{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:NHL3VJVTJCTWHMRNAQOXI7K735","short_pith_number":"pith:NHL3VJVT","canonical_record":{"source":{"id":"2606.04697","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2026-06-03T10:23:59Z","cross_cats_sorted":[],"title_canon_sha256":"31c09dd05daec06eecc8ed587ccc5307f3402a01921f46a6529ad5e3ca1f8b42","abstract_canon_sha256":"bd4919285623bf257f2b9b13a87ed3c2323e34224984687b7ca9b9e71a061fcb"},"schema_version":"1.0"},"canonical_sha256":"69d7baa6b348a763b22d041d747d5fdf74d50d6d8fdd33e39d8956a9f455e659","source":{"kind":"arxiv","id":"2606.04697","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.04697","created_at":"2026-06-04T01:09:25Z"},{"alias_kind":"arxiv_version","alias_value":"2606.04697v1","created_at":"2026-06-04T01:09:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.04697","created_at":"2026-06-04T01:09:25Z"},{"alias_kind":"pith_short_12","alias_value":"NHL3VJVTJCTW","created_at":"2026-06-04T01:09:25Z"},{"alias_kind":"pith_short_16","alias_value":"NHL3VJVTJCTWHMRN","created_at":"2026-06-04T01:09:25Z"},{"alias_kind":"pith_short_8","alias_value":"NHL3VJVT","created_at":"2026-06-04T01:09:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:NHL3VJVTJCTWHMRNAQOXI7K735","target":"record","payload":{"canonical_record":{"source":{"id":"2606.04697","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2026-06-03T10:23:59Z","cross_cats_sorted":[],"title_canon_sha256":"31c09dd05daec06eecc8ed587ccc5307f3402a01921f46a6529ad5e3ca1f8b42","abstract_canon_sha256":"bd4919285623bf257f2b9b13a87ed3c2323e34224984687b7ca9b9e71a061fcb"},"schema_version":"1.0"},"canonical_sha256":"69d7baa6b348a763b22d041d747d5fdf74d50d6d8fdd33e39d8956a9f455e659","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-04T01:09:25.398450Z","signature_b64":"Jfe70md6R4skVJEE1x915l0R0xepFbyAu+E/Ku0SGcbvbpiLOn3NGB3JzECU02FiaQx9//eSkTW3ggoBegvECg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"69d7baa6b348a763b22d041d747d5fdf74d50d6d8fdd33e39d8956a9f455e659","last_reissued_at":"2026-06-04T01:09:25.397724Z","signature_status":"signed_v1","first_computed_at":"2026-06-04T01:09:25.397724Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.04697","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":"2026-06-04T01:09:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ez16XrdSarxHkXkWKQiPa69zw5f+w+CeZopxiXdYn8HlfAlydcOxaCvhV8mABqs8XgtlljPNBR3h5e+BXdoxDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T19:41:42.525676Z"},"content_sha256":"90c59a17faa94ed7bb50e14031ae9a7ca3a63c6a8126bdd1bd78bfbdea3b104a","schema_version":"1.0","event_id":"sha256:90c59a17faa94ed7bb50e14031ae9a7ca3a63c6a8126bdd1bd78bfbdea3b104a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:NHL3VJVTJCTWHMRNAQOXI7K735","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Randomized separations in black-box TFNP","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Fedor Kiselev","submitted_at":"2026-06-03T10:23:59Z","abstract_excerpt":"We study the relationship between deterministic and randomized black-box reducibility between problems in TFNP. Our main contribution is a general technique that establishes equivalence between these reducibility types from specific TFNP problems to any TFNP problem. In particular, we show that this equivalence holds for reductions from complete problems in PPP, PPAD, PPA, and $t$-PPP. In turn, it strengthens all known black-box separations, originating from these classes, to randomized separations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.04697","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/2606.04697/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":"2026-06-04T01:09:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fEO0s43YJThrksST/q6IbbtEXkFMwBtB8x1Q5Iwp4YvErRBxwDwQ/D1fb1JbHZgC521SEuJZOIN9xTQ9/sZDBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T19:41:42.526165Z"},"content_sha256":"089c8386af80e303505a5795217107217b5427472d26f9592c57a8a65cad6e18","schema_version":"1.0","event_id":"sha256:089c8386af80e303505a5795217107217b5427472d26f9592c57a8a65cad6e18"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NHL3VJVTJCTWHMRNAQOXI7K735/bundle.json","state_url":"https://pith