{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:JCZCSV3TLX7OFD3WZC57DHN34I","short_pith_number":"pith:JCZCSV3T","canonical_record":{"source":{"id":"1605.07115","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-05-23T17:44:44Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"10dc4879e06c70d3b4e97b7adaf8df5ea34d8e4b98e87c535317f878622c7146","abstract_canon_sha256":"947da73048025c3432a8e68f17142239ed0ea6b4392bf7ae4992b690a55b3283"},"schema_version":"1.0"},"canonical_sha256":"48b22957735dfee28f76c8bbf19dbbe20d38e204fe577fe1269b11c4707b0fc0","source":{"kind":"arxiv","id":"1605.07115","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.07115","created_at":"2026-05-18T01:14:09Z"},{"alias_kind":"arxiv_version","alias_value":"1605.07115v1","created_at":"2026-05-18T01:14:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.07115","created_at":"2026-05-18T01:14:09Z"},{"alias_kind":"pith_short_12","alias_value":"JCZCSV3TLX7O","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"JCZCSV3TLX7OFD3W","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"JCZCSV3T","created_at":"2026-05-18T12:30:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:JCZCSV3TLX7OFD3WZC57DHN34I","target":"record","payload":{"canonical_record":{"source":{"id":"1605.07115","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-05-23T17:44:44Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"10dc4879e06c70d3b4e97b7adaf8df5ea34d8e4b98e87c535317f878622c7146","abstract_canon_sha256":"947da73048025c3432a8e68f17142239ed0ea6b4392bf7ae4992b690a55b3283"},"schema_version":"1.0"},"canonical_sha256":"48b22957735dfee28f76c8bbf19dbbe20d38e204fe577fe1269b11c4707b0fc0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:14:09.902980Z","signature_b64":"YEB00kGAKPdF2O6JUnLTU5UEePxroKJA5lq1m1lZT9qHGU84TLOmWTA3vSBUHEu35w6g/wWcOa7oBM543cLDCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"48b22957735dfee28f76c8bbf19dbbe20d38e204fe577fe1269b11c4707b0fc0","last_reissued_at":"2026-05-18T01:14:09.902427Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:14:09.902427Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1605.07115","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":"2026-05-18T01:14:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MKFybbfMzuA3bR66GPEobnVRiROvVl11P2tiX4V0tIjOkbTHL4b597j9RULhRnHIv6le6R7J80H6KZl6LEn4Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T23:07:10.005677Z"},"content_sha256":"a65d4e9f00a9d8651ec80bc908c04d3866655b6ba4b4b709fcc3424ce81de5e4","schema_version":"1.0","event_id":"sha256:a65d4e9f00a9d8651ec80bc908c04d3866655b6ba4b4b709fcc3424ce81de5e4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:JCZCSV3TLX7OFD3WZC57DHN34I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Differential calculus over N-graded commutative rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"G. Sardanashvily, W. Wachowski","submitted_at":"2016-05-23T17:44:44Z","abstract_excerpt":"The Chevalley-Eilenberg differential calculus and differential operators over N-graded commutative rings are constructed. This is a straightforward generalization of the differential calculus over commutative rings, and it is the most general case of the differential calculus over rings that is not the non-commutative geometry. Since any N-graded ring possesses the associated Z_2-graded structure, this also is the case of the graded differential calculus over Grassmann algebras and the supergeometry and field theory on graded manifolds."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.07115","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":"2026-05-18T01:14:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dh3QvEedDrWVcAdq+mXTLxow/yfeIshRP36dD5KleTKSkuU1IQ3OQq50iob3OFYOZzAOSUuVCJ0W6x57Fd2BBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T23:07:10.006033Z"},"content_sha256":"b321ab5ce427a6966cda0466a5ac4e5094bbf0f97164048838c7a0f4c1de01a8","schema_version":"1.0","event_id":"sha256:b321ab5ce427a6966cda0466a5ac4e5094bbf0f97164048838c7a0f4c1de01a8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JCZCSV3TLX7OFD3WZC57DHN34I/bundle.json","state_url":"https://