{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:NCHITO4OGIIZ3MQRIJE2TN5VSC","short_pith_number":"pith:NCHITO4O","canonical_record":{"source":{"id":"2304.00506","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AT","submitted_at":"2023-04-02T10:48:31Z","cross_cats_sorted":[],"title_canon_sha256":"7abc26ac7bfb2d48633b2f49929d88ef8f0a795b6269d207dfbbcfca1d9c0926","abstract_canon_sha256":"6ea31e901ef29a5a484ab3fa2af5cea9077ee5c7efef598c32e0c4bd53274eaa"},"schema_version":"1.0"},"canonical_sha256":"688e89bb8e32119db2114249a9b7b59098dc34904a997543c0569a7f11a46422","source":{"kind":"arxiv","id":"2304.00506","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2304.00506","created_at":"2026-07-05T05:57:18Z"},{"alias_kind":"arxiv_version","alias_value":"2304.00506v1","created_at":"2026-07-05T05:57:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2304.00506","created_at":"2026-07-05T05:57:18Z"},{"alias_kind":"pith_short_12","alias_value":"NCHITO4OGIIZ","created_at":"2026-07-05T05:57:18Z"},{"alias_kind":"pith_short_16","alias_value":"NCHITO4OGIIZ3MQR","created_at":"2026-07-05T05:57:18Z"},{"alias_kind":"pith_short_8","alias_value":"NCHITO4O","created_at":"2026-07-05T05:57:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:NCHITO4OGIIZ3MQRIJE2TN5VSC","target":"record","payload":{"canonical_record":{"source":{"id":"2304.00506","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AT","submitted_at":"2023-04-02T10:48:31Z","cross_cats_sorted":[],"title_canon_sha256":"7abc26ac7bfb2d48633b2f49929d88ef8f0a795b6269d207dfbbcfca1d9c0926","abstract_canon_sha256":"6ea31e901ef29a5a484ab3fa2af5cea9077ee5c7efef598c32e0c4bd53274eaa"},"schema_version":"1.0"},"canonical_sha256":"688e89bb8e32119db2114249a9b7b59098dc34904a997543c0569a7f11a46422","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:57:18.528944Z","signature_b64":"XyoejcXAEkO4vJvSVsU+13b40pdK2uEFEmI1rgci34ShT7xaj5VySX3F8vNY8aDLHMQrasvsljd2o6n+AZCSDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"688e89bb8e32119db2114249a9b7b59098dc34904a997543c0569a7f11a46422","last_reissued_at":"2026-07-05T05:57:18.528517Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:57:18.528517Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2304.00506","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":"2026-07-05T05:57:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nijGsH+ApRo5PMQ5LOjOIanqfmi2QCwgen8svfyd7nwdNwbWPrNz/qpLRVRzBNfIyvRV1ZS7rdngrfaAW4Y8Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T20:28:00.045994Z"},"content_sha256":"f276e2ae5948a74ea99b747bb2f766aaefb0aa4540becfab3a83853bcc67cb22","schema_version":"1.0","event_id":"sha256:f276e2ae5948a74ea99b747bb2f766aaefb0aa4540becfab3a83853bcc67cb22"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:NCHITO4OGIIZ3MQRIJE2TN5VSC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Noncommutative Gr\\\"obner Bases and Ext groups; Application to the Steenrod Algebra","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Weinan Lin","submitted_at":"2023-04-02T10:48:31Z","abstract_excerpt":"We consider a theory of noncommutative Gr\\\"obner bases on decreasingly filtered algebras whose associated graded algebras are commutative. We transfer many algorithms that use commutative Gr\\\"obner bases to this context. As an important application, we implement very efficient algorithms to compute the Ext groups over the Steenrod algebra $\\mathscr{A}$ at the prime $2$. Especially, the cohomology of the Steenrod algebra $Ext_{\\mathscr{A}}^{*, *}(\\mathbb{F}_2, \\mathbb{F}_2)$, which plays an important role in algebraic topology, is calculated up to total degree of 261, including the ring structu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.00506","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/2304.00506/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":"2026-07-05T05:57:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8RRSQGEHS/+9kS2OkEi141Ioba6w3gaJIbTFp5rIZ0ZUZSsLDfpO7injOz3wB+NmZ639/Ho3JhZO/L+SWpMhAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T20:28:00.046738Z"},"content_sha256":"c778d19cc36234903c632dc9fe141ee2b3c8cd392b2c93458efc105efa0e8164","schema_version":"1.0","event_id":"sha256:c778d19cc36234903c632dc9fe141ee2b3c8cd392b2c93458efc105efa0e8164"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NCHITO4OGIIZ3MQRIJE2TN5VSC/bundle.json","state_url":"https://pith.science/pith/