{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:VKR56RLYJPXIQR2OD6XFXMRCNJ","short_pith_number":"pith:VKR56RLY","canonical_record":{"source":{"id":"2104.02225","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2021-04-06T01:29:47Z","cross_cats_sorted":["hep-ph","math-ph","math.MP"],"title_canon_sha256":"ee199019cb2228c6aabbfe60cd68189997aca620e9f47d2d01e173f8aaf5ab31","abstract_canon_sha256":"e7447510799fcc2a6353c5eb770eba710b87c375fc46c427a35406d8e63fa226"},"schema_version":"1.0"},"canonical_sha256":"aaa3df45784bee88474e1fae5bb2226a58247b1bbdf3e4ae9ba6a957e886bd8c","source":{"kind":"arxiv","id":"2104.02225","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2104.02225","created_at":"2026-07-05T02:29:15Z"},{"alias_kind":"arxiv_version","alias_value":"2104.02225v1","created_at":"2026-07-05T02:29:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2104.02225","created_at":"2026-07-05T02:29:15Z"},{"alias_kind":"pith_short_12","alias_value":"VKR56RLYJPXI","created_at":"2026-07-05T02:29:15Z"},{"alias_kind":"pith_short_16","alias_value":"VKR56RLYJPXIQR2O","created_at":"2026-07-05T02:29:15Z"},{"alias_kind":"pith_short_8","alias_value":"VKR56RLY","created_at":"2026-07-05T02:29:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:VKR56RLYJPXIQR2OD6XFXMRCNJ","target":"record","payload":{"canonical_record":{"source":{"id":"2104.02225","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2021-04-06T01:29:47Z","cross_cats_sorted":["hep-ph","math-ph","math.MP"],"title_canon_sha256":"ee199019cb2228c6aabbfe60cd68189997aca620e9f47d2d01e173f8aaf5ab31","abstract_canon_sha256":"e7447510799fcc2a6353c5eb770eba710b87c375fc46c427a35406d8e63fa226"},"schema_version":"1.0"},"canonical_sha256":"aaa3df45784bee88474e1fae5bb2226a58247b1bbdf3e4ae9ba6a957e886bd8c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:29:15.837704Z","signature_b64":"6b3PyriPy9QX+2fwuP1FgtkFffGPacoG000LfCBpumnHSbZQcDk3+9Ttf4Nq2a/KoRWVkkEJO4UyfyDw4FKpCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aaa3df45784bee88474e1fae5bb2226a58247b1bbdf3e4ae9ba6a957e886bd8c","last_reissued_at":"2026-07-05T02:29:15.837302Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:29:15.837302Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2104.02225","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":"2026-07-05T02:29:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sO6R2kpEQ7CqCog8WsbHDwMJNmpBaYmJkfPTBlX1zj784Se7DwkzwyHUrg/7JYpf8XHnqZ/xXonkx+riLoTzAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-26T21:11:00.351389Z"},"content_sha256":"67fd11ed547a85cd519b8f265238e21045427c98bfd793533e7bab465d836faf","schema_version":"1.0","event_id":"sha256:67fd11ed547a85cd519b8f265238e21045427c98bfd793533e7bab465d836faf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:VKR56RLYJPXIQR2OD6XFXMRCNJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Golden Ratio and Hydrodynamics","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-ph","math-ph","math.MP"],"primary_cat":"math.DS","authors_text":"Boris Khesin, Hanchun Wang","submitted_at":"2021-04-06T01:29:47Z","abstract_excerpt":"There are useful and useless golden ratios. The useful one helps in traffic. The useless and rather mysterious one arises in hydrodynamics of point vortices, which we discuss in detail."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2104.02225","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2104.02225/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":"2026-07-05T02:29:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CkyHsAfUbPwKnJWH6Swy4lIO2JZ3TkjZbZHRQeQtGjzZRaMTEv9+pPLLuBRLM86ImFIf1mgUmXHNxbZU5sXIAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-26T21:11:00.351769Z"},"content_sha256":"ba2bc9b55b9c47bc52aa943638c19e4464ac340d1ea31623905efff5456176cb","schema_version":"1.0","event_id":"sha256:ba2bc9b55b9c47bc52aa943638c19e4464ac340d1ea31623905efff5456176cb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VKR56RLYJPXIQR2OD6XFXMRCNJ/bundle.json","state_url":"https://pith.