{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:CGUHWY5F4TQAYNJFGB4FGMBWHL","short_pith_number":"pith:CGUHWY5F","canonical_record":{"source":{"id":"1710.00950","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-10-03T01:00:19Z","cross_cats_sorted":[],"title_canon_sha256":"f066a57f3391b69158ff154873f30ee6f1cbab1e222fb011493457236c606d93","abstract_canon_sha256":"64ea5cb3a9674444410286750a91f56ee7064dbaa0771884c1a53a72b6484550"},"schema_version":"1.0"},"canonical_sha256":"11a87b63a5e4e00c352530785330363ac975f6ba9a045cda43d5dcdd8edf336e","source":{"kind":"arxiv","id":"1710.00950","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.00950","created_at":"2026-05-18T00:33:47Z"},{"alias_kind":"arxiv_version","alias_value":"1710.00950v1","created_at":"2026-05-18T00:33:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.00950","created_at":"2026-05-18T00:33:47Z"},{"alias_kind":"pith_short_12","alias_value":"CGUHWY5F4TQA","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"CGUHWY5F4TQAYNJF","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"CGUHWY5F","created_at":"2026-05-18T12:31:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:CGUHWY5F4TQAYNJFGB4FGMBWHL","target":"record","payload":{"canonical_record":{"source":{"id":"1710.00950","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-10-03T01:00:19Z","cross_cats_sorted":[],"title_canon_sha256":"f066a57f3391b69158ff154873f30ee6f1cbab1e222fb011493457236c606d93","abstract_canon_sha256":"64ea5cb3a9674444410286750a91f56ee7064dbaa0771884c1a53a72b6484550"},"schema_version":"1.0"},"canonical_sha256":"11a87b63a5e4e00c352530785330363ac975f6ba9a045cda43d5dcdd8edf336e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:33:47.389060Z","signature_b64":"v+AT7YO+6xIhTMJW2t9Ry4bR1/ghgWEadjtddPwlGLdcA1FugoiE2P9bbmh/wEDCJX8/c4jvAEeywN2YExRPBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"11a87b63a5e4e00c352530785330363ac975f6ba9a045cda43d5dcdd8edf336e","last_reissued_at":"2026-05-18T00:33:47.388431Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:33:47.388431Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.00950","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":"2026-05-18T00:33:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ENRVm1s64RbbOZKGBuOGNPcAkeEWerl5+AGgfndwgYBNEgAYuhAZELtd4Ey/wA6Ss+pTomwYn/VM51xGEzQsBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T00:08:27.285445Z"},"content_sha256":"39cfd3f53d65b371f6f1251ef7fbac6cc47a64b0b5a260c9061e3b300941bf7a","schema_version":"1.0","event_id":"sha256:39cfd3f53d65b371f6f1251ef7fbac6cc47a64b0b5a260c9061e3b300941bf7a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:CGUHWY5F4TQAYNJFGB4FGMBWHL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimal Matroid Partitioning Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Hanna Sumita, Kazuhisa Makino, Kei Kimura, Yasushi Kawase","submitted_at":"2017-10-03T01:00:19Z","abstract_excerpt":"This paper studies optimal matroid partitioning problems for various objective functions. In the problem, we are given a finite set $E$ and $k$ weighted matroids $(E, \\mathcal{I}_i, w_i)$, $i = 1, \\dots, k$, and our task is to find a minimum partition $(I_1,\\dots,I_k)$ of $E$ such that $I_i \\in \\mathcal{I}_i$ for all $i$. For each objective function, we give a polynomial-time algorithm or prove NP-hardness. In particular, for the case when the given weighted matroids are identical and the objective function is the sum of the maximum weight in each set (i.e., $\\sum_{i=1}^k\\max_{e\\in I_i}w_i(e)$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.00950","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":"2026-05-18T00:33:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DXI8HOKN67qichSz73WNxiRpl21Hyh7BV5YLeGiCjLXWZxr0pdGZErtq6jSgC8uSIL4YbBKMCWXQ75WkT7LPBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T00:08:27.285831Z"},"content_sha256":"9e8cddd36f58a60cb76bfd01901b84e45f487cdb12b40fddcc60810662e4a095","schema_version":"1.0","event_id":"sha256:9e8cddd36f58a60cb76bfd01901b84e45f487cdb12b40fddcc60810662e4a095"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CGUHWY5F4TQAYNJFGB4FGMBWHL/bundle.json","state_url":"https://pith.science/