{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:CODZXMUQWYCK5PPCTCTKS727BT","short_pith_number":"pith:CODZXMUQ","canonical_record":{"source":{"id":"1503.05602","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-03-18T22:22:14Z","cross_cats_sorted":["math.AG","math.LO"],"title_canon_sha256":"8014c066892c431c474eea23e00e458f4f5be1dbafacdcb77973591b3674428c","abstract_canon_sha256":"ba0e6618457885afa01297295d6978aa13cea73e6168fa803943414544f92271"},"schema_version":"1.0"},"canonical_sha256":"13879bb290b604aebde298a6a97f5f0ce18df1f3a62212b74845c517ec402a88","source":{"kind":"arxiv","id":"1503.05602","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.05602","created_at":"2026-05-18T00:50:35Z"},{"alias_kind":"arxiv_version","alias_value":"1503.05602v2","created_at":"2026-05-18T00:50:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.05602","created_at":"2026-05-18T00:50:35Z"},{"alias_kind":"pith_short_12","alias_value":"CODZXMUQWYCK","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"CODZXMUQWYCK5PPC","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"CODZXMUQ","created_at":"2026-05-18T12:29:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:CODZXMUQWYCK5PPCTCTKS727BT","target":"record","payload":{"canonical_record":{"source":{"id":"1503.05602","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-03-18T22:22:14Z","cross_cats_sorted":["math.AG","math.LO"],"title_canon_sha256":"8014c066892c431c474eea23e00e458f4f5be1dbafacdcb77973591b3674428c","abstract_canon_sha256":"ba0e6618457885afa01297295d6978aa13cea73e6168fa803943414544f92271"},"schema_version":"1.0"},"canonical_sha256":"13879bb290b604aebde298a6a97f5f0ce18df1f3a62212b74845c517ec402a88","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:50:35.968426Z","signature_b64":"Lc77YCq2wc+c02ovLmRGtI8i785YI86S+V/GXXatOwtFpkVQ/2m6sHP18l1vGQDR0/23MVBtPnKPGWtv1HazCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"13879bb290b604aebde298a6a97f5f0ce18df1f3a62212b74845c517ec402a88","last_reissued_at":"2026-05-18T00:50:35.967612Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:50:35.967612Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.05602","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:50:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MigytbulTrYiKutUPulBSTp1OcEJxSElh2vibgdkFxyNHRPdBArFtj9Y8NNC+pVifXWYlJ2FrmtjRKoNcdFyAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T11:13:13.624628Z"},"content_sha256":"763ee9e3a38060bd0ea410abda385746f3ea183c2421b0b04c0f8c4a6f392b48","schema_version":"1.0","event_id":"sha256:763ee9e3a38060bd0ea410abda385746f3ea183c2421b0b04c0f8c4a6f392b48"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:CODZXMUQWYCK5PPCTCTKS727BT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A note on probability and Hilbert's VI problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.LO"],"primary_cat":"math.PR","authors_text":"Alberto Gandolfi","submitted_at":"2015-03-18T22:22:14Z","abstract_excerpt":"This work has been prompted by the surprising lack of mathematical coherence in the common usage of some of the fundamental entities in the theory of probability, with an inherent risk of contradiction. While disentangling the intricacies, we realized that the same issue has been raised many times, with only partial solutions, notably by Boole, Hilbert, De Finetti and Renyi, among others. In particular, a restoration of foundational coherence in the usage of probability theory appears to be a missing piece in the solution of Hilbert VI problem.\n  Here we solve the problem by a new formalizatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.05602","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T00:50:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JrHH++5vj3UlwFI+q9dedyhST2uREi/stRjVdoW2RV6HSQnq//M6hVSbzNZF4evJz6BMA9/gXsK04tHaugebDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T11:13:13.624977Z"},"content_sha256":"d07fd9e8843211389a1444799e8064bafcba33e3fe0ef5137072659d22cf0c71","schema_version":"1.0","event_id":"sha256:d07fd9e8843211389a1444799e8064bafcba33e3fe0ef5137072659d22cf0c71"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CODZXMUQWYCK5PPCTCTKS727BT/bundle.json","state_url":"https://pith.science/pith/CODZXMUQWYCK5PPCTCTKS727BT