{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:KKJOZYCN4O3FRF54IWLFANMBVY","short_pith_number":"pith:KKJOZYCN","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"},"canonical_sha256":"5292ece04de3b65897bc4596503581ae30b1782459881c034f2e0fc53beb7814","source":{"kind":"arxiv","id":"1710.01639","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.01639","created_at":"2026-05-18T00:33:40Z"},{"alias_kind":"arxiv_version","alias_value":"1710.01639v1","created_at":"2026-05-18T00:33:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.01639","created_at":"2026-05-18T00:33:40Z"},{"alias_kind":"pith_short_12","alias_value":"KKJOZYCN4O3F","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"KKJOZYCN4O3FRF54","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"KKJOZYCN","created_at":"2026-05-18T12:31:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:KKJOZYCN4O3FRF54IWLFANMBVY","target":"record","payload":{"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"},"canonical_sha256":"5292ece04de3b65897bc4596503581ae30b1782459881c034f2e0fc53beb7814","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"},"source_kind":"arxiv","source_id":"1710.01639","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:33:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nLo7wc5eM4+XqYjobU6mtY0u3A8ppwUlpq2nCvxxGoHwCxzlIgusNRLD0fLlqeBmhBBL0Uf1JfD9e9KBKriiCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T11:41:14.391002Z"},"content_sha256":"85fade74c0615c46d2a9ce3dc7b9fe8ffedf829ff176a61d7273595589db9f4f","schema_version":"1.0","event_id":"sha256:85fade74c0615c46d2a9ce3dc7b9fe8ffedf829ff176a61d7273595589db9f4f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:KKJOZYCN4O3FRF54IWLFANMBVY","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:33:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EkBmE27fKw7b8ivM3YZZMUTDoJjMk8l/hYZRyVjoKt1aHvaNI7m+VtqfClisldXa/3HqY0oNjGCgVwJsd4zJDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T11:41:14.391690Z"},"content_sha256":"22d921e8f87d874bf32acb58ebf4a0501258979824edfcd2f1954f20bda5eedc","schema_version":"1.0","event_id":"sha256:22d921e8f87d874bf32acb58ebf4a0501258979824edfcd2f1954f20bda5eedc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KKJOZYCN4O3FRF54IWLFANMBVY/bundle.json","state_url":"https://pith.science/pith/KKJOZYCN4O3FRF54IWLFANMBVY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KKJOZYCN4O3FRF54IWLFANMBVY/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-31T11:41:14Z","links":{"resolver":"https://pith.science/pith/KKJOZYCN4O3FRF54IWLFANMBVY","bundle":"https://pith.science/pith/KKJOZYCN4O3FRF54IWLFANMBVY/bundle.json","state":"https://pith.science/pith/KKJOZYCN4O3FRF54IWLFANMBVY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KKJOZYCN4O3FRF54IWLFANMBVY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:KKJOZYCN4O3FRF54IWLFANMBVY","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"f630d62447d157fa3ef1f521748f6adc65304b6fb5dd31871256ddf3ee278217","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-10-04T14:52:30Z","title_canon_sha256":"94f81f50d95b4a81ac859cce9d2f4def0abf9deee8e1637bfe5c29b3230a1a64"},"schema_version":"1.0","source":{"id":"1710.01639","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.01639","created_at":"2026-05-18T00:33:40Z"},{"alias_kind":"arxiv_version","alias_value":"1710.01639v1","created_at":"2026-05-18T00:33:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.01639","created_at":"2026-05-18T00:33:40Z"},{"alias_kind":"pith_short_12","alias_value":"KKJOZYCN4O3F","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"KKJOZYCN4O3FRF54","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"KKJOZYCN","created_at":"2026-05-18T12:31:24Z"}],"graph_snapshots":[{"event_id":"sha256:22d921e8f87d874bf32acb58ebf4a0501258979824edfcd2f1954f20bda5eedc","target":"graph","created_at":"2026-05-18T00:33:40Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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","authors_text":"Adri\\'an Pastine, Daniel A. Jaume, Gonzalo Molina, Mart\\'in D. Safe","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-10-04T14:52:30Z","title":"A $\\{-1,0,1\\}$- and sparsest basis for the null space of a forest in optimal time"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.01639","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:85fade74c0615c46d2a9ce3dc7b9fe8ffedf829ff176a61d7273595589db9f4f","target":"record","created_at":"2026-05-18T00:33:40Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"f630d62447d157fa3ef1f521748f6adc65304b6fb5dd31871256ddf3ee278217","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-10-04T14:52:30Z","title_canon_sha256":"94f81f50d95b4a81ac859cce9d2f4def0abf9deee8e1637bfe5c29b3230a1a64"},"schema_version":"1.0","source":{"id":"1710.01639","kind":"arxiv","version":1}},"canonical_sha256":"5292ece04de3b65897bc4596503581ae30b1782459881c034f2e0fc53beb7814","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5292ece04de3b65897bc4596503581ae30b1782459881c034f2e0fc53beb7814","first_computed_at":"2026-05-18T00:33:40.300568Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:33:40.300568Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lv+hy2hTDu3rdvkIWwPenuC8U5S3XI4ENV4t9wwMKHIhB2AExsV574CCA5gYuICotnvTwUQ68nt0HC3l+X35Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T00:33:40.301187Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.01639","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:85fade74c0615c46d2a9ce3dc7b9fe8ffedf829ff176a61d7273595589db9f4f","sha256:22d921e8f87d874bf32acb58ebf4a0501258979824edfcd2f1954f20bda5eedc"],"state_sha256":"5a58b4c9b8b19dd94cf6208f017a08ed04fc478b279395885df5b528b33b2c05"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SZKUOuKUwNhHA8acjoIigxrNwwMEp6XgE864jVF/rt08OO+7VQdifvfja19SeGDhj2yw1eImzxIhouXricOmBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T11:41:14.395664Z","bundle_sha256":"207c29acf7169ecabc32f7856a4f19284b15c3cdeb6e2f3a418a253162543cd2"}}