{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2005:K7OZBCZEELFHG2EZFA62IHYMYS","short_pith_number":"pith:K7OZBCZE","schema_version":"1.0","canonical_sha256":"57dd908b2422ca736899283da41f0cc4919b1287852410544e64d926c928f058","source":{"kind":"arxiv","id":"math/0501053","version":2},"attestation_state":"computed","paper":{"title":"The Johnson homomorphism and the second cohomology of IA_n","license":"","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Alexandra Pettet","submitted_at":"2005-01-04T23:01:27Z","abstract_excerpt":"Let F_n be the free group on n generators. Define IA_n to be group of automorphisms of F_n that act trivially on first homology. The Johnson homomorphism in this setting is a map from IA_n to its abelianization. The first goal of this paper is to determine how much this map contributes to the second rational cohomology of IA_n.\n  A descending central series of IA_n is given by the subgroups K_n^(i) which act trivially on F_n/F_n^(i+1), the free rank n, degree i nilpotent group. It is a conjecture of Andreadakis that K_n^(i) is equal to the lower central series of IA_n; indeed K_n^(2) is known "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"math/0501053","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.GR","submitted_at":"2005-01-04T23:01:27Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"cbc47e7f1ee956347c3e829a32db5d43e915548e20969aef25931a6647180324","abstract_canon_sha256":"8e9a8d75b91efb514f2057bee99769b9deeb2c394b6a7618e6e9e0945f633fbb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:32.135006Z","signature_b64":"djC/4t4IJvI9Y1a6biZvxnGC+RSnHMTuekl8ADZUGZsElCU1VkpC1Aug2G4ayFBemlHDbZurkmXt2UIEK0s5Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"57dd908b2422ca736899283da41f0cc4919b1287852410544e64d926c928f058","last_reissued_at":"2026-05-18T02:41:32.134604Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:32.134604Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Johnson homomorphism and the second cohomology of IA_n","license":"","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Alexandra Pettet","submitted_at":"2005-01-04T23:01:27Z","abstract_excerpt":"Let F_n be the free group on n generators. Define IA_n to be group of automorphisms of F_n that act trivially on first homology. The Johnson homomorphism in this setting is a map from IA_n to its abelianization. The first goal of this paper is to determine how much this map contributes to the second rational cohomology of IA_n.\n  A descending central series of IA_n is given by the subgroups K_n^(i) which act trivially on F_n/F_n^(i+1), the free rank n, degree i nilpotent group. It is a conjecture of Andreadakis that K_n^(i) is equal to the lower central series of IA_n; indeed K_n^(2) is known "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0501053","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"math/0501053","created_at":"2026-05-18T02:41:32.134676+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0501053v2","created_at":"2026-05-18T02:41:32.134676+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0501053","created_at":"2026-05-18T02:41:32.134676+00:00"},{"alias_kind":"pith_short_12","alias_value":"K7OZBCZEELFH","created_at":"2026-05-18T12:25:53.335082+00:00"},{"alias_kind":"pith_short_16","alias_value":"K7OZBCZEELFHG2EZ","created_at":"2026-05-18T12:25:53.335082+00:00"},{"alias_kind":"pith_short_8","alias_value":"K7OZBCZE","created_at":"2026-05-18T12:25:53.335082+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2509.03742","citing_title":"Johnson homomorphisms and the second rational cohomology of handlebody Torelli groups","ref_index":30,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/K7OZBCZEELFHG2EZFA62IHYMYS","json":"https://pith.science/pith/K7OZBCZEELFHG2EZFA62IHYMYS.json","graph_json":"https://pith.science/api/pith-number/K7OZBCZEELFHG2EZFA62IHYMYS/graph.json","events_json":"https://pith.science/api/pith-number/K7OZBCZEELFHG2EZFA62IHYMYS/events.json","paper":"https://pith.science/paper/K7OZBCZE"},"agent_actions":{"view_html":"https://pith.science/pith/K7OZBCZEELFHG2EZFA62IHYMYS","download_json":"https://pith.science/pith/K7OZBCZEELFHG2EZFA62IHYMYS.json","view_paper":"https://pith.science/paper/K7OZBCZE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0501053&json=true","fetch_graph":"https://pith.science/api/pith-number/K7OZBCZEELFHG2EZFA62IHYMYS/graph.json","fetch_events":"https://pith.science/api/pith-number/K7OZBCZEELFHG2EZFA62IHYMYS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/K7OZBCZEELFHG2EZFA62IHYMYS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/K7OZBCZEELFHG2EZFA62IHYMYS/action/storage_attestation","attest_author":"https://pith.science/pith/K7OZBCZEELFHG2EZFA62IHYMYS/action/author_attestation","sign_citation":"https://pith.science/pith/K7OZBCZEELFHG2EZFA62IHYMYS/action/citation_signature","submit_replication":"https://pith.science/pith/K7OZBCZEELFHG2EZFA62IHYMYS/action/replication_record"}},"created_at":"2026-05-18T02:41:32.134676+00:00","updated_at":"2026-05-18T02:41:32.134676+00:00"}