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CODZXMUQWYCK5PPCTCTKS727BT/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":"2026-06-07T11:13:13Z","links":{"resolver":"https://pith.science/pith/CODZXMUQWYCK5PPCTCTKS727BT","bundle":"https://pith.science/pith/CODZXMUQWYCK5PPCTCTKS727BT/bundle.json","state":"https://pith.science/pith/CODZXMUQWYCK5PPCTCTKS727BT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CODZXMUQWYCK5PPCTCTKS727BT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:CODZXMUQWYCK5PPCTCTKS727BT","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":"ba0e6618457885afa01297295d6978aa13cea73e6168fa803943414544f92271","cross_cats_sorted":["math.AG","math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-03-18T22:22:14Z","title_canon_sha256":"8014c066892c431c474eea23e00e458f4f5be1dbafacdcb77973591b3674428c"},"schema_version":"1.0","source":{"id":"1503.05602","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.05602","created_at":"2026-05-18T00:50:35Z"},{"alias_kind":"arxiv_version","alias_value":"1503.05602v2","created_at":"2026-05-18T00:50:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.05602","created_at":"2026-05-18T00:50:35Z"},{"alias_kind":"pith_short_12","alias_value":"CODZXMUQWYCK","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"CODZXMUQWYCK5PPC","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"CODZXMUQ","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:d07fd9e8843211389a1444799e8064bafcba33e3fe0ef5137072659d22cf0c71","target":"graph","created_at":"2026-05-18T00:50:35Z","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"},"paper":{"abstract_excerpt":"This work has been prompted by the surprising lack of mathematical coherence in the common usage of some of the fundamental entities in the theory of probability, with an inherent risk of contradiction. While disentangling the intricacies, we realized that the same issue has been raised many times, with only partial solutions, notably by Boole, Hilbert, De Finetti and Renyi, among others. In particular, a restoration of foundational coherence in the usage of probability theory appears to be a missing piece in the solution of Hilbert VI problem.\n  Here we solve the problem by a new formalizatio","authors_text":"Alberto Gandolfi","cross_cats":["math.AG","math.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-03-18T22:22:14Z","title":"A note on probability and Hilbert's VI problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.05602","kind":"arxiv","version":2},"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":"sha256:763ee9e3a38060bd0ea410abda385746f3ea183c2421b0b04c0f8c4a6f392b48","target":"record","created_at":"2026-05-18T00:50:35Z","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":"ba0e6618457885afa01297295d6978aa13cea73e6168fa803943414544f92271","cross_cats_sorted":["math.AG","math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-03-18T22:22:14Z","title_canon_sha256":"8014c066892c431c474eea23e00e458f4f5be1dbafacdcb77973591b3674428c"},"schema_version":"1.0","source":{"id":"1503.05602","kind":"arxiv","version":2}},"canonical_sha256":"13879bb290b604aebde298a6a97f5f0ce18df1f3a62212b74845c517ec402a88","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"13879bb290b604aebde298a6a97f5f0ce18df1f3a62212b74845c517ec402a88","first_computed_at":"2026-05-18T00:50:35.967612Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:50:35.967612Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Lc77YCq2wc+c02ovLmRGtI8i785YI86S+V/GXXatOwtFpkVQ/2m6sHP18l1vGQDR0/23MVBtPnKPGWtv1HazCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:50:35.968426Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.05602","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:763ee9e3a38060bd0ea410abda385746f3ea183c2421b0b04c0f8c4a6f392b48","sha256:d07fd9e8843211389a1444799e8064bafcba33e3fe0ef5137072659d22cf0c71"],"state_sha256":"bf19dd31789af20ff87990fae40efc6b1367f44fa850bdb7f3663a8477aa0692"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l5q1gu0GzVTgWTqdbdNeDGRlxXLB0PVMPmkZ+wVptcc8gRRfhtpecWkKFjejgIbWdB/kDfWdJKMFWG68KpYsBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T11:13:13.627208Z","bundle_sha256":"d6bd892ebbe48a93cd3f5f8700f0c853ed14906cc31309d7e5d6417ea0e2231b"}}