.science/pith/NHL3VJVTJCTWHMRNAQOXI7K735/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NHL3VJVTJCTWHMRNAQOXI7K735/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":"2026-08-21T19:41:42Z","links":{"resolver":"https://pith.science/pith/NHL3VJVTJCTWHMRNAQOXI7K735","bundle":"https://pith.science/pith/NHL3VJVTJCTWHMRNAQOXI7K735/bundle.json","state":"https://pith.science/pith/NHL3VJVTJCTWHMRNAQOXI7K735/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NHL3VJVTJCTWHMRNAQOXI7K735/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:NHL3VJVTJCTWHMRNAQOXI7K735","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":"bd4919285623bf257f2b9b13a87ed3c2323e34224984687b7ca9b9e71a061fcb","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2026-06-03T10:23:59Z","title_canon_sha256":"31c09dd05daec06eecc8ed587ccc5307f3402a01921f46a6529ad5e3ca1f8b42"},"schema_version":"1.0","source":{"id":"2606.04697","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.04697","created_at":"2026-06-04T01:09:25Z"},{"alias_kind":"arxiv_version","alias_value":"2606.04697v1","created_at":"2026-06-04T01:09:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.04697","created_at":"2026-06-04T01:09:25Z"},{"alias_kind":"pith_short_12","alias_value":"NHL3VJVTJCTW","created_at":"2026-06-04T01:09:25Z"},{"alias_kind":"pith_short_16","alias_value":"NHL3VJVTJCTWHMRN","created_at":"2026-06-04T01:09:25Z"},{"alias_kind":"pith_short_8","alias_value":"NHL3VJVT","created_at":"2026-06-04T01:09:25Z"}],"graph_snapshots":[{"event_id":"sha256:089c8386af80e303505a5795217107217b5427472d26f9592c57a8a65cad6e18","target":"graph","created_at":"2026-06-04T01:09:25Z","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/2606.04697/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the relationship between deterministic and randomized black-box reducibility between problems in TFNP. Our main contribution is a general technique that establishes equivalence between these reducibility types from specific TFNP problems to any TFNP problem. In particular, we show that this equivalence holds for reductions from complete problems in PPP, PPAD, PPA, and $t$-PPP. In turn, it strengthens all known black-box separations, originating from these classes, to randomized separations.","authors_text":"Fedor Kiselev","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2026-06-03T10:23:59Z","title":"Randomized separations in black-box TFNP"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.04697","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":"sha256:90c59a17faa94ed7bb50e14031ae9a7ca3a63c6a8126bdd1bd78bfbdea3b104a","target":"record","created_at":"2026-06-04T01:09:25Z","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":"bd4919285623bf257f2b9b13a87ed3c2323e34224984687b7ca9b9e71a061fcb","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2026-06-03T10:23:59Z","title_canon_sha256":"31c09dd05daec06eecc8ed587ccc5307f3402a01921f46a6529ad5e3ca1f8b42"},"schema_version":"1.0","source":{"id":"2606.04697","kind":"arxiv","version":1}},"canonical_sha256":"69d7baa6b348a763b22d041d747d5fdf74d50d6d8fdd33e39d8956a9f455e659","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"69d7baa6b348a763b22d041d747d5fdf74d50d6d8fdd33e39d8956a9f455e659","first_computed_at":"2026-06-04T01:09:25.397724Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-04T01:09:25.397724Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Jfe70md6R4skVJEE1x915l0R0xepFbyAu+E/Ku0SGcbvbpiLOn3NGB3JzECU02FiaQx9//eSkTW3ggoBegvECg==","signature_status":"signed_v1","signed_at":"2026-06-04T01:09:25.398450Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.04697","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:90c59a17faa94ed7bb50e14031ae9a7ca3a63c6a8126bdd1bd78bfbdea3b104a","sha256:089c8386af80e303505a5795217107217b5427472d26f9592c57a8a65cad6e18"],"state_sha256":"5c9599340e605b5fce4f332068f45e2e735e22e8e57bf767dffef19224bae6f7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wV7Eze4GaFqj0HN2Xj8fYzZstbwqhcYmY/6UOeDimd+AlNCK0+MvSMU4e01plSxafgOxCXvV1QSA4Ms3fiOnBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-21T19:41:42.530723Z","bundle_sha256":"701f7d248b49f4fbacdc175d2c20bfb00680e647eecb06c79e393fd179374b11"}}