{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:N7JYZEGBL65IQLAHQOSPRBWGQV","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":"3c87c3254a563f5f84a249682d9b291e99973d7bd4aa397353f5a3afbc5904c9","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-01-14T20:57:31Z","title_canon_sha256":"120f20f6464b83b94be95e7c051bc8629b50b9c50a4180774bfc2ebf15d1fcc8"},"schema_version":"1.0","source":{"id":"1501.03489","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.03489","created_at":"2026-05-18T02:29:23Z"},{"alias_kind":"arxiv_version","alias_value":"1501.03489v1","created_at":"2026-05-18T02:29:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.03489","created_at":"2026-05-18T02:29:23Z"},{"alias_kind":"pith_short_12","alias_value":"N7JYZEGBL65I","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"N7JYZEGBL65IQLAH","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"N7JYZEGB","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:3eac1f3c2c775595df3c34c2b7f1e7064941f67ec39e428601638464a9b84dc6","target":"graph","created_at":"2026-05-18T02:29:23Z","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 use Fox calculus to assign a marked polytope to a `nice' group presentation with two generators and one relator. Relating the marked vertices to Novikov-Sikorav homology we show that they determine the Bieri-Neumann-Strebel invariant of the group. Furthermore we show that in many cases the marked polytope is an invariant of the underlying group and that in those cases the marked polytope also determines the minimal complexity of all the associated HNN-splittings.","authors_text":"Stefan Friedl, Stephan Tillmann","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-01-14T20:57:31Z","title":"Two-generator one-relator groups and marked polytopes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.03489","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":"sha256:45852fd4ecdc3fc532cd3bc722152158559ca0b94136db0c491ddc37a9aea6f9","target":"record","created_at":"2026-05-18T02:29:23Z","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":"3c87c3254a563f5f84a249682d9b291e99973d7bd4aa397353f5a3afbc5904c9","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-01-14T20:57:31Z","title_canon_sha256":"120f20f6464b83b94be95e7c051bc8629b50b9c50a4180774bfc2ebf15d1fcc8"},"schema_version":"1.0","source":{"id":"1501.03489","kind":"arxiv","version":1}},"canonical_sha256":"6fd38c90c15fba882c0783a4f886c685759c96582fe680ec75ebea1ef36e08f4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6fd38c90c15fba882c0783a4f886c685759c96582fe680ec75ebea1ef36e08f4","first_computed_at":"2026-05-18T02:29:23.921430Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:29:23.921430Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RdwFSUGvHqGyjwL9vQw2er4IL7FhyRZt3tIrs3X7e0re+H5aaFbX57L8jdzz//xWA0LmkafBtibxNyf1WIdQCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:29:23.921836Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.03489","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:45852fd4ecdc3fc532cd3bc722152158559ca0b94136db0c491ddc37a9aea6f9","sha256:3eac1f3c2c775595df3c34c2b7f1e7064941f67ec39e428601638464a9b84dc6"],"state_sha256":"a7991f951caf78c4a94767092da870b1d03d3f9f7337537b5f2077a3847802c4"}