{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:V4MUSEP65YO7SLWRB6ZL6Q2O75","short_pith_number":"pith:V4MUSEP6","canonical_record":{"source":{"id":"1312.3552","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-12-12T17:21:20Z","cross_cats_sorted":[],"title_canon_sha256":"6c48c56bafe76c5cadd84a634561f3d873a32aa5537805cc88f6f00412f023b7","abstract_canon_sha256":"419d9f9df36fad7c93c8cebc388a5dcd6ef28c7f5094bee1595c92d9f7416a25"},"schema_version":"1.0"},"canonical_sha256":"af194911feee1df92ed10fb2bf434eff7da58d7443cd4e9761abd2e13a522b82","source":{"kind":"arxiv","id":"1312.3552","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.3552","created_at":"2026-05-18T03:04:50Z"},{"alias_kind":"arxiv_version","alias_value":"1312.3552v1","created_at":"2026-05-18T03:04:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.3552","created_at":"2026-05-18T03:04:50Z"},{"alias_kind":"pith_short_12","alias_value":"V4MUSEP65YO7","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"V4MUSEP65YO7SLWR","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"V4MUSEP6","created_at":"2026-05-18T12:28:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:V4MUSEP65YO7SLWRB6ZL6Q2O75","target":"record","payload":{"canonical_record":{"source":{"id":"1312.3552","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-12-12T17:21:20Z","cross_cats_sorted":[],"title_canon_sha256":"6c48c56bafe76c5cadd84a634561f3d873a32aa5537805cc88f6f00412f023b7","abstract_canon_sha256":"419d9f9df36fad7c93c8cebc388a5dcd6ef28c7f5094bee1595c92d9f7416a25"},"schema_version":"1.0"},"canonical_sha256":"af194911feee1df92ed10fb2bf434eff7da58d7443cd4e9761abd2e13a522b82","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:04:50.572221Z","signature_b64":"YTcb7cq5bJMwDv15PdXuF7bYgh9BfcS0Z2/J3ErTVL4pNp+6H48+Y+L+Em02h/L6l9+8x3fIYznmCNASvwo2Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"af194911feee1df92ed10fb2bf434eff7da58d7443cd4e9761abd2e13a522b82","last_reissued_at":"2026-05-18T03:04:50.571452Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:04:50.571452Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1312.3552","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":"2026-05-18T03:04:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VUx6w0Iwq1Imv4KMDpUgS8suDDsKBJniOPcoAoCzhAXeTdjcnFTTV78ut8LFKxNdgnET5KiShwihpUBdSg+ABQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T06:48:27.356693Z"},"content_sha256":"30a78c1fa8d23554ef5b3676cb51c6a211fb0816cf27c731f0278c392e573258","schema_version":"1.0","event_id":"sha256:30a78c1fa8d23554ef5b3676cb51c6a211fb0816cf27c731f0278c392e573258"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:V4MUSEP65YO7SLWRB6ZL6Q2O75","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Counting Popular Matchings in House Allocation Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Nitesh Jha, Rupam Acharyya, Sourav Chakraborty","submitted_at":"2013-12-12T17:21:20Z","abstract_excerpt":"We study the problem of counting the number of popular matchings in a given instance. A popular matching instance consists of agents A and houses H, where each agent ranks a subset of houses according to their preferences. A matching is an assignment of agents to houses. A matching M is more popular than matching M' if the number of agents that prefer M to M' is more than the number of people that prefer M' to M. A matching M is called popular if there exists no matching more popular than M. McDermid and Irving gave a poly-time algorithm for counting the number of popular matchings when the pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.3552","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":"2026-05-18T03:04:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u675HyU6zBIxKEs1r+/wfAg3AlF7yLsFqjPUf2K7m4qnzeIv2Oo26rwpOyD2QSYE4EpwoL+Xj4al9aKKrdfbCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T06:48:27.357045Z"},"content_sha256":"3bf4d62471b50c39e63130d812a297f16641b117f673e1ce0cb95ad09d10ae91","schema_version":"1.0","event_id":"sha256:3bf4d62471b50c39e63130d812a297f16641b117f673e1ce0cb95ad09d10ae91"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V4MUSEP65YO7SLWRB6ZL6Q2O75/bundle.json","state_url":"https://pith.science