{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:W26TS7PGTX7TKZJEK2ZGCOXH75","short_pith_number":"pith:W26TS7PG","canonical_record":{"source":{"id":"0908.1808","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-08-12T23:13:27Z","cross_cats_sorted":[],"title_canon_sha256":"62ab26f29fde94ce19c7e896fad826b97bcc92a12a013ed4836fd423fe8fd190","abstract_canon_sha256":"9778b063d91d9ffbc48fbb44b1658e2640d760df0d8be9284d6be424a21ebaa5"},"schema_version":"1.0"},"canonical_sha256":"b6bd397de69dff35652456b2613ae7ff6358339f313645c1d6186d01e05414c4","source":{"kind":"arxiv","id":"0908.1808","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0908.1808","created_at":"2026-05-18T03:40:26Z"},{"alias_kind":"arxiv_version","alias_value":"0908.1808v1","created_at":"2026-05-18T03:40:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0908.1808","created_at":"2026-05-18T03:40:26Z"},{"alias_kind":"pith_short_12","alias_value":"W26TS7PGTX7T","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"W26TS7PGTX7TKZJE","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"W26TS7PG","created_at":"2026-05-18T12:26:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:W26TS7PGTX7TKZJEK2ZGCOXH75","target":"record","payload":{"canonical_record":{"source":{"id":"0908.1808","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-08-12T23:13:27Z","cross_cats_sorted":[],"title_canon_sha256":"62ab26f29fde94ce19c7e896fad826b97bcc92a12a013ed4836fd423fe8fd190","abstract_canon_sha256":"9778b063d91d9ffbc48fbb44b1658e2640d760df0d8be9284d6be424a21ebaa5"},"schema_version":"1.0"},"canonical_sha256":"b6bd397de69dff35652456b2613ae7ff6358339f313645c1d6186d01e05414c4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:40:26.000849Z","signature_b64":"04zM1FjnjeDbqOQjbXI2l4XznZnOyLXhd0S9YlyO0d2c/MiAog9GaXJRQaHy7bh00XFZdYaTx1juqBqcMRlcBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b6bd397de69dff35652456b2613ae7ff6358339f313645c1d6186d01e05414c4","last_reissued_at":"2026-05-18T03:40:26.000013Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:40:26.000013Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0908.1808","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":"2026-05-18T03:40:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"goNXV+RBfd3Skhx7thuR/+I/uHWxJoOnI4Nh1ptFl57h0udpPVk9QpCSrcSQSE9RgcaRAdvEqtlIRO8WMM4GDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T01:56:13.290243Z"},"content_sha256":"5cdba05746e5665451272ffca091e60310c23bd4295c0920fbd13d5b1ed723dd","schema_version":"1.0","event_id":"sha256:5cdba05746e5665451272ffca091e60310c23bd4295c0920fbd13d5b1ed723dd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:W26TS7PGTX7TKZJEK2ZGCOXH75","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Parasurface groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"K. Bou-Rabee","submitted_at":"2009-08-12T23:13:27Z","abstract_excerpt":"A residually nilpotent group is \\emph{$k$-parafree} if all of its lower central series quotients match those of a free group of rank $k$. Magnus proved that $k$-parafree groups of rank $k$ are themselves free. We mimic this theory with surface groups playing the role of free groups. Our main result shows that the analog of Magnus' Theorem is false in this setting."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0908.1808","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":"2026-05-18T03:40:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FoKptRfrw3bOGR4Yqbih5uB3MH5wEDqJCfdGfh65Nw5kbWkzwHZxHGu3VO6Oh2+ULvTQpmIOLh/vnqSlvmKvCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T01:56:13.290598Z"},"content_sha256":"c11467bf726043c62ce8f2054a338c40d343e2c86d4157eabf3792e6454cf9ce","schema_version":"1.0","event_id":"sha256:c11467bf726043c62ce8f2054a338c40d343e2c86d4157eabf3792e6454cf9ce"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/W26TS7PGTX7TKZJEK2ZGCOXH75/bundle.json","state_url":"https://pith.science