{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:RJSQE3XSOGRBVOPGL5FDDEIZ66","short_pith_number":"pith:RJSQE3XS","canonical_record":{"source":{"id":"1310.1306","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-04T14:59:10Z","cross_cats_sorted":[],"title_canon_sha256":"2d10e343fd28c5c9a50fdbf9dc6adbbd273438f8d827c93714416f3b6b818400","abstract_canon_sha256":"aa4fba2cedfc32997971f1d55071389ca92f08336fa490fcb25fa781f3d4e4f4"},"schema_version":"1.0"},"canonical_sha256":"8a65026ef271a21ab9e65f4a319119f79f29b0521719ee10cad056cdac232c6f","source":{"kind":"arxiv","id":"1310.1306","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.1306","created_at":"2026-05-18T02:45:23Z"},{"alias_kind":"arxiv_version","alias_value":"1310.1306v2","created_at":"2026-05-18T02:45:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.1306","created_at":"2026-05-18T02:45:23Z"},{"alias_kind":"pith_short_12","alias_value":"RJSQE3XSOGRB","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"RJSQE3XSOGRBVOPG","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"RJSQE3XS","created_at":"2026-05-18T12:27:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:RJSQE3XSOGRBVOPGL5FDDEIZ66","target":"record","payload":{"canonical_record":{"source":{"id":"1310.1306","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-04T14:59:10Z","cross_cats_sorted":[],"title_canon_sha256":"2d10e343fd28c5c9a50fdbf9dc6adbbd273438f8d827c93714416f3b6b818400","abstract_canon_sha256":"aa4fba2cedfc32997971f1d55071389ca92f08336fa490fcb25fa781f3d4e4f4"},"schema_version":"1.0"},"canonical_sha256":"8a65026ef271a21ab9e65f4a319119f79f29b0521719ee10cad056cdac232c6f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:45:23.317740Z","signature_b64":"mGD3BjvmZvmj3tsC92T7zr7ndpwbnbdSKIiWTDKVQS0p6UzySihNiNxQwCehTT035hhuk/WPLDMa3IKrIzDZCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8a65026ef271a21ab9e65f4a319119f79f29b0521719ee10cad056cdac232c6f","last_reissued_at":"2026-05-18T02:45:23.317289Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:45:23.317289Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.1306","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":"2026-05-18T02:45:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JTiRqdRkzntEATGMk0Yi+mlBNbF/gnWUu0T8LFwEcPPyW6J7EufApgeUo7phFEC+hFjOkB4go+EZVrnLdGBIAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T22:46:40.537440Z"},"content_sha256":"5026ff9cac779b1027ee6731d7724298b197e102383c13bed92b23cb3936a5e9","schema_version":"1.0","event_id":"sha256:5026ff9cac779b1027ee6731d7724298b197e102383c13bed92b23cb3936a5e9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:RJSQE3XSOGRBVOPGL5FDDEIZ66","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bit flipping and time to recover","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Anton Muratov, Sergei Zuyev","submitted_at":"2013-10-04T14:59:10Z","abstract_excerpt":"We call `bits' a sequence of devices indexed by positive integers, where every device can be in two states: $0$ (idle) and $1$ (active). Start from the `ground state' of the system when all bits are in $0$-state. In our first Binary Flipping (BF) model, the evolution of the system is the following: at each time step choose one bit from a given distribution $\\mathcal{P}$ on the integers independently of anything else, then flip the state of this bit to the opposite. In our second Damaged Bits (DB) model a `damaged' state is added: each selected idling bit changes to active, but selecting an act"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.1306","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":"2026-05-18T02:45:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wcB8dTwatj9Cyj+jrd8CAL755IRUpSLCyUSCWxKA/ukI8COWnfFg76RaJ2g4SxrsKeEdB9rumhzT2tTcnPguAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T22:46:40.538150Z"},"content_sha256":"6a5599fa699ade634eab68b9ecdc949fccfec88b073d0e907da962b639bc0448","schema_version":"1.0","event_id":"sha256:6a5599fa699ade634eab68b9ecdc949fccfec88b073d0e907da962b639bc0448"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RJSQE3XSOGRBVOPGL5FDDEIZ66/bundle.json","state_url":