NCHITO4OGIIZ3MQRIJE2TN5VSC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NCHITO4OGIIZ3MQRIJE2TN5VSC/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":"2026-08-05T20:28:00Z","links":{"resolver":"https://pith.science/pith/NCHITO4OGIIZ3MQRIJE2TN5VSC","bundle":"https://pith.science/pith/NCHITO4OGIIZ3MQRIJE2TN5VSC/bundle.json","state":"https://pith.science/pith/NCHITO4OGIIZ3MQRIJE2TN5VSC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NCHITO4OGIIZ3MQRIJE2TN5VSC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:NCHITO4OGIIZ3MQRIJE2TN5VSC","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":"6ea31e901ef29a5a484ab3fa2af5cea9077ee5c7efef598c32e0c4bd53274eaa","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AT","submitted_at":"2023-04-02T10:48:31Z","title_canon_sha256":"7abc26ac7bfb2d48633b2f49929d88ef8f0a795b6269d207dfbbcfca1d9c0926"},"schema_version":"1.0","source":{"id":"2304.00506","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2304.00506","created_at":"2026-07-05T05:57:18Z"},{"alias_kind":"arxiv_version","alias_value":"2304.00506v1","created_at":"2026-07-05T05:57:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2304.00506","created_at":"2026-07-05T05:57:18Z"},{"alias_kind":"pith_short_12","alias_value":"NCHITO4OGIIZ","created_at":"2026-07-05T05:57:18Z"},{"alias_kind":"pith_short_16","alias_value":"NCHITO4OGIIZ3MQR","created_at":"2026-07-05T05:57:18Z"},{"alias_kind":"pith_short_8","alias_value":"NCHITO4O","created_at":"2026-07-05T05:57:18Z"}],"graph_snapshots":[{"event_id":"sha256:c778d19cc36234903c632dc9fe141ee2b3c8cd392b2c93458efc105efa0e8164","target":"graph","created_at":"2026-07-05T05:57:18Z","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/2304.00506/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider a theory of noncommutative Gr\\\"obner bases on decreasingly filtered algebras whose associated graded algebras are commutative. We transfer many algorithms that use commutative Gr\\\"obner bases to this context. As an important application, we implement very efficient algorithms to compute the Ext groups over the Steenrod algebra $\\mathscr{A}$ at the prime $2$. Especially, the cohomology of the Steenrod algebra $Ext_{\\mathscr{A}}^{*, *}(\\mathbb{F}_2, \\mathbb{F}_2)$, which plays an important role in algebraic topology, is calculated up to total degree of 261, including the ring structu","authors_text":"Weinan Lin","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AT","submitted_at":"2023-04-02T10:48:31Z","title":"Noncommutative Gr\\\"obner Bases and Ext groups; Application to the Steenrod Algebra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.00506","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:f276e2ae5948a74ea99b747bb2f766aaefb0aa4540becfab3a83853bcc67cb22","target":"record","created_at":"2026-07-05T05:57:18Z","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":"6ea31e901ef29a5a484ab3fa2af5cea9077ee5c7efef598c32e0c4bd53274eaa","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AT","submitted_at":"2023-04-02T10:48:31Z","title_canon_sha256":"7abc26ac7bfb2d48633b2f49929d88ef8f0a795b6269d207dfbbcfca1d9c0926"},"schema_version":"1.0","source":{"id":"2304.00506","kind":"arxiv","version":1}},"canonical_sha256":"688e89bb8e32119db2114249a9b7b59098dc34904a997543c0569a7f11a46422","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"688e89bb8e32119db2114249a9b7b59098dc34904a997543c0569a7f11a46422","first_computed_at":"2026-07-05T05:57:18.528517Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:57:18.528517Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XyoejcXAEkO4vJvSVsU+13b40pdK2uEFEmI1rgci34ShT7xaj5VySX3F8vNY8aDLHMQrasvsljd2o6n+AZCSDg==","signature_status":"signed_v1","signed_at":"2026-07-05T05:57:18.528944Z","signed_message":"canonical_sha256_bytes"},"source_id":"2304.00506","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f276e2ae5948a74ea99b747bb2f766aaefb0aa4540becfab3a83853bcc67cb22","sha256:c778d19cc36234903c632dc9fe141ee2b3c8cd392b2c93458efc105efa0e8164"],"state_sha256":"13549ef3eb1ebf52065c6a744da988270be96d2cbaea24e6e2aa6eaf52337dcc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GxGM7/eMfkbyeVVasvPTlCt2YPsmAekN2db0IJyceyTipXAHBeEaafoNc8DkIo5ofEUhKOx5MsdnUn3EJEoeCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T20:28:00.059370Z","bundle_sha256":"4b8070127296c7e2e9be635599076eb480d3163e11fe7ca2c31efcd54c2c0f29"}}