{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:Q47AFKKY62WIJQDKLLUQONMCEQ","short_pith_number":"pith:Q47AFKKY","canonical_record":{"source":{"id":"1106.5890","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2011-06-29T09:57:43Z","cross_cats_sorted":[],"title_canon_sha256":"4e5950ce032b271cde7353efa3f1c8658dcf6ee71b4e76af703034e0f03e28c1","abstract_canon_sha256":"f8edde19054f4b321d4170590d802ba0b45b9f51e24c5a300fc863d2875dbbae"},"schema_version":"1.0"},"canonical_sha256":"873e02a958f6ac84c06a5ae9073582243532b79d4286cb67d33d0d5f426075ef","source":{"kind":"arxiv","id":"1106.5890","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.5890","created_at":"2026-05-18T04:19:04Z"},{"alias_kind":"arxiv_version","alias_value":"1106.5890v1","created_at":"2026-05-18T04:19:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.5890","created_at":"2026-05-18T04:19:04Z"},{"alias_kind":"pith_short_12","alias_value":"Q47AFKKY62WI","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"Q47AFKKY62WIJQDK","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"Q47AFKKY","created_at":"2026-05-18T12:26:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:Q47AFKKY62WIJQDKLLUQONMCEQ","target":"record","payload":{"canonical_record":{"source":{"id":"1106.5890","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2011-06-29T09:57:43Z","cross_cats_sorted":[],"title_canon_sha256":"4e5950ce032b271cde7353efa3f1c8658dcf6ee71b4e76af703034e0f03e28c1","abstract_canon_sha256":"f8edde19054f4b321d4170590d802ba0b45b9f51e24c5a300fc863d2875dbbae"},"schema_version":"1.0"},"canonical_sha256":"873e02a958f6ac84c06a5ae9073582243532b79d4286cb67d33d0d5f426075ef","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:19:04.979299Z","signature_b64":"BI1NPoaAyVaxjQIYzn3HXguggARsoJFQT/jRJrWXNDZWvS5XUMDpjMryCs/jyvvA1fN/FLlpXJBNOWIUex8PDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"873e02a958f6ac84c06a5ae9073582243532b79d4286cb67d33d0d5f426075ef","last_reissued_at":"2026-05-18T04:19:04.978782Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:19:04.978782Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1106.5890","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":"2026-05-18T04:19:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"69+NxZiQqOW/sNzR4FycrEgtfx4H6o4cf0lycCWDPldKsSF7esNL45QVXdisQEgzlL0gY3S0McKxDwa1VOxyDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T14:53:34.245801Z"},"content_sha256":"5e1f245ec6bc5dd37bb6ae81f6826c29a627538f03e2ca68b556c28e3f47d83e","schema_version":"1.0","event_id":"sha256:5e1f245ec6bc5dd37bb6ae81f6826c29a627538f03e2ca68b556c28e3f47d83e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:Q47AFKKY62WIJQDKLLUQONMCEQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Comparison of Lex Bounds for Multiset Variables in Constraint Programming","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.AI","authors_text":"Jimmy Ho-Man Lee, May Hiu-Chun Woo, Toby Walsh, Yat-Chiu Law","submitted_at":"2011-06-29T09:57:43Z","abstract_excerpt":"Set and multiset variables in constraint programming have typically been represented using subset bounds. However, this is a weak representation that neglects potentially useful information about a set such as its cardinality. For set variables, the length-lex (LL) representation successfully provides information about the length (cardinality) and position in the lexicographic ordering. For multiset variables, where elements can be repeated, we consider richer representations that take into account additional information. We study eight different representations in which we maintain bounds acc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.5890","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":"2026-05-18T04:19:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pb35fYD97Dm4XgX2zOSaR+LHYxAFES+soL/dPu8jGSo8lom8MrneplvZIiL6R4QfOe0TIi+rsjUZBZeejR3VBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T14:53:34.246300Z"},"content_sha256":"060131994b84546ce137cc29e0d21c1c35f75df2592e5d95081575d22f3076d1","schema_version":"1.0","event_id":"sha256:060131994b84546ce137cc29e0d21c1c35f75df2592e5d95081575d22f3076d1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Q47AFKKY62WIJQDKLLUQONMCEQ/bundle.json","state_url