{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:5IOKLJN4PU4FDKK77GR6F2CWA5","short_pith_number":"pith:5IOKLJN4","canonical_record":{"source":{"id":"2606.23352","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.RA","submitted_at":"2026-06-22T13:54:24Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"bfcac844e8495460f25181c34db50f04f8be595e52917b4c66ace3444a625811","abstract_canon_sha256":"18949e426b75d57476ee3c6ee6a6bc86aa645592f946d163b15c204303f6ae0b"},"schema_version":"1.0"},"canonical_sha256":"ea1ca5a5bc7d3851a95ff9a3e2e8560772603d3560ec727ee91870526c404629","source":{"kind":"arxiv","id":"2606.23352","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.23352","created_at":"2026-06-23T03:14:17Z"},{"alias_kind":"arxiv_version","alias_value":"2606.23352v1","created_at":"2026-06-23T03:14:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.23352","created_at":"2026-06-23T03:14:17Z"},{"alias_kind":"pith_short_12","alias_value":"5IOKLJN4PU4F","created_at":"2026-06-23T03:14:17Z"},{"alias_kind":"pith_short_16","alias_value":"5IOKLJN4PU4FDKK7","created_at":"2026-06-23T03:14:17Z"},{"alias_kind":"pith_short_8","alias_value":"5IOKLJN4","created_at":"2026-06-23T03:14:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:5IOKLJN4PU4FDKK77GR6F2CWA5","target":"record","payload":{"canonical_record":{"source":{"id":"2606.23352","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.RA","submitted_at":"2026-06-22T13:54:24Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"bfcac844e8495460f25181c34db50f04f8be595e52917b4c66ace3444a625811","abstract_canon_sha256":"18949e426b75d57476ee3c6ee6a6bc86aa645592f946d163b15c204303f6ae0b"},"schema_version":"1.0"},"canonical_sha256":"ea1ca5a5bc7d3851a95ff9a3e2e8560772603d3560ec727ee91870526c404629","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-23T03:14:17.559067Z","signature_b64":"t6Pvf04H1FVSWo4+A5W1yCV7yhBVKbk5e7p93FjWXh1myEs3KAG55Bqj94Y3G2PpctboblWCLQMX99ARdtKbCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ea1ca5a5bc7d3851a95ff9a3e2e8560772603d3560ec727ee91870526c404629","last_reissued_at":"2026-06-23T03:14:17.558688Z","signature_status":"signed_v1","first_computed_at":"2026-06-23T03:14:17.558688Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.23352","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":"2026-06-23T03:14:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t/96UoGWIYcDV4c/ExULvQQlTJc1acIz+Er+HBU8bQeaiSyVIjGBO3tNViI/Go1UX0PKtAwWSjSNW9BdCU3ZCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T02:44:59.037154Z"},"content_sha256":"34be9d73d5aba46d0ed4fe345559b8d8a4cf0b5dd995846c1ec96dfe3482ef97","schema_version":"1.0","event_id":"sha256:34be9d73d5aba46d0ed4fe345559b8d8a4cf0b5dd995846c1ec96dfe3482ef97"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:5IOKLJN4PU4FDKK77GR6F2CWA5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Graded differential polynomial rings","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.RA","authors_text":"Yassine Ait Mohamed","submitted_at":"2026-06-22T13:54:24Z","abstract_excerpt":"Let $R$ be a $\\Gamma$-graded ring and $\\delta$ a derivation of $R$. We determine exactly when the differential polynomial ring $R[t;\\delta]$ admits a grading compatible with that of $R$: this happens if and only if $\\delta$ is a $\\gamma$-derivation for some $\\gamma$ in the centralizer of the support, in which case the grading is explicit and unique once $\\deg(t)$ is fixed. Over an arbitrary group, we establish graded analogues of the classical simplicity, primeness, and Noetherianity theorems; in characteristic zero, $R[t;\\delta]$ is gr-simple if and only if $R$ is $\\delta$-gr-simple and $\\del"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.23352","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.23352/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-23T03:14:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4r/FRLxen4p+set0L/iI47J1204fP1H2/eFYVw3xQqd9Flmwpg/A8/GuvDAiX3609KicMEvGq4jAq0H4ut1eBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T02:44:59.037551Z"},"content_sha256":"1cb8423dfc7bc6d04e403659e11a74132118d4ff05197cde1ef30f4a88766a46","schema_version":"1.0","event_id":"sha256:1cb8423dfc7bc6d04e403659e11a74132118d4ff05197cde1ef30f4a88766a46"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5IOKLJN4PU4FDKK77GR6F2CWA5/bundle.json","state_url":"https://pith.science/pith/5IOKLJN4PU4FDKK77GR6F