{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:NNOODLCCMJUOL5GFCI2NOYFPDH","short_pith_number":"pith:NNOODLCC","canonical_record":{"source":{"id":"1104.1937","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-04-11T13:21:18Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"598e499f0f8c38fe1e3161008ee11fa86392d807d8b1028823beea6a8f365c3a","abstract_canon_sha256":"b2d76ec4193b9b8bc413cb57d0154843098b11252653fb4dbf38b9529b45bfa9"},"schema_version":"1.0"},"canonical_sha256":"6b5ce1ac426268e5f4c51234d760af19c36919150ae3e05a9b67fab074fdb6fe","source":{"kind":"arxiv","id":"1104.1937","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.1937","created_at":"2026-05-18T03:54:37Z"},{"alias_kind":"arxiv_version","alias_value":"1104.1937v3","created_at":"2026-05-18T03:54:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.1937","created_at":"2026-05-18T03:54:37Z"},{"alias_kind":"pith_short_12","alias_value":"NNOODLCCMJUO","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"NNOODLCCMJUOL5GF","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"NNOODLCC","created_at":"2026-05-18T12:26:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:NNOODLCCMJUOL5GFCI2NOYFPDH","target":"record","payload":{"canonical_record":{"source":{"id":"1104.1937","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-04-11T13:21:18Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"598e499f0f8c38fe1e3161008ee11fa86392d807d8b1028823beea6a8f365c3a","abstract_canon_sha256":"b2d76ec4193b9b8bc413cb57d0154843098b11252653fb4dbf38b9529b45bfa9"},"schema_version":"1.0"},"canonical_sha256":"6b5ce1ac426268e5f4c51234d760af19c36919150ae3e05a9b67fab074fdb6fe","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:54:37.754091Z","signature_b64":"XFieqXnqHCuB3P3mq4/P/nzCM6tLP46rqk+uArHD0uQv7t7bFLWR3qTYLoh+UycVyZAMP4nRWmrDHUOuU4m4CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6b5ce1ac426268e5f4c51234d760af19c36919150ae3e05a9b67fab074fdb6fe","last_reissued_at":"2026-05-18T03:54:37.753301Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:54:37.753301Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1104.1937","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:54:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jbLdL9amirVIUBdYZo9BgQQe7wE/0EQg2bbXMyl0WAvDDk/Wm6z2JeAi4fuzjZhIqi+k6s/8Htnrg3aC8+O7Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T16:02:06.461620Z"},"content_sha256":"f40b10d77f05343bc7a78da7c427b959e11e9cc88357195e01e7530e75b68094","schema_version":"1.0","event_id":"sha256:f40b10d77f05343bc7a78da7c427b959e11e9cc88357195e01e7530e75b68094"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:NNOODLCCMJUOL5GFCI2NOYFPDH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An algorithm for computing compatibly Frobenius split subvarieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"Karl Schwede, Mordechai Katzman","submitted_at":"2011-04-11T13:21:18Z","abstract_excerpt":"Let $R$ be a ring of prime characteristic $p$, and let $F^e_* R$ denote $R$ viewed as an $R$-module via the $e$th iterated Frobenius map. Given a surjective map $\\phi : F^e_* R \\to R$ (for example a Frobenius splitting), we exhibit an algorithm which produces all the $\\phi$-compatible ideals.\n  We also explore a variant of this algorithm under the hypothesis that $\\phi$ is not necessarily a Frobenius splitting (or even surjective). This algorithm, and the original, have been implemented in Macaulay2."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.1937","kind":"arxiv","version":3},"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":"2026-05-18T03:54:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pOpTN4hQTx2QMd9eA4xNtaEJLYkki/aVH4siiL17zf2V/ghmHOODb6UNYFtfqeVxojvYWq48vmJkJuVNSOB9DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T16:02:06.461960Z"},"content_sha256":"af2c70584e835f28bdd9b0d929b654f6931b9c54df7c3e493b13dcb3dcb1aa1d","schema_version":"1.0","event_id":"sha256:af2c70584e835f28bdd9b0d929b654f6931b9c54df7c3e493b13dcb3dcb1aa1d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NNOODLCCMJUOL5GFCI2NOYFPDH/bundle.json","state_url":"https