{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:FZ5YTF7CZ5D36C6ECD762TE4OP","short_pith_number":"pith:FZ5YTF7C","canonical_record":{"source":{"id":"2412.01995","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-12-02T22:04:31Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"660628bd4fc722f90ca2dc7a4792ac9300c7a7c2b848efe1cb42ae519ef0ea8a","abstract_canon_sha256":"48dd1ac261741206f214286c0359913c57d6c726540bd4ee41c6649ae0f51aca"},"schema_version":"1.0"},"canonical_sha256":"2e7b8997e2cf47bf0bc410ffed4c9c73ef487b44705e363ba910ee6f7b955e5f","source":{"kind":"arxiv","id":"2412.01995","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.01995","created_at":"2026-07-05T09:57:49Z"},{"alias_kind":"arxiv_version","alias_value":"2412.01995v2","created_at":"2026-07-05T09:57:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.01995","created_at":"2026-07-05T09:57:49Z"},{"alias_kind":"pith_short_12","alias_value":"FZ5YTF7CZ5D3","created_at":"2026-07-05T09:57:49Z"},{"alias_kind":"pith_short_16","alias_value":"FZ5YTF7CZ5D36C6E","created_at":"2026-07-05T09:57:49Z"},{"alias_kind":"pith_short_8","alias_value":"FZ5YTF7C","created_at":"2026-07-05T09:57:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:FZ5YTF7CZ5D36C6ECD762TE4OP","target":"record","payload":{"canonical_record":{"source":{"id":"2412.01995","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-12-02T22:04:31Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"660628bd4fc722f90ca2dc7a4792ac9300c7a7c2b848efe1cb42ae519ef0ea8a","abstract_canon_sha256":"48dd1ac261741206f214286c0359913c57d6c726540bd4ee41c6649ae0f51aca"},"schema_version":"1.0"},"canonical_sha256":"2e7b8997e2cf47bf0bc410ffed4c9c73ef487b44705e363ba910ee6f7b955e5f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:57:49.152626Z","signature_b64":"dL7Lii3xY4QEy25UukImFNaI1sMbDo96WdWJFo1Wh3Va9kdGoSt+LG03YOeGAAUuhTuUnrSknMN5ogFykWqnAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2e7b8997e2cf47bf0bc410ffed4c9c73ef487b44705e363ba910ee6f7b955e5f","last_reissued_at":"2026-07-05T09:57:49.152117Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:57:49.152117Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2412.01995","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:57:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w26RHKbJIAwV44oj/zbhTeBPRhOyCHf/Qvkw/ztxXiKhWOhRKYNjKjMv0xKjubghX6DZwmJCbHvKNQx6VKs4Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T10:27:55.389229Z"},"content_sha256":"3257e33d9ff46a2a212165dcb6419f5cfbacc49422b63b2dc739a924824d3727","schema_version":"1.0","event_id":"sha256:3257e33d9ff46a2a212165dcb6419f5cfbacc49422b63b2dc739a924824d3727"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:FZ5YTF7CZ5D36C6ECD762TE4OP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Exciting games and Monge-Amp\\`ere equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Julio Backhoff, Xin Zhang, Zhizhang Wang","submitted_at":"2024-12-02T22:04:31Z","abstract_excerpt":"We consider a competition between $d+1$ players, and aim to identify the \"most exciting game'' of this kind. This is translated, mathematically, into a stochastic optimization problem over martingales that live on the $d$-dimensional subprobability simplex $\\Delta$ and terminate on the vertices of $\\Delta$ (so-called win-martingales), with a cost function related to a scaling limit of Shannon entropies. We uncover a surprising connection between this problem and the seemingly unrelated field of Monge-Amp\\`{e}re equations: If $g$ solves \\begin{equation*} \\begin{cases} g(x)=\\log \\det\\left(\\frac{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.01995","kind":"arxiv","version":2},"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/2412.01995/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":"2026-07-05T09:57:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RhAiz3bE5efgv2SXWGSmZrVVqoWU4390NwuDMzDgshPnSOcsm4CtmafDgaxtJiab7/9JiHPnTCxSCBEvCndABg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T10:27:55.389620Z"},"content_sha256":"c9e48d4c35d0b6cc2566342d6a3d346af1ba27eebf7a13bdc891b74343d21938","schema_version":"1.0","event_id":"sha256:c9e48d4c35d0b6cc2566342d6a3d346af1ba27eebf7a13bdc891b74343d21938"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FZ5YTF7CZ5D36C6ECD762TE4OP/bundle.json","state_url":"https://pith.science