{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:ZZZFFRLSLRJ55CNQCKWC3X6WGM","short_pith_number":"pith:ZZZFFRLS","canonical_record":{"source":{"id":"1707.05404","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-07-17T22:13:53Z","cross_cats_sorted":["cs.CC","cs.GT"],"title_canon_sha256":"dc00608e61c521457b9f4363343c050e10ad25f68de2204b45ebfe56b0212285","abstract_canon_sha256":"83acbe1172ce427d399db341b82fa6289e54e739f27176fdffd0d4ba2c517feb"},"schema_version":"1.0"},"canonical_sha256":"ce7252c5725c53de89b012ac2ddfd6330eb726302cfb4844eb111d5f663c58b8","source":{"kind":"arxiv","id":"1707.05404","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.05404","created_at":"2026-05-18T00:40:02Z"},{"alias_kind":"arxiv_version","alias_value":"1707.05404v1","created_at":"2026-05-18T00:40:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.05404","created_at":"2026-05-18T00:40:02Z"},{"alias_kind":"pith_short_12","alias_value":"ZZZFFRLSLRJ5","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZZZFFRLSLRJ55CNQ","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZZZFFRLS","created_at":"2026-05-18T12:31:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:ZZZFFRLSLRJ55CNQCKWC3X6WGM","target":"record","payload":{"canonical_record":{"source":{"id":"1707.05404","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-07-17T22:13:53Z","cross_cats_sorted":["cs.CC","cs.GT"],"title_canon_sha256":"dc00608e61c521457b9f4363343c050e10ad25f68de2204b45ebfe56b0212285","abstract_canon_sha256":"83acbe1172ce427d399db341b82fa6289e54e739f27176fdffd0d4ba2c517feb"},"schema_version":"1.0"},"canonical_sha256":"ce7252c5725c53de89b012ac2ddfd6330eb726302cfb4844eb111d5f663c58b8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:02.443529Z","signature_b64":"rp0dt+Sh5fJFlZk0oSD1Mn6zKZLPjKoOQZpzxWbtTbi4pm6crhpRsPz0xZaLpSWHsj3UGg+bIXrysnz2wndXAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ce7252c5725c53de89b012ac2ddfd6330eb726302cfb4844eb111d5f663c58b8","last_reissued_at":"2026-05-18T00:40:02.442975Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:02.442975Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1707.05404","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":"2026-05-18T00:40:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cRXZNIYiwPACC2wN7wVrOyJ2VJlFVcSf9+j5Hweld961+Yl7phMG3GxZ7+KZ7ltheOPmDT2z2VCtioTaMueeBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T22:12:37.820457Z"},"content_sha256":"06aadb21247ef407dc67d67c359fc95d5b13492e05772b425f6470b9af3a6e54","schema_version":"1.0","event_id":"sha256:06aadb21247ef407dc67d67c359fc95d5b13492e05772b425f6470b9af3a6e54"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:ZZZFFRLSLRJ55CNQCKWC3X6WGM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Treewidth and Stable Marriage","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.GT"],"primary_cat":"cs.DS","authors_text":"Meirav Zehavi, Saket Saurabh, Sushmita Gupta","submitted_at":"2017-07-17T22:13:53Z","abstract_excerpt":"Stable Marriage is a fundamental problem to both computer science and economics. Four well-known NP-hard optimization versions of this problem are the Sex-Equal Stable Marriage (SESM), Balanced Stable Marriage (BSM), max-Stable Marriage with Ties (max-SMT) and min-Stable Marriage with Ties (min-SMT) problems. In this paper, we analyze these problems from the viewpoint of Parameterized Complexity. We conduct the first study of these problems with respect to the parameter treewidth. First, we study the treewidth $\\mathtt{tw}$ of the primal graph. We establish that all four problems are W[1]-hard"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.05404","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":"2026-05-18T00:40:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TCblcDqlqg2t3t5yvGa0TPsyWhNZ/+4flGxRFGUe/BLIoKVLtg0Y/2Gw2PUPPPqdnmELPLZivI0OSfiVRqPkDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T22:12:37.821132Z"},"content_sha256":"edaeff2485f07342f524b1332ccbcd5964ed431fd305c578f667f676c776080b","schema_version":"1.0","event_id":"sha256:edaeff2485f07342f524b1332ccbcd5964ed431fd305c578f667f676c776080b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZZZFFRLSLRJ55CNQCKWC3X6WGM/bundle.json","state_url":"https://pith.science/pith/ZZZFFRLSLRJ55CNQCKWC3X6WGM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZZZFFRLSLRJ55CNQCKWC3X6WGM/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":"2026-06-05T22:12:37Z","links":{"resolver":"https://pith.science/pith/ZZZFFRLSLRJ55CNQCKWC3X6WGM","bundle":"https://pith.science/pith/ZZZFFRLSLRJ55CNQCKWC3X6WGM/bundle.json","state":"https://pith.science/pith/ZZZFFRLSLRJ55CNQCKWC3X6WGM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZZZFFRLSLRJ55CNQCKWC3X6WGM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:ZZZFFRLSLRJ55CNQCKWC3X6WGM","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":"83acbe1172ce427d399db341b82fa6289e54e739f27176fdffd0d4ba2c517feb","cross_cats_sorted":["cs.CC","cs.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-07-17T22:13:53Z","title_canon_sha256":"dc00608e61c521457b9f4363343c050e10ad25f68de2204b45ebfe56b0212285"},"schema_version":"1.0","source":{"id":"1707.05404","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.05404","created_at":"2026-05-18T00:40:02Z"},{"alias_kind":"arxiv_version","alias_value":"1707.05404v1","created_at":"2026-05-18T00:40:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.05404","created_at":"2026-05-18T00:40:02Z"},{"alias_kind":"pith_short_12","alias_value":"ZZZFFRLSLRJ5","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZZZFFRLSLRJ55CNQ","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZZZFFRLS","created_at":"2026-05-18T12:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:edaeff2485f07342f524b1332ccbcd5964ed431fd305c578f667f676c776080b","target":"graph","created_at":"2026-05-18T00:40:02Z","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":"Stable Marriage is a fundamental problem to both computer science and economics. Four well-known NP-hard optimization versions of this problem are the Sex-Equal Stable Marriage (SESM), Balanced Stable Marriage (BSM), max-Stable Marriage with Ties (max-SMT) and min-Stable Marriage with Ties (min-SMT) problems. In this paper, we analyze these problems from the viewpoint of Parameterized Complexity. We conduct the first study of these problems with respect to the parameter treewidth. First, we study the treewidth $\\mathtt{tw}$ of the primal graph. We establish that all four problems are W[1]-hard","authors_text":"Meirav Zehavi, Saket Saurabh, Sushmita Gupta","cross_cats":["cs.CC","cs.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-07-17T22:13:53Z","title":"On Treewidth and Stable Marriage"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.05404","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":"sha256:06aadb21247ef407dc67d67c359fc95d5b13492e05772b425f6470b9af3a6e54","target":"record","created_at":"2026-05-18T00:40:02Z","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":"83acbe1172ce427d399db341b82fa6289e54e739f27176fdffd0d4ba2c517feb","cross_cats_sorted":["cs.CC","cs.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-07-17T22:13:53Z","title_canon_sha256":"dc00608e61c521457b9f4363343c050e10ad25f68de2204b45ebfe56b0212285"},"schema_version":"1.0","source":{"id":"1707.05404","kind":"arxiv","version":1}},"canonical_sha256":"ce7252c5725c53de89b012ac2ddfd6330eb726302cfb4844eb111d5f663c58b8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ce7252c5725c53de89b012ac2ddfd6330eb726302cfb4844eb111d5f663c58b8","first_computed_at":"2026-05-18T00:40:02.442975Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:02.442975Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rp0dt+Sh5fJFlZk0oSD1Mn6zKZLPjKoOQZpzxWbtTbi4pm6crhpRsPz0xZaLpSWHsj3UGg+bIXrysnz2wndXAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:02.443529Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.05404","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:06aadb21247ef407dc67d67c359fc95d5b13492e05772b425f6470b9af3a6e54","sha256:edaeff2485f07342f524b1332ccbcd5964ed431fd305c578f667f676c776080b"],"state_sha256":"a63a555718e7657f93c33f0efaccdeaf3ac7f05b0548ba8f3be998ac286bb827"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Gao/Eh8KSlSoeBSpfj+dmKz9tNrFa+4E4D4SgtrxEdWLujwom5nrcOlq9AfShYJWxKQlnUA/SlQm4uYP71wcCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T22:12:37.825274Z","bundle_sha256":"06fd0072eaaf1a862eea38af1913e0626f056231026555b7028d74ac68598fc1"}}