{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:ZZXWXWO6BLOUZD2WSGXBLY4GE6","short_pith_number":"pith:ZZXWXWO6","canonical_record":{"source":{"id":"1901.07082","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2019-01-21T21:10:34Z","cross_cats_sorted":["hep-th","math.AG","nlin.SI"],"title_canon_sha256":"8a3f0376e2a2e86a66c9cbd0090929295800aa33085f41e9cad8dfffa85e95fe","abstract_canon_sha256":"e2f67026c936ebd6f1504f7f89f5f451f257b127a9bed7ca1526327d3a9401af"},"schema_version":"1.0"},"canonical_sha256":"ce6f6bd9de0add4c8f5691ae15e38627b48c2270b9e3c2ebba032cfc334ed751","source":{"kind":"arxiv","id":"1901.07082","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.07082","created_at":"2026-05-17T23:47:17Z"},{"alias_kind":"arxiv_version","alias_value":"1901.07082v1","created_at":"2026-05-17T23:47:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.07082","created_at":"2026-05-17T23:47:17Z"},{"alias_kind":"pith_short_12","alias_value":"ZZXWXWO6BLOU","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"ZZXWXWO6BLOUZD2W","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"ZZXWXWO6","created_at":"2026-05-18T12:33:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:ZZXWXWO6BLOUZD2WSGXBLY4GE6","target":"record","payload":{"canonical_record":{"source":{"id":"1901.07082","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2019-01-21T21:10:34Z","cross_cats_sorted":["hep-th","math.AG","nlin.SI"],"title_canon_sha256":"8a3f0376e2a2e86a66c9cbd0090929295800aa33085f41e9cad8dfffa85e95fe","abstract_canon_sha256":"e2f67026c936ebd6f1504f7f89f5f451f257b127a9bed7ca1526327d3a9401af"},"schema_version":"1.0"},"canonical_sha256":"ce6f6bd9de0add4c8f5691ae15e38627b48c2270b9e3c2ebba032cfc334ed751","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:17.367738Z","signature_b64":"GgBAjc9PBZWdpqfR1wk8FDCvIsCRNu7tgWYQg+NnXb1J8l7OfLbPGaWlRIGUMlK85tL7vgGBhkbaoE6FFdy+BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ce6f6bd9de0add4c8f5691ae15e38627b48c2270b9e3c2ebba032cfc334ed751","last_reissued_at":"2026-05-17T23:47:17.367095Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:17.367095Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1901.07082","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":"2026-05-17T23:47:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l0WXCHFrNT8HFMntgUDAbRHb04sNyyfEll3rfuyhXeZ8aDb+Hp2ZantF69/9OokEa7CeQkhHx8SlNccoU4V9Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T04:08:26.089618Z"},"content_sha256":"841103d74eb3950d6d660f6659b6a417b358b53c580c78fa11bdac2f05674d9f","schema_version":"1.0","event_id":"sha256:841103d74eb3950d6d660f6659b6a417b358b53c580c78fa11bdac2f05674d9f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:ZZXWXWO6BLOUZD2WSGXBLY4GE6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Poisson structures on loop spaces of $\\mathbb{C} P^n$ and an $r$-matrix associated with the universal elliptic curve","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.AG","nlin.SI"],"primary_cat":"math.QA","authors_text":"Alexander Odesskii","submitted_at":"2019-01-21T21:10:34Z","abstract_excerpt":"We construct a family of Poisson structures of hydrodynamic type on the loop space of $\\mathbb{C} P^{n-1}$. This family is parametrized by the moduli space of elliptic curves or, in other words, by the modular parameter $\\tau$. This family can be lifted to a homogeneous Poisson structure on the loop space of $\\mathbb{C}^n$ but in order to do that we need to upgrade the modular parameter $\\tau$ to an additional field $\\tau(x)$ with Poisson brackets $\\{\\tau(x),\\tau(y)\\}=0,~~\\{\\tau(x),z_a(y)\\}=2\\pi i~ z_a(y)~\\delta^{\\prime}(x-y)$ where $z_1,...,z_n$ are coordinates on $\\mathbb{C}^n$. These homoge"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.07082","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":"2026-05-17T23:47:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xFODPFQpWaB+Rb4hIGr+u44E4LL5uzJdXUpZHHzYjQeDmNHGxqeyCYA87OXZ6mDL8Gazb/gZrNmucMUqWlgxBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T04:08:26.090342Z"},"content_sha256":"2c55caed00a2ca521d6cf1f8150bcb2ebe744da414928bf470ad6fb7490236c9","schema_version":"1.0","event_id":"sha256:2c55caed00a2ca521d6cf1f8150bcb2ebe744da414928bf470ad6fb7490236c9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZZXWXWO6BLOUZD2WSGXBLY4GE6/bundle.json","state_url":"https://pith.science/pith/ZZXWXWO6BLOUZD2WSGXBLY4GE6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZZXWXWO6BLOUZD2WSGXBLY4GE6/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":"2026-05-26T04:08:26Z","links":{"resolver":"https://pith.science/pith/ZZXWXWO6BLOUZD2WSGXBLY4GE6","bundle":"https://pith.science/pith/ZZXWXWO6BLOUZD2WSGXBLY4GE6/bundle.json","state":"https://pith.science/pith/ZZXWXWO6BLOUZD2WSGXBLY4GE6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZZXWXWO6BLOUZD2WSGXBLY4GE6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:ZZXWXWO6BLOUZD2WSGXBLY4GE6","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":"e2f67026c936ebd6f1504f7f89f5f451f257b127a9bed7ca1526327d3a9401af","cross_cats_sorted":["hep-th","math.AG","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2019-01-21T21:10:34Z","title_canon_sha256":"8a3f0376e2a2e86a66c9cbd0090929295800aa33085f41e9cad8dfffa85e95fe"},"schema_version":"1.0","source":{"id":"1901.07082","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.07082","created_at":"2026-05-17T23:47:17Z"},{"alias_kind":"arxiv_version","alias_value":"1901.07082v1","created_at":"2026-05-17T23:47:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.07082","created_at":"2026-05-17T23:47:17Z"},{"alias_kind":"pith_short_12","alias_value":"ZZXWXWO6BLOU","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"ZZXWXWO6BLOUZD2W","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"ZZXWXWO6","created_at":"2026-05-18T12:33:33Z"}],"graph_snapshots":[{"event_id":"sha256:2c55caed00a2ca521d6cf1f8150bcb2ebe744da414928bf470ad6fb7490236c9","target":"graph","created_at":"2026-05-17T23:47:17Z","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":"We construct a family of Poisson structures of hydrodynamic type on the loop space of $\\mathbb{C} P^{n-1}$. This family is parametrized by the moduli space of elliptic curves or, in other words, by the modular parameter $\\tau$. This family can be lifted to a homogeneous Poisson structure on the loop space of $\\mathbb{C}^n$ but in order to do that we need to upgrade the modular parameter $\\tau$ to an additional field $\\tau(x)$ with Poisson brackets $\\{\\tau(x),\\tau(y)\\}=0,~~\\{\\tau(x),z_a(y)\\}=2\\pi i~ z_a(y)~\\delta^{\\prime}(x-y)$ where $z_1,...,z_n$ are coordinates on $\\mathbb{C}^n$. These homoge","authors_text":"Alexander Odesskii","cross_cats":["hep-th","math.AG","nlin.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2019-01-21T21:10:34Z","title":"Poisson structures on loop spaces of $\\mathbb{C} P^n$ and an $r$-matrix associated with the universal elliptic curve"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.07082","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":"sha256:841103d74eb3950d6d660f6659b6a417b358b53c580c78fa11bdac2f05674d9f","target":"record","created_at":"2026-05-17T23:47:17Z","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":"e2f67026c936ebd6f1504f7f89f5f451f257b127a9bed7ca1526327d3a9401af","cross_cats_sorted":["hep-th","math.AG","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2019-01-21T21:10:34Z","title_canon_sha256":"8a3f0376e2a2e86a66c9cbd0090929295800aa33085f41e9cad8dfffa85e95fe"},"schema_version":"1.0","source":{"id":"1901.07082","kind":"arxiv","version":1}},"canonical_sha256":"ce6f6bd9de0add4c8f5691ae15e38627b48c2270b9e3c2ebba032cfc334ed751","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ce6f6bd9de0add4c8f5691ae15e38627b48c2270b9e3c2ebba032cfc334ed751","first_computed_at":"2026-05-17T23:47:17.367095Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:17.367095Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GgBAjc9PBZWdpqfR1wk8FDCvIsCRNu7tgWYQg+NnXb1J8l7OfLbPGaWlRIGUMlK85tL7vgGBhkbaoE6FFdy+BQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:17.367738Z","signed_message":"canonical_sha256_bytes"},"source_id":"1901.07082","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:841103d74eb3950d6d660f6659b6a417b358b53c580c78fa11bdac2f05674d9f","sha256:2c55caed00a2ca521d6cf1f8150bcb2ebe744da414928bf470ad6fb7490236c9"],"state_sha256":"15cb40d5ff785b4a2621beed494d336593b4eab8da32dce798ede25fdfb991db"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wYzT87PAYFQI/xhwKiGMvzjnWGRKAJQIQiErKSfG+a1dlk+xNOZjSxrJ8RXcm49I0islrU7PmbIoU4/r2XtaBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T04:08:26.093788Z","bundle_sha256":"ce51e180c426f447b9f0d73ebdea45099b97ed94d369e8ab83b8350bce399771"}}