{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:P4VRDB3TLY74NDMUDXF2URNGO2","short_pith_number":"pith:P4VRDB3T","canonical_record":{"source":{"id":"1306.4263","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2013-06-18T16:34:18Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"eefeff82551da55197768f4c6634a65a7029bc7d0aa1eeb0b5033afa429034d5","abstract_canon_sha256":"b651e99c985686dc04211a01eab0535ff5196ddb6aa0dddc24be1613d8469be5"},"schema_version":"1.0"},"canonical_sha256":"7f2b1187735e3fc68d941dcbaa45a676bd1792b9654f4ed7d25c0fe4794126cf","source":{"kind":"arxiv","id":"1306.4263","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.4263","created_at":"2026-05-18T03:20:36Z"},{"alias_kind":"arxiv_version","alias_value":"1306.4263v1","created_at":"2026-05-18T03:20:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.4263","created_at":"2026-05-18T03:20:36Z"},{"alias_kind":"pith_short_12","alias_value":"P4VRDB3TLY74","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"P4VRDB3TLY74NDMU","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"P4VRDB3T","created_at":"2026-05-18T12:27:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:P4VRDB3TLY74NDMUDXF2URNGO2","target":"record","payload":{"canonical_record":{"source":{"id":"1306.4263","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2013-06-18T16:34:18Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"eefeff82551da55197768f4c6634a65a7029bc7d0aa1eeb0b5033afa429034d5","abstract_canon_sha256":"b651e99c985686dc04211a01eab0535ff5196ddb6aa0dddc24be1613d8469be5"},"schema_version":"1.0"},"canonical_sha256":"7f2b1187735e3fc68d941dcbaa45a676bd1792b9654f4ed7d25c0fe4794126cf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:20:36.632369Z","signature_b64":"0orQxf7xzg2SwrRllKkm6sVoEjNKoaoLR5zKGT1ItFN8UdQF0BNuag4qvHiDDPP2KcqsQFSleTO89vO4qT/pDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7f2b1187735e3fc68d941dcbaa45a676bd1792b9654f4ed7d25c0fe4794126cf","last_reissued_at":"2026-05-18T03:20:36.631568Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:20:36.631568Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1306.4263","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":"2026-05-18T03:20:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m+XSuyKUf0ziihTaYIzKV6GeQ/WarKWPeeQZXRtgvBUdXLDkJDDCmT2ixvr8Vd+bP9oLY17HfdYaRyWiDj+ZBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T05:27:34.426691Z"},"content_sha256":"be4e8113d26b91c77aef40b4083849f033df98adc56f41ff0fbf8fca86ca0602","schema_version":"1.0","event_id":"sha256:be4e8113d26b91c77aef40b4083849f033df98adc56f41ff0fbf8fca86ca0602"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:P4VRDB3TLY74NDMUDXF2URNGO2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Ore Polynomials in Sage","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.SC","authors_text":"Fredrik Johansson, Manuel Kauers, Maximilian Jaroschek","submitted_at":"2013-06-18T16:34:18Z","abstract_excerpt":"We present a Sage implementation of Ore algebras. The main features for the most common instances include basic arithmetic and actions; gcrd and lclm; D-finite closure properties; natural transformations between related algebras; guessing; desingularization; solvers for polynomials, rational functions and (generalized) power series. This paper is a tutorial on how to use the package."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.4263","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":"2026-05-18T03:20:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KP11kSCYhF3bAH9QgNTAekYJS9NTVoG8jTv6EqJvUI8L28a4wXB+be4POyq9gnPPc3BcWT/pcGwROGwlDjVdCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T05:27:34.427111Z"},"content_sha256":"e7f692728c845f7ea8e793de4dbba41fabaa39ca01acf58d4d0e21c460932c54","schema_version":"1.0","event_id":"sha256:e7f692728c845f7ea8e793de4dbba41fabaa39ca01acf58d4d0e21c460932c54"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P4VRDB3TLY74NDMUDXF2URNGO2/bundle.json","