{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:SYE53VAYGLTVZIW33MTRTQITYP","short_pith_number":"pith:SYE53VAY","canonical_record":{"source":{"id":"1611.01291","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2016-11-04T09:27:34Z","cross_cats_sorted":[],"title_canon_sha256":"4f51e29f96ba1c0a2257e8b97a5ca65c74b8054d72d1bc7379c9ea4aa1a630e8","abstract_canon_sha256":"9afa201a5cf8a9177df2ac1e22f92d5616652facdd33882bb238f8ed32228522"},"schema_version":"1.0"},"canonical_sha256":"9609ddd41832e75ca2dbdb2719c113c3d134eef158e36c02d1a00ce9e227c3f7","source":{"kind":"arxiv","id":"1611.01291","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.01291","created_at":"2026-05-18T00:36:03Z"},{"alias_kind":"arxiv_version","alias_value":"1611.01291v1","created_at":"2026-05-18T00:36:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.01291","created_at":"2026-05-18T00:36:03Z"},{"alias_kind":"pith_short_12","alias_value":"SYE53VAYGLTV","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SYE53VAYGLTVZIW3","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SYE53VAY","created_at":"2026-05-18T12:30:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:SYE53VAYGLTVZIW33MTRTQITYP","target":"record","payload":{"canonical_record":{"source":{"id":"1611.01291","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2016-11-04T09:27:34Z","cross_cats_sorted":[],"title_canon_sha256":"4f51e29f96ba1c0a2257e8b97a5ca65c74b8054d72d1bc7379c9ea4aa1a630e8","abstract_canon_sha256":"9afa201a5cf8a9177df2ac1e22f92d5616652facdd33882bb238f8ed32228522"},"schema_version":"1.0"},"canonical_sha256":"9609ddd41832e75ca2dbdb2719c113c3d134eef158e36c02d1a00ce9e227c3f7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:36:03.740782Z","signature_b64":"WKATAcehWrI1xJHuUbliDgUX0oKfZeyI0BMZ7p7qsEqXpppUWcvrwpxFws6nAJLDqeUuwWYWGNESM6D/7Kh3Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9609ddd41832e75ca2dbdb2719c113c3d134eef158e36c02d1a00ce9e227c3f7","last_reissued_at":"2026-05-18T00:36:03.740136Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:36:03.740136Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.01291","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":"2026-05-18T00:36:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Sm65kH+ANr9s+SFyFPfwwrCIRq6/sGy2N2PI6pCiVoCMZviLcs7xYCaRk6BkGgUe1fUqy4SGyqvmv9GzOzPmBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T20:26:11.375127Z"},"content_sha256":"619fd2a8f43c54b7440ff39f15995a70a395848dee2592a775bca501adfc2a1b","schema_version":"1.0","event_id":"sha256:619fd2a8f43c54b7440ff39f15995a70a395848dee2592a775bca501adfc2a1b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:SYE53VAYGLTVZIW33MTRTQITYP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Tighter Hard Instances for PPSZ","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Dominik Scheder, Navid Talebanfard, Pavel Pudl\\'ak","submitted_at":"2016-11-04T09:27:34Z","abstract_excerpt":"We construct uniquely satisfiable $k$-CNF formulas that are hard for the algorithm PPSZ. Firstly, we construct graph-instances on which \"weak PPSZ\" has savings of at most $(2 + \\epsilon) / k$; the saving of an algorithm on an input formula with $n$ variables is the largest $\\gamma$ such that the algorithm succeeds (i.e. finds a satisfying assignment) with probability at least $2^{ - (1 - \\gamma) n}$. Since PPSZ (both weak and strong) is known to have savings of at least $\\frac{\\pi^2 + o(1)}{6k}$, this is optimal up to the constant factor. In particular, for $k=3$, our upper bound is $2^{0.333\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.01291","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":"2026-05-18T00:36:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+8cDmpmepZl+CxKVQojKfwiDUC/0I+4DU57xa/+4lIIc77wKXVua6gTCTCRjIShBax2y9fjVMPUAX1dDp69BDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T20:26:11.375481Z"},"content_sha256":"ab5cf925fbacaca35d7c4a5ff8306dbd9e0832396b6ad20f4bd1fcfa4842af8c","schema_version":"1.0","event_id":"sha256:ab5cf925fbacaca35d7c4a5ff8306dbd9e0832396b6ad20f4bd1fcfa4842af8c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SYE53VAYGLTVZIW33MTRTQITYP/bundle.json","state_url":"https://