{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:J4BC5VNOHVNR6NXFQRIRKFL4VL","short_pith_number":"pith:J4BC5VNO","canonical_record":{"source":{"id":"1610.09445","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.DG","submitted_at":"2016-10-29T03:18:31Z","cross_cats_sorted":[],"title_canon_sha256":"f5459e6bc43d4344e568e100a7b1047dd762154cfb263dcbf8768d20998d0dd9","abstract_canon_sha256":"5ef73df1764df50d9ef6230afa82a61c8e0322a4a0a5f631707b764e60131c3b"},"schema_version":"1.0"},"canonical_sha256":"4f022ed5ae3d5b1f36e5845115157caad4de1762190ed30ab56d25cc3d23336b","source":{"kind":"arxiv","id":"1610.09445","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.09445","created_at":"2026-05-18T00:46:55Z"},{"alias_kind":"arxiv_version","alias_value":"1610.09445v2","created_at":"2026-05-18T00:46:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.09445","created_at":"2026-05-18T00:46:55Z"},{"alias_kind":"pith_short_12","alias_value":"J4BC5VNOHVNR","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"J4BC5VNOHVNR6NXF","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"J4BC5VNO","created_at":"2026-05-18T12:30:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:J4BC5VNOHVNR6NXFQRIRKFL4VL","target":"record","payload":{"canonical_record":{"source":{"id":"1610.09445","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.DG","submitted_at":"2016-10-29T03:18:31Z","cross_cats_sorted":[],"title_canon_sha256":"f5459e6bc43d4344e568e100a7b1047dd762154cfb263dcbf8768d20998d0dd9","abstract_canon_sha256":"5ef73df1764df50d9ef6230afa82a61c8e0322a4a0a5f631707b764e60131c3b"},"schema_version":"1.0"},"canonical_sha256":"4f022ed5ae3d5b1f36e5845115157caad4de1762190ed30ab56d25cc3d23336b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:55.409124Z","signature_b64":"I2rNpYYO9q3SE+1/BBdTGQLWOGaj5RwnnV4UCFcxs0RPAXFOoN3eo7rkirAhkb9iQfSuTJw/OO9xX9PB0udWBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4f022ed5ae3d5b1f36e5845115157caad4de1762190ed30ab56d25cc3d23336b","last_reissued_at":"2026-05-18T00:46:55.408564Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:55.408564Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.09445","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":"2026-05-18T00:46:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WQW44ML9T+jWOeF9InqUZPtroEhB+A7ceW2pdMzAb7U7IWkwYyvSpzAb+K/nhoH42E7JpeC0W+uOGDzlFy8iBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T08:12:16.224238Z"},"content_sha256":"40848e2ca1e52ca8862630145c939ec25973e9099b5dd5288cf37b636a3436aa","schema_version":"1.0","event_id":"sha256:40848e2ca1e52ca8862630145c939ec25973e9099b5dd5288cf37b636a3436aa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:J4BC5VNOHVNR6NXFQRIRKFL4VL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Toric Poisson Structures of Type $(1,1)$ and their Cohomology","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Arlo Caine, Berit Nilsen Givens","submitted_at":"2016-10-29T03:18:31Z","abstract_excerpt":"We classify real Poisson structures on complex toric manifolds of type $(1,1)$ and initiate an investigation of their Poisson cohomology. For smooth toric varieties, such structures are necessarily algebraic and are homogeneous quadratic in each of the distinguished holomorphic coordinate charts determined by the open cones of the associated simplicial fan. As an approximation to the smooth cohomology problem in each ${\\mathbb C}^n$ chart, we consider the Poisson differential on the complex of polynomial multi-vector fields. For the algebraic problem, we compute $H^0$ and $H^1$ under the assum"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.09445","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":""},"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":"2026-05-18T00:46:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7BvVZVIH6A0m414nbSHBSrew+ctcG4tudndetqBhzVX0QULL9gwl1pqBON2B9QRvJDRms5XXqfNSc2VMdyhfBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T08:12:16.224927Z"},"content_sha256":"a541f4af1b385a6b8f801ac3edc7c01fc2dd06794a15f89f330477426d121a0e","schema_version":"1.0","event_id":"sha256:a541f4af1b385a6b8f801ac3edc7c01fc2dd06794a15f89f330477426d121a0e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/J4BC5VNOHVNR6NXFQRIRKFL4VL/bundle.json","state_url