{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:SF6T4ACBXTS64ETGBECR3UQICJ","short_pith_number":"pith:SF6T4ACB","canonical_record":{"source":{"id":"2507.07532","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-07-10T08:28:46Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"1556d8c6f3634b3580e76329996f9b48e5816867bcf61d9be5d6cb27aaccc1a9","abstract_canon_sha256":"3233eba82bdb5ddf140c5af4697129df0c5e94fb2d3185d0d21032980252d93d"},"schema_version":"1.0"},"canonical_sha256":"917d3e0041bce5ee126609051dd208127064176b7d0cd160a284b24c6d0fa64d","source":{"kind":"arxiv","id":"2507.07532","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.07532","created_at":"2026-06-23T01:12:46Z"},{"alias_kind":"arxiv_version","alias_value":"2507.07532v4","created_at":"2026-06-23T01:12:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.07532","created_at":"2026-06-23T01:12:46Z"},{"alias_kind":"pith_short_12","alias_value":"SF6T4ACBXTS6","created_at":"2026-06-23T01:12:46Z"},{"alias_kind":"pith_short_16","alias_value":"SF6T4ACBXTS64ETG","created_at":"2026-06-23T01:12:46Z"},{"alias_kind":"pith_short_8","alias_value":"SF6T4ACB","created_at":"2026-06-23T01:12:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:SF6T4ACBXTS64ETGBECR3UQICJ","target":"record","payload":{"canonical_record":{"source":{"id":"2507.07532","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-07-10T08:28:46Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"1556d8c6f3634b3580e76329996f9b48e5816867bcf61d9be5d6cb27aaccc1a9","abstract_canon_sha256":"3233eba82bdb5ddf140c5af4697129df0c5e94fb2d3185d0d21032980252d93d"},"schema_version":"1.0"},"canonical_sha256":"917d3e0041bce5ee126609051dd208127064176b7d0cd160a284b24c6d0fa64d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-23T01:12:46.321288Z","signature_b64":"g+qiulLmSwO+EZ05NppgXvAu6KFu2rfBW/2EgcsgHBb49FLTaOHi+/B7hj9Q02wokGC578HuKYZSLUMMAkL0Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"917d3e0041bce5ee126609051dd208127064176b7d0cd160a284b24c6d0fa64d","last_reissued_at":"2026-06-23T01:12:46.320705Z","signature_status":"signed_v1","first_computed_at":"2026-06-23T01:12:46.320705Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2507.07532","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-23T01:12:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LlEHPngY/SHrexism4Ox0tVA1aI9f3898lQkDrOh3yg46GkFRRhXH2zVzbTQw+Cja67UKzg7dcbBS4Iy+87cCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T22:23:33.558037Z"},"content_sha256":"e8246dea01a3d888b4d7080edc1336b58a41f98cc48657c88f7b118af09f4cc7","schema_version":"1.0","event_id":"sha256:e8246dea01a3d888b4d7080edc1336b58a41f98cc48657c88f7b118af09f4cc7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:SF6T4ACBXTS64ETGBECR3UQICJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Neural Concept Verifier: Scaling Prover-Verifier Games via Concept Encodings","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"cs.LG","authors_text":"Berkant Turan, David Steinmann, Kristian Kersting, Sebastian Pokutta, Suhrab Asadulla, Wolfgang Stammer","submitted_at":"2025-07-10T08:28:46Z","abstract_excerpt":"While Prover-Verifier Games (PVGs) offer a promising path toward verifiability in nonlinear classification models, they have not yet been applied to complex inputs such as high-dimensional images. Conversely, expressive concept encodings effectively allow to translate such data into interpretable concepts but are often utilised in the context of low-capacity linear predictors. In this work, we push towards real-world verifiability by combining the strengths of both approaches. We introduce Neural Concept Verifier (NCV), a unified framework combining PVGs for formal verifiability with concept e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.07532","kind":"arxiv","version":4},"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/2507.07532/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":"2026-06-23T01:12:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YcMu9S4zeq9Jb9ysdHdWbDh/lHYb8BW9vGxjP23rQ4MWYJKDfIx8Q+A9Zu9/++/p0NrYPm1LG4E6cBcMNJBXCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T22:23:33.558946Z"},"content_sha256":"1121d72f6a71cccbe30c79ddd086df2bffe7f51a0b865803917cf9fdeb62f74b","schema_version":"1.0","event_id":"sha256:1121d72f6a71cccbe30c79ddd086df2bffe7f51a0b865803917cf9fdeb62f74b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SF6T4ACBXTS64ETGBECR3UQICJ/bundle.json","state_url":"https://pith.science