{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:T7Q3OTLRTXCQ5W5VBQQFFPJNJR","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":"11c1de3ed4e5b08c9f99f9b83bb58f23b4807b59fe217fd6fbc60e439486a540","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2018-08-02T22:50:39Z","title_canon_sha256":"cc9e2f6dc827068527ed8d7faf01389507c553993d42fd90288e7ac297ddd115"},"schema_version":"1.0","source":{"id":"1808.01041","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.01041","created_at":"2026-05-18T00:08:59Z"},{"alias_kind":"arxiv_version","alias_value":"1808.01041v1","created_at":"2026-05-18T00:08:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.01041","created_at":"2026-05-18T00:08:59Z"},{"alias_kind":"pith_short_12","alias_value":"T7Q3OTLRTXCQ","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"T7Q3OTLRTXCQ5W5V","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"T7Q3OTLR","created_at":"2026-05-18T12:32:53Z"}],"graph_snapshots":[{"event_id":"sha256:7c8f3199d2a6dc73acb9b162be077bae9bac5018c438de7192fad61e755fb4d6","target":"graph","created_at":"2026-05-18T00:08:59Z","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":"We compute and compare profitabilities of stubborn mining strategies that are variations of selfish mining. These are deviant mining strategies violating Bitcoin's network protocol rules. We apply the foundational set-up from our previous companion article on the profitability of selfish mining, and the new martingale techniques to get a closed-form computation for the revenue ratio, which is the correct benchmark for profitability. Catalan numbers and Catalan distributions appear in the closed-form computations. This marks the first appearance of Catalan numbers in the Mathematics of the Bitc","authors_text":"Cyril Grunspan, Ricardo P\\'erez-Marco","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2018-08-02T22:50:39Z","title":"On profitability of stubborn mining"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.01041","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":"sha256:972bd7c2243e2ab1e32bb837f2b8ad07c7371da1d5b3e24478aa8b8bf4a64e6c","target":"record","created_at":"2026-05-18T00:08:59Z","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":"11c1de3ed4e5b08c9f99f9b83bb58f23b4807b59fe217fd6fbc60e439486a540","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2018-08-02T22:50:39Z","title_canon_sha256":"cc9e2f6dc827068527ed8d7faf01389507c553993d42fd90288e7ac297ddd115"},"schema_version":"1.0","source":{"id":"1808.01041","kind":"arxiv","version":1}},"canonical_sha256":"9fe1b74d719dc50edbb50c2052bd2d4c7bd24c021fd25eb06b83d1ec6a0bf0a4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9fe1b74d719dc50edbb50c2052bd2d4c7bd24c021fd25eb06b83d1ec6a0bf0a4","first_computed_at":"2026-05-18T00:08:59.252494Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:08:59.252494Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XSPYCScFS5muHbSAE00VsdehqBPffJ5p3q2bZA+MrWZjRwnduy8EG1wYbFyxRvJo7ZPrhLRg14tTczPaUrUUDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:08:59.253007Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.01041","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:972bd7c2243e2ab1e32bb837f2b8ad07c7371da1d5b3e24478aa8b8bf4a64e6c","sha256:7c8f3199d2a6dc73acb9b162be077bae9bac5018c438de7192fad61e755fb4d6"],"state_sha256":"99e53dd139a0c621c32b6b3df6a869e054066b2b72f45b56373d1de80a1d32d8"}