{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:R66GWKFFP35MYABZ4LLV4QB75Q","short_pith_number":"pith:R66GWKFF","canonical_record":{"source":{"id":"1712.04849","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-12-13T16:37:57Z","cross_cats_sorted":[],"title_canon_sha256":"a5c8cc9861342600041fe42ee194fd60b5f2c106ae0d34aac9fc1fe861ff1a6b","abstract_canon_sha256":"44390a1c6b473740c44b945ecfed6795285a901bab36ec828a52f44f7870c441"},"schema_version":"1.0"},"canonical_sha256":"8fbc6b28a57efacc0039e2d75e403fec3825f36e3724dffbcb503c73e629d44d","source":{"kind":"arxiv","id":"1712.04849","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.04849","created_at":"2026-05-18T00:28:03Z"},{"alias_kind":"arxiv_version","alias_value":"1712.04849v1","created_at":"2026-05-18T00:28:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.04849","created_at":"2026-05-18T00:28:03Z"},{"alias_kind":"pith_short_12","alias_value":"R66GWKFFP35M","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"R66GWKFFP35MYABZ","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"R66GWKFF","created_at":"2026-05-18T12:31:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:R66GWKFFP35MYABZ4LLV4QB75Q","target":"record","payload":{"canonical_record":{"source":{"id":"1712.04849","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-12-13T16:37:57Z","cross_cats_sorted":[],"title_canon_sha256":"a5c8cc9861342600041fe42ee194fd60b5f2c106ae0d34aac9fc1fe861ff1a6b","abstract_canon_sha256":"44390a1c6b473740c44b945ecfed6795285a901bab36ec828a52f44f7870c441"},"schema_version":"1.0"},"canonical_sha256":"8fbc6b28a57efacc0039e2d75e403fec3825f36e3724dffbcb503c73e629d44d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:28:03.297024Z","signature_b64":"mMUpTZbkOw0n/PHOVwLfUZvR3YqBXZhZVveTNsocud16du16Hc1bQW43DzHepxQbhXJkdhOdF6XYkrY188+tCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8fbc6b28a57efacc0039e2d75e403fec3825f36e3724dffbcb503c73e629d44d","last_reissued_at":"2026-05-18T00:28:03.296433Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:28:03.296433Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1712.04849","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":"2026-05-18T00:28:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OohHT952FprBf26w5EK2MzUBJHHGW7MhMyICqvgttI0kHjwgVNcZX/5euhVew8tIrI+sy7yPTnWeaSo5HDKCDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T19:14:02.128337Z"},"content_sha256":"6e4e0c5943ef8394a6f7dd5ad787b2be1248a22c6f34677b3574980f71a8d4c5","schema_version":"1.0","event_id":"sha256:6e4e0c5943ef8394a6f7dd5ad787b2be1248a22c6f34677b3574980f71a8d4c5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:R66GWKFFP35MYABZ4LLV4QB75Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Group algebras whose units satisfy a Laurent Polynomial Identity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"\\'Angel del R\\'io, Jairo Z. Gon\\c{c}alves, Osnel Broche","submitted_at":"2017-12-13T16:37:57Z","abstract_excerpt":"Let $KG$ be the group algebra of a torsion group $G$ over a field $K$. We show that if the units of $KG$ satisfy a Laurent polynomial identity which is not satisfied by the units of the relative free algebra $K[\\alpha,\\beta : \\alpha^2=\\beta^2=0]$ then $KG$ satisfies a polynomial identity. This extends Hartley Conjecture which states that if the units of $KG$ satisfies a group identity then $KG$ satisfies a polynomial identity. As an application of our results we prove that if the units of $KG$ satisfies a Laurent polynomial identity with a support of cardinality at most 3 then $KG$ satisfies a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.04849","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":"2026-05-18T00:28:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vLEd6IXBCNHfkqu+w5l5QGQ57UU+vDyJtYoaDki44kQUY1WHT/Rm1ePu11nKPNlaVY1mjTfwmhYkWk4WsRnCAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T19:14:02.128684Z"},"content_sha256":"38b1986f11f5ac17ffe4b8e1393c77b73b59c80b5aed62b66f5a29571c09802e","schema_version":"1.0","event_id":"sha256:38b1986f11f5ac17ffe4b8e1393c77b73b59c80b5aed62b66f5a29571c09802e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/R66GWKFFP35MYABZ4LLV4QB75Q/bundle.json","state_url":"https://pith.science