":"https://pith.science/pith/J4BC5VNOHVNR6NXFQRIRKFL4VL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/J4BC5VNOHVNR6NXFQRIRKFL4VL/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":"2026-06-11T08:12:16Z","links":{"resolver":"https://pith.science/pith/J4BC5VNOHVNR6NXFQRIRKFL4VL","bundle":"https://pith.science/pith/J4BC5VNOHVNR6NXFQRIRKFL4VL/bundle.json","state":"https://pith.science/pith/J4BC5VNOHVNR6NXFQRIRKFL4VL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/J4BC5VNOHVNR6NXFQRIRKFL4VL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:J4BC5VNOHVNR6NXFQRIRKFL4VL","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":"5ef73df1764df50d9ef6230afa82a61c8e0322a4a0a5f631707b764e60131c3b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.DG","submitted_at":"2016-10-29T03:18:31Z","title_canon_sha256":"f5459e6bc43d4344e568e100a7b1047dd762154cfb263dcbf8768d20998d0dd9"},"schema_version":"1.0","source":{"id":"1610.09445","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.09445","created_at":"2026-05-18T00:46:55Z"},{"alias_kind":"arxiv_version","alias_value":"1610.09445v2","created_at":"2026-05-18T00:46:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.09445","created_at":"2026-05-18T00:46:55Z"},{"alias_kind":"pith_short_12","alias_value":"J4BC5VNOHVNR","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"J4BC5VNOHVNR6NXF","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"J4BC5VNO","created_at":"2026-05-18T12:30:22Z"}],"graph_snapshots":[{"event_id":"sha256:a541f4af1b385a6b8f801ac3edc7c01fc2dd06794a15f89f330477426d121a0e","target":"graph","created_at":"2026-05-18T00:46:55Z","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 classify real Poisson structures on complex toric manifolds of type $(1,1)$ and initiate an investigation of their Poisson cohomology. For smooth toric varieties, such structures are necessarily algebraic and are homogeneous quadratic in each of the distinguished holomorphic coordinate charts determined by the open cones of the associated simplicial fan. As an approximation to the smooth cohomology problem in each ${\\mathbb C}^n$ chart, we consider the Poisson differential on the complex of polynomial multi-vector fields. For the algebraic problem, we compute $H^0$ and $H^1$ under the assum","authors_text":"Arlo Caine, Berit Nilsen Givens","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.DG","submitted_at":"2016-10-29T03:18:31Z","title":"On Toric Poisson Structures of Type $(1,1)$ and their Cohomology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.09445","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":"sha256:40848e2ca1e52ca8862630145c939ec25973e9099b5dd5288cf37b636a3436aa","target":"record","created_at":"2026-05-18T00:46:55Z","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":"5ef73df1764df50d9ef6230afa82a61c8e0322a4a0a5f631707b764e60131c3b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.DG","submitted_at":"2016-10-29T03:18:31Z","title_canon_sha256":"f5459e6bc43d4344e568e100a7b1047dd762154cfb263dcbf8768d20998d0dd9"},"schema_version":"1.0","source":{"id":"1610.09445","kind":"arxiv","version":2}},"canonical_sha256":"4f022ed5ae3d5b1f36e5845115157caad4de1762190ed30ab56d25cc3d23336b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4f022ed5ae3d5b1f36e5845115157caad4de1762190ed30ab56d25cc3d23336b","first_computed_at":"2026-05-18T00:46:55.408564Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:55.408564Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"I2rNpYYO9q3SE+1/BBdTGQLWOGaj5RwnnV4UCFcxs0RPAXFOoN3eo7rkirAhkb9iQfSuTJw/OO9xX9PB0udWBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:55.409124Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.09445","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:40848e2ca1e52ca8862630145c939ec25973e9099b5dd5288cf37b636a3436aa","sha256:a541f4af1b385a6b8f801ac3edc7c01fc2dd06794a15f89f330477426d121a0e"],"state_sha256":"aabc31f82734259fe3f52611a8e6dc7a0cb36bb620f5dcacdf43058b7bf7b9f0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yLFKcmG7YG6Rp26rGkoVZowBX82nhmalMokEEp8q/mSF5c2Z+u2UA4BGAV5DJureri0jQczUTFCQ4sfZarC+DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T08:12:16.229293Z","bundle_sha256":"832123bd794d5587c04e8c1e03c9bb7aaf67db27b14871e683b931509aefa9ed"}}