{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:DJCLIB6W4V73KW5TLUICTCBYRC","short_pith_number":"pith:DJCLIB6W","canonical_record":{"source":{"id":"1304.0145","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2013-03-30T23:21:56Z","cross_cats_sorted":[],"title_canon_sha256":"bd85c5694d91c98e58f4e2e9196930fa2cb328f195e819431d48c2640e030285","abstract_canon_sha256":"a07734f97a41e17539edfdf5e712f3cfa5afd3e5a8775725b6fb2a67be77d4a7"},"schema_version":"1.0"},"canonical_sha256":"1a44b407d6e57fb55bb35d102988388885f6201b210ddf59d4484aa63aca0eb7","source":{"kind":"arxiv","id":"1304.0145","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.0145","created_at":"2026-05-18T03:29:25Z"},{"alias_kind":"arxiv_version","alias_value":"1304.0145v1","created_at":"2026-05-18T03:29:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.0145","created_at":"2026-05-18T03:29:25Z"},{"alias_kind":"pith_short_12","alias_value":"DJCLIB6W4V73","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"DJCLIB6W4V73KW5T","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"DJCLIB6W","created_at":"2026-05-18T12:27:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:DJCLIB6W4V73KW5TLUICTCBYRC","target":"record","payload":{"canonical_record":{"source":{"id":"1304.0145","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2013-03-30T23:21:56Z","cross_cats_sorted":[],"title_canon_sha256":"bd85c5694d91c98e58f4e2e9196930fa2cb328f195e819431d48c2640e030285","abstract_canon_sha256":"a07734f97a41e17539edfdf5e712f3cfa5afd3e5a8775725b6fb2a67be77d4a7"},"schema_version":"1.0"},"canonical_sha256":"1a44b407d6e57fb55bb35d102988388885f6201b210ddf59d4484aa63aca0eb7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:29:25.871586Z","signature_b64":"ZrrvDjESAZHcM4t7nfX6rkcaD7cX2STwQUMKui/Wr87t+HZfIzUccpvUgCbrZZWHE5LNjfNyBfFW+FmUQfbpCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1a44b407d6e57fb55bb35d102988388885f6201b210ddf59d4484aa63aca0eb7","last_reissued_at":"2026-05-18T03:29:25.871019Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:29:25.871019Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.0145","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":"2026-05-18T03:29:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y7WRsk51heP9tQtRxTjFI9fp4jgA6hBa21E3tjXkDlm2+rrEZl2jIrQAFZZgVevJdoUxTNMfK8sE7lCTinYSDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-24T03:07:32.495496Z"},"content_sha256":"0f6f9f1f380e2ace3185e8733edc0bc2f19ea415cfeb3f41153f88be95b6ed8e","schema_version":"1.0","event_id":"sha256:0f6f9f1f380e2ace3185e8733edc0bc2f19ea415cfeb3f41153f88be95b6ed8e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:DJCLIB6W4V73KW5TLUICTCBYRC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Phase Transition and Network Structure in Realistic SAT Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.AI","authors_text":"Soumya C. Kambhampati, Thomas Liu","submitted_at":"2013-03-30T23:21:56Z","abstract_excerpt":"A fundamental question in Computer Science is understanding when a specific class of problems go from being computationally easy to hard. Because of its generality and applications, the problem of Boolean Satisfiability (aka SAT) is often used as a vehicle for investigating this question. A signal result from these studies is that the hardness of SAT problems exhibits a dramatic easy-to-hard phase transition with respect to the problem constrainedness. Past studies have however focused mostly on SAT instances generated using uniform random distributions, where all constraints are independently"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.0145","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":"2026-05-18T03:29:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bHCwJvCds6plplhhheNO8yKjd2K9pjX53e6p6r4WRA/e6iPEWNV5zadpVhJ27Dx5xUypJCriZO8hwuKYzJ2sCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-24T03:07:32.496020Z"},"content_sha256":"11bed95266923a049548e711500af939e78012cf20e701ee7ad9bfcd7370de47","schema_version":"1.0","event_id":"sha256:11bed95266923a049548e711500af939e78012cf20e701ee7ad9bfcd7370de47"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DJCLIB6W4V73KW5TLUICTCBYRC/bundle.json","state