{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:7IVSMIUQGHROVWRSPMSJQZOXGP","short_pith_number":"pith:7IVSMIUQ","canonical_record":{"source":{"id":"1609.04055","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-09-13T21:10:31Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"0bf9ddf7fa08633c12b00edd4ba16df70a052c69b5f9e199914c563efdf97a05","abstract_canon_sha256":"f4ce4bfbbca57e6141a3e10ec92e817ef7ea0fd3000222fedad30619bf94cc10"},"schema_version":"1.0"},"canonical_sha256":"fa2b26229031e2eada327b249865d733fb5d7cbfaa9cebd8c95ba96114d13517","source":{"kind":"arxiv","id":"1609.04055","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.04055","created_at":"2026-05-18T01:04:40Z"},{"alias_kind":"arxiv_version","alias_value":"1609.04055v1","created_at":"2026-05-18T01:04:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.04055","created_at":"2026-05-18T01:04:40Z"},{"alias_kind":"pith_short_12","alias_value":"7IVSMIUQGHRO","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"7IVSMIUQGHROVWRS","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"7IVSMIUQ","created_at":"2026-05-18T12:30:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:7IVSMIUQGHROVWRSPMSJQZOXGP","target":"record","payload":{"canonical_record":{"source":{"id":"1609.04055","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-09-13T21:10:31Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"0bf9ddf7fa08633c12b00edd4ba16df70a052c69b5f9e199914c563efdf97a05","abstract_canon_sha256":"f4ce4bfbbca57e6141a3e10ec92e817ef7ea0fd3000222fedad30619bf94cc10"},"schema_version":"1.0"},"canonical_sha256":"fa2b26229031e2eada327b249865d733fb5d7cbfaa9cebd8c95ba96114d13517","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:40.786533Z","signature_b64":"59nWOOcrmv4L+5L61zkbdY+NBtFVFZRbU1te3bqARrS1L9/spHu/qpk6SiU6s4x/OogNRWaj99rvqnYwDLhSBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fa2b26229031e2eada327b249865d733fb5d7cbfaa9cebd8c95ba96114d13517","last_reissued_at":"2026-05-18T01:04:40.785816Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:40.785816Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.04055","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":"2026-05-18T01:04:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1la+LHIE9ouTO5N7ZINTaUqdX7eou4P6FB3EdEwE0j0g0o7JT5ZYXj347ABi1j4Sm3nMa7/vkTedj34GfLrfCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T12:09:04.887949Z"},"content_sha256":"fa434dd8428f4c9a5c38fce6e902f46091e579b575d1bdb7720fe4a88b7b72e0","schema_version":"1.0","event_id":"sha256:fa434dd8428f4c9a5c38fce6e902f46091e579b575d1bdb7720fe4a88b7b72e0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:7IVSMIUQGHROVWRSPMSJQZOXGP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Differential smoothness of skew polynomial rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.RA","authors_text":"Christian Lomp, Tomasz Brzezi\\'nski","submitted_at":"2016-09-13T21:10:31Z","abstract_excerpt":"It is shown that, under some natural assumptions, the tensor product of differentially smooth algebras and the skew-polynomial rings over differentially smooth algebras are differentially smooth."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.04055","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":"2026-05-18T01:04:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8SkiBZsjcrQErXlJSsZzAA26wINd9wX1fHXkHUYxp02wIxZznUTyXRIFbDMrWkqbDo2OAlcsYEaiwYlCN0TyDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T12:09:04.888280Z"},"content_sha256":"bff112690e62d2d1fcefd0c70b5a2f349c7460001c32763afd342183ab56d558","schema_version":"1.0","event_id":"sha256:bff112690e62d2d1fcefd0c70b5a2f349c7460001c32763afd342183ab56d558"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7IVSMIUQGHROVWRSPMSJQZOXGP/bundle.json","state_url":"https://pith.science/pith/7IVSMIUQGHROVWRSPMSJQZOXGP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7IVSMIUQGHROVWRSPMSJQZOXGP/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":"2026-06-01T12:09:04Z","links":{"resolver":"https://pith.science/pith/7IVSMIUQGHROVWRSPMSJQZOXGP","bundle":"https://pith.science/pith/7IVSMIUQGHROVWRSPMSJQZOXGP/bundle.json","state":"https://pith.science/pith/7IVSMIUQGHROVWRSPMSJQZOXGP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7IVSMIUQGHROVWRSPMSJQZOXGP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:7IVSMIUQGHROVWRSPMSJQZOXGP","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":"f4ce4bfbbca57e6141a3e10ec92e817ef7ea0fd3000222fedad30619bf94cc10","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-09-13T21:10:31Z","title_canon_sha256":"0bf9ddf7fa08633c12b00edd4ba16df70a052c69b5f9e199914c563efdf97a05"},"schema_version":"1.0","source":{"id":"1609.04055","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.04055","created_at":"2026-05-18T01:04:40Z"},{"alias_kind":"arxiv_version","alias_value":"1609.04055v1","created_at":"2026-05-18T01:04:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.04055","created_at":"2026-05-18T01:04:40Z"},{"alias_kind":"pith_short_12","alias_value":"7IVSMIUQGHRO","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"7IVSMIUQGHROVWRS","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"7IVSMIUQ","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:bff112690e62d2d1fcefd0c70b5a2f349c7460001c32763afd342183ab56d558","target":"graph","created_at":"2026-05-18T01:04:40Z","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":"It is shown that, under some natural assumptions, the tensor product of differentially smooth algebras and the skew-polynomial rings over differentially smooth algebras are differentially smooth.","authors_text":"Christian Lomp, Tomasz Brzezi\\'nski","cross_cats":["math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-09-13T21:10:31Z","title":"Differential smoothness of skew polynomial rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.04055","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:fa434dd8428f4c9a5c38fce6e902f46091e579b575d1bdb7720fe4a88b7b72e0","target":"record","created_at":"2026-05-18T01:04:40Z","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":"f4ce4bfbbca57e6141a3e10ec92e817ef7ea0fd3000222fedad30619bf94cc10","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-09-13T21:10:31Z","title_canon_sha256":"0bf9ddf7fa08633c12b00edd4ba16df70a052c69b5f9e199914c563efdf97a05"},"schema_version":"1.0","source":{"id":"1609.04055","kind":"arxiv","version":1}},"canonical_sha256":"fa2b26229031e2eada327b249865d733fb5d7cbfaa9cebd8c95ba96114d13517","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fa2b26229031e2eada327b249865d733fb5d7cbfaa9cebd8c95ba96114d13517","first_computed_at":"2026-05-18T01:04:40.785816Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:40.785816Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"59nWOOcrmv4L+5L61zkbdY+NBtFVFZRbU1te3bqARrS1L9/spHu/qpk6SiU6s4x/OogNRWaj99rvqnYwDLhSBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:40.786533Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.04055","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fa434dd8428f4c9a5c38fce6e902f46091e579b575d1bdb7720fe4a88b7b72e0","sha256:bff112690e62d2d1fcefd0c70b5a2f349c7460001c32763afd342183ab56d558"],"state_sha256":"61c744d8522316866e58da1bf867014ab55aecfc31778bc5b6f209995f8a9a00"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x6eh3x/IQmsH9+Nc4OV16cvaIJM3FuIiwkMuwP7KWzFD2p1BDDDKOzu3eNKbTDoNQeN9jDcuafi4NrW4Hu23Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T12:09:04.890251Z","bundle_sha256":"a3f66300e5f1594b748361c4e8b8ecb5e49082dd236f53dff3d768c6211d8176"}}