{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:SRIN6TGOUXHCRQ2JNMC777H7Z6","short_pith_number":"pith:SRIN6TGO","canonical_record":{"source":{"id":"1601.03244","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-01-13T13:55:55Z","cross_cats_sorted":[],"title_canon_sha256":"fa0ee97a87da542153ff5349883cce821e41a8a9154601f571e5e78f16a13553","abstract_canon_sha256":"7a1074755fbe0fc53f2d9c88c47ee1daf3b18b3378b9274b7eb60b77b6ae7097"},"schema_version":"1.0"},"canonical_sha256":"9450df4ccea5ce28c3496b05fffcffcf8cba0d7739d69567b7f09d03e8665ede","source":{"kind":"arxiv","id":"1601.03244","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.03244","created_at":"2026-05-18T00:51:22Z"},{"alias_kind":"arxiv_version","alias_value":"1601.03244v1","created_at":"2026-05-18T00:51:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.03244","created_at":"2026-05-18T00:51:22Z"},{"alias_kind":"pith_short_12","alias_value":"SRIN6TGOUXHC","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SRIN6TGOUXHCRQ2J","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SRIN6TGO","created_at":"2026-05-18T12:30:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:SRIN6TGOUXHCRQ2JNMC777H7Z6","target":"record","payload":{"canonical_record":{"source":{"id":"1601.03244","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-01-13T13:55:55Z","cross_cats_sorted":[],"title_canon_sha256":"fa0ee97a87da542153ff5349883cce821e41a8a9154601f571e5e78f16a13553","abstract_canon_sha256":"7a1074755fbe0fc53f2d9c88c47ee1daf3b18b3378b9274b7eb60b77b6ae7097"},"schema_version":"1.0"},"canonical_sha256":"9450df4ccea5ce28c3496b05fffcffcf8cba0d7739d69567b7f09d03e8665ede","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:51:22.627019Z","signature_b64":"zN7MOgk+bPlhZzKcCNcN3QwfTH5MUvvQAzSHnPZuvkRMR6ORkel0oeuTySUkBI28YppxrmxyHGDydhGI5Pk6BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9450df4ccea5ce28c3496b05fffcffcf8cba0d7739d69567b7f09d03e8665ede","last_reissued_at":"2026-05-18T00:51:22.626322Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:51:22.626322Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1601.03244","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":"2026-05-18T00:51:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2mliTA5McY8DpP9tzkZnqK3NiHocPJDTwjXiIgtJFrtis9Wj1faJ++5Dk6lmoz8yUzHkr9YtIU48m42h3pv7CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T15:27:34.269198Z"},"content_sha256":"3608e88f1c767a8e0cc7917953a9855e7b5ef99ae9871d3582995fdfb4352e3a","schema_version":"1.0","event_id":"sha256:3608e88f1c767a8e0cc7917953a9855e7b5ef99ae9871d3582995fdfb4352e3a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:SRIN6TGOUXHCRQ2JNMC777H7Z6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A kinetic equation for economic value estimation with irrationality and herding","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ansgar J\\\"ungel, Bertram D\\\"uring, Lara Trussardi","submitted_at":"2016-01-13T13:55:55Z","abstract_excerpt":"A kinetic inhomogeneous Boltzmann-type equation is proposed to model the dynamics of the number of agents in a large market depending on the estimated value of an asset and the rationality of the agents. The interaction rules take into account the interplay of the agents with sources of public information, herding phenomena, and irrationality of the individuals. In the formal grazing collision limit, a nonlinear nonlocal Fokker-Planck equation with anisotropic (or incomplete) diffusion is derived. The existence of global-in-time weak solutions to the Fokker-Planck initial-boundary-value proble"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.03244","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":"2026-05-18T00:51:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Jvv9nfd9dwbLhTZn01Tdob1N9jZTkniAkkuVPGYj5zWTlYRNBw2xFJq3DR3+RBf5I3mcO0eLmsso33wyx1ODDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T15:27:34.269839Z"},"content_sha256":"b5c11f85e72059e2326c41e9f2d5bcbc0373da8d2892d5ceeffac2ce28de324a","schema_version":"1.0","event_id":"sha256:b5c11f85e72059e2326c41e9f2d5bcbc0373da8d2892d5ceeffac2ce28de324a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SRIN6TGOUXHCRQ2JNMC777H7Z6/bundle.json","state_url":"https