{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:LS56IK4SFCZEJI3W34YZB7JQK3","short_pith_number":"pith:LS56IK4S","canonical_record":{"source":{"id":"1708.01122","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-08-03T13:12:03Z","cross_cats_sorted":[],"title_canon_sha256":"a9d3f1c101441cf04d86980f81905f488161645bf55666b11cfc432b81e0df8d","abstract_canon_sha256":"f6e480aa5e8d062e7990d195ee6a7ebcc4f2678dece28639ee227b85e1f1b4b2"},"schema_version":"1.0"},"canonical_sha256":"5cbbe42b9228b244a376df3190fd3056f2af5f3f49363b4a41c183f6cbc5f878","source":{"kind":"arxiv","id":"1708.01122","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.01122","created_at":"2026-05-18T00:38:40Z"},{"alias_kind":"arxiv_version","alias_value":"1708.01122v1","created_at":"2026-05-18T00:38:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.01122","created_at":"2026-05-18T00:38:40Z"},{"alias_kind":"pith_short_12","alias_value":"LS56IK4SFCZE","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"LS56IK4SFCZEJI3W","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"LS56IK4S","created_at":"2026-05-18T12:31:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:LS56IK4SFCZEJI3W34YZB7JQK3","target":"record","payload":{"canonical_record":{"source":{"id":"1708.01122","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-08-03T13:12:03Z","cross_cats_sorted":[],"title_canon_sha256":"a9d3f1c101441cf04d86980f81905f488161645bf55666b11cfc432b81e0df8d","abstract_canon_sha256":"f6e480aa5e8d062e7990d195ee6a7ebcc4f2678dece28639ee227b85e1f1b4b2"},"schema_version":"1.0"},"canonical_sha256":"5cbbe42b9228b244a376df3190fd3056f2af5f3f49363b4a41c183f6cbc5f878","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:38:40.588959Z","signature_b64":"en7Kv4w88memQiH8Jm3eu2gfA96ARtbtHEVTd3GTlBrblVKfgfWEuEU4/fjWygHWJKYMIimeGYbomCYLHzgoBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5cbbe42b9228b244a376df3190fd3056f2af5f3f49363b4a41c183f6cbc5f878","last_reissued_at":"2026-05-18T00:38:40.588384Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:38:40.588384Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1708.01122","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":"2026-05-18T00:38:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lq/Q0Oco6vWYsEhpxamP2O8+9gcEx64LeKCLIhz60eptWQif7kJaYQ6MgD+LUUN1SVM9kFV5k5eXVDD41MuDDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T04:46:54.392310Z"},"content_sha256":"875e371e4161e24e375b2b9d587101f96eb6b7182d804638ca608cb63ca84979","schema_version":"1.0","event_id":"sha256:875e371e4161e24e375b2b9d587101f96eb6b7182d804638ca608cb63ca84979"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:LS56IK4SFCZEJI3W34YZB7JQK3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Solving and Sampling with Many Solutions: Satisfiability and Other Hard Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Emo Welzl, Jean Cardinal, Jerri Nummenpalo","submitted_at":"2017-08-03T13:12:03Z","abstract_excerpt":"We investigate parameterizing hard combinatorial problems by the size of the solution set compared to all solution candidates. Our main result is a uniform sampling algorithm for satisfying assignments of 2-CNF formulas that runs in expected time $O^*(\\varepsilon^{-0.617})$ where $\\varepsilon$ is the fraction of assignments that are satisfying. This improves significantly over the trivial sampling bound of expected $\\Theta^*(\\varepsilon^{-1})$, and on all previous algorithms whenever $\\varepsilon = \\Omega(0.708^n)$. We also consider algorithms for 3-SAT with an $\\varepsilon$ fraction of satisf"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.01122","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":"2026-05-18T00:38:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gshYrb9craYjpxuZlgcz7KNgCIajP1kN/DCFr4QnY9g5WoLd2UfyId+jB5oq+7TfXhPlkI6O3jbgfy3sZuOZAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T04:46:54.392677Z"},"content_sha256":"fb02a14a2a358558f08f5a730367e6cd923d3123c0caef1f3e5fd7a944497f74","schema_version":"1.0","event_id":"sha256:fb02a14a2a358558f08f5a730367e6cd923d3123c0caef1f3e5fd7a944497f74"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LS56IK4SFCZEJI3W34YZB7JQK3/bundle.json","state_url":"https://