://pith.science/pith/NNOODLCCMJUOL5GFCI2NOYFPDH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NNOODLCCMJUOL5GFCI2NOYFPDH/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":"2026-06-22T16:02:06Z","links":{"resolver":"https://pith.science/pith/NNOODLCCMJUOL5GFCI2NOYFPDH","bundle":"https://pith.science/pith/NNOODLCCMJUOL5GFCI2NOYFPDH/bundle.json","state":"https://pith.science/pith/NNOODLCCMJUOL5GFCI2NOYFPDH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NNOODLCCMJUOL5GFCI2NOYFPDH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:NNOODLCCMJUOL5GFCI2NOYFPDH","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":"b2d76ec4193b9b8bc413cb57d0154843098b11252653fb4dbf38b9529b45bfa9","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-04-11T13:21:18Z","title_canon_sha256":"598e499f0f8c38fe1e3161008ee11fa86392d807d8b1028823beea6a8f365c3a"},"schema_version":"1.0","source":{"id":"1104.1937","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.1937","created_at":"2026-05-18T03:54:37Z"},{"alias_kind":"arxiv_version","alias_value":"1104.1937v3","created_at":"2026-05-18T03:54:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.1937","created_at":"2026-05-18T03:54:37Z"},{"alias_kind":"pith_short_12","alias_value":"NNOODLCCMJUO","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"NNOODLCCMJUOL5GF","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"NNOODLCC","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:af2c70584e835f28bdd9b0d929b654f6931b9c54df7c3e493b13dcb3dcb1aa1d","target":"graph","created_at":"2026-05-18T03:54:37Z","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":"Let $R$ be a ring of prime characteristic $p$, and let $F^e_* R$ denote $R$ viewed as an $R$-module via the $e$th iterated Frobenius map. Given a surjective map $\\phi : F^e_* R \\to R$ (for example a Frobenius splitting), we exhibit an algorithm which produces all the $\\phi$-compatible ideals.\n  We also explore a variant of this algorithm under the hypothesis that $\\phi$ is not necessarily a Frobenius splitting (or even surjective). This algorithm, and the original, have been implemented in Macaulay2.","authors_text":"Karl Schwede, Mordechai Katzman","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-04-11T13:21:18Z","title":"An algorithm for computing compatibly Frobenius split subvarieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.1937","kind":"arxiv","version":3},"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:f40b10d77f05343bc7a78da7c427b959e11e9cc88357195e01e7530e75b68094","target":"record","created_at":"2026-05-18T03:54:37Z","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":"b2d76ec4193b9b8bc413cb57d0154843098b11252653fb4dbf38b9529b45bfa9","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-04-11T13:21:18Z","title_canon_sha256":"598e499f0f8c38fe1e3161008ee11fa86392d807d8b1028823beea6a8f365c3a"},"schema_version":"1.0","source":{"id":"1104.1937","kind":"arxiv","version":3}},"canonical_sha256":"6b5ce1ac426268e5f4c51234d760af19c36919150ae3e05a9b67fab074fdb6fe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6b5ce1ac426268e5f4c51234d760af19c36919150ae3e05a9b67fab074fdb6fe","first_computed_at":"2026-05-18T03:54:37.753301Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:54:37.753301Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XFieqXnqHCuB3P3mq4/P/nzCM6tLP46rqk+uArHD0uQv7t7bFLWR3qTYLoh+UycVyZAMP4nRWmrDHUOuU4m4CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:54:37.754091Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.1937","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f40b10d77f05343bc7a78da7c427b959e11e9cc88357195e01e7530e75b68094","sha256:af2c70584e835f28bdd9b0d929b654f6931b9c54df7c3e493b13dcb3dcb1aa1d"],"state_sha256":"5b2ab2cf00f58bdabcc5ca4d2156625d589447fe31a1bf36a801ad7844916451"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lrv/CK6I8KDfGUH8hAbFpeGN0+7EBfyxt1D2zaBlpeFsyh2tLealpECB/W2SX2GILuwCPIkOhrMDtYUz9QGeDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T16:02:06.463898Z","bundle_sha256":"3a3f51fec94fb6d0a29c764c0a9ba0012eecb7b917577fdacaa0db752a9ea104"}}