://pith.science/pith/SRIN6TGOUXHCRQ2JNMC777H7Z6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SRIN6TGOUXHCRQ2JNMC777H7Z6/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":"2026-05-28T15:27:34Z","links":{"resolver":"https://pith.science/pith/SRIN6TGOUXHCRQ2JNMC777H7Z6","bundle":"https://pith.science/pith/SRIN6TGOUXHCRQ2JNMC777H7Z6/bundle.json","state":"https://pith.science/pith/SRIN6TGOUXHCRQ2JNMC777H7Z6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SRIN6TGOUXHCRQ2JNMC777H7Z6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:SRIN6TGOUXHCRQ2JNMC777H7Z6","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":"7a1074755fbe0fc53f2d9c88c47ee1daf3b18b3378b9274b7eb60b77b6ae7097","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-01-13T13:55:55Z","title_canon_sha256":"fa0ee97a87da542153ff5349883cce821e41a8a9154601f571e5e78f16a13553"},"schema_version":"1.0","source":{"id":"1601.03244","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.03244","created_at":"2026-05-18T00:51:22Z"},{"alias_kind":"arxiv_version","alias_value":"1601.03244v1","created_at":"2026-05-18T00:51:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.03244","created_at":"2026-05-18T00:51:22Z"},{"alias_kind":"pith_short_12","alias_value":"SRIN6TGOUXHC","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SRIN6TGOUXHCRQ2J","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SRIN6TGO","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:b5c11f85e72059e2326c41e9f2d5bcbc0373da8d2892d5ceeffac2ce28de324a","target":"graph","created_at":"2026-05-18T00:51:22Z","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 kinetic inhomogeneous Boltzmann-type equation is proposed to model the dynamics of the number of agents in a large market depending on the estimated value of an asset and the rationality of the agents. The interaction rules take into account the interplay of the agents with sources of public information, herding phenomena, and irrationality of the individuals. In the formal grazing collision limit, a nonlinear nonlocal Fokker-Planck equation with anisotropic (or incomplete) diffusion is derived. The existence of global-in-time weak solutions to the Fokker-Planck initial-boundary-value proble","authors_text":"Ansgar J\\\"ungel, Bertram D\\\"uring, Lara Trussardi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-01-13T13:55:55Z","title":"A kinetic equation for economic value estimation with irrationality and herding"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.03244","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":"sha256:3608e88f1c767a8e0cc7917953a9855e7b5ef99ae9871d3582995fdfb4352e3a","target":"record","created_at":"2026-05-18T00:51:22Z","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":"7a1074755fbe0fc53f2d9c88c47ee1daf3b18b3378b9274b7eb60b77b6ae7097","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-01-13T13:55:55Z","title_canon_sha256":"fa0ee97a87da542153ff5349883cce821e41a8a9154601f571e5e78f16a13553"},"schema_version":"1.0","source":{"id":"1601.03244","kind":"arxiv","version":1}},"canonical_sha256":"9450df4ccea5ce28c3496b05fffcffcf8cba0d7739d69567b7f09d03e8665ede","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9450df4ccea5ce28c3496b05fffcffcf8cba0d7739d69567b7f09d03e8665ede","first_computed_at":"2026-05-18T00:51:22.626322Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:51:22.626322Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zN7MOgk+bPlhZzKcCNcN3QwfTH5MUvvQAzSHnPZuvkRMR6ORkel0oeuTySUkBI28YppxrmxyHGDydhGI5Pk6BA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:51:22.627019Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.03244","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3608e88f1c767a8e0cc7917953a9855e7b5ef99ae9871d3582995fdfb4352e3a","sha256:b5c11f85e72059e2326c41e9f2d5bcbc0373da8d2892d5ceeffac2ce28de324a"],"state_sha256":"9402eedddea7356d0fea6db643465e89425754f01cb9c276a5928c99776d354c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vmnjGj84SgOBa9qeRkXLRRuGTVnl6d6JpdO3q1YZcXayToRGBAUrlD+PQrOAWIA60YZyOAQ78pFj/3SAtbKqAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T15:27:34.273104Z","bundle_sha256":"db63ab563d5c8305b9b9a08a7e9b8bc1fe0b424847a0e9188612dcf3356be980"}}