{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:NXK274ZP67BOUSZA5T7IS3TLKC","short_pith_number":"pith:NXK274ZP","canonical_record":{"source":{"id":"2506.19276","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2025-06-24T03:12:39Z","cross_cats_sorted":["cond-mat.dis-nn","cs.IT","cs.LG","math.IT"],"title_canon_sha256":"8fdd6d0f9be7508b00f4192c81ece18e2dfb00974a2e3732e4a1038dfa1ef303","abstract_canon_sha256":"d25439d2d4eb0190bbee52daadd241d1c6aa8fa30cd0d9f3bea5efe4a185455a"},"schema_version":"1.0"},"canonical_sha256":"6dd5aff32ff7c2ea4b20ecfe896e6b50b903e515becb2dda3b4fbc26665f6e4e","source":{"kind":"arxiv","id":"2506.19276","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.19276","created_at":"2026-07-05T11:26:12Z"},{"alias_kind":"arxiv_version","alias_value":"2506.19276v1","created_at":"2026-07-05T11:26:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.19276","created_at":"2026-07-05T11:26:12Z"},{"alias_kind":"pith_short_12","alias_value":"NXK274ZP67BO","created_at":"2026-07-05T11:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"NXK274ZP67BOUSZA","created_at":"2026-07-05T11:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"NXK274ZP","created_at":"2026-07-05T11:26:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:NXK274ZP67BOUSZA5T7IS3TLKC","target":"record","payload":{"canonical_record":{"source":{"id":"2506.19276","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2025-06-24T03:12:39Z","cross_cats_sorted":["cond-mat.dis-nn","cs.IT","cs.LG","math.IT"],"title_canon_sha256":"8fdd6d0f9be7508b00f4192c81ece18e2dfb00974a2e3732e4a1038dfa1ef303","abstract_canon_sha256":"d25439d2d4eb0190bbee52daadd241d1c6aa8fa30cd0d9f3bea5efe4a185455a"},"schema_version":"1.0"},"canonical_sha256":"6dd5aff32ff7c2ea4b20ecfe896e6b50b903e515becb2dda3b4fbc26665f6e4e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:26:12.536741Z","signature_b64":"vemDY1pFUAbbrdAljliSQHRYITKjm81gdqZcwYqklAjJV5jD0Hltw2TO25mhvBXC4e5+XoaR/G7r435Kp3uDCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6dd5aff32ff7c2ea4b20ecfe896e6b50b903e515becb2dda3b4fbc26665f6e4e","last_reissued_at":"2026-07-05T11:26:12.536322Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:26:12.536322Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.19276","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":"2026-07-05T11:26:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JDX92TQcQPWVDMGi6tuoaH8EMJyxvNgFVq5VwbtHdc7C202fkBnUYOzF+NeFbfGhHd98V1qVZJkljxUqgY1ZCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T08:03:42.525346Z"},"content_sha256":"1264bc0787b7572c3ba545a9dbcf7f5a7a4a50d58e31a6137b0a1c3beb1c7e7c","schema_version":"1.0","event_id":"sha256:1264bc0787b7572c3ba545a9dbcf7f5a7a4a50d58e31a6137b0a1c3beb1c7e7c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:NXK274ZP67BOUSZA5T7IS3TLKC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rare dense solutions clusters in asymmetric binary perceptrons -- local entropy via fully lifted RDT","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.dis-nn","cs.IT","cs.LG","math.IT"],"primary_cat":"stat.ML","authors_text":"Mihailo Stojnic","submitted_at":"2025-06-24T03:12:39Z","abstract_excerpt":"We study classical asymmetric binary perceptron (ABP) and associated \\emph{local entropy} (LE) as potential source of its algorithmic hardness. Isolation of \\emph{typical} ABP solutions in SAT phase seemingly suggests a universal algorithmic hardness. Paradoxically, efficient algorithms do exist even for constraint densities $\\alpha$ fairly close but at a finite distance (\\emph{computational gap}) from the capacity. In recent years, existence of rare large dense clusters and magical ability of fast algorithms to find them have been posited as the conceptual resolution of this paradox. Monotoni"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.19276","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/2506.19276/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":"2026-07-05T11:26:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jtFxSR2Mc8x55qmlohcRVM9Gg9M2IihDTc3kMKxOBeFVZAv1bMkpVB+yg2ckoAo9y0MDuanpUA4vS8CuRX1DCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T08:03:42.525854Z"},"content_sha256":"e9487dd60e09baa3c03df27042b3e6d99a85ed0895eaaab1c996a15d1493b37e","schema_version":"1.0","event_id":"sha256:e9487dd60e09baa3c03df27042b3e6d99a85ed0895eaaab1c996a15d1493b37e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NXK274ZP67BOUSZA5T7IS3TLKC/bundle.json","state_url":"https://pith.science/pith/NXK274ZP67BOUSZA5T7IS3TLKC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NXK274ZP67BOUSZA5T7IS3TLKC/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":"2026-08-06T08:03:42Z","links":{"resolver":"https://pith.science/pith/NXK274ZP67BOUSZA5T7IS3TLKC","bundle":"https://pith.science/pith/NXK274ZP67BOUSZA5T7IS3TLKC/bundle.json","state":"https://pith.science/pith/NXK274ZP67BOUSZA5T7IS3TLKC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NXK274ZP67BOUSZA5T7IS3TLKC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:NXK274ZP67BOUSZA5T7IS3TLKC","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":"d25439d2d4eb0190bbee52daadd241d1c6aa8fa30cd0d9f3bea5efe4a185455a","cross_cats_sorted":["cond-mat.dis-nn","cs.IT","cs.LG","math.IT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2025-06-24T03:12:39Z","title_canon_sha256":"8fdd6d0f9be7508b00f4192c81ece18e2dfb00974a2e3732e4a1038dfa1ef303"},"schema_version":"1.0","source":{"id":"2506.19276","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.19276","created_at":"2026-07-05T11:26:12Z"},{"alias_kind":"arxiv_version","alias_value":"2506.19276v1","created_at":"2026-07-05T11:26:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.19276","created_at":"2026-07-05T11:26:12Z"},{"alias_kind":"pith_short_12","alias_value":"NXK274ZP67BO","created_at":"2026-07-05T11:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"NXK274ZP67BOUSZA","created_at":"2026-07-05T11:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"NXK274ZP","created_at":"2026-07-05T11:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:e9487dd60e09baa3c03df27042b3e6d99a85ed0895eaaab1c996a15d1493b37e","target":"graph","created_at":"2026-07-05T11:26:12Z","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/2506.19276/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study classical asymmetric binary perceptron (ABP) and associated \\emph{local entropy} (LE) as potential source of its algorithmic hardness. Isolation of \\emph{typical} ABP solutions in SAT phase seemingly suggests a universal algorithmic hardness. Paradoxically, efficient algorithms do exist even for constraint densities $\\alpha$ fairly close but at a finite distance (\\emph{computational gap}) from the capacity. In recent years, existence of rare large dense clusters and magical ability of fast algorithms to find them have been posited as the conceptual resolution of this paradox. Monotoni","authors_text":"Mihailo Stojnic","cross_cats":["cond-mat.dis-nn","cs.IT","cs.LG","math.IT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2025-06-24T03:12:39Z","title":"Rare dense solutions clusters in asymmetric binary perceptrons -- local entropy via fully lifted RDT"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.19276","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":"sha256:1264bc0787b7572c3ba545a9dbcf7f5a7a4a50d58e31a6137b0a1c3beb1c7e7c","target":"record","created_at":"2026-07-05T11:26:12Z","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":"d25439d2d4eb0190bbee52daadd241d1c6aa8fa30cd0d9f3bea5efe4a185455a","cross_cats_sorted":["cond-mat.dis-nn","cs.IT","cs.LG","math.IT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2025-06-24T03:12:39Z","title_canon_sha256":"8fdd6d0f9be7508b00f4192c81ece18e2dfb00974a2e3732e4a1038dfa1ef303"},"schema_version":"1.0","source":{"id":"2506.19276","kind":"arxiv","version":1}},"canonical_sha256":"6dd5aff32ff7c2ea4b20ecfe896e6b50b903e515becb2dda3b4fbc26665f6e4e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6dd5aff32ff7c2ea4b20ecfe896e6b50b903e515becb2dda3b4fbc26665f6e4e","first_computed_at":"2026-07-05T11:26:12.536322Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:26:12.536322Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vemDY1pFUAbbrdAljliSQHRYITKjm81gdqZcwYqklAjJV5jD0Hltw2TO25mhvBXC4e5+XoaR/G7r435Kp3uDCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:26:12.536741Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.19276","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1264bc0787b7572c3ba545a9dbcf7f5a7a4a50d58e31a6137b0a1c3beb1c7e7c","sha256:e9487dd60e09baa3c03df27042b3e6d99a85ed0895eaaab1c996a15d1493b37e"],"state_sha256":"bc32c90618a1979b3b282a8a274de1323b5819cb5ac962ea0a80cda19266a266"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bPpDW/0YUGOMpIeHB2f86BccxggKPEcIozmlGtUL2alMz4BO6jpgVJGsQ0SWKwbuvRZ+FKRhC0QL00dOE0LpBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T08:03:42.529449Z","bundle_sha256":"aab4b7f24f405c29182947b0b7fb560058b1074fcde859c078f6f74a61588d67"}}