{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:Y7CAX72OEBXRIHFCIYX2UWZ652","short_pith_number":"pith:Y7CAX72O","canonical_record":{"source":{"id":"1312.1304","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-12-04T19:57:25Z","cross_cats_sorted":[],"title_canon_sha256":"b6bccd273ff3aa8583dcb19fd8ab173481310598ba4ac3d9d98a368e0b943bdb","abstract_canon_sha256":"550289d3b2192beacb4f8bd75927342c7a870e63a7649a95fcaf68a60261a2ff"},"schema_version":"1.0"},"canonical_sha256":"c7c40bff4e206f141ca2462faa5b3eee9a57abd2a532a6630a91452e73cec3e0","source":{"kind":"arxiv","id":"1312.1304","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.1304","created_at":"2026-05-18T03:05:28Z"},{"alias_kind":"arxiv_version","alias_value":"1312.1304v1","created_at":"2026-05-18T03:05:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.1304","created_at":"2026-05-18T03:05:28Z"},{"alias_kind":"pith_short_12","alias_value":"Y7CAX72OEBXR","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"Y7CAX72OEBXRIHFC","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"Y7CAX72O","created_at":"2026-05-18T12:28:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:Y7CAX72OEBXRIHFCIYX2UWZ652","target":"record","payload":{"canonical_record":{"source":{"id":"1312.1304","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-12-04T19:57:25Z","cross_cats_sorted":[],"title_canon_sha256":"b6bccd273ff3aa8583dcb19fd8ab173481310598ba4ac3d9d98a368e0b943bdb","abstract_canon_sha256":"550289d3b2192beacb4f8bd75927342c7a870e63a7649a95fcaf68a60261a2ff"},"schema_version":"1.0"},"canonical_sha256":"c7c40bff4e206f141ca2462faa5b3eee9a57abd2a532a6630a91452e73cec3e0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:05:28.863987Z","signature_b64":"kh7cCBQK9pcOOQ9YxHWD/lTuU/bq6Y60cqisPdO3rMHZFq8d2jmAdnTwEK4YwuZk/MjAQz0iSi2TjKKFNYoxDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c7c40bff4e206f141ca2462faa5b3eee9a57abd2a532a6630a91452e73cec3e0","last_reissued_at":"2026-05-18T03:05:28.863465Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:05:28.863465Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1312.1304","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":"2026-05-18T03:05:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AXC9kLSwM3fsFFpYevyixe0AoE0yIdlutc2b9BCeHTalBOo265HdNzeaH2N5eXnDYn7mzy7LZVBPQdBcRfSdDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T08:31:19.557200Z"},"content_sha256":"b0e0a2e470e2e29636e900e18ed2c9b612757796d2ec9d722e9f427b26d72fb3","schema_version":"1.0","event_id":"sha256:b0e0a2e470e2e29636e900e18ed2c9b612757796d2ec9d722e9f427b26d72fb3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:Y7CAX72OEBXRIHFCIYX2UWZ652","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the asymptotic behavior of a Boltzmann-type price formation model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Luis Caffarelli, Marie-Therese Wolfram, Martin Burger, Peter A. Markowich","submitted_at":"2013-12-04T19:57:25Z","abstract_excerpt":"In this paper we study the asymptotic behavior of a Boltzmann type price formation model, which describes the trading dynamics in a financial market. In many of these markets trading happens at high frequencies and low transactions costs. This observation motivates the study of the limit as the number of transactions $k$ tends to infinity, the transaction cost $a$ to zero and $ka=const$. Furthermore we illustrate the price dynamics with numerical simulations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.1304","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":"2026-05-18T03:05:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ptBcUEIXEucm2TrtUkNUj0+s55eUU2sQZQsQ/jfhk/T8nLwv1EcmrK2uk9Uy+zYYxXUk5anyo0umePoFNx5/Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T08:31:19.557772Z"},"content_sha256":"a77f2e17a27e3a212feb1b239d629e2cc267f8d47edc9ed53116685bf2a678c6","schema_version":"1.0","event_id":"sha256:a77f2e17a27e3a212feb1b239d629e2cc267f8d47edc9ed53116685bf2a678c6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Y7CAX72OEBXRIHFCIYX2UWZ652/bundle.json","state_url":"