{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:XSLMXPXHUR3TTUXQ6KZNWIHZTD","short_pith_number":"pith:XSLMXPXH","schema_version":"1.0","canonical_sha256":"bc96cbbee7a47739d2f0f2b2db20f998d08aaabffd1458642b355c7491265b7a","source":{"kind":"arxiv","id":"1706.10027","version":2},"attestation_state":"computed","paper":{"title":"Matrix Method for Persistence Modules on Commutative Ladders of Finite Type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.RT","authors_text":"Emerson G. Escolar, Hideto Asashiba, Hiroshi Takeuchi, Yasuaki Hiraoka","submitted_at":"2017-06-30T05:42:45Z","abstract_excerpt":"The theory of persistence modules on the commutative ladders $CL_n(\\tau)$ provides an extension of persistent homology. However, an efficient algorithm to compute the generalized persistence diagrams is still lacking. In this work, we view a persistence module $M$ on $CL_n(\\tau)$ as a morphism between zigzag modules, which can be expressed in a block matrix form. For the representation finite case ($n\\leq 4)$, we provide an algorithm that uses certain permissible row and column operations to compute a normal form of the block matrix. In this form an indecomposable decomposition of $M$, and thu"},"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":"1706.10027","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-06-30T05:42:45Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"8df64addc1f85d5cf63671a118c0635c12cbb250355d2694090f0d03c65fac7a","abstract_canon_sha256":"afa17b344ff7352b2a5c60de657329af2312b95251b7e997bb3a3ce3771b3472"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:00.533527Z","signature_b64":"XY8LMaabtzH8thkc2yQE6BxYz4MBMryAt2yqq2nhYeIOMSsM1B0gYD5DyflWgCI7Z9+DjYtcRIZWuHEH5Ei4Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bc96cbbee7a47739d2f0f2b2db20f998d08aaabffd1458642b355c7491265b7a","last_reissued_at":"2026-05-18T00:05:00.533095Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:00.533095Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Matrix Method for Persistence Modules on Commutative Ladders of Finite Type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.RT","authors_text":"Emerson G. Escolar, Hideto Asashiba, Hiroshi Takeuchi, Yasuaki Hiraoka","submitted_at":"2017-06-30T05:42:45Z","abstract_excerpt":"The theory of persistence modules on the commutative ladders $CL_n(\\tau)$ provides an extension of persistent homology. However, an efficient algorithm to compute the generalized persistence diagrams is still lacking. In this work, we view a persistence module $M$ on $CL_n(\\tau)$ as a morphism between zigzag modules, which can be expressed in a block matrix form. For the representation finite case ($n\\leq 4)$, we provide an algorithm that uses certain permissible row and column operations to compute a normal form of the block matrix. In this form an indecomposable decomposition of $M$, and thu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.10027","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":""},"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":"1706.10027","created_at":"2026-05-18T00:05:00.533159+00:00"},{"alias_kind":"arxiv_version","alias_value":"1706.10027v2","created_at":"2026-05-18T00:05:00.533159+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.10027","created_at":"2026-05-18T00:05:00.533159+00:00"},{"alias_kind":"pith_short_12","alias_value":"XSLMXPXHUR3T","created_at":"2026-05-18T12:31:56.362134+00:00"},{"alias_kind":"pith_short_16","alias_value":"XSLMXPXHUR3TTUXQ","created_at":"2026-05-18T12:31:56.362134+00:00"},{"alias_kind":"pith_short_8","alias_value":"XSLMXPXH","created_at":"2026-05-18T12:31:56.362134+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/XSLMXPXHUR3TTUXQ6KZNWIHZTD","json":"https://pith.science/pith/XSLMXPXHUR3TTUXQ6KZNWIHZTD.json","graph_json":"https://pith.science/api/pith-number/XSLMXPXHUR3TTUXQ6KZNWIHZTD/graph.json","events_json":"https://pith.science/api/pith-number/XSLMXPXHUR3TTUXQ6KZNWIHZTD/events.json","paper":"https://pith.science/paper/XSLMXPXH"},"agent_actions":{"view_html":"https://pith.science/pith/XSLMXPXHUR3TTUXQ6KZNWIHZTD","download_json":"https://pith.science/pith/XSLMXPXHUR3TTUXQ6KZNWIHZTD.json","view_paper":"https://pith.science/paper/XSLMXPXH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1706.10027&json=true","fetch_graph":"https://pith.science/api/pith-number/XSLMXPXHUR3TTUXQ6KZNWIHZTD/graph.json","fetch_events":"https://pith.science/api/pith-number/XSLMXPXHUR3TTUXQ6KZNWIHZTD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XSLMXPXHUR3TTUXQ6KZNWIHZTD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XSLMXPXHUR3TTUXQ6KZNWIHZTD/action/storage_attestation","attest_author":"https://pith.science/pith/XSLMXPXHUR3TTUXQ6KZNWIHZTD/action/author_attestation","sign_citation":"https://pith.science/pith/XSLMXPXHUR3TTUXQ6KZNWIHZTD/action/citation_signature","submit_replication":"https://pith.science/pith/XSLMXPXHUR3TTUXQ6KZNWIHZTD/action/replication_record"}},"created_at":"2026-05-18T00:05:00.533159+00:00","updated_at":"2026-05-18T00:05:00.533159+00:00"}