/pith/W26TS7PGTX7TKZJEK2ZGCOXH75/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/W26TS7PGTX7TKZJEK2ZGCOXH75/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":"2026-07-03T01:56:13Z","links":{"resolver":"https://pith.science/pith/W26TS7PGTX7TKZJEK2ZGCOXH75","bundle":"https://pith.science/pith/W26TS7PGTX7TKZJEK2ZGCOXH75/bundle.json","state":"https://pith.science/pith/W26TS7PGTX7TKZJEK2ZGCOXH75/state.json","well_known_bundle":"https://pith.science/.well-known/pith/W26TS7PGTX7TKZJEK2ZGCOXH75/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:W26TS7PGTX7TKZJEK2ZGCOXH75","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":"9778b063d91d9ffbc48fbb44b1658e2640d760df0d8be9284d6be424a21ebaa5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-08-12T23:13:27Z","title_canon_sha256":"62ab26f29fde94ce19c7e896fad826b97bcc92a12a013ed4836fd423fe8fd190"},"schema_version":"1.0","source":{"id":"0908.1808","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0908.1808","created_at":"2026-05-18T03:40:26Z"},{"alias_kind":"arxiv_version","alias_value":"0908.1808v1","created_at":"2026-05-18T03:40:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0908.1808","created_at":"2026-05-18T03:40:26Z"},{"alias_kind":"pith_short_12","alias_value":"W26TS7PGTX7T","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"W26TS7PGTX7TKZJE","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"W26TS7PG","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:c11467bf726043c62ce8f2054a338c40d343e2c86d4157eabf3792e6454cf9ce","target":"graph","created_at":"2026-05-18T03:40:26Z","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":"A residually nilpotent group is \\emph{$k$-parafree} if all of its lower central series quotients match those of a free group of rank $k$. Magnus proved that $k$-parafree groups of rank $k$ are themselves free. We mimic this theory with surface groups playing the role of free groups. Our main result shows that the analog of Magnus' Theorem is false in this setting.","authors_text":"K. Bou-Rabee","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-08-12T23:13:27Z","title":"Parasurface groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0908.1808","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":"sha256:5cdba05746e5665451272ffca091e60310c23bd4295c0920fbd13d5b1ed723dd","target":"record","created_at":"2026-05-18T03:40:26Z","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":"9778b063d91d9ffbc48fbb44b1658e2640d760df0d8be9284d6be424a21ebaa5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-08-12T23:13:27Z","title_canon_sha256":"62ab26f29fde94ce19c7e896fad826b97bcc92a12a013ed4836fd423fe8fd190"},"schema_version":"1.0","source":{"id":"0908.1808","kind":"arxiv","version":1}},"canonical_sha256":"b6bd397de69dff35652456b2613ae7ff6358339f313645c1d6186d01e05414c4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b6bd397de69dff35652456b2613ae7ff6358339f313645c1d6186d01e05414c4","first_computed_at":"2026-05-18T03:40:26.000013Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:40:26.000013Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"04zM1FjnjeDbqOQjbXI2l4XznZnOyLXhd0S9YlyO0d2c/MiAog9GaXJRQaHy7bh00XFZdYaTx1juqBqcMRlcBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:40:26.000849Z","signed_message":"canonical_sha256_bytes"},"source_id":"0908.1808","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5cdba05746e5665451272ffca091e60310c23bd4295c0920fbd13d5b1ed723dd","sha256:c11467bf726043c62ce8f2054a338c40d343e2c86d4157eabf3792e6454cf9ce"],"state_sha256":"edd75e264feee0504989aceed71390b0e0b620f889d4c430d1ac7a9601a7138c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dtoVO0t1/WxtKjpZRC7VOB/mnCe0j7VMWcV5AhzmUtGbZbnFY/t38gxFn/9MH8iHUPHW+VcHem9D161I72gfAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T01:56:13.292439Z","bundle_sha256":"cdeef51823fe436ea402574e62646d3d1d093148f5e3dad84f26d978bf5f179a"}}