science/pith/VKR56RLYJPXIQR2OD6XFXMRCNJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VKR56RLYJPXIQR2OD6XFXMRCNJ/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":"2026-07-26T21:11:00Z","links":{"resolver":"https://pith.science/pith/VKR56RLYJPXIQR2OD6XFXMRCNJ","bundle":"https://pith.science/pith/VKR56RLYJPXIQR2OD6XFXMRCNJ/bundle.json","state":"https://pith.science/pith/VKR56RLYJPXIQR2OD6XFXMRCNJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VKR56RLYJPXIQR2OD6XFXMRCNJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:VKR56RLYJPXIQR2OD6XFXMRCNJ","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":"e7447510799fcc2a6353c5eb770eba710b87c375fc46c427a35406d8e63fa226","cross_cats_sorted":["hep-ph","math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2021-04-06T01:29:47Z","title_canon_sha256":"ee199019cb2228c6aabbfe60cd68189997aca620e9f47d2d01e173f8aaf5ab31"},"schema_version":"1.0","source":{"id":"2104.02225","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2104.02225","created_at":"2026-07-05T02:29:15Z"},{"alias_kind":"arxiv_version","alias_value":"2104.02225v1","created_at":"2026-07-05T02:29:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2104.02225","created_at":"2026-07-05T02:29:15Z"},{"alias_kind":"pith_short_12","alias_value":"VKR56RLYJPXI","created_at":"2026-07-05T02:29:15Z"},{"alias_kind":"pith_short_16","alias_value":"VKR56RLYJPXIQR2O","created_at":"2026-07-05T02:29:15Z"},{"alias_kind":"pith_short_8","alias_value":"VKR56RLY","created_at":"2026-07-05T02:29:15Z"}],"graph_snapshots":[{"event_id":"sha256:ba2bc9b55b9c47bc52aa943638c19e4464ac340d1ea31623905efff5456176cb","target":"graph","created_at":"2026-07-05T02:29:15Z","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/2104.02225/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"There are useful and useless golden ratios. The useful one helps in traffic. The useless and rather mysterious one arises in hydrodynamics of point vortices, which we discuss in detail.","authors_text":"Boris Khesin, Hanchun Wang","cross_cats":["hep-ph","math-ph","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2021-04-06T01:29:47Z","title":"The Golden Ratio and Hydrodynamics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2104.02225","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":"sha256:67fd11ed547a85cd519b8f265238e21045427c98bfd793533e7bab465d836faf","target":"record","created_at":"2026-07-05T02:29:15Z","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":"e7447510799fcc2a6353c5eb770eba710b87c375fc46c427a35406d8e63fa226","cross_cats_sorted":["hep-ph","math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2021-04-06T01:29:47Z","title_canon_sha256":"ee199019cb2228c6aabbfe60cd68189997aca620e9f47d2d01e173f8aaf5ab31"},"schema_version":"1.0","source":{"id":"2104.02225","kind":"arxiv","version":1}},"canonical_sha256":"aaa3df45784bee88474e1fae5bb2226a58247b1bbdf3e4ae9ba6a957e886bd8c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aaa3df45784bee88474e1fae5bb2226a58247b1bbdf3e4ae9ba6a957e886bd8c","first_computed_at":"2026-07-05T02:29:15.837302Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:29:15.837302Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6b3PyriPy9QX+2fwuP1FgtkFffGPacoG000LfCBpumnHSbZQcDk3+9Ttf4Nq2a/KoRWVkkEJO4UyfyDw4FKpCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T02:29:15.837704Z","signed_message":"canonical_sha256_bytes"},"source_id":"2104.02225","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:67fd11ed547a85cd519b8f265238e21045427c98bfd793533e7bab465d836faf","sha256:ba2bc9b55b9c47bc52aa943638c19e4464ac340d1ea31623905efff5456176cb"],"state_sha256":"a5cc68c32ddaaa0aee93cb960a3aa238233b79c2cab7d69276d60c77c907c2b6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Fm0S51STbKuFRCmW0AeTON4tUFsaYdXhhQK+RLDQJWV1bKw8eXIsBZJyjl13DLCd+B3CCci5u6z9TJPvMlDxCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-26T21:11:00.353984Z","bundle_sha256":"1383f5a5b57b8a624e23941db76eaa015c82cac5bea21b87d485baa8e6e0fcac"}}