{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:NR4KNXNPZTN5PS22VDUNEDL4AI","short_pith_number":"pith:NR4KNXNP","schema_version":"1.0","canonical_sha256":"6c78a6ddafccdbd7cb5aa8e8d20d7c023c44eb4bb4d6c60868dde59d171b9b7c","source":{"kind":"arxiv","id":"1210.4030","version":3},"attestation_state":"computed","paper":{"title":"Sur l'homologie des groupes d'automorphismes des groupes libres \\`a coefficients polynomiaux","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT"],"primary_cat":"math.AT","authors_text":"Aur\\'elien Djament (LMJL), Christine Vespa (IRMA)","submitted_at":"2012-10-15T13:42:09Z","abstract_excerpt":"We study in this article stable homology of automorphism groups of free groups with coefficients twisted by a poynomial functor. We show that this homology is zero for a reduced covariant polynomial functor. For a reduced contravariant functor, we compute the first homology group, which is in general non zero. Our methods relie on the use of functor categories. ---On \\'etudie dans cet article l'homologie stable des groupes d'automorphismes des groupes libres \\`a coefficients tordus par un foncteur polynomial. On montre que cette homologie est nulle pour un foncteur polynomial covariant r\\'edui"},"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":"1210.4030","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-10-15T13:42:09Z","cross_cats_sorted":["math.KT"],"title_canon_sha256":"f0cfc22f381869faaaf52a7f494df64da94baca66ba4a2e820ee7a3d26cd20af","abstract_canon_sha256":"41513b60d5576b77af9da642976f91f899de92fa6446db8d3e9ac1b5bf2b1987"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:13:56.168237Z","signature_b64":"T8JtdgV0CLkNXVSYTbmJqqaukTTbTrkqIbQl85P3e7ozAJtivJGtq+vT30aRE2if1wRGIqbMBhOOJ3MEtV0cBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6c78a6ddafccdbd7cb5aa8e8d20d7c023c44eb4bb4d6c60868dde59d171b9b7c","last_reissued_at":"2026-05-18T03:13:56.167643Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:13:56.167643Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sur l'homologie des groupes d'automorphismes des groupes libres \\`a coefficients polynomiaux","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT"],"primary_cat":"math.AT","authors_text":"Aur\\'elien Djament (LMJL), Christine Vespa (IRMA)","submitted_at":"2012-10-15T13:42:09Z","abstract_excerpt":"We study in this article stable homology of automorphism groups of free groups with coefficients twisted by a poynomial functor. We show that this homology is zero for a reduced covariant polynomial functor. For a reduced contravariant functor, we compute the first homology group, which is in general non zero. Our methods relie on the use of functor categories. ---On \\'etudie dans cet article l'homologie stable des groupes d'automorphismes des groupes libres \\`a coefficients tordus par un foncteur polynomial. On montre que cette homologie est nulle pour un foncteur polynomial covariant r\\'edui"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.4030","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1210.4030","created_at":"2026-05-18T03:13:56.167719+00:00"},{"alias_kind":"arxiv_version","alias_value":"1210.4030v3","created_at":"2026-05-18T03:13:56.167719+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.4030","created_at":"2026-05-18T03:13:56.167719+00:00"},{"alias_kind":"pith_short_12","alias_value":"NR4KNXNPZTN5","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_16","alias_value":"NR4KNXNPZTN5PS22","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_8","alias_value":"NR4KNXNP","created_at":"2026-05-18T12:27:16.716162+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/NR4KNXNPZTN5PS22VDUNEDL4AI","json":"https://pith.science/pith/NR4KNXNPZTN5PS22VDUNEDL4AI.json","graph_json":"https://pith.science/api/pith-number/NR4KNXNPZTN5PS22VDUNEDL4AI/graph.json","events_json":"https://pith.science/api/pith-number/NR4KNXNPZTN5PS22VDUNEDL4AI/events.json","paper":"https://pith.science/paper/NR4KNXNP"},"agent_actions":{"view_html":"https://pith.science/pith/NR4KNXNPZTN5PS22VDUNEDL4AI","download_json":"https://pith.science/pith/NR4KNXNPZTN5PS22VDUNEDL4AI.json","view_paper":"https://pith.science/paper/NR4KNXNP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1210.4030&json=true","fetch_graph":"https://pith.science/api/pith-number/NR4KNXNPZTN5PS22VDUNEDL4AI/graph.json","fetch_events":"https://pith.science/api/pith-number/NR4KNXNPZTN5PS22VDUNEDL4AI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NR4KNXNPZTN5PS22VDUNEDL4AI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NR4KNXNPZTN5PS22VDUNEDL4AI/action/storage_attestation","attest_author":"https://pith.science/pith/NR4KNXNPZTN5PS22VDUNEDL4AI/action/author_attestation","sign_citation":"https://pith.science/pith/NR4KNXNPZTN5PS22VDUNEDL4AI/action/citation_signature","submit_replication":"https://pith.science/pith/NR4KNXNPZTN5PS22VDUNEDL4AI/action/replication_record"}},"created_at":"2026-05-18T03:13:56.167719+00:00","updated_at":"2026-05-18T03:13:56.167719+00:00"}