_url":"https://pith.science/pith/DJCLIB6W4V73KW5TLUICTCBYRC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DJCLIB6W4V73KW5TLUICTCBYRC/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":"2026-08-24T03:07:32Z","links":{"resolver":"https://pith.science/pith/DJCLIB6W4V73KW5TLUICTCBYRC","bundle":"https://pith.science/pith/DJCLIB6W4V73KW5TLUICTCBYRC/bundle.json","state":"https://pith.science/pith/DJCLIB6W4V73KW5TLUICTCBYRC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DJCLIB6W4V73KW5TLUICTCBYRC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:DJCLIB6W4V73KW5TLUICTCBYRC","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":"a07734f97a41e17539edfdf5e712f3cfa5afd3e5a8775725b6fb2a67be77d4a7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2013-03-30T23:21:56Z","title_canon_sha256":"bd85c5694d91c98e58f4e2e9196930fa2cb328f195e819431d48c2640e030285"},"schema_version":"1.0","source":{"id":"1304.0145","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.0145","created_at":"2026-05-18T03:29:25Z"},{"alias_kind":"arxiv_version","alias_value":"1304.0145v1","created_at":"2026-05-18T03:29:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.0145","created_at":"2026-05-18T03:29:25Z"},{"alias_kind":"pith_short_12","alias_value":"DJCLIB6W4V73","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"DJCLIB6W4V73KW5T","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"DJCLIB6W","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:11bed95266923a049548e711500af939e78012cf20e701ee7ad9bfcd7370de47","target":"graph","created_at":"2026-05-18T03:29:25Z","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":"A fundamental question in Computer Science is understanding when a specific class of problems go from being computationally easy to hard. Because of its generality and applications, the problem of Boolean Satisfiability (aka SAT) is often used as a vehicle for investigating this question. A signal result from these studies is that the hardness of SAT problems exhibits a dramatic easy-to-hard phase transition with respect to the problem constrainedness. Past studies have however focused mostly on SAT instances generated using uniform random distributions, where all constraints are independently","authors_text":"Soumya C. Kambhampati, Thomas Liu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2013-03-30T23:21:56Z","title":"Phase Transition and Network Structure in Realistic SAT Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.0145","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":"sha256:0f6f9f1f380e2ace3185e8733edc0bc2f19ea415cfeb3f41153f88be95b6ed8e","target":"record","created_at":"2026-05-18T03:29:25Z","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":"a07734f97a41e17539edfdf5e712f3cfa5afd3e5a8775725b6fb2a67be77d4a7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2013-03-30T23:21:56Z","title_canon_sha256":"bd85c5694d91c98e58f4e2e9196930fa2cb328f195e819431d48c2640e030285"},"schema_version":"1.0","source":{"id":"1304.0145","kind":"arxiv","version":1}},"canonical_sha256":"1a44b407d6e57fb55bb35d102988388885f6201b210ddf59d4484aa63aca0eb7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1a44b407d6e57fb55bb35d102988388885f6201b210ddf59d4484aa63aca0eb7","first_computed_at":"2026-05-18T03:29:25.871019Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:29:25.871019Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZrrvDjESAZHcM4t7nfX6rkcaD7cX2STwQUMKui/Wr87t+HZfIzUccpvUgCbrZZWHE5LNjfNyBfFW+FmUQfbpCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:29:25.871586Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.0145","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0f6f9f1f380e2ace3185e8733edc0bc2f19ea415cfeb3f41153f88be95b6ed8e","sha256:11bed95266923a049548e711500af939e78012cf20e701ee7ad9bfcd7370de47"],"state_sha256":"591e3e0bff9b2f07afd1faf798d1bda93d207b5f8335782be9a69a4803de1dbc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jRYKREa1bWbepm4MMQbEz8QCRfraGeXNWRIoG1Lel8NKkVR7PFW8H+3m4YWPG9Rb3HeYyBSQrBg37YznIXNFAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-24T03:07:32.500077Z","bundle_sha256":"f2242f10f67714e6ac8a868ed457dcd2ed4298d1a8b352e9eb81d366c074197b"}}