{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:JIGN73VOGSYT2MTFKOKCLYWFSE","short_pith_number":"pith:JIGN73VO","canonical_record":{"source":{"id":"1903.07040","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-03-17T07:42:03Z","cross_cats_sorted":["math.DS","math.GT"],"title_canon_sha256":"8fccd12505c1a4e83818af5c9bf454250fbb708b3dbf732ead9a1641285d2c55","abstract_canon_sha256":"57246780c1c6fa7270b95ab413df8fd4c0448bf38637bc35e8851203d21b7c67"},"schema_version":"1.0"},"canonical_sha256":"4a0cdfeeae34b13d3265539425e2c59121e2b2f0b889b0834f6f3268a5788cd5","source":{"kind":"arxiv","id":"1903.07040","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.07040","created_at":"2026-05-17T23:50:44Z"},{"alias_kind":"arxiv_version","alias_value":"1903.07040v2","created_at":"2026-05-17T23:50:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.07040","created_at":"2026-05-17T23:50:44Z"},{"alias_kind":"pith_short_12","alias_value":"JIGN73VOGSYT","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"JIGN73VOGSYT2MTF","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"JIGN73VO","created_at":"2026-05-18T12:33:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:JIGN73VOGSYT2MTFKOKCLYWFSE","target":"record","payload":{"canonical_record":{"source":{"id":"1903.07040","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-03-17T07:42:03Z","cross_cats_sorted":["math.DS","math.GT"],"title_canon_sha256":"8fccd12505c1a4e83818af5c9bf454250fbb708b3dbf732ead9a1641285d2c55","abstract_canon_sha256":"57246780c1c6fa7270b95ab413df8fd4c0448bf38637bc35e8851203d21b7c67"},"schema_version":"1.0"},"canonical_sha256":"4a0cdfeeae34b13d3265539425e2c59121e2b2f0b889b0834f6f3268a5788cd5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:44.384593Z","signature_b64":"LCAxxXk8SK8hfcNPpriSaVJZd7VZ7YPG4/krnT3sJTo3fYchgUdBY4Owbv5GhvmF65OnxKk1bwtFPxAF0EfAAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4a0cdfeeae34b13d3265539425e2c59121e2b2f0b889b0834f6f3268a5788cd5","last_reissued_at":"2026-05-17T23:50:44.383881Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:44.383881Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1903.07040","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:50:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kf8vjc8TaYlrNgKvh2AYvXnixw4oMeosg4xi/Sg8WaU6wsrGuvYbSKjn2N3sMvWRjFyErkheQ4jEbk2fEKo4Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T02:31:37.062111Z"},"content_sha256":"91b44eeea3caa9fa4c23d72f4052b54f13e84141c9065153959897fd84e0e36a","schema_version":"1.0","event_id":"sha256:91b44eeea3caa9fa4c23d72f4052b54f13e84141c9065153959897fd84e0e36a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:JIGN73VOGSYT2MTFKOKCLYWFSE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generic-case complexity of Whitehead's algorithm, revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.GT"],"primary_cat":"math.GR","authors_text":"Ilya Kapovich","submitted_at":"2019-03-17T07:42:03Z","abstract_excerpt":"In \\cite{KSS06} it was shown that with respect to the simple non-backtracking random walk on the free group $F_N=F(a_1,\\dots,a_N)$ the Whitehead algorithm has strongly linear time generic-case complexity and that \"generic\" elements of $F_N$ are \"strictly minimal\" in their $Out(F_N)$-orbits. Here we generalize these results, with appropriate modifications, to a much wider class of random processes generating elements of $F_N$. We introduce the notion of a ''$(M,\\lambda, \\epsilon)$-minimal\" conjugacy class $[w]$ in $F_N$, where $M\\ge 1, \\lambda>1$ and $0<\\epsilon<1$. Roughly, being $(M,\\lambda, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.07040","kind":"arxiv","version":2},"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":"2026-05-17T23:50:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TSw+9SIMcISwX7No0Ld6zx3FlAGTJpctORFYaFaLsjshk9e0fbKF9bgKdynxUor4/b7bV8mlF5OkNZzyMMLKBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T02:31:37.063047Z"},"content_sha256":"d72eff759e464a4bf75368fd430de7aac2065d408d668af75169a39b47d3de9c","schema_version":"1.0","event_id":"sha256:d72eff759e464a4bf75368fd430de7aac2065d408d668af75169a39b47d3de9c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JIGN73VOGSYT2MTFKOKCLYWFSE/bundle.json","state_url":"https://pith.science/pith