{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:UQ7ZN3ECZXKTWKQU4WJCK7BYR5","short_pith_number":"pith:UQ7ZN3EC","canonical_record":{"source":{"id":"1907.05037","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2019-07-11T08:10:06Z","cross_cats_sorted":["econ.TH"],"title_canon_sha256":"95422284c3a19b8dfe1613591f2b49abe88740ac4893239cce51b7f1a471b31f","abstract_canon_sha256":"83e65bf17e72f7f5e823818119db1d03b73d603dcb5be6a36d615c8b11bec5f3"},"schema_version":"1.0"},"canonical_sha256":"a43f96ec82cdd53b2a14e592257c388f52e10c2537c56d5ee1c11bb33740b953","source":{"kind":"arxiv","id":"1907.05037","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.05037","created_at":"2026-07-05T06:49:38Z"},{"alias_kind":"arxiv_version","alias_value":"1907.05037v3","created_at":"2026-07-05T06:49:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.05037","created_at":"2026-07-05T06:49:38Z"},{"alias_kind":"pith_short_12","alias_value":"UQ7ZN3ECZXKT","created_at":"2026-07-05T06:49:38Z"},{"alias_kind":"pith_short_16","alias_value":"UQ7ZN3ECZXKTWKQU","created_at":"2026-07-05T06:49:38Z"},{"alias_kind":"pith_short_8","alias_value":"UQ7ZN3EC","created_at":"2026-07-05T06:49:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:UQ7ZN3ECZXKTWKQU4WJCK7BYR5","target":"record","payload":{"canonical_record":{"source":{"id":"1907.05037","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2019-07-11T08:10:06Z","cross_cats_sorted":["econ.TH"],"title_canon_sha256":"95422284c3a19b8dfe1613591f2b49abe88740ac4893239cce51b7f1a471b31f","abstract_canon_sha256":"83e65bf17e72f7f5e823818119db1d03b73d603dcb5be6a36d615c8b11bec5f3"},"schema_version":"1.0"},"canonical_sha256":"a43f96ec82cdd53b2a14e592257c388f52e10c2537c56d5ee1c11bb33740b953","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:49:38.490308Z","signature_b64":"9x+TGPqrTC1Z68WmXUPb+u+rlrvmuTp6aeRCk9NOvvVowMKLGQqN82tgqNgy1i3aevFMbHwO3IrVq4aRwkkJCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a43f96ec82cdd53b2a14e592257c388f52e10c2537c56d5ee1c11bb33740b953","last_reissued_at":"2026-07-05T06:49:38.489954Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:49:38.489954Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1907.05037","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T06:49:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g6Jqryjz6qTa3pBf8Jmjr01r6Ov1RjWRsJo7iuRhVPk63M0wmkCv33ljH9VrXTCuq3t/ukyezx0qJqDD3lIPAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T17:24:44.066858Z"},"content_sha256":"9915856cfb79662c34976e7acbf30cee0257da4b4a8556010c04f171db908168","schema_version":"1.0","event_id":"sha256:9915856cfb79662c34976e7acbf30cee0257da4b4a8556010c04f171db908168"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:UQ7ZN3ECZXKTWKQU4WJCK7BYR5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Proportional Dynamics in Exchange Economies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["econ.TH"],"primary_cat":"cs.GT","authors_text":"Nikhil R. Devanur, Simina Br\\^anzei, Yuval Rabani","submitted_at":"2019-07-11T08:10:06Z","abstract_excerpt":"We study the Proportional Response dynamic in exchange economies, where each player starts with some amount of money and a good. Every day, the players bring one unit of their good and submit bids on goods they like, each good gets allocated in proportion to the bid amounts, and each seller collects the bids received. Then every player updates the bids proportionally to the contribution of each good in their utility. This dynamic models a process of learning how to bid and has been studied in a series of papers on Fisher and production markets, but not in exchange economies. Our main results a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.05037","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1907.05037/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T06:49:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k0Y1LMtMchdZBJEOoSsfiGvZ/qK+bBBCr3uGhol44wwbdHGGiPDgVGHpWfiyHjdMYx0vxaD/rwkjtT5VvjNoBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T17:24:44.067562Z"},"content_sha256":"b61aec6b2a132bbd351ee0c17f830230843bb7fd679b1bf5b6745e020f8b373f","schema_version":"1.0","event_id":"sha256:b61aec6b2a132bbd351ee0c17f830230843bb7fd679b1bf5b6745e020f8b373f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UQ7ZN3ECZXKTWKQU4WJCK7BYR5/bundle.json","state_url":"https://pith.science/pith/UQ7ZN3ECZXKTWKQU4WJCK7BYR5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UQ7ZN3ECZXKTWKQU4WJCK7BYR5/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":"2026-08-16T17:24:44Z","links":{"resolver":"https://pith.science/pith/UQ7ZN3ECZXKTWKQU4WJCK7BYR5","bundle":"https://pith.science/pith/UQ7ZN3ECZXKTWKQU4WJCK7BYR5/bundle.json","state":"https://pith.science/pith/UQ7ZN3ECZXKTWKQU4WJCK7BYR5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UQ7ZN3ECZXKTWKQU4WJCK7BYR5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:UQ7ZN3ECZXKTWKQU4WJCK7BYR5","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":"83e65bf17e72f7f5e823818119db1d03b73d603dcb5be6a36d615c8b11bec5f3","cross_cats_sorted":["econ.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2019-07-11T08:10:06Z","title_canon_sha256":"95422284c3a19b8dfe1613591f2b49abe88740ac4893239cce51b7f1a471b31f"},"schema_version":"1.0","source":{"id":"1907.05037","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.05037","created_at":"2026-07-05T06:49:38Z"},{"alias_kind":"arxiv_version","alias_value":"1907.05037v3","created_at":"2026-07-05T06:49:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.05037","created_at":"2026-07-05T06:49:38Z"},{"alias_kind":"pith_short_12","alias_value":"UQ7ZN3ECZXKT","created_at":"2026-07-05T06:49:38Z"},{"alias_kind":"pith_short_16","alias_value":"UQ7ZN3ECZXKTWKQU","created_at":"2026-07-05T06:49:38Z"},{"alias_kind":"pith_short_8","alias_value":"UQ7ZN3EC","created_at":"2026-07-05T06:49:38Z"}],"graph_snapshots":[{"event_id":"sha256:b61aec6b2a132bbd351ee0c17f830230843bb7fd679b1bf5b6745e020f8b373f","target":"graph","created_at":"2026-07-05T06:49:38Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1907.05037/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the Proportional Response dynamic in exchange economies, where each player starts with some amount of money and a good. Every day, the players bring one unit of their good and submit bids on goods they like, each good gets allocated in proportion to the bid amounts, and each seller collects the bids received. Then every player updates the bids proportionally to the contribution of each good in their utility. This dynamic models a process of learning how to bid and has been studied in a series of papers on Fisher and production markets, but not in exchange economies. Our main results a","authors_text":"Nikhil R. Devanur, Simina Br\\^anzei, Yuval Rabani","cross_cats":["econ.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2019-07-11T08:10:06Z","title":"Proportional Dynamics in Exchange Economies"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.05037","kind":"arxiv","version":3},"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":"sha256:9915856cfb79662c34976e7acbf30cee0257da4b4a8556010c04f171db908168","target":"record","created_at":"2026-07-05T06:49:38Z","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":"83e65bf17e72f7f5e823818119db1d03b73d603dcb5be6a36d615c8b11bec5f3","cross_cats_sorted":["econ.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2019-07-11T08:10:06Z","title_canon_sha256":"95422284c3a19b8dfe1613591f2b49abe88740ac4893239cce51b7f1a471b31f"},"schema_version":"1.0","source":{"id":"1907.05037","kind":"arxiv","version":3}},"canonical_sha256":"a43f96ec82cdd53b2a14e592257c388f52e10c2537c56d5ee1c11bb33740b953","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a43f96ec82cdd53b2a14e592257c388f52e10c2537c56d5ee1c11bb33740b953","first_computed_at":"2026-07-05T06:49:38.489954Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:49:38.489954Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9x+TGPqrTC1Z68WmXUPb+u+rlrvmuTp6aeRCk9NOvvVowMKLGQqN82tgqNgy1i3aevFMbHwO3IrVq4aRwkkJCg==","signature_status":"signed_v1","signed_at":"2026-07-05T06:49:38.490308Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.05037","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9915856cfb79662c34976e7acbf30cee0257da4b4a8556010c04f171db908168","sha256:b61aec6b2a132bbd351ee0c17f830230843bb7fd679b1bf5b6745e020f8b373f"],"state_sha256":"67b072bff3016849f2748bc624b47570ccc89059a526082328af2bb782b2c18c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+4E9k/sRg6FkwBsssM2ZYy02TuP9a2NJbXGFE5hqv3IUuaI2H0OJNI/LzTasxEW+335bTbP6l6tuUO9rVEiKCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T17:24:44.074319Z","bundle_sha256":"0217b51a95e44b3e9633ae35d811d3ea14331e51df79a5b0643f7a030effcd92"}}