{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:RUOQNAF4AHZ7VVYADTF4FY54YS","short_pith_number":"pith:RUOQNAF4","canonical_record":{"source":{"id":"2606.07516","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-06-05T17:59:46Z","cross_cats_sorted":[],"title_canon_sha256":"1ed07c8e6c6176325edc8cae387e4e5e615075fdecb195c62c8c7d7a3d5ff0c1","abstract_canon_sha256":"ad92f784997eaf832f3d62a698d97dd23cbe688d0a5762d778b9485fbf5acddc"},"schema_version":"1.0"},"canonical_sha256":"8d1d0680bc01f3fad7001ccbc2e3bcc4ac9f9187ad68ff5ea67e8f03bf81820c","source":{"kind":"arxiv","id":"2606.07516","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.07516","created_at":"2026-06-08T01:05:32Z"},{"alias_kind":"arxiv_version","alias_value":"2606.07516v1","created_at":"2026-06-08T01:05:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.07516","created_at":"2026-06-08T01:05:32Z"},{"alias_kind":"pith_short_12","alias_value":"RUOQNAF4AHZ7","created_at":"2026-06-08T01:05:32Z"},{"alias_kind":"pith_short_16","alias_value":"RUOQNAF4AHZ7VVYA","created_at":"2026-06-08T01:05:32Z"},{"alias_kind":"pith_short_8","alias_value":"RUOQNAF4","created_at":"2026-06-08T01:05:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:RUOQNAF4AHZ7VVYADTF4FY54YS","target":"record","payload":{"canonical_record":{"source":{"id":"2606.07516","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-06-05T17:59:46Z","cross_cats_sorted":[],"title_canon_sha256":"1ed07c8e6c6176325edc8cae387e4e5e615075fdecb195c62c8c7d7a3d5ff0c1","abstract_canon_sha256":"ad92f784997eaf832f3d62a698d97dd23cbe688d0a5762d778b9485fbf5acddc"},"schema_version":"1.0"},"canonical_sha256":"8d1d0680bc01f3fad7001ccbc2e3bcc4ac9f9187ad68ff5ea67e8f03bf81820c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-08T01:05:32.345918Z","signature_b64":"ay7j2zhNNNeY9iuj8wAEkYD5+QtceEdcynCCzMPhjdcBU3In1JOQ97ANTSnyUC47kl/lmJgJYLUZy+KIBEwxAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8d1d0680bc01f3fad7001ccbc2e3bcc4ac9f9187ad68ff5ea67e8f03bf81820c","last_reissued_at":"2026-06-08T01:05:32.344982Z","signature_status":"signed_v1","first_computed_at":"2026-06-08T01:05:32.344982Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.07516","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":"2026-06-08T01:05:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hGg0rRNemrgkVqTL/j5DiZ3RGsB8w4+ayLwUSYSnWcQrVDESYnIVV1HQmXgL9K7bRfeuDAfNWr4Avg2Isg6vCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T21:26:06.828728Z"},"content_sha256":"900098232aaac30f755efbf08177f9eec6145d14bcfc5885df383b0c86bb86fb","schema_version":"1.0","event_id":"sha256:900098232aaac30f755efbf08177f9eec6145d14bcfc5885df383b0c86bb86fb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:RUOQNAF4AHZ7VVYADTF4FY54YS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Counterintuitive problems in discrete probability","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Bernardo Busoni, Gianmarco Bet, Luca Avena","submitted_at":"2026-06-05T17:59:46Z","abstract_excerpt":"This manuscript contains a collection of counterintuitive problems in discrete probability, together with detailed solutions. The dataset was constructed as part of a broader research project investigating the capabilities of the latest-generation Large Language Models (LLMs) in solving discrete probability problems, in order to assess whether LLMs tend to make systematic reasoning errors associated with known cognitive biases. The problems collected here are specifically designed to challenge heuristic reasoning strategies that often lead to intuitively appealing but mathematically incorrect "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.07516","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/2606.07516/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":"2026-06-08T01:05:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zcbEmDmhspmt9waf+eq/KVLkUozz12VqhJsFzZQVVtwlcdRxzSQi4+GCqEjZaux6hrdc4A4MLd2PnwNnyHcXCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T21:26:06.829092Z"},"content_sha256":"19b2d5f184aa5cae89a1f2782e00eebfd6d7308b03cc34cb502279487a11f472","schema_version":"1.0","event_id":"sha256:19b2d5f184aa5cae89a1f2782e00eebfd6d7308b03cc34cb502279487a11f472"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RUOQNAF4AHZ7VVYADTF4FY54YS/bundle.json","state_url":"https://pith.