{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:QFUCRJYP6GVGT6HXVN3SWTN4CA","short_pith_number":"pith:QFUCRJYP","canonical_record":{"source":{"id":"1312.1819","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-12-06T10:06:20Z","cross_cats_sorted":[],"title_canon_sha256":"16e85777ee7be0de3c0a716f18975282f290c03bfab7a0a036d274febe86f89f","abstract_canon_sha256":"934ceb5cc61d9c54f9855182288fe811d22a8d736cd3361fcf92c94cd93ce4de"},"schema_version":"1.0"},"canonical_sha256":"816828a70ff1aa69f8f7ab772b4dbc10367e26e6b82414a918cecb024b9e4d0f","source":{"kind":"arxiv","id":"1312.1819","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.1819","created_at":"2026-05-18T03:05:19Z"},{"alias_kind":"arxiv_version","alias_value":"1312.1819v1","created_at":"2026-05-18T03:05:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.1819","created_at":"2026-05-18T03:05:19Z"},{"alias_kind":"pith_short_12","alias_value":"QFUCRJYP6GVG","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"QFUCRJYP6GVGT6HX","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"QFUCRJYP","created_at":"2026-05-18T12:27:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:QFUCRJYP6GVGT6HXVN3SWTN4CA","target":"record","payload":{"canonical_record":{"source":{"id":"1312.1819","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-12-06T10:06:20Z","cross_cats_sorted":[],"title_canon_sha256":"16e85777ee7be0de3c0a716f18975282f290c03bfab7a0a036d274febe86f89f","abstract_canon_sha256":"934ceb5cc61d9c54f9855182288fe811d22a8d736cd3361fcf92c94cd93ce4de"},"schema_version":"1.0"},"canonical_sha256":"816828a70ff1aa69f8f7ab772b4dbc10367e26e6b82414a918cecb024b9e4d0f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:05:19.678234Z","signature_b64":"hqxVLx/QJeD8TI67yvY+VFYMawSCzTiLW5Qf7r5KOyAGXHq+HmheStz6ZkUBb0fxYu9CN2a+fGYDjLHQ9r1vDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"816828a70ff1aa69f8f7ab772b4dbc10367e26e6b82414a918cecb024b9e4d0f","last_reissued_at":"2026-05-18T03:05:19.677862Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:05:19.677862Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1312.1819","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":"2026-05-18T03:05:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mWcjpb6sTQbyBBcJuoF/aQwM33wcmGdvEBTxDrF8Cr9EX7mVZNOeYz+uSxDUOhrAkIk7zhMVcX12j2au/6KfCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T00:20:36.276920Z"},"content_sha256":"70611b028083e10329621e9cee206a7d68fbc93a0473642a0836f2401e406645","schema_version":"1.0","event_id":"sha256:70611b028083e10329621e9cee206a7d68fbc93a0473642a0836f2401e406645"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:QFUCRJYP6GVGT6HXVN3SWTN4CA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Exponential lower bounds on the size of approximate formulations in the natural encoding for Capacitated Facility Location","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Stavros G. Kolliopoulos, Yannis Moysoglou","submitted_at":"2013-12-06T10:06:20Z","abstract_excerpt":"The metric capacitated facility location is a well-studied problem for which, while constant factor approximations are known, no efficient relaxation with constant integrality gap is known. The question whether there is such a relaxation is among the most important open problems of approximation algorithms \\cite{ShmoysWbook}.\n  In this paper we show that, if one is restricted to linear programs that use the natural encoding for facility location, at least an exponential number of constraints is needed to achieve a constant gap. Our proof does not assume any special property of the relaxation s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.1819","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":"2026-05-18T03:05:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VY2RYeNwpw3JLSQFk/S6pGZ/Z/s2kQTKyatBi3MJrhuLFKGCI/nYqyY2AwMbinNihO5R6el24CALRlAqXI+ZAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T00:20:36.277592Z"},"content_sha256":"6d1fda2de2a0d8eacaf0a250178fc050bdcaa82d7175e74bf63df20abde4ec99","schema_version":"1.0","event_id":"sha256:6d1fda2de2a0d8eacaf0a250178fc050bdcaa82d7175e74bf63df20abde4ec99"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QFUCRJYP6GVGT6HXVN3SWTN4CA/bundle.json","state_url":"https