{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:KAY3ZESWKUKRCNK2YJGJVE5OXH","short_pith_number":"pith:KAY3ZESW","canonical_record":{"source":{"id":"1904.08343","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-04-17T16:12:54Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"6070b31bcc9d87f892015ef8733f7cd6cac7c5ea849b1cd5bee714cf40251a9b","abstract_canon_sha256":"720f9e5e38bf02d9f697d33e13f38e130d38d1c3eefb271571a673d1f16275a5"},"schema_version":"1.0"},"canonical_sha256":"5031bc9256551511355ac24c9a93aeb9f5b9f0796f9971115198a77a138a7ca9","source":{"kind":"arxiv","id":"1904.08343","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.08343","created_at":"2026-05-17T23:48:17Z"},{"alias_kind":"arxiv_version","alias_value":"1904.08343v1","created_at":"2026-05-17T23:48:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.08343","created_at":"2026-05-17T23:48:17Z"},{"alias_kind":"pith_short_12","alias_value":"KAY3ZESWKUKR","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"KAY3ZESWKUKRCNK2","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"KAY3ZESW","created_at":"2026-05-18T12:33:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:KAY3ZESWKUKRCNK2YJGJVE5OXH","target":"record","payload":{"canonical_record":{"source":{"id":"1904.08343","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-04-17T16:12:54Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"6070b31bcc9d87f892015ef8733f7cd6cac7c5ea849b1cd5bee714cf40251a9b","abstract_canon_sha256":"720f9e5e38bf02d9f697d33e13f38e130d38d1c3eefb271571a673d1f16275a5"},"schema_version":"1.0"},"canonical_sha256":"5031bc9256551511355ac24c9a93aeb9f5b9f0796f9971115198a77a138a7ca9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:48:17.981300Z","signature_b64":"C1Gi2q2mFm5glaCEqHah3kOCKUf2YFNW8u4Nyf6z/tTpUgoTWSJEDW9/2V6Cad/zcv/gyp76ZIAJOKnX7QIcCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5031bc9256551511355ac24c9a93aeb9f5b9f0796f9971115198a77a138a7ca9","last_reissued_at":"2026-05-17T23:48:17.980753Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:48:17.980753Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1904.08343","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":"2026-05-17T23:48:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PiyOdgSrfDUGY4Bmob+s1h4rYhamE6yyoMowbTgHW9eT2ZcTdvE3DvwbeBa/EhO7Az8JQV0bRZkv/mAsNgAmBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T04:06:07.710644Z"},"content_sha256":"9542660596edcb1ec9918ea4607e525d9e95ef56a02fbe192bec9e6ffce363a2","schema_version":"1.0","event_id":"sha256:9542660596edcb1ec9918ea4607e525d9e95ef56a02fbe192bec9e6ffce363a2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:KAY3ZESWKUKRCNK2YJGJVE5OXH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The power word problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"math.GR","authors_text":"Armin Wei{\\ss}, Markus Lohrey","submitted_at":"2019-04-17T16:12:54Z","abstract_excerpt":"In this work we introduce a new succinct variant of the word problem in a finitely generated group $G$, which we call the power word problem: the input word may contain powers $p^x$, where $p$ is a finite word over generators of $G$ and $x$ is a binary encoded integer. The power word problem is a restriction of the compressed word problem, where the input word is represented by a straight-line program (i.e., an algebraic circuit over $G$). The main result of the paper states that the power word problem for a finitely generated free group $F$ is AC$^0$-Turing-reducible to the word problem for $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.08343","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":"2026-05-17T23:48:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ylPdahncNUuHr51p2yrC1+yVFncD5l5EX2YzTCHAE/nL2hb5QBMTfo1FQnuoaSOfDS0gQKtUEa+KSPnQo97pDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T04:06:07.711007Z"},"content_sha256":"2bd32754130fe8aca64b4e55b4bd6a00adccbf4a2c85328b725aa400d5bd9389","schema_version":"1.0","event_id":"sha256:2bd32754130fe8aca64b4e55b4bd6a00adccbf4a2c85328b725aa400d5bd9389"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KAY3ZESWKUKRCNK2YJGJVE5OXH/bundle.json","state_url":"https