{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:RCGLXSQZAWNS6OKNV6VIYSD6P3","short_pith_number":"pith:RCGLXSQZ","canonical_record":{"source":{"id":"1609.03137","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-09-11T09:06:57Z","cross_cats_sorted":[],"title_canon_sha256":"823cb16d7c04b96f966353ec33a6cb91922376335337a4ec744f2ee5c39f4b20","abstract_canon_sha256":"92328234e27e4ddc2668b4d3bfb1a44c0cf87c2aac3be24ae4bca6f2f25acd49"},"schema_version":"1.0"},"canonical_sha256":"888cbbca19059b2f394dafaa8c487e7ee2738ceae5978b9e3f5318f5a443ff97","source":{"kind":"arxiv","id":"1609.03137","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.03137","created_at":"2026-05-18T00:43:35Z"},{"alias_kind":"arxiv_version","alias_value":"1609.03137v3","created_at":"2026-05-18T00:43:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.03137","created_at":"2026-05-18T00:43:35Z"},{"alias_kind":"pith_short_12","alias_value":"RCGLXSQZAWNS","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"RCGLXSQZAWNS6OKN","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"RCGLXSQZ","created_at":"2026-05-18T12:30:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:RCGLXSQZAWNS6OKNV6VIYSD6P3","target":"record","payload":{"canonical_record":{"source":{"id":"1609.03137","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-09-11T09:06:57Z","cross_cats_sorted":[],"title_canon_sha256":"823cb16d7c04b96f966353ec33a6cb91922376335337a4ec744f2ee5c39f4b20","abstract_canon_sha256":"92328234e27e4ddc2668b4d3bfb1a44c0cf87c2aac3be24ae4bca6f2f25acd49"},"schema_version":"1.0"},"canonical_sha256":"888cbbca19059b2f394dafaa8c487e7ee2738ceae5978b9e3f5318f5a443ff97","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:35.619108Z","signature_b64":"gHeuS+RKI802lT0VK41ZcmRGvf6w8GFlXCJby5Tak/Nh3ro2QERGRTBlCgkFjZQC7rUZmhsth8fR60/jtZQIDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"888cbbca19059b2f394dafaa8c487e7ee2738ceae5978b9e3f5318f5a443ff97","last_reissued_at":"2026-05-18T00:43:35.618647Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:35.618647Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.03137","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:43:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RcaN5CKLti7t9swtxc1ooWUrQe/DLn0BEQxdoJZwZCMP3HjLhEyj2oTzDkfb09bqjf3C0dYs/nQyDSCV0HU1Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T14:41:44.606765Z"},"content_sha256":"60d4cdc4eac597dda47e888ed651985f4030198912afd2c32391d0fb1e8188d1","schema_version":"1.0","event_id":"sha256:60d4cdc4eac597dda47e888ed651985f4030198912afd2c32391d0fb1e8188d1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:RCGLXSQZAWNS6OKNV6VIYSD6P3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On a general framework for network representability in discrete optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Yuni Iwamasa","submitted_at":"2016-09-11T09:06:57Z","abstract_excerpt":"In discrete optimization, representing an objective function as an $s$-$t$ cut function of a network is a basic technique to design an efficient minimization algorithm. A network representable function can be minimized by computing a minimum $s$-$t$ cut of a directed network, which is a very easy and fastly solved problem. Hence it is natural to ask what functions are network representable. In the case of pseudo Boolean functions (functions on $\\{0,1\\}^n$), it is known that any submodular function on $\\{0,1\\}^3$ is network representable. \\v{Z}ivn\\'y--Cohen--Jeavons showed by using the theory o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.03137","kind":"arxiv","version":3},"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":"2026-05-18T00:43:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wmsVdTT7aDNqr452OKfQdyEV8NG2Y4INKAjFDUScYv40JFH6ltvy+QzaeO72CTeIXwb9+VDdSK5WqM7sya7kAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T14:41:44.607117Z"},"content_sha256":"a70ede15549b5bbf4380fe04a16c03d0f7847de9713381fb7566332fb4081cde","schema_version":"1.0","event_id":"sha256:a70ede15549b5bbf4380fe04a16c03d0f7847de9713381fb7566332fb4081cde"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RCGLXSQZAWNS6OKNV6VIYSD6P3/bundle.json","state_url":"https://pith.science