/pith/FZ5YTF7CZ5D36C6ECD762TE4OP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FZ5YTF7CZ5D36C6ECD762TE4OP/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":"2026-08-13T10:27:55Z","links":{"resolver":"https://pith.science/pith/FZ5YTF7CZ5D36C6ECD762TE4OP","bundle":"https://pith.science/pith/FZ5YTF7CZ5D36C6ECD762TE4OP/bundle.json","state":"https://pith.science/pith/FZ5YTF7CZ5D36C6ECD762TE4OP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FZ5YTF7CZ5D36C6ECD762TE4OP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:FZ5YTF7CZ5D36C6ECD762TE4OP","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":"48dd1ac261741206f214286c0359913c57d6c726540bd4ee41c6649ae0f51aca","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-12-02T22:04:31Z","title_canon_sha256":"660628bd4fc722f90ca2dc7a4792ac9300c7a7c2b848efe1cb42ae519ef0ea8a"},"schema_version":"1.0","source":{"id":"2412.01995","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.01995","created_at":"2026-07-05T09:57:49Z"},{"alias_kind":"arxiv_version","alias_value":"2412.01995v2","created_at":"2026-07-05T09:57:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.01995","created_at":"2026-07-05T09:57:49Z"},{"alias_kind":"pith_short_12","alias_value":"FZ5YTF7CZ5D3","created_at":"2026-07-05T09:57:49Z"},{"alias_kind":"pith_short_16","alias_value":"FZ5YTF7CZ5D36C6E","created_at":"2026-07-05T09:57:49Z"},{"alias_kind":"pith_short_8","alias_value":"FZ5YTF7C","created_at":"2026-07-05T09:57:49Z"}],"graph_snapshots":[{"event_id":"sha256:c9e48d4c35d0b6cc2566342d6a3d346af1ba27eebf7a13bdc891b74343d21938","target":"graph","created_at":"2026-07-05T09:57:49Z","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/2412.01995/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider a competition between $d+1$ players, and aim to identify the \"most exciting game'' of this kind. This is translated, mathematically, into a stochastic optimization problem over martingales that live on the $d$-dimensional subprobability simplex $\\Delta$ and terminate on the vertices of $\\Delta$ (so-called win-martingales), with a cost function related to a scaling limit of Shannon entropies. We uncover a surprising connection between this problem and the seemingly unrelated field of Monge-Amp\\`{e}re equations: If $g$ solves \\begin{equation*} \\begin{cases} g(x)=\\log \\det\\left(\\frac{","authors_text":"Julio Backhoff, Xin Zhang, Zhizhang Wang","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-12-02T22:04:31Z","title":"Exciting games and Monge-Amp\\`ere equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.01995","kind":"arxiv","version":2},"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":"sha256:3257e33d9ff46a2a212165dcb6419f5cfbacc49422b63b2dc739a924824d3727","target":"record","created_at":"2026-07-05T09:57:49Z","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":"48dd1ac261741206f214286c0359913c57d6c726540bd4ee41c6649ae0f51aca","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-12-02T22:04:31Z","title_canon_sha256":"660628bd4fc722f90ca2dc7a4792ac9300c7a7c2b848efe1cb42ae519ef0ea8a"},"schema_version":"1.0","source":{"id":"2412.01995","kind":"arxiv","version":2}},"canonical_sha256":"2e7b8997e2cf47bf0bc410ffed4c9c73ef487b44705e363ba910ee6f7b955e5f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2e7b8997e2cf47bf0bc410ffed4c9c73ef487b44705e363ba910ee6f7b955e5f","first_computed_at":"2026-07-05T09:57:49.152117Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:57:49.152117Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dL7Lii3xY4QEy25UukImFNaI1sMbDo96WdWJFo1Wh3Va9kdGoSt+LG03YOeGAAUuhTuUnrSknMN5ogFykWqnAg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:57:49.152626Z","signed_message":"canonical_sha256_bytes"},"source_id":"2412.01995","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3257e33d9ff46a2a212165dcb6419f5cfbacc49422b63b2dc739a924824d3727","sha256:c9e48d4c35d0b6cc2566342d6a3d346af1ba27eebf7a13bdc891b74343d21938"],"state_sha256":"b1d2dfb254cf24431f68c3b5e6f61237ddf56ce6bdba3914237221e3cdda093f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7DAnjeVEWAUchmnBABMG2kIo88DC5ubPH3w3K6v2J5imWBuJbcEa1Soys8r6KCnn0eE/iYEFbyVoUbTDz+X5BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T10:27:55.392606Z","bundle_sha256":"3add20b943e9d587c3bb8e69d3c8535f3775510b68d26bdaa69a06009a713b01"}}