pith.science/pith/JCZCSV3TLX7OFD3WZC57DHN34I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JCZCSV3TLX7OFD3WZC57DHN34I/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":"2026-05-21T23:07:10Z","links":{"resolver":"https://pith.science/pith/JCZCSV3TLX7OFD3WZC57DHN34I","bundle":"https://pith.science/pith/JCZCSV3TLX7OFD3WZC57DHN34I/bundle.json","state":"https://pith.science/pith/JCZCSV3TLX7OFD3WZC57DHN34I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JCZCSV3TLX7OFD3WZC57DHN34I/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:JCZCSV3TLX7OFD3WZC57DHN34I","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":"947da73048025c3432a8e68f17142239ed0ea6b4392bf7ae4992b690a55b3283","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-05-23T17:44:44Z","title_canon_sha256":"10dc4879e06c70d3b4e97b7adaf8df5ea34d8e4b98e87c535317f878622c7146"},"schema_version":"1.0","source":{"id":"1605.07115","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.07115","created_at":"2026-05-18T01:14:09Z"},{"alias_kind":"arxiv_version","alias_value":"1605.07115v1","created_at":"2026-05-18T01:14:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.07115","created_at":"2026-05-18T01:14:09Z"},{"alias_kind":"pith_short_12","alias_value":"JCZCSV3TLX7O","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"JCZCSV3TLX7OFD3W","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"JCZCSV3T","created_at":"2026-05-18T12:30:25Z"}],"graph_snapshots":[{"event_id":"sha256:b321ab5ce427a6966cda0466a5ac4e5094bbf0f97164048838c7a0f4c1de01a8","target":"graph","created_at":"2026-05-18T01:14:09Z","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":"The Chevalley-Eilenberg differential calculus and differential operators over N-graded commutative rings are constructed. This is a straightforward generalization of the differential calculus over commutative rings, and it is the most general case of the differential calculus over rings that is not the non-commutative geometry. Since any N-graded ring possesses the associated Z_2-graded structure, this also is the case of the graded differential calculus over Grassmann algebras and the supergeometry and field theory on graded manifolds.","authors_text":"G. Sardanashvily, W. Wachowski","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-05-23T17:44:44Z","title":"Differential calculus over N-graded commutative rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.07115","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:a65d4e9f00a9d8651ec80bc908c04d3866655b6ba4b4b709fcc3424ce81de5e4","target":"record","created_at":"2026-05-18T01:14:09Z","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":"947da73048025c3432a8e68f17142239ed0ea6b4392bf7ae4992b690a55b3283","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-05-23T17:44:44Z","title_canon_sha256":"10dc4879e06c70d3b4e97b7adaf8df5ea34d8e4b98e87c535317f878622c7146"},"schema_version":"1.0","source":{"id":"1605.07115","kind":"arxiv","version":1}},"canonical_sha256":"48b22957735dfee28f76c8bbf19dbbe20d38e204fe577fe1269b11c4707b0fc0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"48b22957735dfee28f76c8bbf19dbbe20d38e204fe577fe1269b11c4707b0fc0","first_computed_at":"2026-05-18T01:14:09.902427Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:14:09.902427Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YEB00kGAKPdF2O6JUnLTU5UEePxroKJA5lq1m1lZT9qHGU84TLOmWTA3vSBUHEu35w6g/wWcOa7oBM543cLDCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:14:09.902980Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.07115","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a65d4e9f00a9d8651ec80bc908c04d3866655b6ba4b4b709fcc3424ce81de5e4","sha256:b321ab5ce427a6966cda0466a5ac4e5094bbf0f97164048838c7a0f4c1de01a8"],"state_sha256":"480d64416e393d16ec455a82ad18048f78a274d867e424a10eca1f11744a066b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0o+mqInc1hGfvhFVRe3LmnqAB5iwpzBWP3LCkp7f2kB1PEYXRedBq67V6Cu2TDMWRNbilWJWa9imf2Cr7LoRBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-21T23:07:10.008117Z","bundle_sha256":"1c50bbf48d1c9fd588972d82b1430f08006cc12bc76e7aa01ad679483f95b8aa"}}