{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:MDEF3DDRGN7WHGFCK3CRNGSHTH","short_pith_number":"pith:MDEF3DDR","canonical_record":{"source":{"id":"0904.0724","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-04-04T15:46:58Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"de560a521771850e7f6a47f21906b3078d4a7235e9d1e2745826d5b692f4274c","abstract_canon_sha256":"fc6a0350b1eaf758d5ad736be9bd4cb4908806dfdc6629156f282da5c0424ed3"},"schema_version":"1.0"},"canonical_sha256":"60c85d8c71337f6398a256c5169a4799e352b43f814ee0b20bbc47408c10a36d","source":{"kind":"arxiv","id":"0904.0724","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0904.0724","created_at":"2026-05-18T04:34:09Z"},{"alias_kind":"arxiv_version","alias_value":"0904.0724v3","created_at":"2026-05-18T04:34:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0904.0724","created_at":"2026-05-18T04:34:09Z"},{"alias_kind":"pith_short_12","alias_value":"MDEF3DDRGN7W","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"MDEF3DDRGN7WHGFC","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"MDEF3DDR","created_at":"2026-05-18T12:26:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:MDEF3DDRGN7WHGFCK3CRNGSHTH","target":"record","payload":{"canonical_record":{"source":{"id":"0904.0724","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-04-04T15:46:58Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"de560a521771850e7f6a47f21906b3078d4a7235e9d1e2745826d5b692f4274c","abstract_canon_sha256":"fc6a0350b1eaf758d5ad736be9bd4cb4908806dfdc6629156f282da5c0424ed3"},"schema_version":"1.0"},"canonical_sha256":"60c85d8c71337f6398a256c5169a4799e352b43f814ee0b20bbc47408c10a36d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:34:09.028425Z","signature_b64":"ldnWRsgAtGbuuADXolJVwFcAUTCqZsua6RITN/uPcqNxGjndLkkAHCSjPpgK6seQ/ZctnzAddqw4FvJFbFbTCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"60c85d8c71337f6398a256c5169a4799e352b43f814ee0b20bbc47408c10a36d","last_reissued_at":"2026-05-18T04:34:09.027930Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:34:09.027930Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0904.0724","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:34:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kal3tSArTdvt+PG5RdZbAgehcCu2SbgWQ9gTPrFGGb4sO38VEj6Z0gtYhSq0RNOq+zI9zocGqu3oxXDBsrOvBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T16:19:43.921637Z"},"content_sha256":"31cd1fa1201559f4acff32287239fa76ff7bab0e3f11293ef65336c872444b53","schema_version":"1.0","event_id":"sha256:31cd1fa1201559f4acff32287239fa76ff7bab0e3f11293ef65336c872444b53"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:MDEF3DDRGN7WHGFCK3CRNGSHTH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Virtually geometric words and Whitehead's algorithm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Jason Fox Manning","submitted_at":"2009-04-04T15:46:58Z","abstract_excerpt":"Motivated by a question of Gordon and Wilton, we consider the question of which collections of words are \"virtually geometric\". In particular, we prove that some words (e.g. bbaaccabc) are not virtually geometric."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.0724","kind":"arxiv","version":3},"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":"2026-05-18T04:34:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2dWVxYh/sxcDtyDEAElKEZ0A47uPuHHPIw2+vvX9ZbfXDTLaoOLsF4PbW/xbu597GlpKRH/sj0Ja/Pi5a2i5AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T16:19:43.921968Z"},"content_sha256":"6f66e6ecdb85ddf682f9b4adaaa0f9bc5221f6052a788ce8b7b8ae9dbabb8639","schema_version":"1.0","event_id":"sha256:6f66e6ecdb85ddf682f9b4adaaa0f9bc5221f6052a788ce8b7b8ae9dbabb8639"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MDEF3DDRGN7WHGFCK3CRNGSHTH/bundle.json","state_url":"https://pith.science/pith