://pith.science/pith/KAY3ZESWKUKRCNK2YJGJVE5OXH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KAY3ZESWKUKRCNK2YJGJVE5OXH/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":"2026-05-27T04:06:07Z","links":{"resolver":"https://pith.science/pith/KAY3ZESWKUKRCNK2YJGJVE5OXH","bundle":"https://pith.science/pith/KAY3ZESWKUKRCNK2YJGJVE5OXH/bundle.json","state":"https://pith.science/pith/KAY3ZESWKUKRCNK2YJGJVE5OXH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KAY3ZESWKUKRCNK2YJGJVE5OXH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:KAY3ZESWKUKRCNK2YJGJVE5OXH","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":"720f9e5e38bf02d9f697d33e13f38e130d38d1c3eefb271571a673d1f16275a5","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-04-17T16:12:54Z","title_canon_sha256":"6070b31bcc9d87f892015ef8733f7cd6cac7c5ea849b1cd5bee714cf40251a9b"},"schema_version":"1.0","source":{"id":"1904.08343","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.08343","created_at":"2026-05-17T23:48:17Z"},{"alias_kind":"arxiv_version","alias_value":"1904.08343v1","created_at":"2026-05-17T23:48:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.08343","created_at":"2026-05-17T23:48:17Z"},{"alias_kind":"pith_short_12","alias_value":"KAY3ZESWKUKR","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"KAY3ZESWKUKRCNK2","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"KAY3ZESW","created_at":"2026-05-18T12:33:21Z"}],"graph_snapshots":[{"event_id":"sha256:2bd32754130fe8aca64b4e55b4bd6a00adccbf4a2c85328b725aa400d5bd9389","target":"graph","created_at":"2026-05-17T23:48:17Z","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 this work we introduce a new succinct variant of the word problem in a finitely generated group $G$, which we call the power word problem: the input word may contain powers $p^x$, where $p$ is a finite word over generators of $G$ and $x$ is a binary encoded integer. The power word problem is a restriction of the compressed word problem, where the input word is represented by a straight-line program (i.e., an algebraic circuit over $G$). The main result of the paper states that the power word problem for a finitely generated free group $F$ is AC$^0$-Turing-reducible to the word problem for $","authors_text":"Armin Wei{\\ss}, Markus Lohrey","cross_cats":["cs.CC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-04-17T16:12:54Z","title":"The power word problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.08343","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":"sha256:9542660596edcb1ec9918ea4607e525d9e95ef56a02fbe192bec9e6ffce363a2","target":"record","created_at":"2026-05-17T23:48:17Z","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":"720f9e5e38bf02d9f697d33e13f38e130d38d1c3eefb271571a673d1f16275a5","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-04-17T16:12:54Z","title_canon_sha256":"6070b31bcc9d87f892015ef8733f7cd6cac7c5ea849b1cd5bee714cf40251a9b"},"schema_version":"1.0","source":{"id":"1904.08343","kind":"arxiv","version":1}},"canonical_sha256":"5031bc9256551511355ac24c9a93aeb9f5b9f0796f9971115198a77a138a7ca9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5031bc9256551511355ac24c9a93aeb9f5b9f0796f9971115198a77a138a7ca9","first_computed_at":"2026-05-17T23:48:17.980753Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:48:17.980753Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"C1Gi2q2mFm5glaCEqHah3kOCKUf2YFNW8u4Nyf6z/tTpUgoTWSJEDW9/2V6Cad/zcv/gyp76ZIAJOKnX7QIcCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:48:17.981300Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.08343","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9542660596edcb1ec9918ea4607e525d9e95ef56a02fbe192bec9e6ffce363a2","sha256:2bd32754130fe8aca64b4e55b4bd6a00adccbf4a2c85328b725aa400d5bd9389"],"state_sha256":"610b77efe70fa60901c820bf3e68e446880f7ac157c08051ede22f5fd2c81b57"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z0XCD/phWAqCXyJXprBYN3/C6MT9GUB9fHG7lDL62udZl+oznGLf3feKngevgZcRCfioCo0OANJP/zr1mnbdBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T04:06:07.713729Z","bundle_sha256":"2a787bfb063d6520f1fd6e27a7f9520ccfa311ef20a1767f8e9f71bb88ca41d6"}}