/pith/R66GWKFFP35MYABZ4LLV4QB75Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/R66GWKFFP35MYABZ4LLV4QB75Q/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":"2026-07-01T19:14:02Z","links":{"resolver":"https://pith.science/pith/R66GWKFFP35MYABZ4LLV4QB75Q","bundle":"https://pith.science/pith/R66GWKFFP35MYABZ4LLV4QB75Q/bundle.json","state":"https://pith.science/pith/R66GWKFFP35MYABZ4LLV4QB75Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/R66GWKFFP35MYABZ4LLV4QB75Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:R66GWKFFP35MYABZ4LLV4QB75Q","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":"44390a1c6b473740c44b945ecfed6795285a901bab36ec828a52f44f7870c441","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-12-13T16:37:57Z","title_canon_sha256":"a5c8cc9861342600041fe42ee194fd60b5f2c106ae0d34aac9fc1fe861ff1a6b"},"schema_version":"1.0","source":{"id":"1712.04849","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.04849","created_at":"2026-05-18T00:28:03Z"},{"alias_kind":"arxiv_version","alias_value":"1712.04849v1","created_at":"2026-05-18T00:28:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.04849","created_at":"2026-05-18T00:28:03Z"},{"alias_kind":"pith_short_12","alias_value":"R66GWKFFP35M","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"R66GWKFFP35MYABZ","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"R66GWKFF","created_at":"2026-05-18T12:31:39Z"}],"graph_snapshots":[{"event_id":"sha256:38b1986f11f5ac17ffe4b8e1393c77b73b59c80b5aed62b66f5a29571c09802e","target":"graph","created_at":"2026-05-18T00:28:03Z","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":"Let $KG$ be the group algebra of a torsion group $G$ over a field $K$. We show that if the units of $KG$ satisfy a Laurent polynomial identity which is not satisfied by the units of the relative free algebra $K[\\alpha,\\beta : \\alpha^2=\\beta^2=0]$ then $KG$ satisfies a polynomial identity. This extends Hartley Conjecture which states that if the units of $KG$ satisfies a group identity then $KG$ satisfies a polynomial identity. As an application of our results we prove that if the units of $KG$ satisfies a Laurent polynomial identity with a support of cardinality at most 3 then $KG$ satisfies a","authors_text":"\\'Angel del R\\'io, Jairo Z. Gon\\c{c}alves, Osnel Broche","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-12-13T16:37:57Z","title":"Group algebras whose units satisfy a Laurent Polynomial Identity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.04849","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":"sha256:6e4e0c5943ef8394a6f7dd5ad787b2be1248a22c6f34677b3574980f71a8d4c5","target":"record","created_at":"2026-05-18T00:28:03Z","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":"44390a1c6b473740c44b945ecfed6795285a901bab36ec828a52f44f7870c441","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-12-13T16:37:57Z","title_canon_sha256":"a5c8cc9861342600041fe42ee194fd60b5f2c106ae0d34aac9fc1fe861ff1a6b"},"schema_version":"1.0","source":{"id":"1712.04849","kind":"arxiv","version":1}},"canonical_sha256":"8fbc6b28a57efacc0039e2d75e403fec3825f36e3724dffbcb503c73e629d44d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8fbc6b28a57efacc0039e2d75e403fec3825f36e3724dffbcb503c73e629d44d","first_computed_at":"2026-05-18T00:28:03.296433Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:28:03.296433Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mMUpTZbkOw0n/PHOVwLfUZvR3YqBXZhZVveTNsocud16du16Hc1bQW43DzHepxQbhXJkdhOdF6XYkrY188+tCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:28:03.297024Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.04849","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6e4e0c5943ef8394a6f7dd5ad787b2be1248a22c6f34677b3574980f71a8d4c5","sha256:38b1986f11f5ac17ffe4b8e1393c77b73b59c80b5aed62b66f5a29571c09802e"],"state_sha256":"fe3cd5834de177ace6d6948ed4d3c112f533ba9c0ccdf02977c0d190c23c59a8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CGP0wh1iTIy+D6mLer1L/ISYmX3IenIF1ep6K83YyHw0eROBIkLYgl3S7p/k0a6DMSxsgURlPTqKRe5nICypBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T19:14:02.130585Z","bundle_sha256":"1d2c57d31ae71db7fb973c4e31c0a79953c84da209823682f5013e43a20d8a07"}}