{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:YSLPKP5XMVPWVCLBFU3WLYPAOP","short_pith_number":"pith:YSLPKP5X","canonical_record":{"source":{"id":"1610.04425","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-10-14T12:08:59Z","cross_cats_sorted":[],"title_canon_sha256":"a18f41d2fca1ef26f020ce25a5b5e79842aad1404bb1d25a2dd999adb6eb5626","abstract_canon_sha256":"47ab44ca43c0cbe461e56dc30c2324e0b1cfb10a54865baa18a5d6f796ddfefa"},"schema_version":"1.0"},"canonical_sha256":"c496f53fb7655f6a89612d3765e1e073c9d4f123405b6023385c9842b2a82f35","source":{"kind":"arxiv","id":"1610.04425","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.04425","created_at":"2026-05-18T00:16:39Z"},{"alias_kind":"arxiv_version","alias_value":"1610.04425v3","created_at":"2026-05-18T00:16:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.04425","created_at":"2026-05-18T00:16:39Z"},{"alias_kind":"pith_short_12","alias_value":"YSLPKP5XMVPW","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"YSLPKP5XMVPWVCLB","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"YSLPKP5X","created_at":"2026-05-18T12:30:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:YSLPKP5XMVPWVCLBFU3WLYPAOP","target":"record","payload":{"canonical_record":{"source":{"id":"1610.04425","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-10-14T12:08:59Z","cross_cats_sorted":[],"title_canon_sha256":"a18f41d2fca1ef26f020ce25a5b5e79842aad1404bb1d25a2dd999adb6eb5626","abstract_canon_sha256":"47ab44ca43c0cbe461e56dc30c2324e0b1cfb10a54865baa18a5d6f796ddfefa"},"schema_version":"1.0"},"canonical_sha256":"c496f53fb7655f6a89612d3765e1e073c9d4f123405b6023385c9842b2a82f35","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:16:39.105487Z","signature_b64":"XmHonUWV2TyxVz7E8mtY64JIfQrq3F07MWksm5/arps5mboJ2eyGZFY2eLCRQpam3SJpchoWtjL24p9KA5nMAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c496f53fb7655f6a89612d3765e1e073c9d4f123405b6023385c9842b2a82f35","last_reissued_at":"2026-05-18T00:16:39.104895Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:16:39.104895Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.04425","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:16:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NEBGbT2xiYzQ9WY/UOqqhIOoh0vIOrKpz737AuaSJDLTJfh/+lcoDdGym4W9/jJYWrJzbT3SLfts2vhOQWO1AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T05:12:03.965856Z"},"content_sha256":"b07398be1ad67aa5cb65caf1a9042bece926c4460e8cb33d7d7303629fb9fdd3","schema_version":"1.0","event_id":"sha256:b07398be1ad67aa5cb65caf1a9042bece926c4460e8cb33d7d7303629fb9fdd3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:YSLPKP5XMVPWVCLBFU3WLYPAOP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Verbally prime T-ideals and graded division algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Eli Aljadeff, Yakov Karasik","submitted_at":"2016-10-14T12:08:59Z","abstract_excerpt":"Let $F$ be an algebraically closed field of characteristic zero and let $G$ be a finite group. We consider graded Verbally prime $T$-ideals in the free $G$-graded algebra. It turns out that equivalent definitions in the ordinary case (i.e. ungraded) extend to nonequivalent definitions in the graded case, namely verbally prime $G$-graded $T$-ideals and strongly verbally prime $T$-ideals. At first, following Kemer's ideas, we classify $G$-graded verbally prime $T$-ideals. The main bulk of the paper is devoted to the stronger notion. We classify $G$-graded strongly verbally prime $T$-ideals which"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.04425","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:16:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"34Lx9j/McWvBlzU0VXlW2z5gBBuFEiElMHzF1lYRKOHCnOPzwx9zY/7QRac7BHGE24wf2p8xS7QOwdIkhuCABw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T05:12:03.966199Z"},"content_sha256":"deef9de135f7e9f062acbcf5e303c65b2cb319c888399eecdaa1089e56f49b13","schema_version":"1.0","event_id":"sha256:deef9de135f7e9f062acbcf5e303c65b2cb319c888399eecdaa1089e56f49b13"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YSLPKP5XMVPWVCLBFU3WLYPAOP/bundle.json","state_url":"https://pith.science/pith/YSLPKP5XMVPWVCLBFU3WLYPAOP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YSLPKP5XMVPWVCLBFU3WLYPAOP/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":"2026-06-02T05:12:03Z","links":{"resolver":"https://pith.science/pith/YSLPKP5XMVPWVCLBFU3WLYPAOP","bundle":"https://pith.science/pith/YSLPKP5XMVPWVCLBFU3WLYPAOP/bundle.json","state":"https://pith.science/pith/YSLPKP5XMVPWVCLBFU3WLYPAOP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YSLPKP5XMVPWVCLBFU3WLYPAOP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:YSLPKP5XMVPWVCLBFU3WLYPAOP","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":"47ab44ca43c0cbe461e56dc30c2324e0b1cfb10a54865baa18a5d6f796ddfefa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-10-14T12:08:59Z","title_canon_sha256":"a18f41d2fca1ef26f020ce25a5b5e79842aad1404bb1d25a2dd999adb6eb5626"},"schema_version":"1.0","source":{"id":"1610.04425","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.04425","created_at":"2026-05-18T00:16:39Z"},{"alias_kind":"arxiv_version","alias_value":"1610.04425v3","created_at":"2026-05-18T00:16:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.04425","created_at":"2026-05-18T00:16:39Z"},{"alias_kind":"pith_short_12","alias_value":"YSLPKP5XMVPW","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"YSLPKP5XMVPWVCLB","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"YSLPKP5X","created_at":"2026-05-18T12:30:53Z"}],"graph_snapshots":[{"event_id":"sha256:deef9de135f7e9f062acbcf5e303c65b2cb319c888399eecdaa1089e56f49b13","target":"graph","created_at":"2026-05-18T00:16:39Z","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 $F$ be an algebraically closed field of characteristic zero and let $G$ be a finite group. We consider graded Verbally prime $T$-ideals in the free $G$-graded algebra. It turns out that equivalent definitions in the ordinary case (i.e. ungraded) extend to nonequivalent definitions in the graded case, namely verbally prime $G$-graded $T$-ideals and strongly verbally prime $T$-ideals. At first, following Kemer's ideas, we classify $G$-graded verbally prime $T$-ideals. The main bulk of the paper is devoted to the stronger notion. We classify $G$-graded strongly verbally prime $T$-ideals which","authors_text":"Eli Aljadeff, Yakov Karasik","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-10-14T12:08:59Z","title":"Verbally prime T-ideals and graded division algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.04425","kind":"arxiv","version":3},"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:b07398be1ad67aa5cb65caf1a9042bece926c4460e8cb33d7d7303629fb9fdd3","target":"record","created_at":"2026-05-18T00:16:39Z","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":"47ab44ca43c0cbe461e56dc30c2324e0b1cfb10a54865baa18a5d6f796ddfefa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-10-14T12:08:59Z","title_canon_sha256":"a18f41d2fca1ef26f020ce25a5b5e79842aad1404bb1d25a2dd999adb6eb5626"},"schema_version":"1.0","source":{"id":"1610.04425","kind":"arxiv","version":3}},"canonical_sha256":"c496f53fb7655f6a89612d3765e1e073c9d4f123405b6023385c9842b2a82f35","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c496f53fb7655f6a89612d3765e1e073c9d4f123405b6023385c9842b2a82f35","first_computed_at":"2026-05-18T00:16:39.104895Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:16:39.104895Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XmHonUWV2TyxVz7E8mtY64JIfQrq3F07MWksm5/arps5mboJ2eyGZFY2eLCRQpam3SJpchoWtjL24p9KA5nMAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:16:39.105487Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.04425","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b07398be1ad67aa5cb65caf1a9042bece926c4460e8cb33d7d7303629fb9fdd3","sha256:deef9de135f7e9f062acbcf5e303c65b2cb319c888399eecdaa1089e56f49b13"],"state_sha256":"4f3f6b22dbc80338eed426dc43c346f9fe971d33cbc86408e4f82a08ef3dbec5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JqQ8tQLbDkZwGOcd0fbcHFeuLKN+OQB4XipiB09Pp4+pcVR2KyHSZ/RJQqc7/IQRP2RL5FfxC+uXNQ6niZaeDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T05:12:03.968106Z","bundle_sha256":"cabec8be62e8ddaf2bde5ca0a2bd608efcbacc5e7d303f30000b0c1a57956c09"}}