{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:KFVSE4UYQG6GUXUPMOLKMFXNA3","short_pith_number":"pith:KFVSE4UY","canonical_record":{"source":{"id":"1708.00477","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-08-01T19:09:48Z","cross_cats_sorted":[],"title_canon_sha256":"37422534028386aa84efb89ec3262d23c04fb2698b47818dde1aa6f72bfa4c1a","abstract_canon_sha256":"c8ea9d17a24bb1da1ef4f76adcfcf2837afbb53f3952383bb6d421429ea1508e"},"schema_version":"1.0"},"canonical_sha256":"516b22729881bc6a5e8f6396a616ed06db45e2c0e442bd035cf533d22b367be6","source":{"kind":"arxiv","id":"1708.00477","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.00477","created_at":"2026-05-18T00:38:45Z"},{"alias_kind":"arxiv_version","alias_value":"1708.00477v1","created_at":"2026-05-18T00:38:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.00477","created_at":"2026-05-18T00:38:45Z"},{"alias_kind":"pith_short_12","alias_value":"KFVSE4UYQG6G","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"KFVSE4UYQG6GUXUP","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"KFVSE4UY","created_at":"2026-05-18T12:31:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:KFVSE4UYQG6GUXUPMOLKMFXNA3","target":"record","payload":{"canonical_record":{"source":{"id":"1708.00477","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-08-01T19:09:48Z","cross_cats_sorted":[],"title_canon_sha256":"37422534028386aa84efb89ec3262d23c04fb2698b47818dde1aa6f72bfa4c1a","abstract_canon_sha256":"c8ea9d17a24bb1da1ef4f76adcfcf2837afbb53f3952383bb6d421429ea1508e"},"schema_version":"1.0"},"canonical_sha256":"516b22729881bc6a5e8f6396a616ed06db45e2c0e442bd035cf533d22b367be6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:38:45.643948Z","signature_b64":"MrME1AASV/4ECopmTtPBAjuXznHdaUTgXv8RSvEUipBc3DyD+3nTjtO4mesmozTijoiL5DUI3WxRDO/K/EHKDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"516b22729881bc6a5e8f6396a616ed06db45e2c0e442bd035cf533d22b367be6","last_reissued_at":"2026-05-18T00:38:45.643395Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:38:45.643395Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1708.00477","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":"2026-05-18T00:38:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iwfeQGqHjME4lgTyMvvkEeznxafGv/yDcF6U2rFAuAiaPjmYtCduplp3WA9yz653pqKjbHY6N31pnjL73WnuDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T03:16:56.719075Z"},"content_sha256":"d139df3c0455bba93ee5149d95b0aa6cc8d061ebd6d7f820828994cccb16d097","schema_version":"1.0","event_id":"sha256:d139df3c0455bba93ee5149d95b0aa6cc8d061ebd6d7f820828994cccb16d097"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:KFVSE4UYQG6GUXUPMOLKMFXNA3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Approximability of word maps by homomorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Alexander Bors","submitted_at":"2017-08-01T19:09:48Z","abstract_excerpt":"Generalizing a recent result of Mann, we show that there is an explicit function $f:\\left(0,1\\right]\\rightarrow\\left(0,1\\right]$ such that for every reduced word $w$, say in $d$ variables, there is an explicit reduced word $v$ in at most $3d$ variables (nontrivial if the length of $w$ is at least $2$) such that for all $\\rho\\in\\left(0,1\\right]$, the following holds: If $G$ is any finite group for which the word map $w_G:G^d\\rightarrow G$ agrees with some fixed homomorphism $G^d\\rightarrow G$ on at least $\\rho|G|^d$ many arguments, then the word map $v_G:G^{3d}\\rightarrow G$ has a fiber of size"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.00477","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":"2026-05-18T00:38:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o4i879fExQwsLcVa+hzRUqIRO9VirfOczHIouCjQji23WJziUg54/s+iKw8ay5NFG3YGKsLzZiFBkFPQ8xKNBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T03:16:56.719739Z"},"content_sha256":"cfcd30407fbb60e9bad712204c15e23cbcc938e5f475964c68d61a2183172638","schema_version":"1.0","event_id":"sha256:cfcd30407fbb60e9bad712204c15e23cbcc938e5f475964c68d61a2183172638"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KFVSE4UYQG6GUXUPMOLKMFXNA3/bundle.json","state_url":"https://pith