545809150e3a5692777e25d5a7d501884382b6d8d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ezpy8Ghe3BpKg2pRVr1oY6xNpMBA7tNwaaNA8bv9PPKET8mFbfAzu+vuQzklS1J7wEsK5Yksxs9haCrzcWysDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T21:28:30.539282Z","bundle_sha256":"35399826f77c7ae9fa844f2d40a4c08445cae6632af60b34c05a4fbf55dfc69f"}}