{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:J6H2FWX73DESZAV7C54VTXQ7RI","short_pith_number":"pith:J6H2FWX7","schema_version":"1.0","canonical_sha256":"4f8fa2daffd8c92c82bf177959de1f8a3e027b910149f742afac09ab12cc4026","source":{"kind":"arxiv","id":"2109.01003","version":2},"attestation_state":"computed","paper":{"title":"The homotopy Lie algebra of a Tor-independent tensor product","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"David A. Jorgensen, Josh Pollitz, Luigi Ferraro, Mohsen Gheibi, Nicholas Packauskas","submitted_at":"2021-09-02T14:59:03Z","abstract_excerpt":"In this article we investigate a pair of surjective local ring maps $S_1\\leftarrow R\\to S_2$ and their relation to the canonical projection $R\\to S_1\\otimes_R S_2$, where $S_1,S_2$ are Tor-independent over $R$. Our main result asserts a structural connection between the homotopy Lie algebra of $S:=S_1\\otimes_R S_2$, denoted $\\pi(S)$, in terms of those of $R,S_1$ and $S_2$. Namely, $\\pi(S)$ is the pullback of (adjusted) Lie algebras along the maps $\\pi(S_i)\\to \\pi(R)$ in various cases, including when the maps above have residual characteristic zero. Consequences to the main theorem include stru"},"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":"2109.01003","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2021-09-02T14:59:03Z","cross_cats_sorted":[],"title_canon_sha256":"5db4efa88abcfc7b20346e041ea7723e69a889b2a3c2dd7b0d9230951c21bdf9","abstract_canon_sha256":"613b6d9202860469ae0d14bbe322b9bf0bdb376d150e94c44f7e0839e892b7ad"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:41:51.965406Z","signature_b64":"Yg2jnZpBafpQIX68a/xuC0V7yFEOiqRdR9fiduyRCZFM7b26XY0DmFyiFBOMdULv4XqLdebLgrKJUHn1AA2PAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4f8fa2daffd8c92c82bf177959de1f8a3e027b910149f742afac09ab12cc4026","last_reissued_at":"2026-07-05T04:41:51.965054Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:41:51.965054Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The homotopy Lie algebra of a Tor-independent tensor product","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"David A. Jorgensen, Josh Pollitz, Luigi Ferraro, Mohsen Gheibi, Nicholas Packauskas","submitted_at":"2021-09-02T14:59:03Z","abstract_excerpt":"In this article we investigate a pair of surjective local ring maps $S_1\\leftarrow R\\to S_2$ and their relation to the canonical projection $R\\to S_1\\otimes_R S_2$, where $S_1,S_2$ are Tor-independent over $R$. Our main result asserts a structural connection between the homotopy Lie algebra of $S:=S_1\\otimes_R S_2$, denoted $\\pi(S)$, in terms of those of $R,S_1$ and $S_2$. Namely, $\\pi(S)$ is the pullback of (adjusted) Lie algebras along the maps $\\pi(S_i)\\to \\pi(R)$ in various cases, including when the maps above have residual characteristic zero. Consequences to the main theorem include stru"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.01003","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2109.01003/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2109.01003","created_at":"2026-07-05T04:41:51.965108+00:00"},{"alias_kind":"arxiv_version","alias_value":"2109.01003v2","created_at":"2026-07-05T04:41:51.965108+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.01003","created_at":"2026-07-05T04:41:51.965108+00:00"},{"alias_kind":"pith_short_12","alias_value":"J6H2FWX73DES","created_at":"2026-07-05T04:41:51.965108+00:00"},{"alias_kind":"pith_short_16","alias_value":"J6H2FWX73DESZAV7","created_at":"2026-07-05T04:41:51.965108+00:00"},{"alias_kind":"pith_short_8","alias_value":"J6H2FWX7","created_at":"2026-07-05T04:41:51.965108+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/J6H2FWX73DESZAV7C54VTXQ7RI","json":"https://pith.science/pith/J6H2FWX73DESZAV7C54VTXQ7RI.json","graph_json":"https://pith.science/api/pith-number/J6H2FWX73DESZAV7C54VTXQ7RI/graph.json","events_json":"https://pith.science/api/pith-number/J6H2FWX73DESZAV7C54VTXQ7RI/events.json","paper":"https://pith.science/paper/J6H2FWX7"},"agent_actions":{"view_html":"https://pith.science/pith/J6H2FWX73DESZAV7C54VTXQ7RI","download_json":"https://pith.science/pith/J6H2FWX73DESZAV7C54VTXQ7RI.json","view_paper":"https://pith.science/paper/J6H2FWX7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2109.01003&json=true","fetch_graph":"https://pith.science/api/pith-number/J6H2FWX73DESZAV7C54VTXQ7RI/graph.json","fetch_events":"https://pith.science/api/pith-number/J6H2FWX73DESZAV7C54VTXQ7RI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/J6H2FWX73DESZAV7C54VTXQ7RI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/J6H2FWX73DESZAV7C54VTXQ7RI/action/storage_attestation","attest_author":"https://pith.science/pith/J6H2FWX73DESZAV7C54VTXQ7RI/action/author_attestation","sign_citation":"https://pith.science/pith/J6H2FWX73DESZAV7C54VTXQ7RI/action/citation_signature","submit_replication":"https://pith.science/pith/J6H2FWX73DESZAV7C54VTXQ7RI/action/replication_record"}},"created_at":"2026-07-05T04:41:51.965108+00:00","updated_at":"2026-07-05T04:41:51.965108+00:00"}