pith.science/pith/SYE53VAYGLTVZIW33MTRTQITYP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SYE53VAYGLTVZIW33MTRTQITYP/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":"2026-06-02T20:26:11Z","links":{"resolver":"https://pith.science/pith/SYE53VAYGLTVZIW33MTRTQITYP","bundle":"https://pith.science/pith/SYE53VAYGLTVZIW33MTRTQITYP/bundle.json","state":"https://pith.science/pith/SYE53VAYGLTVZIW33MTRTQITYP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SYE53VAYGLTVZIW33MTRTQITYP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:SYE53VAYGLTVZIW33MTRTQITYP","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":"9afa201a5cf8a9177df2ac1e22f92d5616652facdd33882bb238f8ed32228522","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2016-11-04T09:27:34Z","title_canon_sha256":"4f51e29f96ba1c0a2257e8b97a5ca65c74b8054d72d1bc7379c9ea4aa1a630e8"},"schema_version":"1.0","source":{"id":"1611.01291","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.01291","created_at":"2026-05-18T00:36:03Z"},{"alias_kind":"arxiv_version","alias_value":"1611.01291v1","created_at":"2026-05-18T00:36:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.01291","created_at":"2026-05-18T00:36:03Z"},{"alias_kind":"pith_short_12","alias_value":"SYE53VAYGLTV","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SYE53VAYGLTVZIW3","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SYE53VAY","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:ab5cf925fbacaca35d7c4a5ff8306dbd9e0832396b6ad20f4bd1fcfa4842af8c","target":"graph","created_at":"2026-05-18T00:36:03Z","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 construct uniquely satisfiable $k$-CNF formulas that are hard for the algorithm PPSZ. Firstly, we construct graph-instances on which \"weak PPSZ\" has savings of at most $(2 + \\epsilon) / k$; the saving of an algorithm on an input formula with $n$ variables is the largest $\\gamma$ such that the algorithm succeeds (i.e. finds a satisfying assignment) with probability at least $2^{ - (1 - \\gamma) n}$. Since PPSZ (both weak and strong) is known to have savings of at least $\\frac{\\pi^2 + o(1)}{6k}$, this is optimal up to the constant factor. In particular, for $k=3$, our upper bound is $2^{0.333\\","authors_text":"Dominik Scheder, Navid Talebanfard, Pavel Pudl\\'ak","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2016-11-04T09:27:34Z","title":"Tighter Hard Instances for PPSZ"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.01291","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":"sha256:619fd2a8f43c54b7440ff39f15995a70a395848dee2592a775bca501adfc2a1b","target":"record","created_at":"2026-05-18T00:36:03Z","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":"9afa201a5cf8a9177df2ac1e22f92d5616652facdd33882bb238f8ed32228522","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2016-11-04T09:27:34Z","title_canon_sha256":"4f51e29f96ba1c0a2257e8b97a5ca65c74b8054d72d1bc7379c9ea4aa1a630e8"},"schema_version":"1.0","source":{"id":"1611.01291","kind":"arxiv","version":1}},"canonical_sha256":"9609ddd41832e75ca2dbdb2719c113c3d134eef158e36c02d1a00ce9e227c3f7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9609ddd41832e75ca2dbdb2719c113c3d134eef158e36c02d1a00ce9e227c3f7","first_computed_at":"2026-05-18T00:36:03.740136Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:36:03.740136Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WKATAcehWrI1xJHuUbliDgUX0oKfZeyI0BMZ7p7qsEqXpppUWcvrwpxFws6nAJLDqeUuwWYWGNESM6D/7Kh3Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:36:03.740782Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.01291","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:619fd2a8f43c54b7440ff39f15995a70a395848dee2592a775bca501adfc2a1b","sha256:ab5cf925fbacaca35d7c4a5ff8306dbd9e0832396b6ad20f4bd1fcfa4842af8c"],"state_sha256":"3b73cee6f27f72d744e02daf1cc4959b7cbc857de3b69618c64195da3027bbe1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FTsAD5gvGA1U48P/YhY6uWg4L5Mq0DEKbtXHoMnIED4gF6CIKrlxejaQFz9kDb/hORYSvAyoMWCyECIsNYadDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T20:26:11.377357Z","bundle_sha256":"6f4e377864e3d0cb05d87203953e1d9d053a4a936a9f791d5836c3ea985593f3"}}