pith/CGUHWY5F4TQAYNJFGB4FGMBWHL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CGUHWY5F4TQAYNJFGB4FGMBWHL/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":"2026-06-03T00:08:27Z","links":{"resolver":"https://pith.science/pith/CGUHWY5F4TQAYNJFGB4FGMBWHL","bundle":"https://pith.science/pith/CGUHWY5F4TQAYNJFGB4FGMBWHL/bundle.json","state":"https://pith.science/pith/CGUHWY5F4TQAYNJFGB4FGMBWHL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CGUHWY5F4TQAYNJFGB4FGMBWHL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:CGUHWY5F4TQAYNJFGB4FGMBWHL","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":"64ea5cb3a9674444410286750a91f56ee7064dbaa0771884c1a53a72b6484550","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-10-03T01:00:19Z","title_canon_sha256":"f066a57f3391b69158ff154873f30ee6f1cbab1e222fb011493457236c606d93"},"schema_version":"1.0","source":{"id":"1710.00950","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.00950","created_at":"2026-05-18T00:33:47Z"},{"alias_kind":"arxiv_version","alias_value":"1710.00950v1","created_at":"2026-05-18T00:33:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.00950","created_at":"2026-05-18T00:33:47Z"},{"alias_kind":"pith_short_12","alias_value":"CGUHWY5F4TQA","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"CGUHWY5F4TQAYNJF","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"CGUHWY5F","created_at":"2026-05-18T12:31:10Z"}],"graph_snapshots":[{"event_id":"sha256:9e8cddd36f58a60cb76bfd01901b84e45f487cdb12b40fddcc60810662e4a095","target":"graph","created_at":"2026-05-18T00:33:47Z","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":"This paper studies optimal matroid partitioning problems for various objective functions. In the problem, we are given a finite set $E$ and $k$ weighted matroids $(E, \\mathcal{I}_i, w_i)$, $i = 1, \\dots, k$, and our task is to find a minimum partition $(I_1,\\dots,I_k)$ of $E$ such that $I_i \\in \\mathcal{I}_i$ for all $i$. For each objective function, we give a polynomial-time algorithm or prove NP-hardness. In particular, for the case when the given weighted matroids are identical and the objective function is the sum of the maximum weight in each set (i.e., $\\sum_{i=1}^k\\max_{e\\in I_i}w_i(e)$","authors_text":"Hanna Sumita, Kazuhisa Makino, Kei Kimura, Yasushi Kawase","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-10-03T01:00:19Z","title":"Optimal Matroid Partitioning Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.00950","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":"sha256:39cfd3f53d65b371f6f1251ef7fbac6cc47a64b0b5a260c9061e3b300941bf7a","target":"record","created_at":"2026-05-18T00:33:47Z","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":"64ea5cb3a9674444410286750a91f56ee7064dbaa0771884c1a53a72b6484550","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-10-03T01:00:19Z","title_canon_sha256":"f066a57f3391b69158ff154873f30ee6f1cbab1e222fb011493457236c606d93"},"schema_version":"1.0","source":{"id":"1710.00950","kind":"arxiv","version":1}},"canonical_sha256":"11a87b63a5e4e00c352530785330363ac975f6ba9a045cda43d5dcdd8edf336e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"11a87b63a5e4e00c352530785330363ac975f6ba9a045cda43d5dcdd8edf336e","first_computed_at":"2026-05-18T00:33:47.388431Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:33:47.388431Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"v+AT7YO+6xIhTMJW2t9Ry4bR1/ghgWEadjtddPwlGLdcA1FugoiE2P9bbmh/wEDCJX8/c4jvAEeywN2YExRPBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:33:47.389060Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.00950","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:39cfd3f53d65b371f6f1251ef7fbac6cc47a64b0b5a260c9061e3b300941bf7a","sha256:9e8cddd36f58a60cb76bfd01901b84e45f487cdb12b40fddcc60810662e4a095"],"state_sha256":"2de17cdbfe4461393edff70385be8cbfe8e4eabe4d6d772bad30c19fbd8bba66"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"urSYCVJ6uvfxsPlauXeeUGzOztYeLNM82tNzOWsBw+A60hzU4SKUfKyx06wHigkLGuzR9fzqtOM5d+YCsrn3Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T00:08:27.287762Z","bundle_sha256":"94c3cf58445084a5cdcb2bdfc4ea16d8b8bf71c44c1675819342dc4e1f93c0ca"}}