.science/pith/KFVSE4UYQG6GUXUPMOLKMFXNA3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KFVSE4UYQG6GUXUPMOLKMFXNA3/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":"2026-05-31T03:16:56Z","links":{"resolver":"https://pith.science/pith/KFVSE4UYQG6GUXUPMOLKMFXNA3","bundle":"https://pith.science/pith/KFVSE4UYQG6GUXUPMOLKMFXNA3/bundle.json","state":"https://pith.science/pith/KFVSE4UYQG6GUXUPMOLKMFXNA3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KFVSE4UYQG6GUXUPMOLKMFXNA3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:KFVSE4UYQG6GUXUPMOLKMFXNA3","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":"c8ea9d17a24bb1da1ef4f76adcfcf2837afbb53f3952383bb6d421429ea1508e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-08-01T19:09:48Z","title_canon_sha256":"37422534028386aa84efb89ec3262d23c04fb2698b47818dde1aa6f72bfa4c1a"},"schema_version":"1.0","source":{"id":"1708.00477","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.00477","created_at":"2026-05-18T00:38:45Z"},{"alias_kind":"arxiv_version","alias_value":"1708.00477v1","created_at":"2026-05-18T00:38:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.00477","created_at":"2026-05-18T00:38:45Z"},{"alias_kind":"pith_short_12","alias_value":"KFVSE4UYQG6G","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"KFVSE4UYQG6GUXUP","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"KFVSE4UY","created_at":"2026-05-18T12:31:24Z"}],"graph_snapshots":[{"event_id":"sha256:cfcd30407fbb60e9bad712204c15e23cbcc938e5f475964c68d61a2183172638","target":"graph","created_at":"2026-05-18T00:38:45Z","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":"Generalizing a recent result of Mann, we show that there is an explicit function $f:\\left(0,1\\right]\\rightarrow\\left(0,1\\right]$ such that for every reduced word $w$, say in $d$ variables, there is an explicit reduced word $v$ in at most $3d$ variables (nontrivial if the length of $w$ is at least $2$) such that for all $\\rho\\in\\left(0,1\\right]$, the following holds: If $G$ is any finite group for which the word map $w_G:G^d\\rightarrow G$ agrees with some fixed homomorphism $G^d\\rightarrow G$ on at least $\\rho|G|^d$ many arguments, then the word map $v_G:G^{3d}\\rightarrow G$ has a fiber of size","authors_text":"Alexander Bors","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-08-01T19:09:48Z","title":"Approximability of word maps by homomorphisms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.00477","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:d139df3c0455bba93ee5149d95b0aa6cc8d061ebd6d7f820828994cccb16d097","target":"record","created_at":"2026-05-18T00:38:45Z","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":"c8ea9d17a24bb1da1ef4f76adcfcf2837afbb53f3952383bb6d421429ea1508e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-08-01T19:09:48Z","title_canon_sha256":"37422534028386aa84efb89ec3262d23c04fb2698b47818dde1aa6f72bfa4c1a"},"schema_version":"1.0","source":{"id":"1708.00477","kind":"arxiv","version":1}},"canonical_sha256":"516b22729881bc6a5e8f6396a616ed06db45e2c0e442bd035cf533d22b367be6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"516b22729881bc6a5e8f6396a616ed06db45e2c0e442bd035cf533d22b367be6","first_computed_at":"2026-05-18T00:38:45.643395Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:38:45.643395Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MrME1AASV/4ECopmTtPBAjuXznHdaUTgXv8RSvEUipBc3DyD+3nTjtO4mesmozTijoiL5DUI3WxRDO/K/EHKDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:38:45.643948Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.00477","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d139df3c0455bba93ee5149d95b0aa6cc8d061ebd6d7f820828994cccb16d097","sha256:cfcd30407fbb60e9bad712204c15e23cbcc938e5f475964c68d61a2183172638"],"state_sha256":"4e664f726fe5211281eb53ccaa732ab1449fc0dd1af0008f926fe8e1df4eec24"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MDEnx71Py9f3QcaaobDhX05oukUsVrxsTxTrjScDyVCkMGBI9yFiHawkUfCFedKepnDarHl8P0bPHoJxPxBkDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T03:16:56.723245Z","bundle_sha256":"28a6e2f76f20573064b994b15c4921bebd13c3968254e38a1d05cbcd562d81c1"}}