"https://pith.science/pith/RJSQE3XSOGRBVOPGL5FDDEIZ66/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RJSQE3XSOGRBVOPGL5FDDEIZ66/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":"2026-06-09T22:46:40Z","links":{"resolver":"https://pith.science/pith/RJSQE3XSOGRBVOPGL5FDDEIZ66","bundle":"https://pith.science/pith/RJSQE3XSOGRBVOPGL5FDDEIZ66/bundle.json","state":"https://pith.science/pith/RJSQE3XSOGRBVOPGL5FDDEIZ66/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RJSQE3XSOGRBVOPGL5FDDEIZ66/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:RJSQE3XSOGRBVOPGL5FDDEIZ66","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":"aa4fba2cedfc32997971f1d55071389ca92f08336fa490fcb25fa781f3d4e4f4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-04T14:59:10Z","title_canon_sha256":"2d10e343fd28c5c9a50fdbf9dc6adbbd273438f8d827c93714416f3b6b818400"},"schema_version":"1.0","source":{"id":"1310.1306","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.1306","created_at":"2026-05-18T02:45:23Z"},{"alias_kind":"arxiv_version","alias_value":"1310.1306v2","created_at":"2026-05-18T02:45:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.1306","created_at":"2026-05-18T02:45:23Z"},{"alias_kind":"pith_short_12","alias_value":"RJSQE3XSOGRB","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"RJSQE3XSOGRBVOPG","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"RJSQE3XS","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:6a5599fa699ade634eab68b9ecdc949fccfec88b073d0e907da962b639bc0448","target":"graph","created_at":"2026-05-18T02:45:23Z","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 call `bits' a sequence of devices indexed by positive integers, where every device can be in two states: $0$ (idle) and $1$ (active). Start from the `ground state' of the system when all bits are in $0$-state. In our first Binary Flipping (BF) model, the evolution of the system is the following: at each time step choose one bit from a given distribution $\\mathcal{P}$ on the integers independently of anything else, then flip the state of this bit to the opposite. In our second Damaged Bits (DB) model a `damaged' state is added: each selected idling bit changes to active, but selecting an act","authors_text":"Anton Muratov, Sergei Zuyev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-04T14:59:10Z","title":"Bit flipping and time to recover"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.1306","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":"sha256:5026ff9cac779b1027ee6731d7724298b197e102383c13bed92b23cb3936a5e9","target":"record","created_at":"2026-05-18T02:45:23Z","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":"aa4fba2cedfc32997971f1d55071389ca92f08336fa490fcb25fa781f3d4e4f4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-04T14:59:10Z","title_canon_sha256":"2d10e343fd28c5c9a50fdbf9dc6adbbd273438f8d827c93714416f3b6b818400"},"schema_version":"1.0","source":{"id":"1310.1306","kind":"arxiv","version":2}},"canonical_sha256":"8a65026ef271a21ab9e65f4a319119f79f29b0521719ee10cad056cdac232c6f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8a65026ef271a21ab9e65f4a319119f79f29b0521719ee10cad056cdac232c6f","first_computed_at":"2026-05-18T02:45:23.317289Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:45:23.317289Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mGD3BjvmZvmj3tsC92T7zr7ndpwbnbdSKIiWTDKVQS0p6UzySihNiNxQwCehTT035hhuk/WPLDMa3IKrIzDZCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:45:23.317740Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.1306","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5026ff9cac779b1027ee6731d7724298b197e102383c13bed92b23cb3936a5e9","sha256:6a5599fa699ade634eab68b9ecdc949fccfec88b073d0e907da962b639bc0448"],"state_sha256":"b99a6d99dbaab9d9e65ebbe4d36a57c01152a44ce08d8a5da85a6a3221d7bb17"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2NkGqTuD2k2PV4iSnURF7ICrK/6pGA/U5D6SpdkFI5RNaoQ/bIxrov/ExXBb0cXWl9Ox6Yzhym/g4idAtIT2AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T22:46:40.542090Z","bundle_sha256":"ae231dffb06e6691c2c562f2f35f9aa558033fe09e964932c451f9b82d774164"}}