2CWA5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5IOKLJN4PU4FDKK77GR6F2CWA5/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":"2026-06-28T02:44:59Z","links":{"resolver":"https://pith.science/pith/5IOKLJN4PU4FDKK77GR6F2CWA5","bundle":"https://pith.science/pith/5IOKLJN4PU4FDKK77GR6F2CWA5/bundle.json","state":"https://pith.science/pith/5IOKLJN4PU4FDKK77GR6F2CWA5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5IOKLJN4PU4FDKK77GR6F2CWA5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:5IOKLJN4PU4FDKK77GR6F2CWA5","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":"18949e426b75d57476ee3c6ee6a6bc86aa645592f946d163b15c204303f6ae0b","cross_cats_sorted":["math.AC"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.RA","submitted_at":"2026-06-22T13:54:24Z","title_canon_sha256":"bfcac844e8495460f25181c34db50f04f8be595e52917b4c66ace3444a625811"},"schema_version":"1.0","source":{"id":"2606.23352","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.23352","created_at":"2026-06-23T03:14:17Z"},{"alias_kind":"arxiv_version","alias_value":"2606.23352v1","created_at":"2026-06-23T03:14:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.23352","created_at":"2026-06-23T03:14:17Z"},{"alias_kind":"pith_short_12","alias_value":"5IOKLJN4PU4F","created_at":"2026-06-23T03:14:17Z"},{"alias_kind":"pith_short_16","alias_value":"5IOKLJN4PU4FDKK7","created_at":"2026-06-23T03:14:17Z"},{"alias_kind":"pith_short_8","alias_value":"5IOKLJN4","created_at":"2026-06-23T03:14:17Z"}],"graph_snapshots":[{"event_id":"sha256:1cb8423dfc7bc6d04e403659e11a74132118d4ff05197cde1ef30f4a88766a46","target":"graph","created_at":"2026-06-23T03:14:17Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.23352/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $R$ be a $\\Gamma$-graded ring and $\\delta$ a derivation of $R$. We determine exactly when the differential polynomial ring $R[t;\\delta]$ admits a grading compatible with that of $R$: this happens if and only if $\\delta$ is a $\\gamma$-derivation for some $\\gamma$ in the centralizer of the support, in which case the grading is explicit and unique once $\\deg(t)$ is fixed. Over an arbitrary group, we establish graded analogues of the classical simplicity, primeness, and Noetherianity theorems; in characteristic zero, $R[t;\\delta]$ is gr-simple if and only if $R$ is $\\delta$-gr-simple and $\\del","authors_text":"Yassine Ait Mohamed","cross_cats":["math.AC"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.RA","submitted_at":"2026-06-22T13:54:24Z","title":"Graded differential polynomial rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.23352","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":"sha256:34be9d73d5aba46d0ed4fe345559b8d8a4cf0b5dd995846c1ec96dfe3482ef97","target":"record","created_at":"2026-06-23T03:14:17Z","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":"18949e426b75d57476ee3c6ee6a6bc86aa645592f946d163b15c204303f6ae0b","cross_cats_sorted":["math.AC"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.RA","submitted_at":"2026-06-22T13:54:24Z","title_canon_sha256":"bfcac844e8495460f25181c34db50f04f8be595e52917b4c66ace3444a625811"},"schema_version":"1.0","source":{"id":"2606.23352","kind":"arxiv","version":1}},"canonical_sha256":"ea1ca5a5bc7d3851a95ff9a3e2e8560772603d3560ec727ee91870526c404629","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ea1ca5a5bc7d3851a95ff9a3e2e8560772603d3560ec727ee91870526c404629","first_computed_at":"2026-06-23T03:14:17.558688Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-23T03:14:17.558688Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t6Pvf04H1FVSWo4+A5W1yCV7yhBVKbk5e7p93FjWXh1myEs3KAG55Bqj94Y3G2PpctboblWCLQMX99ARdtKbCw==","signature_status":"signed_v1","signed_at":"2026-06-23T03:14:17.559067Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.23352","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:34be9d73d5aba46d0ed4fe345559b8d8a4cf0b5dd995846c1ec96dfe3482ef97","sha256:1cb8423dfc7bc6d04e403659e11a74132118d4ff05197cde1ef30f4a88766a46"],"state_sha256":"d7cee1bdf327c878ded3145cb134b8cd1fb4af32a9cbb4475795984b323da837"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LqoJP6WszZLnfpkQ/UqieZ1MxSEX2hzI+blPcti8QDkV4nDYmKeuJNBYX/BqVKbzyzuwPL9f3VhJXCoqbq/yBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T02:44:59.039643Z","bundle_sha256":"deacc0491bac3600f796fc121923fbb127caf0f683f268d5087815dd3a2a04e9"}}