/pith/V4MUSEP65YO7SLWRB6ZL6Q2O75/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V4MUSEP65YO7SLWRB6ZL6Q2O75/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":"2026-06-01T06:48:27Z","links":{"resolver":"https://pith.science/pith/V4MUSEP65YO7SLWRB6ZL6Q2O75","bundle":"https://pith.science/pith/V4MUSEP65YO7SLWRB6ZL6Q2O75/bundle.json","state":"https://pith.science/pith/V4MUSEP65YO7SLWRB6ZL6Q2O75/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V4MUSEP65YO7SLWRB6ZL6Q2O75/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:V4MUSEP65YO7SLWRB6ZL6Q2O75","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":"419d9f9df36fad7c93c8cebc388a5dcd6ef28c7f5094bee1595c92d9f7416a25","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-12-12T17:21:20Z","title_canon_sha256":"6c48c56bafe76c5cadd84a634561f3d873a32aa5537805cc88f6f00412f023b7"},"schema_version":"1.0","source":{"id":"1312.3552","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.3552","created_at":"2026-05-18T03:04:50Z"},{"alias_kind":"arxiv_version","alias_value":"1312.3552v1","created_at":"2026-05-18T03:04:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.3552","created_at":"2026-05-18T03:04:50Z"},{"alias_kind":"pith_short_12","alias_value":"V4MUSEP65YO7","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"V4MUSEP65YO7SLWR","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"V4MUSEP6","created_at":"2026-05-18T12:28:04Z"}],"graph_snapshots":[{"event_id":"sha256:3bf4d62471b50c39e63130d812a297f16641b117f673e1ce0cb95ad09d10ae91","target":"graph","created_at":"2026-05-18T03:04:50Z","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":"We study the problem of counting the number of popular matchings in a given instance. A popular matching instance consists of agents A and houses H, where each agent ranks a subset of houses according to their preferences. A matching is an assignment of agents to houses. A matching M is more popular than matching M' if the number of agents that prefer M to M' is more than the number of people that prefer M' to M. A matching M is called popular if there exists no matching more popular than M. McDermid and Irving gave a poly-time algorithm for counting the number of popular matchings when the pr","authors_text":"Nitesh Jha, Rupam Acharyya, Sourav Chakraborty","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-12-12T17:21:20Z","title":"Counting Popular Matchings in House Allocation Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.3552","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":"sha256:30a78c1fa8d23554ef5b3676cb51c6a211fb0816cf27c731f0278c392e573258","target":"record","created_at":"2026-05-18T03:04:50Z","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":"419d9f9df36fad7c93c8cebc388a5dcd6ef28c7f5094bee1595c92d9f7416a25","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-12-12T17:21:20Z","title_canon_sha256":"6c48c56bafe76c5cadd84a634561f3d873a32aa5537805cc88f6f00412f023b7"},"schema_version":"1.0","source":{"id":"1312.3552","kind":"arxiv","version":1}},"canonical_sha256":"af194911feee1df92ed10fb2bf434eff7da58d7443cd4e9761abd2e13a522b82","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"af194911feee1df92ed10fb2bf434eff7da58d7443cd4e9761abd2e13a522b82","first_computed_at":"2026-05-18T03:04:50.571452Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:04:50.571452Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YTcb7cq5bJMwDv15PdXuF7bYgh9BfcS0Z2/J3ErTVL4pNp+6H48+Y+L+Em02h/L6l9+8x3fIYznmCNASvwo2Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:04:50.572221Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.3552","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:30a78c1fa8d23554ef5b3676cb51c6a211fb0816cf27c731f0278c392e573258","sha256:3bf4d62471b50c39e63130d812a297f16641b117f673e1ce0cb95ad09d10ae91"],"state_sha256":"707848cacd3640a31605d5f3d614e5123ef8e47b97a5f9444a5e031988899e3b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lBgXLShG7UTW9gbQXPE+KbVEsRUlaP47Za3AeHu9jcbxITl0FN/6EHVF1l42PtY67NdTrkUVhKpSuK2EFWIgAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T06:48:27.359158Z","bundle_sha256":"39e0808bd3f69c551b1f2ba316239aec683451ed3dba1a87acf24ce189835355"}}