{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:JQUGW4VY2HT7FVNNIZMIIVZLVA","short_pith_number":"pith:JQUGW4VY","schema_version":"1.0","canonical_sha256":"4c286b72b8d1e7f2d5ad465884572ba81d721d6e537aa0cc4290653d4955a7e1","source":{"kind":"arxiv","id":"1403.3683","version":1},"attestation_state":"computed","paper":{"title":"Removal and Contraction Operations in $n$D Generalized Maps for Efficient Homology Computation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CV","authors_text":"Guillaume Damiand, Rocio Gonzalez-Diaz, Samuel Peltier","submitted_at":"2014-03-14T19:45:56Z","abstract_excerpt":"In this paper, we show that contraction operations preserve the homology of $n$D generalized maps, under some conditions. Removal and contraction operations are used to propose an efficient algorithm that compute homology generators of $n$D generalized maps. Its principle consists in simplifying a generalized map as much as possible by using removal and contraction operations. We obtain a generalized map having the same homology than the initial one, while the number of cells decreased significantly.\n  Keywords: $n$D Generalized Maps; Cellular Homology; Homology Generators; Contraction and Rem"},"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":"1403.3683","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2014-03-14T19:45:56Z","cross_cats_sorted":[],"title_canon_sha256":"3ea065b2cf62a72905825ce2f1983114a17d3eb08a0aec13983bd7fa00065fa9","abstract_canon_sha256":"a8376268ff5a5cabff3ffd79bb541084471e00d8c29bb92bf86d9760ad2bd694"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:56:19.668259Z","signature_b64":"pJSlCgwmtoMyKEmJyu06ugXHhYP+AFUAhH31qc102ZZLBB8F1HcyAAX+scKhpVkQpn9RD4nM6jHADatLSCtAAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4c286b72b8d1e7f2d5ad465884572ba81d721d6e537aa0cc4290653d4955a7e1","last_reissued_at":"2026-05-18T02:56:19.667600Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:56:19.667600Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Removal and Contraction Operations in $n$D Generalized Maps for Efficient Homology Computation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CV","authors_text":"Guillaume Damiand, Rocio Gonzalez-Diaz, Samuel Peltier","submitted_at":"2014-03-14T19:45:56Z","abstract_excerpt":"In this paper, we show that contraction operations preserve the homology of $n$D generalized maps, under some conditions. Removal and contraction operations are used to propose an efficient algorithm that compute homology generators of $n$D generalized maps. Its principle consists in simplifying a generalized map as much as possible by using removal and contraction operations. We obtain a generalized map having the same homology than the initial one, while the number of cells decreased significantly.\n  Keywords: $n$D Generalized Maps; Cellular Homology; Homology Generators; Contraction and Rem"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.3683","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":""},"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":"1403.3683","created_at":"2026-05-18T02:56:19.667695+00:00"},{"alias_kind":"arxiv_version","alias_value":"1403.3683v1","created_at":"2026-05-18T02:56:19.667695+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.3683","created_at":"2026-05-18T02:56:19.667695+00:00"},{"alias_kind":"pith_short_12","alias_value":"JQUGW4VY2HT7","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_16","alias_value":"JQUGW4VY2HT7FVNN","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_8","alias_value":"JQUGW4VY","created_at":"2026-05-18T12:28:35.611951+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/JQUGW4VY2HT7FVNNIZMIIVZLVA","json":"https://pith.science/pith/JQUGW4VY2HT7FVNNIZMIIVZLVA.json","graph_json":"https://pith.science/api/pith-number/JQUGW4VY2HT7FVNNIZMIIVZLVA/graph.json","events_json":"https://pith.science/api/pith-number/JQUGW4VY2HT7FVNNIZMIIVZLVA/events.json","paper":"https://pith.science/paper/JQUGW4VY"},"agent_actions":{"view_html":"https://pith.science/pith/JQUGW4VY2HT7FVNNIZMIIVZLVA","download_json":"https://pith.science/pith/JQUGW4VY2HT7FVNNIZMIIVZLVA.json","view_paper":"https://pith.science/paper/JQUGW4VY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1403.3683&json=true","fetch_graph":"https://pith.science/api/pith-number/JQUGW4VY2HT7FVNNIZMIIVZLVA/graph.json","fetch_events":"https://pith.science/api/pith-number/JQUGW4VY2HT7FVNNIZMIIVZLVA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JQUGW4VY2HT7FVNNIZMIIVZLVA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JQUGW4VY2HT7FVNNIZMIIVZLVA/action/storage_attestation","attest_author":"https://pith.science/pith/JQUGW4VY2HT7FVNNIZMIIVZLVA/action/author_attestation","sign_citation":"https://pith.science/pith/JQUGW4VY2HT7FVNNIZMIIVZLVA/action/citation_signature","submit_replication":"https://pith.science/pith/JQUGW4VY2HT7FVNNIZMIIVZLVA/action/replication_record"}},"created_at":"2026-05-18T02:56:19.667695+00:00","updated_at":"2026-05-18T02:56:19.667695+00:00"}