pith.science/pith/LS56IK4SFCZEJI3W34YZB7JQK3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LS56IK4SFCZEJI3W34YZB7JQK3/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":"2026-06-03T04:46:54Z","links":{"resolver":"https://pith.science/pith/LS56IK4SFCZEJI3W34YZB7JQK3","bundle":"https://pith.science/pith/LS56IK4SFCZEJI3W34YZB7JQK3/bundle.json","state":"https://pith.science/pith/LS56IK4SFCZEJI3W34YZB7JQK3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LS56IK4SFCZEJI3W34YZB7JQK3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:LS56IK4SFCZEJI3W34YZB7JQK3","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":"f6e480aa5e8d062e7990d195ee6a7ebcc4f2678dece28639ee227b85e1f1b4b2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-08-03T13:12:03Z","title_canon_sha256":"a9d3f1c101441cf04d86980f81905f488161645bf55666b11cfc432b81e0df8d"},"schema_version":"1.0","source":{"id":"1708.01122","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.01122","created_at":"2026-05-18T00:38:40Z"},{"alias_kind":"arxiv_version","alias_value":"1708.01122v1","created_at":"2026-05-18T00:38:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.01122","created_at":"2026-05-18T00:38:40Z"},{"alias_kind":"pith_short_12","alias_value":"LS56IK4SFCZE","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"LS56IK4SFCZEJI3W","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"LS56IK4S","created_at":"2026-05-18T12:31:28Z"}],"graph_snapshots":[{"event_id":"sha256:fb02a14a2a358558f08f5a730367e6cd923d3123c0caef1f3e5fd7a944497f74","target":"graph","created_at":"2026-05-18T00:38:40Z","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 investigate parameterizing hard combinatorial problems by the size of the solution set compared to all solution candidates. Our main result is a uniform sampling algorithm for satisfying assignments of 2-CNF formulas that runs in expected time $O^*(\\varepsilon^{-0.617})$ where $\\varepsilon$ is the fraction of assignments that are satisfying. This improves significantly over the trivial sampling bound of expected $\\Theta^*(\\varepsilon^{-1})$, and on all previous algorithms whenever $\\varepsilon = \\Omega(0.708^n)$. We also consider algorithms for 3-SAT with an $\\varepsilon$ fraction of satisf","authors_text":"Emo Welzl, Jean Cardinal, Jerri Nummenpalo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-08-03T13:12:03Z","title":"Solving and Sampling with Many Solutions: Satisfiability and Other Hard Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.01122","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":"sha256:875e371e4161e24e375b2b9d587101f96eb6b7182d804638ca608cb63ca84979","target":"record","created_at":"2026-05-18T00:38:40Z","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":"f6e480aa5e8d062e7990d195ee6a7ebcc4f2678dece28639ee227b85e1f1b4b2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-08-03T13:12:03Z","title_canon_sha256":"a9d3f1c101441cf04d86980f81905f488161645bf55666b11cfc432b81e0df8d"},"schema_version":"1.0","source":{"id":"1708.01122","kind":"arxiv","version":1}},"canonical_sha256":"5cbbe42b9228b244a376df3190fd3056f2af5f3f49363b4a41c183f6cbc5f878","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5cbbe42b9228b244a376df3190fd3056f2af5f3f49363b4a41c183f6cbc5f878","first_computed_at":"2026-05-18T00:38:40.588384Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:38:40.588384Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"en7Kv4w88memQiH8Jm3eu2gfA96ARtbtHEVTd3GTlBrblVKfgfWEuEU4/fjWygHWJKYMIimeGYbomCYLHzgoBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:38:40.588959Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.01122","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:875e371e4161e24e375b2b9d587101f96eb6b7182d804638ca608cb63ca84979","sha256:fb02a14a2a358558f08f5a730367e6cd923d3123c0caef1f3e5fd7a944497f74"],"state_sha256":"ab11fe9854441cf2f1423c4f9f97de97b07f9d7230089996c9f0504e6ef5f9fb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fG1dvYxm3CHQLow9JSJWZLhdW9AYym1mZoSy/obhnaVW8qF0UufPB3kqlUblq7PXRxzBu9AjYdohLH48LVA2Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T04:46:54.394662Z","bundle_sha256":"1147a18213a3a37a8e782db89850782ab42777b904a9ad32a36493a2913e0a39"}}