{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:RBB3IJXPYRWIDSEXRGMTJI2HWR","short_pith_number":"pith:RBB3IJXP","canonical_record":{"source":{"id":"1902.01513","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2019-02-05T01:32:56Z","cross_cats_sorted":["math.CO","math.PR"],"title_canon_sha256":"a7e126444e2e00f824646b91e26eeb8b8c62da19c60342128776679478a29bfb","abstract_canon_sha256":"66f74f2cecede6b5934b31fddb8605ca25108f52e7f2eb9ddc8bfb24156fb696"},"schema_version":"1.0"},"canonical_sha256":"8843b426efc46c81c897899934a347b46e8d6fabe38737d0910f6cc834113b91","source":{"kind":"arxiv","id":"1902.01513","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.01513","created_at":"2026-05-17T23:54:47Z"},{"alias_kind":"arxiv_version","alias_value":"1902.01513v1","created_at":"2026-05-17T23:54:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.01513","created_at":"2026-05-17T23:54:47Z"},{"alias_kind":"pith_short_12","alias_value":"RBB3IJXPYRWI","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"RBB3IJXPYRWIDSEX","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"RBB3IJXP","created_at":"2026-05-18T12:33:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:RBB3IJXPYRWIDSEXRGMTJI2HWR","target":"record","payload":{"canonical_record":{"source":{"id":"1902.01513","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2019-02-05T01:32:56Z","cross_cats_sorted":["math.CO","math.PR"],"title_canon_sha256":"a7e126444e2e00f824646b91e26eeb8b8c62da19c60342128776679478a29bfb","abstract_canon_sha256":"66f74f2cecede6b5934b31fddb8605ca25108f52e7f2eb9ddc8bfb24156fb696"},"schema_version":"1.0"},"canonical_sha256":"8843b426efc46c81c897899934a347b46e8d6fabe38737d0910f6cc834113b91","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:47.471076Z","signature_b64":"ODOzGG/DyhISjLCDfpy17Tgx2dYxrYt24ph7r62P5hcGz9ywnslU0cwxS/lC9Lp2xn8vf/b4H6Q0hUP1dnjzAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8843b426efc46c81c897899934a347b46e8d6fabe38737d0910f6cc834113b91","last_reissued_at":"2026-05-17T23:54:47.470429Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:47.470429Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1902.01513","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":"2026-05-17T23:54:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XroFF/HhbXWgB11s2LkODDwZ5MmaCdn5u/aODBPj0/jQxaChizzAp/SDoo98JB7744MHwF5UGOjgs9RgKtNlBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T19:54:11.853305Z"},"content_sha256":"e1029a6927db63d023410f8b1f11ec375d93d8c21fbb0f834254f9c937d19c4d","schema_version":"1.0","event_id":"sha256:e1029a6927db63d023410f8b1f11ec375d93d8c21fbb0f834254f9c937d19c4d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:RBB3IJXPYRWIDSEXRGMTJI2HWR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bitcoin Selfish Mining and Dyck Words","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.PR"],"primary_cat":"cs.CR","authors_text":"Cyril Grunspan, Ricardo P\\'erez-Marco","submitted_at":"2019-02-05T01:32:56Z","abstract_excerpt":"We give a straightforward proof for the formula giving the long-term apparent hashrate of the Selfish Mining strategy in Bitcoin using only elementary probabilities and combinatorics, and more precisely, Dyck words. There is no need to compute stationary probabilities on Markov chain nor stopping times for Poisson processes as it was previously done. We consider also several other block withholding strategies."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.01513","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":""},"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":"2026-05-17T23:54:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E5ikM5ZHcQxfyfzMkgSqYXjEbV9hbE3URl+6QTqytbJJducyQHOmiEl1ILKt9vXuuI0D253BRyAz6UyM1xwlDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T19:54:11.854065Z"},"content_sha256":"0d3dec3b687e2d8eced04fe87be4e82514da41d58b8bc718ccccb4b97fa6bf21","schema_version":"1.0","event_id":"sha256:0d3dec3b687e2d8eced04fe87be4e82514da41d58b8bc718ccccb4b97fa6bf21"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RBB3IJXPYRWIDSEXRGMTJI2HWR/bundle.json