{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:2TN5JHT4M4KXI3RG75BN2C3GB3","short_pith_number":"pith:2TN5JHT4","canonical_record":{"source":{"id":"2605.22885","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.AI","submitted_at":"2026-05-21T02:20:26Z","cross_cats_sorted":["cs.CL","cs.LG","cs.LO"],"title_canon_sha256":"ed5412ad9422dcdd659246d5fe216471d67d3a15ab5c5700ce097c53887a9028","abstract_canon_sha256":"5552f64973ffa2734f2f8a8e24bdd88b0bb82250162e78bf57d2a8cd4036630b"},"schema_version":"1.0"},"canonical_sha256":"d4dbd49e7c6715746e26ff42dd0b660eec6bece48aced007c42756da8c2806ba","source":{"kind":"arxiv","id":"2605.22885","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.22885","created_at":"2026-05-25T02:01:28Z"},{"alias_kind":"arxiv_version","alias_value":"2605.22885v1","created_at":"2026-05-25T02:01:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.22885","created_at":"2026-05-25T02:01:28Z"},{"alias_kind":"pith_short_12","alias_value":"2TN5JHT4M4KX","created_at":"2026-05-25T02:01:28Z"},{"alias_kind":"pith_short_16","alias_value":"2TN5JHT4M4KXI3RG","created_at":"2026-05-25T02:01:28Z"},{"alias_kind":"pith_short_8","alias_value":"2TN5JHT4","created_at":"2026-05-25T02:01:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:2TN5JHT4M4KXI3RG75BN2C3GB3","target":"record","payload":{"canonical_record":{"source":{"id":"2605.22885","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.AI","submitted_at":"2026-05-21T02:20:26Z","cross_cats_sorted":["cs.CL","cs.LG","cs.LO"],"title_canon_sha256":"ed5412ad9422dcdd659246d5fe216471d67d3a15ab5c5700ce097c53887a9028","abstract_canon_sha256":"5552f64973ffa2734f2f8a8e24bdd88b0bb82250162e78bf57d2a8cd4036630b"},"schema_version":"1.0"},"canonical_sha256":"d4dbd49e7c6715746e26ff42dd0b660eec6bece48aced007c42756da8c2806ba","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-25T02:01:28.644967Z","signature_b64":"Qgb/WarzcTv3yfgNzxmn+jfWnwPCXT2oGtiQbSwmB/KEl3pGcm1FWVwGa70rX2MAgT6zXYFSLv5ReS9dlJzIAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d4dbd49e7c6715746e26ff42dd0b660eec6bece48aced007c42756da8c2806ba","last_reissued_at":"2026-05-25T02:01:28.644392Z","signature_status":"signed_v1","first_computed_at":"2026-05-25T02:01:28.644392Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.22885","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":"2026-05-25T02:01:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BBMHmOJyJ83zD3GYxKJAzIi3ZHLquCy5BumXkHHeglQ1/Cf92PoDo95W4hbI5LMw30LvTe52SP1gXGkdegehAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T23:47:21.506430Z"},"content_sha256":"1f1df6064a815762327db3747ffa46bdcf8dc8c6dd6999c4b4251c7c4dced4d3","schema_version":"1.0","event_id":"sha256:1f1df6064a815762327db3747ffa46bdcf8dc8c6dd6999c4b4251c7c4dced4d3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:2TN5JHT4M4KXI3RG75BN2C3GB3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"ImProver 2: Iteratively Self-Improving LMs for Neurosymbolic Proof Optimization","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CL","cs.LG","cs.LO"],"primary_cat":"cs.AI","authors_text":"Jeremy Avigad, Riyaz Ahuja, Sean Welleck, Tate Rowney","submitted_at":"2026-05-21T02:20:26Z","abstract_excerpt":"Formal mathematics libraries are rapidly expanding, creating a growing need to refactor verified proofs for maintainability and to improve training data quality for neural provers. However, scalable proof optimization is hindered by heterogeneous and heuristically specified objectives, scarce data, and high training and inference costs. To overcome these challenges, we introduce ImProver 2, a neurosymbolic framework for automated proof optimization in Lean 4. ImProver 2 combines a data-efficient expert-iteration pipeline with a scaffold that exposes formal structure alongside lightweight infor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.22885","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.22885/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":"2026-05-25T02:01:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"keT14xhcOXzdSdS1jBu6Bel7xfO82bMAQ477kSicibFzlYP9hSiSfDaA+W+ajTlQBcThxJx6jK5EqklPeFf3Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T23:47:21.507118Z"},"content_sha256":"3b90c60db2a5347e81595e3571ac63d86d5597ca31b3695099ef15c10ae43700","schema_version":"1.0","event_id":"sha256:3b90c60db2a5347e81595e3571ac63d86d5597ca31b3695099ef15c10ae43700"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2TN5JHT4M4KXI3RG75BN2C3GB3/bundle.json","state_url":"https://pith.science/pith/2TN5JHT4M