{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:A6FOD7VJ632PMURPRMKJSCIXHD","short_pith_number":"pith:A6FOD7VJ","canonical_record":{"source":{"id":"1810.00418","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-09-30T16:37:04Z","cross_cats_sorted":[],"title_canon_sha256":"e3a3f9d56cee07096b9aa6e509e3fbc7b5320bf98688b97e73c62a24002414aa","abstract_canon_sha256":"fd02ee56e83eb2963da93e011088375f1bb2bc924fa83ba75c56c8d688b6fe80"},"schema_version":"1.0"},"canonical_sha256":"078ae1fea9f6f4f6522f8b1499091738e5dea0ac77a69ed0b7422408839f04d5","source":{"kind":"arxiv","id":"1810.00418","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.00418","created_at":"2026-05-18T00:04:27Z"},{"alias_kind":"arxiv_version","alias_value":"1810.00418v1","created_at":"2026-05-18T00:04:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.00418","created_at":"2026-05-18T00:04:27Z"},{"alias_kind":"pith_short_12","alias_value":"A6FOD7VJ632P","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"A6FOD7VJ632PMURP","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"A6FOD7VJ","created_at":"2026-05-18T12:32:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:A6FOD7VJ632PMURPRMKJSCIXHD","target":"record","payload":{"canonical_record":{"source":{"id":"1810.00418","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-09-30T16:37:04Z","cross_cats_sorted":[],"title_canon_sha256":"e3a3f9d56cee07096b9aa6e509e3fbc7b5320bf98688b97e73c62a24002414aa","abstract_canon_sha256":"fd02ee56e83eb2963da93e011088375f1bb2bc924fa83ba75c56c8d688b6fe80"},"schema_version":"1.0"},"canonical_sha256":"078ae1fea9f6f4f6522f8b1499091738e5dea0ac77a69ed0b7422408839f04d5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:27.932915Z","signature_b64":"blJ/U/1v2WrbVqXPO2QGynTxDBtzHwMKyqr6bL2B/5HLmiVmV8n0fOUGy/HYZSa63ar7gh2/7nX12Rk583i1AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"078ae1fea9f6f4f6522f8b1499091738e5dea0ac77a69ed0b7422408839f04d5","last_reissued_at":"2026-05-18T00:04:27.932406Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:27.932406Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.00418","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":"2026-05-18T00:04:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UT/w6kzjnjqPaRYtNoBrE0TpQVc0cGlFluP3LznHzaO8Spr8gQTmFeOZXIZr09kLCpF9HcXEqmB4qqJ2WtSdCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T11:44:09.824044Z"},"content_sha256":"14922123f2ec246ae4769603d66a2c26c0d80e3906fcf053a137bb8443ebf428","schema_version":"1.0","event_id":"sha256:14922123f2ec246ae4769603d66a2c26c0d80e3906fcf053a137bb8443ebf428"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:A6FOD7VJ632PMURPRMKJSCIXHD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Carr-Nadtochiy's Weak Reflection Principle for Markov Chains on $\\mathbf{Z}^d$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Yuri Imamura","submitted_at":"2018-09-30T16:37:04Z","abstract_excerpt":"The present paper establishes a discrete version of the result obtained by P. Carr and S. Nadtochiy (2011) for 1-dimensional diffusion processes. Our result is for Markov chains on $\\mathbf{Z}^d$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.00418","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":"2026-05-18T00:04:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"phAPstQ0VyVYlprJ+4Yu/DFzbOWw2fqAqu3jbBN/Sh5jgtBREDb3ghMjHykF25wQJAl4pVsU3aFzdsoXjxutCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T11:44:09.824397Z"},"content_sha256":"a25c78890e018e7d6d6a3c0c720aeb09fffa3f9cae5fa3e5ef015664efa68b18","schema_version":"1.0","event_id":"sha256:a25c78890e018e7d6d6a3c0c720aeb09fffa3f9cae5fa3e5ef015664efa68b18"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/A6FOD7VJ632PMURPRMKJSCIXHD/bundle.json","state_url":"https://pith.science