","state_url":"https://pith.science/pith/RBB3IJXPYRWIDSEXRGMTJI2HWR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RBB3IJXPYRWIDSEXRGMTJI2HWR/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":"2026-06-09T19:54:11Z","links":{"resolver":"https://pith.science/pith/RBB3IJXPYRWIDSEXRGMTJI2HWR","bundle":"https://pith.science/pith/RBB3IJXPYRWIDSEXRGMTJI2HWR/bundle.json","state":"https://pith.science/pith/RBB3IJXPYRWIDSEXRGMTJI2HWR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RBB3IJXPYRWIDSEXRGMTJI2HWR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:RBB3IJXPYRWIDSEXRGMTJI2HWR","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":"66f74f2cecede6b5934b31fddb8605ca25108f52e7f2eb9ddc8bfb24156fb696","cross_cats_sorted":["math.CO","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2019-02-05T01:32:56Z","title_canon_sha256":"a7e126444e2e00f824646b91e26eeb8b8c62da19c60342128776679478a29bfb"},"schema_version":"1.0","source":{"id":"1902.01513","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.01513","created_at":"2026-05-17T23:54:47Z"},{"alias_kind":"arxiv_version","alias_value":"1902.01513v1","created_at":"2026-05-17T23:54:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.01513","created_at":"2026-05-17T23:54:47Z"},{"alias_kind":"pith_short_12","alias_value":"RBB3IJXPYRWI","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"RBB3IJXPYRWIDSEX","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"RBB3IJXP","created_at":"2026-05-18T12:33:27Z"}],"graph_snapshots":[{"event_id":"sha256:0d3dec3b687e2d8eced04fe87be4e82514da41d58b8bc718ccccb4b97fa6bf21","target":"graph","created_at":"2026-05-17T23:54:47Z","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 give a straightforward proof for the formula giving the long-term apparent hashrate of the Selfish Mining strategy in Bitcoin using only elementary probabilities and combinatorics, and more precisely, Dyck words. There is no need to compute stationary probabilities on Markov chain nor stopping times for Poisson processes as it was previously done. We consider also several other block withholding strategies.","authors_text":"Cyril Grunspan, Ricardo P\\'erez-Marco","cross_cats":["math.CO","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2019-02-05T01:32:56Z","title":"Bitcoin Selfish Mining and Dyck Words"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.01513","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:e1029a6927db63d023410f8b1f11ec375d93d8c21fbb0f834254f9c937d19c4d","target":"record","created_at":"2026-05-17T23:54:47Z","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":"66f74f2cecede6b5934b31fddb8605ca25108f52e7f2eb9ddc8bfb24156fb696","cross_cats_sorted":["math.CO","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2019-02-05T01:32:56Z","title_canon_sha256":"a7e126444e2e00f824646b91e26eeb8b8c62da19c60342128776679478a29bfb"},"schema_version":"1.0","source":{"id":"1902.01513","kind":"arxiv","version":1}},"canonical_sha256":"8843b426efc46c81c897899934a347b46e8d6fabe38737d0910f6cc834113b91","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8843b426efc46c81c897899934a347b46e8d6fabe38737d0910f6cc834113b91","first_computed_at":"2026-05-17T23:54:47.470429Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:47.470429Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ODOzGG/DyhISjLCDfpy17Tgx2dYxrYt24ph7r62P5hcGz9ywnslU0cwxS/lC9Lp2xn8vf/b4H6Q0hUP1dnjzAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:47.471076Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.01513","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e1029a6927db63d023410f8b1f11ec375d93d8c21fbb0f834254f9c937d19c4d","sha256:0d3dec3b687e2d8eced04fe87be4e82514da41d58b8bc718ccccb4b97fa6bf21"],"state_sha256":"06ef339c52e119bbb4945830624c291dff680771baa97b71ad66d5383aa942a2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m87Ue8aAiyA7c0o+RgQlGnmvcasGZrKkqQm7EetB735+QxACaavqaQybZo75jY+ABRLLvTFt+AwIOtvxnJqzDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T19:54:11.857975Z","bundle_sha256":"203da4ee62438edc9b5633ec998054022f76902eb78cb5bcbadf5eb9e2e9ef83"}}