https://pith.science/pith/Y7CAX72OEBXRIHFCIYX2UWZ652/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Y7CAX72OEBXRIHFCIYX2UWZ652/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":"2026-06-04T08:31:19Z","links":{"resolver":"https://pith.science/pith/Y7CAX72OEBXRIHFCIYX2UWZ652","bundle":"https://pith.science/pith/Y7CAX72OEBXRIHFCIYX2UWZ652/bundle.json","state":"https://pith.science/pith/Y7CAX72OEBXRIHFCIYX2UWZ652/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Y7CAX72OEBXRIHFCIYX2UWZ652/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:Y7CAX72OEBXRIHFCIYX2UWZ652","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":"550289d3b2192beacb4f8bd75927342c7a870e63a7649a95fcaf68a60261a2ff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-12-04T19:57:25Z","title_canon_sha256":"b6bccd273ff3aa8583dcb19fd8ab173481310598ba4ac3d9d98a368e0b943bdb"},"schema_version":"1.0","source":{"id":"1312.1304","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.1304","created_at":"2026-05-18T03:05:28Z"},{"alias_kind":"arxiv_version","alias_value":"1312.1304v1","created_at":"2026-05-18T03:05:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.1304","created_at":"2026-05-18T03:05:28Z"},{"alias_kind":"pith_short_12","alias_value":"Y7CAX72OEBXR","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"Y7CAX72OEBXRIHFC","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"Y7CAX72O","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:a77f2e17a27e3a212feb1b239d629e2cc267f8d47edc9ed53116685bf2a678c6","target":"graph","created_at":"2026-05-18T03:05:28Z","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":"In this paper we study the asymptotic behavior of a Boltzmann type price formation model, which describes the trading dynamics in a financial market. In many of these markets trading happens at high frequencies and low transactions costs. This observation motivates the study of the limit as the number of transactions $k$ tends to infinity, the transaction cost $a$ to zero and $ka=const$. Furthermore we illustrate the price dynamics with numerical simulations.","authors_text":"Luis Caffarelli, Marie-Therese Wolfram, Martin Burger, Peter A. Markowich","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-12-04T19:57:25Z","title":"On the asymptotic behavior of a Boltzmann-type price formation model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.1304","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:b0e0a2e470e2e29636e900e18ed2c9b612757796d2ec9d722e9f427b26d72fb3","target":"record","created_at":"2026-05-18T03:05:28Z","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":"550289d3b2192beacb4f8bd75927342c7a870e63a7649a95fcaf68a60261a2ff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-12-04T19:57:25Z","title_canon_sha256":"b6bccd273ff3aa8583dcb19fd8ab173481310598ba4ac3d9d98a368e0b943bdb"},"schema_version":"1.0","source":{"id":"1312.1304","kind":"arxiv","version":1}},"canonical_sha256":"c7c40bff4e206f141ca2462faa5b3eee9a57abd2a532a6630a91452e73cec3e0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c7c40bff4e206f141ca2462faa5b3eee9a57abd2a532a6630a91452e73cec3e0","first_computed_at":"2026-05-18T03:05:28.863465Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:05:28.863465Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kh7cCBQK9pcOOQ9YxHWD/lTuU/bq6Y60cqisPdO3rMHZFq8d2jmAdnTwEK4YwuZk/MjAQz0iSi2TjKKFNYoxDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:05:28.863987Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.1304","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b0e0a2e470e2e29636e900e18ed2c9b612757796d2ec9d722e9f427b26d72fb3","sha256:a77f2e17a27e3a212feb1b239d629e2cc267f8d47edc9ed53116685bf2a678c6"],"state_sha256":"a9c9c01687be4274fae92ef8d8d83066e7b42f5e68a55b1d86420cc6c678669f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OjL/d4KTayBn1wzEWdDYsNh98p+rlpbP5WfR1weHPzP5PEVOFookn30fa8iX3ms0c3sipOufBZglxqGcRhf+Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T08:31:19.561511Z","bundle_sha256":"41ac9b8ecf6689b0fc70c9e9294c8327eb3a98ec2112e10540beb4c65ae46cf7"}}