{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:4PYQ52AWGC7IZRRRFRHDTMD3XW","short_pith_number":"pith:4PYQ52AW","canonical_record":{"source":{"id":"math/0610855","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2006-10-27T16:07:48Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"3c2fde7349fa449d9a0c2837f7fee0acd17f75988645fd737266cbd88c8c8640","abstract_canon_sha256":"c3fec9837232e6b643160a9dffa8167eb2763d11bcb54f1b02b2b78ce8945f6f"},"schema_version":"1.0"},"canonical_sha256":"e3f10ee81630be8cc6312c4e39b07bbdbc3c57027c0e3e20739b06cc945c693d","source":{"kind":"arxiv","id":"math/0610855","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0610855","created_at":"2026-05-18T02:31:02Z"},{"alias_kind":"arxiv_version","alias_value":"math/0610855v4","created_at":"2026-05-18T02:31:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0610855","created_at":"2026-05-18T02:31:02Z"},{"alias_kind":"pith_short_12","alias_value":"4PYQ52AWGC7I","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"4PYQ52AWGC7IZRRR","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"4PYQ52AW","created_at":"2026-05-18T12:25:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:4PYQ52AWGC7IZRRRFRHDTMD3XW","target":"record","payload":{"canonical_record":{"source":{"id":"math/0610855","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2006-10-27T16:07:48Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"3c2fde7349fa449d9a0c2837f7fee0acd17f75988645fd737266cbd88c8c8640","abstract_canon_sha256":"c3fec9837232e6b643160a9dffa8167eb2763d11bcb54f1b02b2b78ce8945f6f"},"schema_version":"1.0"},"canonical_sha256":"e3f10ee81630be8cc6312c4e39b07bbdbc3c57027c0e3e20739b06cc945c693d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:31:02.704874Z","signature_b64":"I1Z8JDWGjPi0RBJ+1A2OqksUd5Ck08UvQNR//DOkFQOfihN1RMXlX8K7NEAhFeoEyk2bnrsdrsdf/GXF2B2DDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e3f10ee81630be8cc6312c4e39b07bbdbc3c57027c0e3e20739b06cc945c693d","last_reissued_at":"2026-05-18T02:31:02.704374Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:31:02.704374Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0610855","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:31:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aUOoUT3xRyG0Q9rYhLVsYQCMvWKw40NYTKOkr/Ww1z3PjHwLn0NV3wikwfGqvgfZQNShOslVAOS4un2YaN5cAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T23:18:08.909243Z"},"content_sha256":"9a251bc1154aba6afd6ef4f8e9404613bfc54800e5901a8aa7b9cd7ba7c00e47","schema_version":"1.0","event_id":"sha256:9a251bc1154aba6afd6ef4f8e9404613bfc54800e5901a8aa7b9cd7ba7c00e47"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:4PYQ52AWGC7IZRRRFRHDTMD3XW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On finite-difference approximations for normalized Bellman equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"math.OC","authors_text":"David \\v{S}i\\v{s}ka, Istv\\'an Gy\\\"ongy","submitted_at":"2006-10-27T16:07:48Z","abstract_excerpt":"A class of stochastic optimal control problems involving optimal stopping is considered. Methods of Krylov are adapted to investigate the numerical solutions of the corresponding normalized Bellman equations and to estimate the rate of convergence of finite difference approximations for the optimal reward functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0610855","kind":"arxiv","version":4},"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":"2026-05-18T02:31:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L5PIHvkR06tpVRF/L7rA15sVJtdSL1I30e9IRm/SVVMDxMA8qWSgyCYn4ZCPS1MRKDs0KuFJjEwlqFTlyFsIDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T23:18:08.909649Z"},"content_sha256":"8a159ccfd9f2a49ab0089dc73af3a219e7b49f2606baa25bdb6394eda71fb4be","schema_version":"1.0","event_id":"sha256:8a159ccfd9f2a49ab0089dc73af3a219e7b49f2606baa25bdb6394eda71fb4be"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4PYQ52AWGC7IZRRRFRHDTMD3XW/bundle.json","state_url":"https://pith.science/pith/4PYQ52AWGC7IZRRRFRHDTMD3XW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4PYQ52AWGC7IZRRRFRHDTMD3XW/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":"2026-05-27T23:18:08Z","links":{"resolver":"https://pith.science/pith/4PYQ52AWGC7IZRRRFRHDTMD3XW","bundle":"https://pith.science/pith/4PYQ52AWGC7IZRRRFRHDTMD3XW/bundle.json","state":"https://pith.science/pith/4PYQ52AWGC7IZRRRFRHDTMD3XW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4PYQ52AWGC7IZRRRFRHDTMD3XW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:4PYQ52AWGC7IZRRRFRHDTMD3XW","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":"c3fec9837232e6b643160a9dffa8167eb2763d11bcb54f1b02b2b78ce8945f6f","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2006-10-27T16:07:48Z","title_canon_sha256":"3c2fde7349fa449d9a0c2837f7fee0acd17f75988645fd737266cbd88c8c8640"},"schema_version":"1.0","source":{"id":"math/0610855","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0610855","created_at":"2026-05-18T02:31:02Z"},{"alias_kind":"arxiv_version","alias_value":"math/0610855v4","created_at":"2026-05-18T02:31:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0610855","created_at":"2026-05-18T02:31:02Z"},{"alias_kind":"pith_short_12","alias_value":"4PYQ52AWGC7I","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"4PYQ52AWGC7IZRRR","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"4PYQ52AW","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:8a159ccfd9f2a49ab0089dc73af3a219e7b49f2606baa25bdb6394eda71fb4be","target":"graph","created_at":"2026-05-18T02:31:02Z","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":"A class of stochastic optimal control problems involving optimal stopping is considered. Methods of Krylov are adapted to investigate the numerical solutions of the corresponding normalized Bellman equations and to estimate the rate of convergence of finite difference approximations for the optimal reward functions.","authors_text":"David \\v{S}i\\v{s}ka, Istv\\'an Gy\\\"ongy","cross_cats":["math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2006-10-27T16:07:48Z","title":"On finite-difference approximations for normalized Bellman equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0610855","kind":"arxiv","version":4},"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":"sha256:9a251bc1154aba6afd6ef4f8e9404613bfc54800e5901a8aa7b9cd7ba7c00e47","target":"record","created_at":"2026-05-18T02:31:02Z","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":"c3fec9837232e6b643160a9dffa8167eb2763d11bcb54f1b02b2b78ce8945f6f","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2006-10-27T16:07:48Z","title_canon_sha256":"3c2fde7349fa449d9a0c2837f7fee0acd17f75988645fd737266cbd88c8c8640"},"schema_version":"1.0","source":{"id":"math/0610855","kind":"arxiv","version":4}},"canonical_sha256":"e3f10ee81630be8cc6312c4e39b07bbdbc3c57027c0e3e20739b06cc945c693d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e3f10ee81630be8cc6312c4e39b07bbdbc3c57027c0e3e20739b06cc945c693d","first_computed_at":"2026-05-18T02:31:02.704374Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:31:02.704374Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"I1Z8JDWGjPi0RBJ+1A2OqksUd5Ck08UvQNR//DOkFQOfihN1RMXlX8K7NEAhFeoEyk2bnrsdrsdf/GXF2B2DDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:31:02.704874Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0610855","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9a251bc1154aba6afd6ef4f8e9404613bfc54800e5901a8aa7b9cd7ba7c00e47","sha256:8a159ccfd9f2a49ab0089dc73af3a219e7b49f2606baa25bdb6394eda71fb4be"],"state_sha256":"0be9cb046592d6147a9a7bd5f359dbd9d9efc1f46f71da1f65333350131190a7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wLotzTxt4Hdasxd34VyShXFIfLRrWzK265H+aA4YaRpJDcsP1jZIqCkvZ5s+GOUhktJezcRPNBxfhMrlIR1UCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T23:18:08.911956Z","bundle_sha256":"d172030206fc703de4dac0a44f59ef7358c0b091491b603d85fe5aeb01723b93"}}