{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:NFPUHMVQDKEXJQT3YM7E5BLF2Y","short_pith_number":"pith:NFPUHMVQ","canonical_record":{"source":{"id":"2601.04045","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LO","submitted_at":"2026-01-07T16:00:43Z","cross_cats_sorted":[],"title_canon_sha256":"228e0af27f31d21033f2007a79afb4e4dca9bb7c33dfeb4ba9530df88cd68e2b","abstract_canon_sha256":"61646f8f8091dfa878eee8af51dbd866a23eafacfd009ea01c2d873720e75e9d"},"schema_version":"1.0"},"canonical_sha256":"695f43b2b01a8974c27bc33e4e8565d63c5d2588a7cb79488e38b71cdb97b6ff","source":{"kind":"arxiv","id":"2601.04045","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2601.04045","created_at":"2026-07-23T01:24:19Z"},{"alias_kind":"arxiv_version","alias_value":"2601.04045v2","created_at":"2026-07-23T01:24:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2601.04045","created_at":"2026-07-23T01:24:19Z"},{"alias_kind":"pith_short_12","alias_value":"NFPUHMVQDKEX","created_at":"2026-07-23T01:24:19Z"},{"alias_kind":"pith_short_16","alias_value":"NFPUHMVQDKEXJQT3","created_at":"2026-07-23T01:24:19Z"},{"alias_kind":"pith_short_8","alias_value":"NFPUHMVQ","created_at":"2026-07-23T01:24:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:NFPUHMVQDKEXJQT3YM7E5BLF2Y","target":"record","payload":{"canonical_record":{"source":{"id":"2601.04045","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LO","submitted_at":"2026-01-07T16:00:43Z","cross_cats_sorted":[],"title_canon_sha256":"228e0af27f31d21033f2007a79afb4e4dca9bb7c33dfeb4ba9530df88cd68e2b","abstract_canon_sha256":"61646f8f8091dfa878eee8af51dbd866a23eafacfd009ea01c2d873720e75e9d"},"schema_version":"1.0"},"canonical_sha256":"695f43b2b01a8974c27bc33e4e8565d63c5d2588a7cb79488e38b71cdb97b6ff","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-23T01:24:19.857937Z","signature_b64":"UkPvghOu8mWLjGPfNvfn95CdJCIBA0zjQh1jOAXBctuf6zgbi6Szip3ar1eNoi4IY2S38lFpAUGTNAUvcowFAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"695f43b2b01a8974c27bc33e4e8565d63c5d2588a7cb79488e38b71cdb97b6ff","last_reissued_at":"2026-07-23T01:24:19.857005Z","signature_status":"signed_v1","first_computed_at":"2026-07-23T01:24:19.857005Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2601.04045","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-23T01:24:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6tipi6k7LdB3bYhapVpHhKI+2HnykgjStOj183ZCVcN/v2vMkWh65jyuzJ+idjQjeyO2qErGvLR4PKpMkRXiBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T06:41:02.993596Z"},"content_sha256":"7b80444909133b577b78b3be7e989bc897a07d29b77ced3f59f0d24c4686528e","schema_version":"1.0","event_id":"sha256:7b80444909133b577b78b3be7e989bc897a07d29b77ced3f59f0d24c4686528e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:NFPUHMVQDKEXJQT3YM7E5BLF2Y","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Recursive Program Synthesis from Sketches and Mixed-Quantifier Properties","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Derek Egolf, Stavros Tripakis","submitted_at":"2026-01-07T16:00:43Z","abstract_excerpt":"We present a novel approach for the synthesis of recursive programs from mixed-quantifier first-order logic properties. We solve this problem using a sketching-based, enumerative, counterexample-guided approach. Our algorithm learns syntactic constraints from counterexamples to prune the candidate space and employs a prophylactic pruning technique to avoid enumerating invalid candidates altogether. We implement our technique in a tool called Cataclyst and evaluate it on a suite of 60 benchmarks. We demonstrate that both counterexample generalization and prophylactic pruning significantly impro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2601.04045","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2601.04045/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-23T01:24:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8RGDMLmwTJeZsb20J8l64tZ49AszgMO+6K165WYmMMRDwGEQyOByIuPaLdZIt5QLQb9vmI9sXGTTEyou6e5gAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T06:41:02.994066Z"},"content_sha256":"30e0bf14a856a27fcc7dd17d7a45edbf3ecc53ff31744575b6cb0b6302ab85cf","schema_version":"1.0","event_id":"sha256:30e0bf14a856a27fcc7dd17d7a45edbf3ecc53ff31744575b6cb0b6302ab85cf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NFPUHMVQDKEXJQT3YM7E5BLF2Y/bundle.json","state_url":"https://pith.science/pith/NFPUHMVQDKEXJQT3YM7E5BLF2Y/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NFPUHMVQDKEXJQT3YM7E5BLF2Y/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":"2026-08-14T06:41:02Z","links":{"resolver":"https://pith.science/pith/NFPUHMVQDKEXJQT3YM7E5BLF2Y","bundle":"https://pith.science/pith/NFPUHMVQDKEXJQT3YM7E5BLF2Y/bundle.json","state":"https://pith.science/pith/NFPUHMVQDKEXJQT3YM7E5BLF2Y/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NFPUHMVQDKEXJQT3YM7E5BLF2Y/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:NFPUHMVQDKEXJQT3YM7E5BLF2Y","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":"61646f8f8091dfa878eee8af51dbd866a23eafacfd009ea01c2d873720e75e9d","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LO","submitted_at":"2026-01-07T16:00:43Z","title_canon_sha256":"228e0af27f31d21033f2007a79afb4e4dca9bb7c33dfeb4ba9530df88cd68e2b"},"schema_version":"1.0","source":{"id":"2601.04045","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2601.04045","created_at":"2026-07-23T01:24:19Z"},{"alias_kind":"arxiv_version","alias_value":"2601.04045v2","created_at":"2026-07-23T01:24:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2601.04045","created_at":"2026-07-23T01:24:19Z"},{"alias_kind":"pith_short_12","alias_value":"NFPUHMVQDKEX","created_at":"2026-07-23T01:24:19Z"},{"alias_kind":"pith_short_16","alias_value":"NFPUHMVQDKEXJQT3","created_at":"2026-07-23T01:24:19Z"},{"alias_kind":"pith_short_8","alias_value":"NFPUHMVQ","created_at":"2026-07-23T01:24:19Z"}],"graph_snapshots":[{"event_id":"sha256:30e0bf14a856a27fcc7dd17d7a45edbf3ecc53ff31744575b6cb0b6302ab85cf","target":"graph","created_at":"2026-07-23T01:24:19Z","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/2601.04045/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present a novel approach for the synthesis of recursive programs from mixed-quantifier first-order logic properties. We solve this problem using a sketching-based, enumerative, counterexample-guided approach. Our algorithm learns syntactic constraints from counterexamples to prune the candidate space and employs a prophylactic pruning technique to avoid enumerating invalid candidates altogether. We implement our technique in a tool called Cataclyst and evaluate it on a suite of 60 benchmarks. We demonstrate that both counterexample generalization and prophylactic pruning significantly impro","authors_text":"Derek Egolf, Stavros Tripakis","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LO","submitted_at":"2026-01-07T16:00:43Z","title":"Recursive Program Synthesis from Sketches and Mixed-Quantifier Properties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2601.04045","kind":"arxiv","version":2},"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":"sha256:7b80444909133b577b78b3be7e989bc897a07d29b77ced3f59f0d24c4686528e","target":"record","created_at":"2026-07-23T01:24:19Z","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":"61646f8f8091dfa878eee8af51dbd866a23eafacfd009ea01c2d873720e75e9d","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LO","submitted_at":"2026-01-07T16:00:43Z","title_canon_sha256":"228e0af27f31d21033f2007a79afb4e4dca9bb7c33dfeb4ba9530df88cd68e2b"},"schema_version":"1.0","source":{"id":"2601.04045","kind":"arxiv","version":2}},"canonical_sha256":"695f43b2b01a8974c27bc33e4e8565d63c5d2588a7cb79488e38b71cdb97b6ff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"695f43b2b01a8974c27bc33e4e8565d63c5d2588a7cb79488e38b71cdb97b6ff","first_computed_at":"2026-07-23T01:24:19.857005Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-23T01:24:19.857005Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UkPvghOu8mWLjGPfNvfn95CdJCIBA0zjQh1jOAXBctuf6zgbi6Szip3ar1eNoi4IY2S38lFpAUGTNAUvcowFAg==","signature_status":"signed_v1","signed_at":"2026-07-23T01:24:19.857937Z","signed_message":"canonical_sha256_bytes"},"source_id":"2601.04045","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7b80444909133b577b78b3be7e989bc897a07d29b77ced3f59f0d24c4686528e","sha256:30e0bf14a856a27fcc7dd17d7a45edbf3ecc53ff31744575b6cb0b6302ab85cf"],"state_sha256":"2c9e4fd5bfbdd61c650fc5d153c7c6c530ab87cf65c87af5365788d2473fecb4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9Ar4ose9Vq7E3qwbU1VUXLC0QkRh30QJbtW4Tc8WQaWkwLmIZy3Wyw1JAfvGV8Z9heM+twYuZf4IawJNhCEcCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T06:41:02.998830Z","bundle_sha256":"79cd88f929a30421522caae61eb08dcc6f24466ebc9a1275fc0e90a5a35fb5b8"}}