{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:MDSOCWQFZKGL6X4RZYZDSUGV3N","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":"df28038b7e3f67896271753489ea30d1e25a9fcb1a99ca688f46d8ad72e3bad5","cross_cats_sorted":["cs.AI","cs.LO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-07-19T03:23:22Z","title_canon_sha256":"d187cd1e839714a7617d02e98d832886281b1c683aed8cdbba3a84127d6d69de"},"schema_version":"1.0","source":{"id":"2607.17047","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.17047","created_at":"2026-07-21T01:21:12Z"},{"alias_kind":"arxiv_version","alias_value":"2607.17047v1","created_at":"2026-07-21T01:21:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.17047","created_at":"2026-07-21T01:21:12Z"},{"alias_kind":"pith_short_12","alias_value":"MDSOCWQFZKGL","created_at":"2026-07-21T01:21:12Z"},{"alias_kind":"pith_short_16","alias_value":"MDSOCWQFZKGL6X4R","created_at":"2026-07-21T01:21:12Z"},{"alias_kind":"pith_short_8","alias_value":"MDSOCWQF","created_at":"2026-07-21T01:21:12Z"}],"graph_snapshots":[{"event_id":"sha256:55d6d2978c1f172d2a8a5b94b448fd9dd340c6746a74bbdd48bb05ca89aeb732","target":"graph","created_at":"2026-07-21T01:21:12Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2607.17047/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"LLM constraint reasoners are often evaluated near the random-SAT phase transition, confounding density and solver hardness. We test instance-level transfer while near-matching clause density. At aligned size bins, with near-matched density and matched maximum clause width, we compare proof-hard expander-Tseitin and proof-easy ladder-Tseitin formulas, pigeonhole anchors, and density-mismatched controls. Theory separates their resolution hardness; a solver-specific Glucose mean-conflict proxy differs by up to $51\\times$, and five other solvers preserve the direction. Across three included models","authors_text":"Lucky Verma","cross_cats":["cs.AI","cs.LO"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-07-19T03:23:22Z","title":"Solver-Hard Is Not Model-Hard: A Hardness-Controlled Diagnostic for LLM Constraint Reasoning"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.17047","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":"sha256:4ef1347f2a746a7f266bfa958e66abf097f24f97541e51534d1bc958a1500cdc","target":"record","created_at":"2026-07-21T01:21:12Z","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":"df28038b7e3f67896271753489ea30d1e25a9fcb1a99ca688f46d8ad72e3bad5","cross_cats_sorted":["cs.AI","cs.LO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-07-19T03:23:22Z","title_canon_sha256":"d187cd1e839714a7617d02e98d832886281b1c683aed8cdbba3a84127d6d69de"},"schema_version":"1.0","source":{"id":"2607.17047","kind":"arxiv","version":1}},"canonical_sha256":"60e4e15a05ca8cbf5f91ce323950d5db74ea0819937cb4c2e96bcd03a83a501e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"60e4e15a05ca8cbf5f91ce323950d5db74ea0819937cb4c2e96bcd03a83a501e","first_computed_at":"2026-07-21T01:21:12.135444Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-21T01:21:12.135444Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QxHk8AV7IOykbd6psTtGiEJThGdFIX8uBBXMp6daGt3WEts6fckiiDCJ6TIMf5JzRv58Lline+veXy/RjvRJAQ==","signature_status":"signed_v1","signed_at":"2026-07-21T01:21:12.136289Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.17047","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4ef1347f2a746a7f266bfa958e66abf097f24f97541e51534d1bc958a1500cdc","sha256:55d6d2978c1f172d2a8a5b94b448fd9dd340c6746a74bbdd48bb05ca89aeb732"],"state_sha256":"68e91fc9fb4d7f6a893d835e67450c4f3f656d267dd5f2a6c89a717d68618bc1"}