{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1999:TU2QE7JXXRO72V7BXARMJ4AOXB","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":"c8d285bbb8d9d8190f0ddc5a2298453bcb76fb1a961025a4227849ebd73de0f5","cross_cats_sorted":["math-ph","math.MP","math.PR"],"license":"","primary_cat":"math.CO","submitted_at":"1999-09-05T17:26:16Z","title_canon_sha256":"f39db3b569decca44ba901b9d07a4c61422919b31057babe8ccea94be8795e7b"},"schema_version":"1.0","source":{"id":"math/9909031","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9909031","created_at":"2026-05-18T03:53:18Z"},{"alias_kind":"arxiv_version","alias_value":"math/9909031v4","created_at":"2026-05-18T03:53:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9909031","created_at":"2026-05-18T03:53:18Z"},{"alias_kind":"pith_short_12","alias_value":"TU2QE7JXXRO7","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"TU2QE7JXXRO72V7B","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"TU2QE7JX","created_at":"2026-05-18T12:25:49Z"}],"graph_snapshots":[{"event_id":"sha256:506ce5b4644242739c344ce4ffdc773e4302e53dde237b2c66256c21dc9fa20c","target":"graph","created_at":"2026-05-18T03:53:18Z","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 consider the random 2-satisfiability problem, in which each instance is a formula that is the conjunction of m clauses of the form (x or y), chosen uniformly at random from among all 2-clauses on n Boolean variables and their negations. As m and n tend to infinity in the ratio m/n --> alpha, the problem is known to have a phase transition at alpha_c = 1, below which the probability that the formula is satisfiable tends to one and above which it tends to zero. We determine the finite-size scaling about this transition, namely the scaling of the maximal window W(n,delta) = (alpha_-(n,delta),a","authors_text":"B\\'ela Bollob\\'as, Christian Borgs, David B. Wilson, Jennifer T. Chayes, Jeong Han Kim","cross_cats":["math-ph","math.MP","math.PR"],"headline":"","license":"","primary_cat":"math.CO","submitted_at":"1999-09-05T17:26:16Z","title":"The Scaling Window of the 2-SAT Transition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9909031","kind":"arxiv","version":4},"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":"sha256:8021d0620e08232397f43a1f13a10dc0abebd80d7edac37ba0b473197c5f800f","target":"record","created_at":"2026-05-18T03:53:18Z","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":"c8d285bbb8d9d8190f0ddc5a2298453bcb76fb1a961025a4227849ebd73de0f5","cross_cats_sorted":["math-ph","math.MP","math.PR"],"license":"","primary_cat":"math.CO","submitted_at":"1999-09-05T17:26:16Z","title_canon_sha256":"f39db3b569decca44ba901b9d07a4c61422919b31057babe8ccea94be8795e7b"},"schema_version":"1.0","source":{"id":"math/9909031","kind":"arxiv","version":4}},"canonical_sha256":"9d35027d37bc5dfd57e1b822c4f00eb8796ab5b117f8bbf20a62818fc6a6de8f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9d35027d37bc5dfd57e1b822c4f00eb8796ab5b117f8bbf20a62818fc6a6de8f","first_computed_at":"2026-05-18T03:53:18.005120Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:53:18.005120Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9+qwXgHY/krEcl5fQUIOQfG89Afi4fxmpBR1t0W8hrAlpWd6CQHrf1d733d7v0OmnLMHUgsxlZqxei5Q4n1xDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:53:18.005964Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9909031","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8021d0620e08232397f43a1f13a10dc0abebd80d7edac37ba0b473197c5f800f","sha256:506ce5b4644242739c344ce4ffdc773e4302e53dde237b2c66256c21dc9fa20c"],"state_sha256":"a1e61bbd538d537cc052e71fdad7ed16e34c0df223ca89e20471c32c0142d6da"}