{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:TDLDOGEW2CGE2GD32VRHJE5DI4","short_pith_number":"pith:TDLDOGEW","schema_version":"1.0","canonical_sha256":"98d6371896d08c4d187bd5627493a3471cd04b6d803c165ec31085daa7a63fe7","source":{"kind":"arxiv","id":"2412.19799","version":2},"attestation_state":"computed","paper":{"title":"Computing Direct Sum Decompositions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"Devlin Mallory, Mahrud Sayrafi","submitted_at":"2024-12-27T18:57:35Z","abstract_excerpt":"We describe and prove correctness of two practical algorithms for finding indecomposable summands of finitely generated modules over a finitely generated k-algebra R. The first algorithm applies in the (multi)graded case, which enables the computation of indecomposable summands of coherent sheaves on subvarieties of toric varieties (in particular, for varieties embedded in projective space); the second algorithm applies when R is local and k is a finite field, opening the door to computing decompositions in singularity theory. We also present multiple examples, including some which present pre"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2412.19799","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2024-12-27T18:57:35Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"0c95d1a1b73c13b15278f8e1bf10c6b87317057c3dbbd29348fa06350b53025e","abstract_canon_sha256":"619832ec3dc5159e5524ffe39f1ccf22204babefc466ef501a8b8c75a8513dfa"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-28T02:04:39.607475Z","signature_b64":"axnqg3P2enWoGco1yHQGdqHKeTVqNpZ8lwC1m3BKoRtt96a+PBdOws1PWgCrEcZE58d7lC7sc5pRiJhnjTc2Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"98d6371896d08c4d187bd5627493a3471cd04b6d803c165ec31085daa7a63fe7","last_reissued_at":"2026-05-28T02:04:39.607001Z","signature_status":"signed_v1","first_computed_at":"2026-05-28T02:04:39.607001Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Computing Direct Sum Decompositions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"Devlin Mallory, Mahrud Sayrafi","submitted_at":"2024-12-27T18:57:35Z","abstract_excerpt":"We describe and prove correctness of two practical algorithms for finding indecomposable summands of finitely generated modules over a finitely generated k-algebra R. The first algorithm applies in the (multi)graded case, which enables the computation of indecomposable summands of coherent sheaves on subvarieties of toric varieties (in particular, for varieties embedded in projective space); the second algorithm applies when R is local and k is a finite field, opening the door to computing decompositions in singularity theory. We also present multiple examples, including some which present pre"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.19799","kind":"arxiv","version":2},"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/2412.19799/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2412.19799","created_at":"2026-05-28T02:04:39.607062+00:00"},{"alias_kind":"arxiv_version","alias_value":"2412.19799v2","created_at":"2026-05-28T02:04:39.607062+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.19799","created_at":"2026-05-28T02:04:39.607062+00:00"},{"alias_kind":"pith_short_12","alias_value":"TDLDOGEW2CGE","created_at":"2026-05-28T02:04:39.607062+00:00"},{"alias_kind":"pith_short_16","alias_value":"TDLDOGEW2CGE2GD3","created_at":"2026-05-28T02:04:39.607062+00:00"},{"alias_kind":"pith_short_8","alias_value":"TDLDOGEW","created_at":"2026-05-28T02:04:39.607062+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/TDLDOGEW2CGE2GD32VRHJE5DI4","json":"https://pith.science/pith/TDLDOGEW2CGE2GD32VRHJE5DI4.json","graph_json":"https://pith.science/api/pith-number/TDLDOGEW2CGE2GD32VRHJE5DI4/graph.json","events_json":"https://pith.science/api/pith-number/TDLDOGEW2CGE2GD32VRHJE5DI4/events.json","paper":"https://pith.science/paper/TDLDOGEW"},"agent_actions":{"view_html":"https://pith.science/pith/TDLDOGEW2CGE2GD32VRHJE5DI4","download_json":"https://pith.science/pith/TDLDOGEW2CGE2GD32VRHJE5DI4.json","view_paper":"https://pith.science/paper/TDLDOGEW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2412.19799&json=true","fetch_graph":"https://pith.science/api/pith-number/TDLDOGEW2CGE2GD32VRHJE5DI4/graph.json","fetch_events":"https://pith.science/api/pith-number/TDLDOGEW2CGE2GD32VRHJE5DI4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TDLDOGEW2CGE2GD32VRHJE5DI4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TDLDOGEW2CGE2GD32VRHJE5DI4/action/storage_attestation","attest_author":"https://pith.science/pith/TDLDOGEW2CGE2GD32VRHJE5DI4/action/author_attestation","sign_citation":"https://pith.science/pith/TDLDOGEW2CGE2GD32VRHJE5DI4/action/citation_signature","submit_replication":"https://pith.science/pith/TDLDOGEW2CGE2GD32VRHJE5DI4/action/replication_record"}},"created_at":"2026-05-28T02:04:39.607062+00:00","updated_at":"2026-05-28T02:04:39.607062+00:00"}