{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:BNYYVA6FBAVHRKN2SAR4LCDWZV","short_pith_number":"pith:BNYYVA6F","schema_version":"1.0","canonical_sha256":"0b718a83c5082a78a9ba9023c58876cd4a66ebbd8752a0343e75e9505345f29c","source":{"kind":"arxiv","id":"1010.5136","version":4},"attestation_state":"computed","paper":{"title":"A Mathematical Approach to Order Book Modeling","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"q-fin.TR","authors_text":"Aymen Jedidi, Frederic Abergel","submitted_at":"2010-10-25T14:16:02Z","abstract_excerpt":"Motivated by the desire to bridge the gap between the microscopic description of price formation (agent-based modeling) and the stochastic differential equations approach used classically to describe price evolution at macroscopic time scales, we present a mathematical study of the order book as a multidimensional continuous-time Markov chain and derive several mathematical results in the case of independent Poissonian arrival times. In particular, we show that the cancellation structure is an important factor ensuring the existence of a stationary distribution and the exponential convergence "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1010.5136","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.TR","submitted_at":"2010-10-25T14:16:02Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"ad41ee3b6131d6b4b61d37ac117927e64e92b777c6a54d2705aa006ced59488d","abstract_canon_sha256":"90d0f3e9f293226151df4c838cee6dd22e371207dd77cc9f58026fe9a5087d08"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:23:38.665596Z","signature_b64":"VUiatug40JaudgUowDPZIBcgAvOwk4+2t3Jwh8vAudyJyevep8wmmkDF1yRtnDojQDv8PeSeVdHlxoknbR6dAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0b718a83c5082a78a9ba9023c58876cd4a66ebbd8752a0343e75e9505345f29c","last_reissued_at":"2026-05-18T02:23:38.665069Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:23:38.665069Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Mathematical Approach to Order Book Modeling","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"q-fin.TR","authors_text":"Aymen Jedidi, Frederic Abergel","submitted_at":"2010-10-25T14:16:02Z","abstract_excerpt":"Motivated by the desire to bridge the gap between the microscopic description of price formation (agent-based modeling) and the stochastic differential equations approach used classically to describe price evolution at macroscopic time scales, we present a mathematical study of the order book as a multidimensional continuous-time Markov chain and derive several mathematical results in the case of independent Poissonian arrival times. In particular, we show that the cancellation structure is an important factor ensuring the existence of a stationary distribution and the exponential convergence "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.5136","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1010.5136","created_at":"2026-05-18T02:23:38.665144+00:00"},{"alias_kind":"arxiv_version","alias_value":"1010.5136v4","created_at":"2026-05-18T02:23:38.665144+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.5136","created_at":"2026-05-18T02:23:38.665144+00:00"},{"alias_kind":"pith_short_12","alias_value":"BNYYVA6FBAVH","created_at":"2026-05-18T12:26:05.355336+00:00"},{"alias_kind":"pith_short_16","alias_value":"BNYYVA6FBAVHRKN2","created_at":"2026-05-18T12:26:05.355336+00:00"},{"alias_kind":"pith_short_8","alias_value":"BNYYVA6F","created_at":"2026-05-18T12:26:05.355336+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BNYYVA6FBAVHRKN2SAR4LCDWZV","json":"https://pith.science/pith/BNYYVA6FBAVHRKN2SAR4LCDWZV.json","graph_json":"https://pith.science/api/pith-number/BNYYVA6FBAVHRKN2SAR4LCDWZV/graph.json","events_json":"https://pith.science/api/pith-number/BNYYVA6FBAVHRKN2SAR4LCDWZV/events.json","paper":"https://pith.science/paper/BNYYVA6F"},"agent_actions":{"view_html":"https://pith.science/pith/BNYYVA6FBAVHRKN2SAR4LCDWZV","download_json":"https://pith.science/pith/BNYYVA6FBAVHRKN2SAR4LCDWZV.json","view_paper":"https://pith.science/paper/BNYYVA6F","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1010.5136&json=true","fetch_graph":"https://pith.science/api/pith-number/BNYYVA6FBAVHRKN2SAR4LCDWZV/graph.json","fetch_events":"https://pith.science/api/pith-number/BNYYVA6FBAVHRKN2SAR4LCDWZV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BNYYVA6FBAVHRKN2SAR4LCDWZV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BNYYVA6FBAVHRKN2SAR4LCDWZV/action/storage_attestation","attest_author":"https://pith.science/pith/BNYYVA6FBAVHRKN2SAR4LCDWZV/action/author_attestation","sign_citation":"https://pith.science/pith/BNYYVA6FBAVHRKN2SAR4LCDWZV/action/citation_signature","submit_replication":"https://pith.science/pith/BNYYVA6FBAVHRKN2SAR4LCDWZV/action/replication_record"}},"created_at":"2026-05-18T02:23:38.665144+00:00","updated_at":"2026-05-18T02:23:38.665144+00:00"}