4KXI3RG75BN2C3GB3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2TN5JHT4M4KXI3RG75BN2C3GB3/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":"2026-05-25T23:47:21Z","links":{"resolver":"https://pith.science/pith/2TN5JHT4M4KXI3RG75BN2C3GB3","bundle":"https://pith.science/pith/2TN5JHT4M4KXI3RG75BN2C3GB3/bundle.json","state":"https://pith.science/pith/2TN5JHT4M4KXI3RG75BN2C3GB3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2TN5JHT4M4KXI3RG75BN2C3GB3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:2TN5JHT4M4KXI3RG75BN2C3GB3","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":"5552f64973ffa2734f2f8a8e24bdd88b0bb82250162e78bf57d2a8cd4036630b","cross_cats_sorted":["cs.CL","cs.LG","cs.LO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.AI","submitted_at":"2026-05-21T02:20:26Z","title_canon_sha256":"ed5412ad9422dcdd659246d5fe216471d67d3a15ab5c5700ce097c53887a9028"},"schema_version":"1.0","source":{"id":"2605.22885","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.22885","created_at":"2026-05-25T02:01:28Z"},{"alias_kind":"arxiv_version","alias_value":"2605.22885v1","created_at":"2026-05-25T02:01:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.22885","created_at":"2026-05-25T02:01:28Z"},{"alias_kind":"pith_short_12","alias_value":"2TN5JHT4M4KX","created_at":"2026-05-25T02:01:28Z"},{"alias_kind":"pith_short_16","alias_value":"2TN5JHT4M4KXI3RG","created_at":"2026-05-25T02:01:28Z"},{"alias_kind":"pith_short_8","alias_value":"2TN5JHT4","created_at":"2026-05-25T02:01:28Z"}],"graph_snapshots":[{"event_id":"sha256:3b90c60db2a5347e81595e3571ac63d86d5597ca31b3695099ef15c10ae43700","target":"graph","created_at":"2026-05-25T02:01:28Z","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/2605.22885/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Formal mathematics libraries are rapidly expanding, creating a growing need to refactor verified proofs for maintainability and to improve training data quality for neural provers. However, scalable proof optimization is hindered by heterogeneous and heuristically specified objectives, scarce data, and high training and inference costs. To overcome these challenges, we introduce ImProver 2, a neurosymbolic framework for automated proof optimization in Lean 4. ImProver 2 combines a data-efficient expert-iteration pipeline with a scaffold that exposes formal structure alongside lightweight infor","authors_text":"Jeremy Avigad, Riyaz Ahuja, Sean Welleck, Tate Rowney","cross_cats":["cs.CL","cs.LG","cs.LO"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.AI","submitted_at":"2026-05-21T02:20:26Z","title":"ImProver 2: Iteratively Self-Improving LMs for Neurosymbolic Proof Optimization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.22885","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":"sha256:1f1df6064a815762327db3747ffa46bdcf8dc8c6dd6999c4b4251c7c4dced4d3","target":"record","created_at":"2026-05-25T02:01:28Z","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":"5552f64973ffa2734f2f8a8e24bdd88b0bb82250162e78bf57d2a8cd4036630b","cross_cats_sorted":["cs.CL","cs.LG","cs.LO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.AI","submitted_at":"2026-05-21T02:20:26Z","title_canon_sha256":"ed5412ad9422dcdd659246d5fe216471d67d3a15ab5c5700ce097c53887a9028"},"schema_version":"1.0","source":{"id":"2605.22885","kind":"arxiv","version":1}},"canonical_sha256":"d4dbd49e7c6715746e26ff42dd0b660eec6bece48aced007c42756da8c2806ba","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d4dbd49e7c6715746e26ff42dd0b660eec6bece48aced007c42756da8c2806ba","first_computed_at":"2026-05-25T02:01:28.644392Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-25T02:01:28.644392Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Qgb/WarzcTv3yfgNzxmn+jfWnwPCXT2oGtiQbSwmB/KEl3pGcm1FWVwGa70rX2MAgT6zXYFSLv5ReS9dlJzIAQ==","signature_status":"signed_v1","signed_at":"2026-05-25T02:01:28.644967Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.22885","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1f1df6064a815762327db3747ffa46bdcf8dc8c6dd6999c4b4251c7c4dced4d3","sha256:3b90c60db2a5347e81595e3571ac63d86d5597ca31b3695099ef15c10ae43700"],"state_sha256":"1ed37315799effbc3c25dc90b105e252b3ebb5f302fa1cc3ec135024c58bc474"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tpD/9M4gs6u2Y1E7STVljA49z4rV9YmnUQdajDCb6orxpr+OxRNbQknmFiF4oVBNKvUu08lmxkbfmbdBS3UbDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T23:47:21.510713Z","bundle_sha256":"00bf124794a45a6b973c7597407091e64289656e84f99a37fd0bee737b37021b"}}