/pith/RCGLXSQZAWNS6OKNV6VIYSD6P3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RCGLXSQZAWNS6OKNV6VIYSD6P3/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":"2026-06-05T14:41:44Z","links":{"resolver":"https://pith.science/pith/RCGLXSQZAWNS6OKNV6VIYSD6P3","bundle":"https://pith.science/pith/RCGLXSQZAWNS6OKNV6VIYSD6P3/bundle.json","state":"https://pith.science/pith/RCGLXSQZAWNS6OKNV6VIYSD6P3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RCGLXSQZAWNS6OKNV6VIYSD6P3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:RCGLXSQZAWNS6OKNV6VIYSD6P3","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":"92328234e27e4ddc2668b4d3bfb1a44c0cf87c2aac3be24ae4bca6f2f25acd49","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-09-11T09:06:57Z","title_canon_sha256":"823cb16d7c04b96f966353ec33a6cb91922376335337a4ec744f2ee5c39f4b20"},"schema_version":"1.0","source":{"id":"1609.03137","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.03137","created_at":"2026-05-18T00:43:35Z"},{"alias_kind":"arxiv_version","alias_value":"1609.03137v3","created_at":"2026-05-18T00:43:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.03137","created_at":"2026-05-18T00:43:35Z"},{"alias_kind":"pith_short_12","alias_value":"RCGLXSQZAWNS","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"RCGLXSQZAWNS6OKN","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"RCGLXSQZ","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:a70ede15549b5bbf4380fe04a16c03d0f7847de9713381fb7566332fb4081cde","target":"graph","created_at":"2026-05-18T00:43:35Z","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 discrete optimization, representing an objective function as an $s$-$t$ cut function of a network is a basic technique to design an efficient minimization algorithm. A network representable function can be minimized by computing a minimum $s$-$t$ cut of a directed network, which is a very easy and fastly solved problem. Hence it is natural to ask what functions are network representable. In the case of pseudo Boolean functions (functions on $\\{0,1\\}^n$), it is known that any submodular function on $\\{0,1\\}^3$ is network representable. \\v{Z}ivn\\'y--Cohen--Jeavons showed by using the theory o","authors_text":"Yuni Iwamasa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-09-11T09:06:57Z","title":"On a general framework for network representability in discrete optimization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.03137","kind":"arxiv","version":3},"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":"sha256:60d4cdc4eac597dda47e888ed651985f4030198912afd2c32391d0fb1e8188d1","target":"record","created_at":"2026-05-18T00:43:35Z","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":"92328234e27e4ddc2668b4d3bfb1a44c0cf87c2aac3be24ae4bca6f2f25acd49","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-09-11T09:06:57Z","title_canon_sha256":"823cb16d7c04b96f966353ec33a6cb91922376335337a4ec744f2ee5c39f4b20"},"schema_version":"1.0","source":{"id":"1609.03137","kind":"arxiv","version":3}},"canonical_sha256":"888cbbca19059b2f394dafaa8c487e7ee2738ceae5978b9e3f5318f5a443ff97","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"888cbbca19059b2f394dafaa8c487e7ee2738ceae5978b9e3f5318f5a443ff97","first_computed_at":"2026-05-18T00:43:35.618647Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:43:35.618647Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gHeuS+RKI802lT0VK41ZcmRGvf6w8GFlXCJby5Tak/Nh3ro2QERGRTBlCgkFjZQC7rUZmhsth8fR60/jtZQIDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:43:35.619108Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.03137","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:60d4cdc4eac597dda47e888ed651985f4030198912afd2c32391d0fb1e8188d1","sha256:a70ede15549b5bbf4380fe04a16c03d0f7847de9713381fb7566332fb4081cde"],"state_sha256":"069d0d31efe76f2ddd180fbdc07b39257f6e4d026522cc347fb4570b837ea3e7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B4NfI1w/4LQpFE16uBTxxuH/aSf5Ey24GnmF8buWj768ONlLXTYzAsTyabXIUnqjUkJO+xcqzGYyuJJN9+cUAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T14:41:44.609150Z","bundle_sha256":"e66ec974f0e2d9773edc738fb3e458a37b8e2e3b94b9543c4471728d866ddc2a"}}