science/pith/RUOQNAF4AHZ7VVYADTF4FY54YS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RUOQNAF4AHZ7VVYADTF4FY54YS/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":"2026-06-29T21:26:06Z","links":{"resolver":"https://pith.science/pith/RUOQNAF4AHZ7VVYADTF4FY54YS","bundle":"https://pith.science/pith/RUOQNAF4AHZ7VVYADTF4FY54YS/bundle.json","state":"https://pith.science/pith/RUOQNAF4AHZ7VVYADTF4FY54YS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RUOQNAF4AHZ7VVYADTF4FY54YS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:RUOQNAF4AHZ7VVYADTF4FY54YS","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":"ad92f784997eaf832f3d62a698d97dd23cbe688d0a5762d778b9485fbf5acddc","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-06-05T17:59:46Z","title_canon_sha256":"1ed07c8e6c6176325edc8cae387e4e5e615075fdecb195c62c8c7d7a3d5ff0c1"},"schema_version":"1.0","source":{"id":"2606.07516","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.07516","created_at":"2026-06-08T01:05:32Z"},{"alias_kind":"arxiv_version","alias_value":"2606.07516v1","created_at":"2026-06-08T01:05:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.07516","created_at":"2026-06-08T01:05:32Z"},{"alias_kind":"pith_short_12","alias_value":"RUOQNAF4AHZ7","created_at":"2026-06-08T01:05:32Z"},{"alias_kind":"pith_short_16","alias_value":"RUOQNAF4AHZ7VVYA","created_at":"2026-06-08T01:05:32Z"},{"alias_kind":"pith_short_8","alias_value":"RUOQNAF4","created_at":"2026-06-08T01:05:32Z"}],"graph_snapshots":[{"event_id":"sha256:19b2d5f184aa5cae89a1f2782e00eebfd6d7308b03cc34cb502279487a11f472","target":"graph","created_at":"2026-06-08T01:05:32Z","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/2606.07516/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This manuscript contains a collection of counterintuitive problems in discrete probability, together with detailed solutions. The dataset was constructed as part of a broader research project investigating the capabilities of the latest-generation Large Language Models (LLMs) in solving discrete probability problems, in order to assess whether LLMs tend to make systematic reasoning errors associated with known cognitive biases. The problems collected here are specifically designed to challenge heuristic reasoning strategies that often lead to intuitively appealing but mathematically incorrect ","authors_text":"Bernardo Busoni, Gianmarco Bet, Luca Avena","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-06-05T17:59:46Z","title":"Counterintuitive problems in discrete probability"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.07516","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":"sha256:900098232aaac30f755efbf08177f9eec6145d14bcfc5885df383b0c86bb86fb","target":"record","created_at":"2026-06-08T01:05:32Z","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":"ad92f784997eaf832f3d62a698d97dd23cbe688d0a5762d778b9485fbf5acddc","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-06-05T17:59:46Z","title_canon_sha256":"1ed07c8e6c6176325edc8cae387e4e5e615075fdecb195c62c8c7d7a3d5ff0c1"},"schema_version":"1.0","source":{"id":"2606.07516","kind":"arxiv","version":1}},"canonical_sha256":"8d1d0680bc01f3fad7001ccbc2e3bcc4ac9f9187ad68ff5ea67e8f03bf81820c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8d1d0680bc01f3fad7001ccbc2e3bcc4ac9f9187ad68ff5ea67e8f03bf81820c","first_computed_at":"2026-06-08T01:05:32.344982Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-08T01:05:32.344982Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ay7j2zhNNNeY9iuj8wAEkYD5+QtceEdcynCCzMPhjdcBU3In1JOQ97ANTSnyUC47kl/lmJgJYLUZy+KIBEwxAw==","signature_status":"signed_v1","signed_at":"2026-06-08T01:05:32.345918Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.07516","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:900098232aaac30f755efbf08177f9eec6145d14bcfc5885df383b0c86bb86fb","sha256:19b2d5f184aa5cae89a1f2782e00eebfd6d7308b03cc34cb502279487a11f472"],"state_sha256":"ab0fe500e3b8cb2d5ee067f56e13b7cee67754b0c5e9ff03cfd6d535e61b5289"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X58UrMDnce3A4aPvB3OdYrZHUpg2GkCPSm4yeZP2js4AhQayyutDQHcTruDDm1+YJyAxLWM9/eTssHpI09xtCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T21:26:06.831008Z","bundle_sha256":"bf8cdf1f8ea074b62f557b410e72f40218e2ca1d197a6c2c96824c7694d5d278"}}