/pith/SF6T4ACBXTS64ETGBECR3UQICJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SF6T4ACBXTS64ETGBECR3UQICJ/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":"2026-08-16T22:23:33Z","links":{"resolver":"https://pith.science/pith/SF6T4ACBXTS64ETGBECR3UQICJ","bundle":"https://pith.science/pith/SF6T4ACBXTS64ETGBECR3UQICJ/bundle.json","state":"https://pith.science/pith/SF6T4ACBXTS64ETGBECR3UQICJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SF6T4ACBXTS64ETGBECR3UQICJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:SF6T4ACBXTS64ETGBECR3UQICJ","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":"3233eba82bdb5ddf140c5af4697129df0c5e94fb2d3185d0d21032980252d93d","cross_cats_sorted":["cs.AI"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-07-10T08:28:46Z","title_canon_sha256":"1556d8c6f3634b3580e76329996f9b48e5816867bcf61d9be5d6cb27aaccc1a9"},"schema_version":"1.0","source":{"id":"2507.07532","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.07532","created_at":"2026-06-23T01:12:46Z"},{"alias_kind":"arxiv_version","alias_value":"2507.07532v4","created_at":"2026-06-23T01:12:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.07532","created_at":"2026-06-23T01:12:46Z"},{"alias_kind":"pith_short_12","alias_value":"SF6T4ACBXTS6","created_at":"2026-06-23T01:12:46Z"},{"alias_kind":"pith_short_16","alias_value":"SF6T4ACBXTS64ETG","created_at":"2026-06-23T01:12:46Z"},{"alias_kind":"pith_short_8","alias_value":"SF6T4ACB","created_at":"2026-06-23T01:12:46Z"}],"graph_snapshots":[{"event_id":"sha256:1121d72f6a71cccbe30c79ddd086df2bffe7f51a0b865803917cf9fdeb62f74b","target":"graph","created_at":"2026-06-23T01:12:46Z","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/2507.07532/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"While Prover-Verifier Games (PVGs) offer a promising path toward verifiability in nonlinear classification models, they have not yet been applied to complex inputs such as high-dimensional images. Conversely, expressive concept encodings effectively allow to translate such data into interpretable concepts but are often utilised in the context of low-capacity linear predictors. In this work, we push towards real-world verifiability by combining the strengths of both approaches. We introduce Neural Concept Verifier (NCV), a unified framework combining PVGs for formal verifiability with concept e","authors_text":"Berkant Turan, David Steinmann, Kristian Kersting, Sebastian Pokutta, Suhrab Asadulla, Wolfgang Stammer","cross_cats":["cs.AI"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-07-10T08:28:46Z","title":"Neural Concept Verifier: Scaling Prover-Verifier Games via Concept Encodings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.07532","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:e8246dea01a3d888b4d7080edc1336b58a41f98cc48657c88f7b118af09f4cc7","target":"record","created_at":"2026-06-23T01:12:46Z","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":"3233eba82bdb5ddf140c5af4697129df0c5e94fb2d3185d0d21032980252d93d","cross_cats_sorted":["cs.AI"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-07-10T08:28:46Z","title_canon_sha256":"1556d8c6f3634b3580e76329996f9b48e5816867bcf61d9be5d6cb27aaccc1a9"},"schema_version":"1.0","source":{"id":"2507.07532","kind":"arxiv","version":4}},"canonical_sha256":"917d3e0041bce5ee126609051dd208127064176b7d0cd160a284b24c6d0fa64d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"917d3e0041bce5ee126609051dd208127064176b7d0cd160a284b24c6d0fa64d","first_computed_at":"2026-06-23T01:12:46.320705Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-23T01:12:46.320705Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"g+qiulLmSwO+EZ05NppgXvAu6KFu2rfBW/2EgcsgHBb49FLTaOHi+/B7hj9Q02wokGC578HuKYZSLUMMAkL0Aw==","signature_status":"signed_v1","signed_at":"2026-06-23T01:12:46.321288Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.07532","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e8246dea01a3d888b4d7080edc1336b58a41f98cc48657c88f7b118af09f4cc7","sha256:1121d72f6a71cccbe30c79ddd086df2bffe7f51a0b865803917cf9fdeb62f74b"],"state_sha256":"82816b47403a4bac363a24ace8f9943ae87704357950fdb71d8212b06c8e17bd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6MvDg7XpZdGNevCCqlCZFHDan1jkh8xmWA9paSUW9oPFhozOkYqIKomof8gRDJElahWml4aZLUlt4EtOAHc/Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T22:23:33.566715Z","bundle_sha256":"6a88b586f1324380f0f12b91c7b27d24c6a894afe5e0415b17e3d254e8876faf"}}