state_url":"https://pith.science/pith/P4VRDB3TLY74NDMUDXF2URNGO2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P4VRDB3TLY74NDMUDXF2URNGO2/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":"2026-05-26T05:27:34Z","links":{"resolver":"https://pith.science/pith/P4VRDB3TLY74NDMUDXF2URNGO2","bundle":"https://pith.science/pith/P4VRDB3TLY74NDMUDXF2URNGO2/bundle.json","state":"https://pith.science/pith/P4VRDB3TLY74NDMUDXF2URNGO2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P4VRDB3TLY74NDMUDXF2URNGO2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:P4VRDB3TLY74NDMUDXF2URNGO2","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":"b651e99c985686dc04211a01eab0535ff5196ddb6aa0dddc24be1613d8469be5","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2013-06-18T16:34:18Z","title_canon_sha256":"eefeff82551da55197768f4c6634a65a7029bc7d0aa1eeb0b5033afa429034d5"},"schema_version":"1.0","source":{"id":"1306.4263","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.4263","created_at":"2026-05-18T03:20:36Z"},{"alias_kind":"arxiv_version","alias_value":"1306.4263v1","created_at":"2026-05-18T03:20:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.4263","created_at":"2026-05-18T03:20:36Z"},{"alias_kind":"pith_short_12","alias_value":"P4VRDB3TLY74","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"P4VRDB3TLY74NDMU","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"P4VRDB3T","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:e7f692728c845f7ea8e793de4dbba41fabaa39ca01acf58d4d0e21c460932c54","target":"graph","created_at":"2026-05-18T03:20:36Z","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":"We present a Sage implementation of Ore algebras. The main features for the most common instances include basic arithmetic and actions; gcrd and lclm; D-finite closure properties; natural transformations between related algebras; guessing; desingularization; solvers for polynomials, rational functions and (generalized) power series. This paper is a tutorial on how to use the package.","authors_text":"Fredrik Johansson, Manuel Kauers, Maximilian Jaroschek","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2013-06-18T16:34:18Z","title":"Ore Polynomials in Sage"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.4263","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:be4e8113d26b91c77aef40b4083849f033df98adc56f41ff0fbf8fca86ca0602","target":"record","created_at":"2026-05-18T03:20:36Z","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":"b651e99c985686dc04211a01eab0535ff5196ddb6aa0dddc24be1613d8469be5","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2013-06-18T16:34:18Z","title_canon_sha256":"eefeff82551da55197768f4c6634a65a7029bc7d0aa1eeb0b5033afa429034d5"},"schema_version":"1.0","source":{"id":"1306.4263","kind":"arxiv","version":1}},"canonical_sha256":"7f2b1187735e3fc68d941dcbaa45a676bd1792b9654f4ed7d25c0fe4794126cf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7f2b1187735e3fc68d941dcbaa45a676bd1792b9654f4ed7d25c0fe4794126cf","first_computed_at":"2026-05-18T03:20:36.631568Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:20:36.631568Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0orQxf7xzg2SwrRllKkm6sVoEjNKoaoLR5zKGT1ItFN8UdQF0BNuag4qvHiDDPP2KcqsQFSleTO89vO4qT/pDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:20:36.632369Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.4263","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:be4e8113d26b91c77aef40b4083849f033df98adc56f41ff0fbf8fca86ca0602","sha256:e7f692728c845f7ea8e793de4dbba41fabaa39ca01acf58d4d0e21c460932c54"],"state_sha256":"b9173eabe86adb81e83dc7a0c675439905debdf1e0f265454e59f84037664618"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/Lrq/SjAH8nnn4REpYaJaLmRNEmPpvGDhN66h7K1aaz8YnYu9SK89anMIpfnn8LNVeY+wbg9LnW5fO/lCDICBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T05:27:34.430855Z","bundle_sha256":"b5591cf987e692be17d70d7aa754720fc7e44873d2bdec9feaf4a3f3995ccff6"}}