://pith.science/pith/QFUCRJYP6GVGT6HXVN3SWTN4CA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QFUCRJYP6GVGT6HXVN3SWTN4CA/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":"2026-06-05T00:20:36Z","links":{"resolver":"https://pith.science/pith/QFUCRJYP6GVGT6HXVN3SWTN4CA","bundle":"https://pith.science/pith/QFUCRJYP6GVGT6HXVN3SWTN4CA/bundle.json","state":"https://pith.science/pith/QFUCRJYP6GVGT6HXVN3SWTN4CA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QFUCRJYP6GVGT6HXVN3SWTN4CA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:QFUCRJYP6GVGT6HXVN3SWTN4CA","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":"934ceb5cc61d9c54f9855182288fe811d22a8d736cd3361fcf92c94cd93ce4de","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-12-06T10:06:20Z","title_canon_sha256":"16e85777ee7be0de3c0a716f18975282f290c03bfab7a0a036d274febe86f89f"},"schema_version":"1.0","source":{"id":"1312.1819","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.1819","created_at":"2026-05-18T03:05:19Z"},{"alias_kind":"arxiv_version","alias_value":"1312.1819v1","created_at":"2026-05-18T03:05:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.1819","created_at":"2026-05-18T03:05:19Z"},{"alias_kind":"pith_short_12","alias_value":"QFUCRJYP6GVG","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"QFUCRJYP6GVGT6HX","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"QFUCRJYP","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:6d1fda2de2a0d8eacaf0a250178fc050bdcaa82d7175e74bf63df20abde4ec99","target":"graph","created_at":"2026-05-18T03:05:19Z","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":"The metric capacitated facility location is a well-studied problem for which, while constant factor approximations are known, no efficient relaxation with constant integrality gap is known. The question whether there is such a relaxation is among the most important open problems of approximation algorithms \\cite{ShmoysWbook}.\n  In this paper we show that, if one is restricted to linear programs that use the natural encoding for facility location, at least an exponential number of constraints is needed to achieve a constant gap. Our proof does not assume any special property of the relaxation s","authors_text":"Stavros G. Kolliopoulos, Yannis Moysoglou","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-12-06T10:06:20Z","title":"Exponential lower bounds on the size of approximate formulations in the natural encoding for Capacitated Facility Location"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.1819","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":"sha256:70611b028083e10329621e9cee206a7d68fbc93a0473642a0836f2401e406645","target":"record","created_at":"2026-05-18T03:05:19Z","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":"934ceb5cc61d9c54f9855182288fe811d22a8d736cd3361fcf92c94cd93ce4de","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-12-06T10:06:20Z","title_canon_sha256":"16e85777ee7be0de3c0a716f18975282f290c03bfab7a0a036d274febe86f89f"},"schema_version":"1.0","source":{"id":"1312.1819","kind":"arxiv","version":1}},"canonical_sha256":"816828a70ff1aa69f8f7ab772b4dbc10367e26e6b82414a918cecb024b9e4d0f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"816828a70ff1aa69f8f7ab772b4dbc10367e26e6b82414a918cecb024b9e4d0f","first_computed_at":"2026-05-18T03:05:19.677862Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:05:19.677862Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hqxVLx/QJeD8TI67yvY+VFYMawSCzTiLW5Qf7r5KOyAGXHq+HmheStz6ZkUBb0fxYu9CN2a+fGYDjLHQ9r1vDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:05:19.678234Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.1819","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:70611b028083e10329621e9cee206a7d68fbc93a0473642a0836f2401e406645","sha256:6d1fda2de2a0d8eacaf0a250178fc050bdcaa82d7175e74bf63df20abde4ec99"],"state_sha256":"0a1bad2da75020e56db8a728416169fa40ffc287e28a2174abe0c4fbbb97959e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bVczW9kP3DzVZNXi64fKTaGs76GOlf2H09C//7Th4CxkoSSrxZ8YjZ/HVeeRhJsVOGE+avnwJqKwq6QM4LzQDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T00:20:36.281391Z","bundle_sha256":"4df80140f25e893ac29da8724d0ce261b96cb77371a3dcbbdfdd5ea25eab3d5f"}}