{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:TQB2YXBXTWIZIWNEO65BHEZUB4","short_pith_number":"pith:TQB2YXBX","schema_version":"1.0","canonical_sha256":"9c03ac5c379d919459a477ba1393340f27ef85c06c3c54df47ee85f51c0c1246","source":{"kind":"arxiv","id":"2308.14979","version":2},"attestation_state":"computed","paper":{"title":"Summand-injectivity of interval covers and monotonicity of interval resolution global dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.RT","authors_text":"Emerson G. Escolar, Shunsuke Tada, Toshitaka Aoki","submitted_at":"2023-08-29T02:13:13Z","abstract_excerpt":"Recently, there is growing interest in the use of relative homology algebra to develop invariants using interval covers and interval resolutions (i.e., right minimal approximations and resolutions relative to interval-decomposable modules) for multi-parameter persistence modules. In this paper, the set of all interval modules over a given poset plays a central role. Firstly, we show that the restriction of interval covers of modules to each indecomposable direct summand is injective. This result suggests a way to simplify the computation of interval covers. Secondly, we show the monotonicity o"},"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":"2308.14979","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2023-08-29T02:13:13Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"088d87dee9cbd0882d0933dd171b3240dbcc7f65d5eec64d98fd41f206e2c5f7","abstract_canon_sha256":"e66f45ac3d54a5ed5ae4177a441878c3329228d9587b74c314c0c5abf3c3e19a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:11:18.074554Z","signature_b64":"RGrecC5pY+E054NdZfg5x3xNXZbSoXpx1MJycBP/Xm/kzEbXbpJNEIhA0u5SSw01VnL+6bGTIi6+epp28W0uBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9c03ac5c379d919459a477ba1393340f27ef85c06c3c54df47ee85f51c0c1246","last_reissued_at":"2026-07-05T07:11:18.074132Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:11:18.074132Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Summand-injectivity of interval covers and monotonicity of interval resolution global dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.RT","authors_text":"Emerson G. Escolar, Shunsuke Tada, Toshitaka Aoki","submitted_at":"2023-08-29T02:13:13Z","abstract_excerpt":"Recently, there is growing interest in the use of relative homology algebra to develop invariants using interval covers and interval resolutions (i.e., right minimal approximations and resolutions relative to interval-decomposable modules) for multi-parameter persistence modules. In this paper, the set of all interval modules over a given poset plays a central role. Firstly, we show that the restriction of interval covers of modules to each indecomposable direct summand is injective. This result suggests a way to simplify the computation of interval covers. Secondly, we show the monotonicity o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.14979","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/2308.14979/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":"2308.14979","created_at":"2026-07-05T07:11:18.074190+00:00"},{"alias_kind":"arxiv_version","alias_value":"2308.14979v2","created_at":"2026-07-05T07:11:18.074190+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2308.14979","created_at":"2026-07-05T07:11:18.074190+00:00"},{"alias_kind":"pith_short_12","alias_value":"TQB2YXBXTWIZ","created_at":"2026-07-05T07:11:18.074190+00:00"},{"alias_kind":"pith_short_16","alias_value":"TQB2YXBXTWIZIWNE","created_at":"2026-07-05T07:11:18.074190+00:00"},{"alias_kind":"pith_short_8","alias_value":"TQB2YXBX","created_at":"2026-07-05T07:11:18.074190+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2501.00322","citing_title":"Bipath Persistence as Zigzag Persistence","ref_index":3,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/TQB2YXBXTWIZIWNEO65BHEZUB4","json":"https://pith.science/pith/TQB2YXBXTWIZIWNEO65BHEZUB4.json","graph_json":"https://pith.science/api/pith-number/TQB2YXBXTWIZIWNEO65BHEZUB4/graph.json","events_json":"https://pith.science/api/pith-number/TQB2YXBXTWIZIWNEO65BHEZUB4/events.json","paper":"https://pith.science/paper/TQB2YXBX"},"agent_actions":{"view_html":"https://pith.science/pith/TQB2YXBXTWIZIWNEO65BHEZUB4","download_json":"https://pith.science/pith/TQB2YXBXTWIZIWNEO65BHEZUB4.json","view_paper":"https://pith.science/paper/TQB2YXBX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2308.14979&json=true","fetch_graph":"https://pith.science/api/pith-number/TQB2YXBXTWIZIWNEO65BHEZUB4/graph.json","fetch_events":"https://pith.science/api/pith-number/TQB2YXBXTWIZIWNEO65BHEZUB4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TQB2YXBXTWIZIWNEO65BHEZUB4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TQB2YXBXTWIZIWNEO65BHEZUB4/action/storage_attestation","attest_author":"https://pith.science/pith/TQB2YXBXTWIZIWNEO65BHEZUB4/action/author_attestation","sign_citation":"https://pith.science/pith/TQB2YXBXTWIZIWNEO65BHEZUB4/action/citation_signature","submit_replication":"https://pith.science/pith/TQB2YXBXTWIZIWNEO65BHEZUB4/action/replication_record"}},"created_at":"2026-07-05T07:11:18.074190+00:00","updated_at":"2026-07-05T07:11:18.074190+00:00"}