/MDEF3DDRGN7WHGFCK3CRNGSHTH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MDEF3DDRGN7WHGFCK3CRNGSHTH/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":"2026-06-23T16:19:43Z","links":{"resolver":"https://pith.science/pith/MDEF3DDRGN7WHGFCK3CRNGSHTH","bundle":"https://pith.science/pith/MDEF3DDRGN7WHGFCK3CRNGSHTH/bundle.json","state":"https://pith.science/pith/MDEF3DDRGN7WHGFCK3CRNGSHTH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MDEF3DDRGN7WHGFCK3CRNGSHTH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:MDEF3DDRGN7WHGFCK3CRNGSHTH","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":"fc6a0350b1eaf758d5ad736be9bd4cb4908806dfdc6629156f282da5c0424ed3","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-04-04T15:46:58Z","title_canon_sha256":"de560a521771850e7f6a47f21906b3078d4a7235e9d1e2745826d5b692f4274c"},"schema_version":"1.0","source":{"id":"0904.0724","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0904.0724","created_at":"2026-05-18T04:34:09Z"},{"alias_kind":"arxiv_version","alias_value":"0904.0724v3","created_at":"2026-05-18T04:34:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0904.0724","created_at":"2026-05-18T04:34:09Z"},{"alias_kind":"pith_short_12","alias_value":"MDEF3DDRGN7W","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"MDEF3DDRGN7WHGFC","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"MDEF3DDR","created_at":"2026-05-18T12:26:00Z"}],"graph_snapshots":[{"event_id":"sha256:6f66e6ecdb85ddf682f9b4adaaa0f9bc5221f6052a788ce8b7b8ae9dbabb8639","target":"graph","created_at":"2026-05-18T04:34:09Z","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":"Motivated by a question of Gordon and Wilton, we consider the question of which collections of words are \"virtually geometric\". In particular, we prove that some words (e.g. bbaaccabc) are not virtually geometric.","authors_text":"Jason Fox Manning","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-04-04T15:46:58Z","title":"Virtually geometric words and Whitehead's algorithm"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.0724","kind":"arxiv","version":3},"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":"sha256:31cd1fa1201559f4acff32287239fa76ff7bab0e3f11293ef65336c872444b53","target":"record","created_at":"2026-05-18T04:34:09Z","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":"fc6a0350b1eaf758d5ad736be9bd4cb4908806dfdc6629156f282da5c0424ed3","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-04-04T15:46:58Z","title_canon_sha256":"de560a521771850e7f6a47f21906b3078d4a7235e9d1e2745826d5b692f4274c"},"schema_version":"1.0","source":{"id":"0904.0724","kind":"arxiv","version":3}},"canonical_sha256":"60c85d8c71337f6398a256c5169a4799e352b43f814ee0b20bbc47408c10a36d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"60c85d8c71337f6398a256c5169a4799e352b43f814ee0b20bbc47408c10a36d","first_computed_at":"2026-05-18T04:34:09.027930Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:34:09.027930Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ldnWRsgAtGbuuADXolJVwFcAUTCqZsua6RITN/uPcqNxGjndLkkAHCSjPpgK6seQ/ZctnzAddqw4FvJFbFbTCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:34:09.028425Z","signed_message":"canonical_sha256_bytes"},"source_id":"0904.0724","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:31cd1fa1201559f4acff32287239fa76ff7bab0e3f11293ef65336c872444b53","sha256:6f66e6ecdb85ddf682f9b4adaaa0f9bc5221f6052a788ce8b7b8ae9dbabb8639"],"state_sha256":"0ca21acc3df2a947c7bebb5485a3e464274208b985036e0e74857fb171ffc553"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tUv6K3rEbXhEffnitbncD7zNpr8VWbFz7shPWufXe/9zaxnDK6zIIAS1xY+MpD6Zx31ZbVISIhNo424DY6w9DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T16:19:43.923910Z","bundle_sha256":"00932d2172397118062d6ee29dc66e0b2498ead1e5698aa76f89a5b9f959e98d"}}