/JIGN73VOGSYT2MTFKOKCLYWFSE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JIGN73VOGSYT2MTFKOKCLYWFSE/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":"2026-06-01T02:31:37Z","links":{"resolver":"https://pith.science/pith/JIGN73VOGSYT2MTFKOKCLYWFSE","bundle":"https://pith.science/pith/JIGN73VOGSYT2MTFKOKCLYWFSE/bundle.json","state":"https://pith.science/pith/JIGN73VOGSYT2MTFKOKCLYWFSE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JIGN73VOGSYT2MTFKOKCLYWFSE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:JIGN73VOGSYT2MTFKOKCLYWFSE","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":"57246780c1c6fa7270b95ab413df8fd4c0448bf38637bc35e8851203d21b7c67","cross_cats_sorted":["math.DS","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-03-17T07:42:03Z","title_canon_sha256":"8fccd12505c1a4e83818af5c9bf454250fbb708b3dbf732ead9a1641285d2c55"},"schema_version":"1.0","source":{"id":"1903.07040","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.07040","created_at":"2026-05-17T23:50:44Z"},{"alias_kind":"arxiv_version","alias_value":"1903.07040v2","created_at":"2026-05-17T23:50:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.07040","created_at":"2026-05-17T23:50:44Z"},{"alias_kind":"pith_short_12","alias_value":"JIGN73VOGSYT","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"JIGN73VOGSYT2MTF","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"JIGN73VO","created_at":"2026-05-18T12:33:21Z"}],"graph_snapshots":[{"event_id":"sha256:d72eff759e464a4bf75368fd430de7aac2065d408d668af75169a39b47d3de9c","target":"graph","created_at":"2026-05-17T23:50:44Z","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":"In \\cite{KSS06} it was shown that with respect to the simple non-backtracking random walk on the free group $F_N=F(a_1,\\dots,a_N)$ the Whitehead algorithm has strongly linear time generic-case complexity and that \"generic\" elements of $F_N$ are \"strictly minimal\" in their $Out(F_N)$-orbits. Here we generalize these results, with appropriate modifications, to a much wider class of random processes generating elements of $F_N$. We introduce the notion of a ''$(M,\\lambda, \\epsilon)$-minimal\" conjugacy class $[w]$ in $F_N$, where $M\\ge 1, \\lambda>1$ and $0<\\epsilon<1$. Roughly, being $(M,\\lambda, ","authors_text":"Ilya Kapovich","cross_cats":["math.DS","math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-03-17T07:42:03Z","title":"Generic-case complexity of Whitehead's algorithm, revisited"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.07040","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":"sha256:91b44eeea3caa9fa4c23d72f4052b54f13e84141c9065153959897fd84e0e36a","target":"record","created_at":"2026-05-17T23:50:44Z","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":"57246780c1c6fa7270b95ab413df8fd4c0448bf38637bc35e8851203d21b7c67","cross_cats_sorted":["math.DS","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-03-17T07:42:03Z","title_canon_sha256":"8fccd12505c1a4e83818af5c9bf454250fbb708b3dbf732ead9a1641285d2c55"},"schema_version":"1.0","source":{"id":"1903.07040","kind":"arxiv","version":2}},"canonical_sha256":"4a0cdfeeae34b13d3265539425e2c59121e2b2f0b889b0834f6f3268a5788cd5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4a0cdfeeae34b13d3265539425e2c59121e2b2f0b889b0834f6f3268a5788cd5","first_computed_at":"2026-05-17T23:50:44.383881Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:50:44.383881Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LCAxxXk8SK8hfcNPpriSaVJZd7VZ7YPG4/krnT3sJTo3fYchgUdBY4Owbv5GhvmF65OnxKk1bwtFPxAF0EfAAw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:50:44.384593Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.07040","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:91b44eeea3caa9fa4c23d72f4052b54f13e84141c9065153959897fd84e0e36a","sha256:d72eff759e464a4bf75368fd430de7aac2065d408d668af75169a39b47d3de9c"],"state_sha256":"39a7896a0c14f673f3c2c001242f280e659c1f8d190e80adc982ddcb22378edf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"veqNDPK+wDjaSM5tq75KwAWtWtFRPDH9vkrzJrtGxWyc3LeDk/OGguip7ziTKwG/hLalDfi+FJfLlIrNcS3BBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T02:31:37.067891Z","bundle_sha256":"740b1eafa7b65e50f2b8d41f68b650ce7e3bd8374dfc0899c79cffd85cb94da8"}}