{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:YG7JGLIZ33YU2AAKJSIA3ZNI6Y","short_pith_number":"pith:YG7JGLIZ","canonical_record":{"source":{"id":"2404.16796","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2024-04-25T17:42:32Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"c22d66c2105487699c2182ab68a9b110957de730d0e41ac8734f3bcb719e35c2","abstract_canon_sha256":"4c42c9ee77ee2f452c6fabfbbd7ef0a2c4a4868eebd683ad912debff73f89624"},"schema_version":"1.0"},"canonical_sha256":"c1be932d19def14d000a4c900de5a8f6127ab4857e4a5abb94385f17f1c5f995","source":{"kind":"arxiv","id":"2404.16796","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.16796","created_at":"2026-07-05T08:12:12Z"},{"alias_kind":"arxiv_version","alias_value":"2404.16796v1","created_at":"2026-07-05T08:12:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.16796","created_at":"2026-07-05T08:12:12Z"},{"alias_kind":"pith_short_12","alias_value":"YG7JGLIZ33YU","created_at":"2026-07-05T08:12:12Z"},{"alias_kind":"pith_short_16","alias_value":"YG7JGLIZ33YU2AAK","created_at":"2026-07-05T08:12:12Z"},{"alias_kind":"pith_short_8","alias_value":"YG7JGLIZ","created_at":"2026-07-05T08:12:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:YG7JGLIZ33YU2AAKJSIA3ZNI6Y","target":"record","payload":{"canonical_record":{"source":{"id":"2404.16796","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2024-04-25T17:42:32Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"c22d66c2105487699c2182ab68a9b110957de730d0e41ac8734f3bcb719e35c2","abstract_canon_sha256":"4c42c9ee77ee2f452c6fabfbbd7ef0a2c4a4868eebd683ad912debff73f89624"},"schema_version":"1.0"},"canonical_sha256":"c1be932d19def14d000a4c900de5a8f6127ab4857e4a5abb94385f17f1c5f995","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:12:12.647709Z","signature_b64":"jXU+dhaRe9WGchwMWA0lKO6mQXoQWnVsAOl0wr9IRyZoW+VAntcLAt7BYGOKtURMIxEjtZAADuf61Yt/TRCcDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c1be932d19def14d000a4c900de5a8f6127ab4857e4a5abb94385f17f1c5f995","last_reissued_at":"2026-07-05T08:12:12.647211Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:12:12.647211Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2404.16796","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":"2026-07-05T08:12:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8s6gaFe1cl1I+KTgVbgDdr8HO+cpZN7cK0ZhyINoQUtWXNA4twRBCvzCTipBiCk+wePCe5QE88zHxUTtzOylDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T12:31:56.679117Z"},"content_sha256":"cf219821a76c51891e9107d29a2255bf30f775b2be41aafef5a6c2265db6a65a","schema_version":"1.0","event_id":"sha256:cf219821a76c51891e9107d29a2255bf30f775b2be41aafef5a6c2265db6a65a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:YG7JGLIZ33YU2AAKJSIA3ZNI6Y","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"SAGBI and Gr\\\"obner Bases Detection","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"Elima Shehu, Timothy Duff, Viktoriia Borovik","submitted_at":"2024-04-25T17:42:32Z","abstract_excerpt":"We introduce a detection algorithm for SAGBI basis in polynomial rings, analogous to a Gr\\\"obner basis detection algorithm previously proposed by Gritzmann and Sturmfels. We also present two accompanying software packages named SagbiGbDetection for Macaulay2 and Julia. Both packages allow the user to find one or more term orders for which a set of input polynomials form either Gr\\\"obner basis for the ideal they generate or a SAGBI basis for the subalgebra. Additionally, we investigate the computational complexity of homogeneous SAGBI detection and apply our implementation to several novel exam"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.16796","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/2404.16796/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":"2026-07-05T08:12:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"69Le70hNy0aniG4PrwOaeD0yvwP9RwlRr67qv7KyV1ZHGCMTx+F0IFLrFhgOQmKkM1NZ8TuY1DZYY4KjYXi6Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T12:31:56.679624Z"},"content_sha256":"65b7e83bcf0e06977ccdedfe5e2e99d49d7ad88fb88589661308d9c5c92bdb89","schema_version":"1.0","event_id":"sha256:65b7e83bcf0e06977ccdedfe5e2e99d49d7ad88fb88589661308d9c5c92bdb89"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YG7JGLIZ33YU2AAKJSIA3ZNI6Y/bundle.json","state_url":"https://