{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1993:FXAR7X7PPQB6ODBJZHWVU4TEQR","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":"169d5a9906a0246e10c3030d1f52606d368973c748320730c8ee4e687f16248d","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"1993-03-17T23:08:38Z","title_canon_sha256":"f46fc959b51111d41823ea612700b6ee980b06a1766c36ec614fc19faf31ce80"},"schema_version":"1.0","source":{"id":"hep-th/9303100","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/9303100","created_at":"2026-05-18T01:38:42Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9303100v1","created_at":"2026-05-18T01:38:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9303100","created_at":"2026-05-18T01:38:42Z"},{"alias_kind":"pith_short_12","alias_value":"FXAR7X7PPQB6","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"FXAR7X7PPQB6ODBJ","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"FXAR7X7P","created_at":"2026-05-18T12:25:47Z"}],"graph_snapshots":[{"event_id":"sha256:3b24e58b70b91e4474a9a1cbb1c058552c09a31eba26d728ad3c262c918a9341","target":"graph","created_at":"2026-05-18T01:38:42Z","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 study the integral representation for the exact solution to nonperturbative $c le 1$ string theory. A generic solution is determined by two functions $W(x)$ and $Q(x)$ which behaive at infinity like $x^p$ and $x^q$ respectively. The integral model for arbitrary $(p,q)$ models is derived which explicitely demonstrates $p-q$ duality of minimal models coupled to gravity. We discuss also the exact solutions to string equation and reduction condition and present several explicit examples.","authors_text":"A.Marshakov, S.Kharchev","cross_cats":[],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"1993-03-17T23:08:38Z","title":"On pq-duality and explicit solutions in $c \\le 1$ $2d$ gravity models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9303100","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":"sha256:22c468f7f7ef4b6a9da91d4c312d4b43a892de4c7206771131dbda473af986c2","target":"record","created_at":"2026-05-18T01:38:42Z","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":"169d5a9906a0246e10c3030d1f52606d368973c748320730c8ee4e687f16248d","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"1993-03-17T23:08:38Z","title_canon_sha256":"f46fc959b51111d41823ea612700b6ee980b06a1766c36ec614fc19faf31ce80"},"schema_version":"1.0","source":{"id":"hep-th/9303100","kind":"arxiv","version":1}},"canonical_sha256":"2dc11fdfef7c03e70c29c9ed5a72648479dd92f538cb140bd4d82c289ecd51b2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2dc11fdfef7c03e70c29c9ed5a72648479dd92f538cb140bd4d82c289ecd51b2","first_computed_at":"2026-05-18T01:38:42.907955Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:42.907955Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9QlOY50sDzfUkFmjzkXyKmLujQUpz+YcZMXZfNvvQh2LMQqbRDIHXRWAnB8Y7tbpPXTZ72yvnzAC/YGXnVWSBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:42.908365Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/9303100","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:22c468f7f7ef4b6a9da91d4c312d4b43a892de4c7206771131dbda473af986c2","sha256:3b24e58b70b91e4474a9a1cbb1c058552c09a31eba26d728ad3c262c918a9341"],"state_sha256":"61a69bc20e966248305977b20d49753327acf2344720116c9b90202d1c197f16"}