":"https://pith.science/pith/Q47AFKKY62WIJQDKLLUQONMCEQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Q47AFKKY62WIJQDKLLUQONMCEQ/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":"2026-06-09T14:53:34Z","links":{"resolver":"https://pith.science/pith/Q47AFKKY62WIJQDKLLUQONMCEQ","bundle":"https://pith.science/pith/Q47AFKKY62WIJQDKLLUQONMCEQ/bundle.json","state":"https://pith.science/pith/Q47AFKKY62WIJQDKLLUQONMCEQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Q47AFKKY62WIJQDKLLUQONMCEQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:Q47AFKKY62WIJQDKLLUQONMCEQ","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":"f8edde19054f4b321d4170590d802ba0b45b9f51e24c5a300fc863d2875dbbae","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2011-06-29T09:57:43Z","title_canon_sha256":"4e5950ce032b271cde7353efa3f1c8658dcf6ee71b4e76af703034e0f03e28c1"},"schema_version":"1.0","source":{"id":"1106.5890","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.5890","created_at":"2026-05-18T04:19:04Z"},{"alias_kind":"arxiv_version","alias_value":"1106.5890v1","created_at":"2026-05-18T04:19:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.5890","created_at":"2026-05-18T04:19:04Z"},{"alias_kind":"pith_short_12","alias_value":"Q47AFKKY62WI","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"Q47AFKKY62WIJQDK","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"Q47AFKKY","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:060131994b84546ce137cc29e0d21c1c35f75df2592e5d95081575d22f3076d1","target":"graph","created_at":"2026-05-18T04:19:04Z","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":"Set and multiset variables in constraint programming have typically been represented using subset bounds. However, this is a weak representation that neglects potentially useful information about a set such as its cardinality. For set variables, the length-lex (LL) representation successfully provides information about the length (cardinality) and position in the lexicographic ordering. For multiset variables, where elements can be repeated, we consider richer representations that take into account additional information. We study eight different representations in which we maintain bounds acc","authors_text":"Jimmy Ho-Man Lee, May Hiu-Chun Woo, Toby Walsh, Yat-Chiu Law","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2011-06-29T09:57:43Z","title":"A Comparison of Lex Bounds for Multiset Variables in Constraint Programming"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.5890","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":"sha256:5e1f245ec6bc5dd37bb6ae81f6826c29a627538f03e2ca68b556c28e3f47d83e","target":"record","created_at":"2026-05-18T04:19:04Z","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":"f8edde19054f4b321d4170590d802ba0b45b9f51e24c5a300fc863d2875dbbae","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2011-06-29T09:57:43Z","title_canon_sha256":"4e5950ce032b271cde7353efa3f1c8658dcf6ee71b4e76af703034e0f03e28c1"},"schema_version":"1.0","source":{"id":"1106.5890","kind":"arxiv","version":1}},"canonical_sha256":"873e02a958f6ac84c06a5ae9073582243532b79d4286cb67d33d0d5f426075ef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"873e02a958f6ac84c06a5ae9073582243532b79d4286cb67d33d0d5f426075ef","first_computed_at":"2026-05-18T04:19:04.978782Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:19:04.978782Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BI1NPoaAyVaxjQIYzn3HXguggARsoJFQT/jRJrWXNDZWvS5XUMDpjMryCs/jyvvA1fN/FLlpXJBNOWIUex8PDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:19:04.979299Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.5890","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5e1f245ec6bc5dd37bb6ae81f6826c29a627538f03e2ca68b556c28e3f47d83e","sha256:060131994b84546ce137cc29e0d21c1c35f75df2592e5d95081575d22f3076d1"],"state_sha256":"5a738b5ea29cf8832f351abce36bed2f9df3db640f3ed2357a45a23573cbc4dc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vj/5OvL1E97zq8ziniqzKcnIuBb0ealB3k232ShnjmfXhMNzZMb/5o97GIX3Uf4oLDQkHsXJI8qrUMhULqGlAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T14:53:34.248230Z","bundle_sha256":"7632fe5c1144a5c81264f4fd2b3925c8f6d5bd3d11a41846e8e983f7168eb213"}}