pith.science/pith/YG7JGLIZ33YU2AAKJSIA3ZNI6Y/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YG7JGLIZ33YU2AAKJSIA3ZNI6Y/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":"2026-08-08T12:31:56Z","links":{"resolver":"https://pith.science/pith/YG7JGLIZ33YU2AAKJSIA3ZNI6Y","bundle":"https://pith.science/pith/YG7JGLIZ33YU2AAKJSIA3ZNI6Y/bundle.json","state":"https://pith.science/pith/YG7JGLIZ33YU2AAKJSIA3ZNI6Y/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YG7JGLIZ33YU2AAKJSIA3ZNI6Y/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:YG7JGLIZ33YU2AAKJSIA3ZNI6Y","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":"4c42c9ee77ee2f452c6fabfbbd7ef0a2c4a4868eebd683ad912debff73f89624","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2024-04-25T17:42:32Z","title_canon_sha256":"c22d66c2105487699c2182ab68a9b110957de730d0e41ac8734f3bcb719e35c2"},"schema_version":"1.0","source":{"id":"2404.16796","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.16796","created_at":"2026-07-05T08:12:12Z"},{"alias_kind":"arxiv_version","alias_value":"2404.16796v1","created_at":"2026-07-05T08:12:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.16796","created_at":"2026-07-05T08:12:12Z"},{"alias_kind":"pith_short_12","alias_value":"YG7JGLIZ33YU","created_at":"2026-07-05T08:12:12Z"},{"alias_kind":"pith_short_16","alias_value":"YG7JGLIZ33YU2AAK","created_at":"2026-07-05T08:12:12Z"},{"alias_kind":"pith_short_8","alias_value":"YG7JGLIZ","created_at":"2026-07-05T08:12:12Z"}],"graph_snapshots":[{"event_id":"sha256:65b7e83bcf0e06977ccdedfe5e2e99d49d7ad88fb88589661308d9c5c92bdb89","target":"graph","created_at":"2026-07-05T08:12:12Z","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/2404.16796/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce a detection algorithm for SAGBI basis in polynomial rings, analogous to a Gr\\\"obner basis detection algorithm previously proposed by Gritzmann and Sturmfels. We also present two accompanying software packages named SagbiGbDetection for Macaulay2 and Julia. Both packages allow the user to find one or more term orders for which a set of input polynomials form either Gr\\\"obner basis for the ideal they generate or a SAGBI basis for the subalgebra. Additionally, we investigate the computational complexity of homogeneous SAGBI detection and apply our implementation to several novel exam","authors_text":"Elima Shehu, Timothy Duff, Viktoriia Borovik","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2024-04-25T17:42:32Z","title":"SAGBI and Gr\\\"obner Bases Detection"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.16796","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:cf219821a76c51891e9107d29a2255bf30f775b2be41aafef5a6c2265db6a65a","target":"record","created_at":"2026-07-05T08:12:12Z","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":"4c42c9ee77ee2f452c6fabfbbd7ef0a2c4a4868eebd683ad912debff73f89624","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2024-04-25T17:42:32Z","title_canon_sha256":"c22d66c2105487699c2182ab68a9b110957de730d0e41ac8734f3bcb719e35c2"},"schema_version":"1.0","source":{"id":"2404.16796","kind":"arxiv","version":1}},"canonical_sha256":"c1be932d19def14d000a4c900de5a8f6127ab4857e4a5abb94385f17f1c5f995","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c1be932d19def14d000a4c900de5a8f6127ab4857e4a5abb94385f17f1c5f995","first_computed_at":"2026-07-05T08:12:12.647211Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:12:12.647211Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jXU+dhaRe9WGchwMWA0lKO6mQXoQWnVsAOl0wr9IRyZoW+VAntcLAt7BYGOKtURMIxEjtZAADuf61Yt/TRCcDw==","signature_status":"signed_v1","signed_at":"2026-07-05T08:12:12.647709Z","signed_message":"canonical_sha256_bytes"},"source_id":"2404.16796","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cf219821a76c51891e9107d29a2255bf30f775b2be41aafef5a6c2265db6a65a","sha256:65b7e83bcf0e06977ccdedfe5e2e99d49d7ad88fb88589661308d9c5c92bdb89"],"state_sha256":"9d8605e3dfa5b0c59d3d9c0dd3b0195d5383e185d9befb9e7e76f3d8019dc6fc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8gAAe7js63fQANXBCCxY5U4bol9/r69/D/dOdLqg8tD2WNnXjgeSWJNU4pWBAsl18i5fHZw3IiR99csL5rPmBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T12:31:56.684101Z","bundle_sha256":"3a4be9f633e5bf016baeb181f31080924390d52455ed0fcea1359226d71cda2b"}}