{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:KKJOZYCN4O3FRF54IWLFANMBVY","short_pith_number":"pith:KKJOZYCN","schema_version":"1.0","canonical_sha256":"5292ece04de3b65897bc4596503581ae30b1782459881c034f2e0fc53beb7814","source":{"kind":"arxiv","id":"1710.01639","version":1},"attestation_state":"computed","paper":{"title":"A $\\{-1,0,1\\}$- and sparsest basis for the null space of a forest in optimal time","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Adri\\'an Pastine, Daniel A. Jaume, Gonzalo Molina, Mart\\'in D. Safe","submitted_at":"2017-10-04T14:52:30Z","abstract_excerpt":"Given a matrix, the Null Space Problem asks for a basis of its null space having the fewest nonzeros. This problem is known to be NP-complete and even hard to approximate. The null space of a forest is the null space of its adjacency matrix. Sander and Sander (2005) and Akbari et al. (2006), independently, proved that the null space of each forest admits a $\\{-1,0,1\\}$-basis. We devise an algorithm for determining a sparsest basis of the null space of any given forest which, in addition, is a $\\{-1,0,1\\}$-basis. Our algorithm is time-optimal in the sense that it takes time at most proportional"},"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":"1710.01639","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-10-04T14:52:30Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"94f81f50d95b4a81ac859cce9d2f4def0abf9deee8e1637bfe5c29b3230a1a64","abstract_canon_sha256":"f630d62447d157fa3ef1f521748f6adc65304b6fb5dd31871256ddf3ee278217"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:33:40.301187Z","signature_b64":"lv+hy2hTDu3rdvkIWwPenuC8U5S3XI4ENV4t9wwMKHIhB2AExsV574CCA5gYuICotnvTwUQ68nt0HC3l+X35Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5292ece04de3b65897bc4596503581ae30b1782459881c034f2e0fc53beb7814","last_reissued_at":"2026-05-18T00:33:40.300568Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:33:40.300568Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A $\\{-1,0,1\\}$- and sparsest basis for the null space of a forest in optimal time","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Adri\\'an Pastine, Daniel A. Jaume, Gonzalo Molina, Mart\\'in D. Safe","submitted_at":"2017-10-04T14:52:30Z","abstract_excerpt":"Given a matrix, the Null Space Problem asks for a basis of its null space having the fewest nonzeros. This problem is known to be NP-complete and even hard to approximate. The null space of a forest is the null space of its adjacency matrix. Sander and Sander (2005) and Akbari et al. (2006), independently, proved that the null space of each forest admits a $\\{-1,0,1\\}$-basis. We devise an algorithm for determining a sparsest basis of the null space of any given forest which, in addition, is a $\\{-1,0,1\\}$-basis. Our algorithm is time-optimal in the sense that it takes time at most proportional"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.01639","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":"1710.01639","created_at":"2026-05-18T00:33:40.300645+00:00"},{"alias_kind":"arxiv_version","alias_value":"1710.01639v1","created_at":"2026-05-18T00:33:40.300645+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.01639","created_at":"2026-05-18T00:33:40.300645+00:00"},{"alias_kind":"pith_short_12","alias_value":"KKJOZYCN4O3F","created_at":"2026-05-18T12:31:24.725408+00:00"},{"alias_kind":"pith_short_16","alias_value":"KKJOZYCN4O3FRF54","created_at":"2026-05-18T12:31:24.725408+00:00"},{"alias_kind":"pith_short_8","alias_value":"KKJOZYCN","created_at":"2026-05-18T12:31:24.725408+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/KKJOZYCN4O3FRF54IWLFANMBVY","json":"https://pith.science/pith/KKJOZYCN4O3FRF54IWLFANMBVY.json","graph_json":"https://pith.science/api/pith-number/KKJOZYCN4O3FRF54IWLFANMBVY/graph.json","events_json":"https://pith.science/api/pith-number/KKJOZYCN4O3FRF54IWLFANMBVY/events.json","paper":"https://pith.science/paper/KKJOZYCN"},"agent_actions":{"view_html":"https://pith.science/pith/KKJOZYCN4O3FRF54IWLFANMBVY","download_json":"https://pith.science/pith/KKJOZYCN4O3FRF54IWLFANMBVY.json","view_paper":"https://pith.science/paper/KKJOZYCN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1710.01639&json=true","fetch_graph":"https://pith.science/api/pith-number/KKJOZYCN4O3FRF54IWLFANMBVY/graph.json","fetch_events":"https://pith.science/api/pith-number/KKJOZYCN4O3FRF54IWLFANMBVY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KKJOZYCN4O3FRF54IWLFANMBVY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KKJOZYCN4O3FRF54IWLFANMBVY/action/storage_attestation","attest_author":"https://pith.science/pith/KKJOZYCN4O3FRF54IWLFANMBVY/action/author_attestation","sign_citation":"https://pith.science/pith/KKJOZYCN4O3FRF54IWLFANMBVY/action/citation_signature","submit_replication":"https://pith.science/pith/KKJOZYCN4O3FRF54IWLFANMBVY/action/replication_record"}},"created_at":"2026-05-18T00:33:40.300645+00:00","updated_at":"2026-05-18T00:33:40.300645+00:00"}