{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:JEVWNMV75TXMDGTHNIDLNCOEFI","short_pith_number":"pith:JEVWNMV7","canonical_record":{"source":{"id":"1509.08575","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-09-29T03:03:26Z","cross_cats_sorted":[],"title_canon_sha256":"a5058f6795084e0ea9d47b25b71c0ce48cadb27984d788edfcb01d0cb9e0d89f","abstract_canon_sha256":"4aa7fd2012ec0c3db76cd66627b63915139ab10dbd7ced1471e73788348d49a6"},"schema_version":"1.0"},"canonical_sha256":"492b66b2bfeceec19a676a06b689c42a2be5843c0b8ae989ccaf3a0212004456","source":{"kind":"arxiv","id":"1509.08575","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.08575","created_at":"2026-05-18T01:22:47Z"},{"alias_kind":"arxiv_version","alias_value":"1509.08575v2","created_at":"2026-05-18T01:22:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.08575","created_at":"2026-05-18T01:22:47Z"},{"alias_kind":"pith_short_12","alias_value":"JEVWNMV75TXM","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JEVWNMV75TXMDGTH","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JEVWNMV7","created_at":"2026-05-18T12:29:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:JEVWNMV75TXMDGTHNIDLNCOEFI","target":"record","payload":{"canonical_record":{"source":{"id":"1509.08575","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-09-29T03:03:26Z","cross_cats_sorted":[],"title_canon_sha256":"a5058f6795084e0ea9d47b25b71c0ce48cadb27984d788edfcb01d0cb9e0d89f","abstract_canon_sha256":"4aa7fd2012ec0c3db76cd66627b63915139ab10dbd7ced1471e73788348d49a6"},"schema_version":"1.0"},"canonical_sha256":"492b66b2bfeceec19a676a06b689c42a2be5843c0b8ae989ccaf3a0212004456","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:47.993646Z","signature_b64":"xcgm8lbWhGbS7piWmDJObwbzEg/mM9YHyxADRf5g3mJ+CQk0aVkf3w+S3dEALj54AJAB11pmjsKl9tiQ7sU3CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"492b66b2bfeceec19a676a06b689c42a2be5843c0b8ae989ccaf3a0212004456","last_reissued_at":"2026-05-18T01:22:47.993060Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:47.993060Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.08575","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:22:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8vQR8v8clpHp+khi19JoGM46CpLLNGFdrTkrb2LtFBVUpBMjkk4WPYKSihgkRj4ESAqAEr09RIXQY3BQ5j0KDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T08:09:11.902810Z"},"content_sha256":"cc19fcf5464bfc4885ec1e1fc90e032383a46f8ed74d8f5d506345ed5f042433","schema_version":"1.0","event_id":"sha256:cc19fcf5464bfc4885ec1e1fc90e032383a46f8ed74d8f5d506345ed5f042433"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:JEVWNMV75TXMDGTHNIDLNCOEFI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On uncrossing games for skew-supermodular functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hiroshi Hirai","submitted_at":"2015-09-29T03:03:26Z","abstract_excerpt":"In this note, we consider the uncrossing game for a skew-supermodular function $f$, which is a two-player game with players, Red and Blue, and abstracts the uncrossing procedure in the cut-covering linear program associated with $f$. Extending the earlier results by Karzanov for $\\{0,1\\}$-valued skew-supermodular functions, we present an improved polynomial time strategy for Red to win, and give a strongly polynomial time uncrossing procedure for dual solutions of the cut-covering LP as its consequence. We also mention its implication on the optimality of laminar solutions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.08575","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:22:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GXDblUJVXS9min0qLiRur1m+8e+xD/o5wbO+Lyptg9q2xBKUZym8gRwIQrXO70jlYmzIg+y9goIf8m4kKbrWBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T08:09:11.903542Z"},"content_sha256":"aa888bcbf7071c472c41b554029a43b9f2e1dde2d70f051f1c64b9b5bad06825","schema_version":"1.0","event_id":"sha256:aa888bcbf7071c472c41b554029a43b9f2e1dde2d70f051f1c64b9b5bad06825"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JEVWNMV75TXMDGTHNIDLNCOEFI/bundle.json","state_url":"https://pith.science/pith/JEVWNMV75TXMDGTHNIDLNCOEFI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JEVWNMV75TXMDGTHNIDLNCOEFI/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":"2026-05-27T08:09:11Z","links":{"resolver":"https://pith.science/pith/JEVWNMV75TXMDGTHNIDLNCOEFI","bundle":"https://pith.science/pith/JEVWNMV75TXMDGTHNIDLNCOEFI/bundle.json","state":"https://pith.science/pith/JEVWNMV75TXMDGTHNIDLNCOEFI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JEVWNMV75TXMDGTHNIDLNCOEFI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:JEVWNMV75TXMDGTHNIDLNCOEFI","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":"4aa7fd2012ec0c3db76cd66627b63915139ab10dbd7ced1471e73788348d49a6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-09-29T03:03:26Z","title_canon_sha256":"a5058f6795084e0ea9d47b25b71c0ce48cadb27984d788edfcb01d0cb9e0d89f"},"schema_version":"1.0","source":{"id":"1509.08575","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.08575","created_at":"2026-05-18T01:22:47Z"},{"alias_kind":"arxiv_version","alias_value":"1509.08575v2","created_at":"2026-05-18T01:22:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.08575","created_at":"2026-05-18T01:22:47Z"},{"alias_kind":"pith_short_12","alias_value":"JEVWNMV75TXM","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JEVWNMV75TXMDGTH","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JEVWNMV7","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:aa888bcbf7071c472c41b554029a43b9f2e1dde2d70f051f1c64b9b5bad06825","target":"graph","created_at":"2026-05-18T01:22:47Z","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":"In this note, we consider the uncrossing game for a skew-supermodular function $f$, which is a two-player game with players, Red and Blue, and abstracts the uncrossing procedure in the cut-covering linear program associated with $f$. Extending the earlier results by Karzanov for $\\{0,1\\}$-valued skew-supermodular functions, we present an improved polynomial time strategy for Red to win, and give a strongly polynomial time uncrossing procedure for dual solutions of the cut-covering LP as its consequence. We also mention its implication on the optimality of laminar solutions.","authors_text":"Hiroshi Hirai","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-09-29T03:03:26Z","title":"On uncrossing games for skew-supermodular functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.08575","kind":"arxiv","version":2},"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:cc19fcf5464bfc4885ec1e1fc90e032383a46f8ed74d8f5d506345ed5f042433","target":"record","created_at":"2026-05-18T01:22:47Z","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":"4aa7fd2012ec0c3db76cd66627b63915139ab10dbd7ced1471e73788348d49a6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-09-29T03:03:26Z","title_canon_sha256":"a5058f6795084e0ea9d47b25b71c0ce48cadb27984d788edfcb01d0cb9e0d89f"},"schema_version":"1.0","source":{"id":"1509.08575","kind":"arxiv","version":2}},"canonical_sha256":"492b66b2bfeceec19a676a06b689c42a2be5843c0b8ae989ccaf3a0212004456","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"492b66b2bfeceec19a676a06b689c42a2be5843c0b8ae989ccaf3a0212004456","first_computed_at":"2026-05-18T01:22:47.993060Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:47.993060Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xcgm8lbWhGbS7piWmDJObwbzEg/mM9YHyxADRf5g3mJ+CQk0aVkf3w+S3dEALj54AJAB11pmjsKl9tiQ7sU3CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:47.993646Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.08575","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cc19fcf5464bfc4885ec1e1fc90e032383a46f8ed74d8f5d506345ed5f042433","sha256:aa888bcbf7071c472c41b554029a43b9f2e1dde2d70f051f1c64b9b5bad06825"],"state_sha256":"b84eaa7f03faf5b0d2dad85d093d06919d9d00fffa600b072b139796f09e9674"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Yc5ib3jLT8pMp1IC3XHJiY/96+awlXX6pnLz4cpO8qPxX4ZxtEKm+ycV5EaXS/1dHGl2TDioacVnTQEPiiKsCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T08:09:11.907219Z","bundle_sha256":"c006bc5cdd66b13d6697ebfbc7a8d06acc2b19ca846f2aa783d634f4987ad564"}}