/pith/A6FOD7VJ632PMURPRMKJSCIXHD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/A6FOD7VJ632PMURPRMKJSCIXHD/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":"2026-06-24T11:44:09Z","links":{"resolver":"https://pith.science/pith/A6FOD7VJ632PMURPRMKJSCIXHD","bundle":"https://pith.science/pith/A6FOD7VJ632PMURPRMKJSCIXHD/bundle.json","state":"https://pith.science/pith/A6FOD7VJ632PMURPRMKJSCIXHD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/A6FOD7VJ632PMURPRMKJSCIXHD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:A6FOD7VJ632PMURPRMKJSCIXHD","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":"fd02ee56e83eb2963da93e011088375f1bb2bc924fa83ba75c56c8d688b6fe80","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-09-30T16:37:04Z","title_canon_sha256":"e3a3f9d56cee07096b9aa6e509e3fbc7b5320bf98688b97e73c62a24002414aa"},"schema_version":"1.0","source":{"id":"1810.00418","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.00418","created_at":"2026-05-18T00:04:27Z"},{"alias_kind":"arxiv_version","alias_value":"1810.00418v1","created_at":"2026-05-18T00:04:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.00418","created_at":"2026-05-18T00:04:27Z"},{"alias_kind":"pith_short_12","alias_value":"A6FOD7VJ632P","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"A6FOD7VJ632PMURP","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"A6FOD7VJ","created_at":"2026-05-18T12:32:13Z"}],"graph_snapshots":[{"event_id":"sha256:a25c78890e018e7d6d6a3c0c720aeb09fffa3f9cae5fa3e5ef015664efa68b18","target":"graph","created_at":"2026-05-18T00:04:27Z","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":"The present paper establishes a discrete version of the result obtained by P. Carr and S. Nadtochiy (2011) for 1-dimensional diffusion processes. Our result is for Markov chains on $\\mathbf{Z}^d$.","authors_text":"Yuri Imamura","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-09-30T16:37:04Z","title":"Carr-Nadtochiy's Weak Reflection Principle for Markov Chains on $\\mathbf{Z}^d$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.00418","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":"sha256:14922123f2ec246ae4769603d66a2c26c0d80e3906fcf053a137bb8443ebf428","target":"record","created_at":"2026-05-18T00:04:27Z","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":"fd02ee56e83eb2963da93e011088375f1bb2bc924fa83ba75c56c8d688b6fe80","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-09-30T16:37:04Z","title_canon_sha256":"e3a3f9d56cee07096b9aa6e509e3fbc7b5320bf98688b97e73c62a24002414aa"},"schema_version":"1.0","source":{"id":"1810.00418","kind":"arxiv","version":1}},"canonical_sha256":"078ae1fea9f6f4f6522f8b1499091738e5dea0ac77a69ed0b7422408839f04d5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"078ae1fea9f6f4f6522f8b1499091738e5dea0ac77a69ed0b7422408839f04d5","first_computed_at":"2026-05-18T00:04:27.932406Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:27.932406Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"blJ/U/1v2WrbVqXPO2QGynTxDBtzHwMKyqr6bL2B/5HLmiVmV8n0fOUGy/HYZSa63ar7gh2/7nX12Rk583i1AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:27.932915Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.00418","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:14922123f2ec246ae4769603d66a2c26c0d80e3906fcf053a137bb8443ebf428","sha256:a25c78890e018e7d6d6a3c0c720aeb09fffa3f9cae5fa3e5ef015664efa68b18"],"state_sha256":"d30bd0a19a54efdb58c58ebfda76800cae5fcc9d03bd84e2fcbf2133da963d9e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bM5ZR4qkPblAUq4DuwYAXxdv7ZOO/96nLirugkX1AvFJWPRL4Dle8UGMlbjloERWj9VEgsl683XSPC4pBEXUBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T11:44:09.826332Z","bundle_sha256":"72b8dca74f9a0e913af9deb441ac1ae1a6876305c12ddcd5c77950e8d6378301"}}