{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:CCR4NQR5IGU6LR4FCYM6R3UZMP","short_pith_number":"pith:CCR4NQR5","canonical_record":{"source":{"id":"1306.6589","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-06-27T18:04:29Z","cross_cats_sorted":["math.MP","math.RA","math.RT","nlin.SI"],"title_canon_sha256":"b491106a79f495b14420a989b6af129834d4254c3bad0b93b5bd4bcdc4200abd","abstract_canon_sha256":"c25c8ed962aabc950b1f823ee010616f8d951ec4eafe44ed30560716c2208589"},"schema_version":"1.0"},"canonical_sha256":"10a3c6c23d41a9e5c7851619e8ee9963fbb140d0f9cbef697142a289f1ce6c31","source":{"kind":"arxiv","id":"1306.6589","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.6589","created_at":"2026-05-18T01:24:11Z"},{"alias_kind":"arxiv_version","alias_value":"1306.6589v3","created_at":"2026-05-18T01:24:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.6589","created_at":"2026-05-18T01:24:11Z"},{"alias_kind":"pith_short_12","alias_value":"CCR4NQR5IGU6","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"CCR4NQR5IGU6LR4F","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"CCR4NQR5","created_at":"2026-05-18T12:27:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:CCR4NQR5IGU6LR4FCYM6R3UZMP","target":"record","payload":{"canonical_record":{"source":{"id":"1306.6589","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-06-27T18:04:29Z","cross_cats_sorted":["math.MP","math.RA","math.RT","nlin.SI"],"title_canon_sha256":"b491106a79f495b14420a989b6af129834d4254c3bad0b93b5bd4bcdc4200abd","abstract_canon_sha256":"c25c8ed962aabc950b1f823ee010616f8d951ec4eafe44ed30560716c2208589"},"schema_version":"1.0"},"canonical_sha256":"10a3c6c23d41a9e5c7851619e8ee9963fbb140d0f9cbef697142a289f1ce6c31","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:24:11.415889Z","signature_b64":"qdUbtQDG+c5bP6fwxLT2B3bV7uEkCgvNVs7hqQUPwibgV6jDxuV4A/2q5A68b+l42Nt4wfyvIdR6Q1xNibUlBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"10a3c6c23d41a9e5c7851619e8ee9963fbb140d0f9cbef697142a289f1ce6c31","last_reissued_at":"2026-05-18T01:24:11.415239Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:24:11.415239Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1306.6589","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":"2026-05-18T01:24:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"km0gAiM9gsvE+51dGH/DC4XTla/BcmpfzFBwEXF0PHwuQCWr0hzt8cpT4SbrHHebtat0w0+HUlbBnZnsx4x4BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T02:25:34.050712Z"},"content_sha256":"e4d55dad55c5777859e3b911a77ec158af2b3ac52a5820ad72fcc00df7c34819","schema_version":"1.0","event_id":"sha256:e4d55dad55c5777859e3b911a77ec158af2b3ac52a5820ad72fcc00df7c34819"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:CCR4NQR5IGU6LR4FCYM6R3UZMP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dirac reduction for Poisson vertex algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.RA","math.RT","nlin.SI"],"primary_cat":"math-ph","authors_text":"Alberto De Sole, Daniele Valeri, Victor G. Kac","submitted_at":"2013-06-27T18:04:29Z","abstract_excerpt":"We construct an analogue of Dirac's reduction for an arbitrary local or non-local Poisson bracket in the general setup of non-local Poisson vertex algebras. This leads to Dirac's reduction of an arbitrary non-local Poisson structure. We apply this construction to an example of a generalized Drinfeld-Sokolov hierarchy."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.6589","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":""},"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":"2026-05-18T01:24:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dqSu8ZU3ki5J0O/DIuWmjiHcTBgy3tRpqXD3rv3XRkARGOz+VTiDqDio/KVtTLJWdpEQ4E7TKpQPNHU+tCNpBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T02:25:34.051283Z"},"content_sha256":"2172dd92c8722ccddeae3d136897e35cebc182a2454e391ce8e4c41a2e816cd0","schema_version":"1.0","event_id":"sha256:2172dd92c8722ccddeae3d136897e35cebc182a2454e391ce8e4c41a2e816cd0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CCR4NQR5IGU6LR4FCYM6R3UZMP/bundle.json","state_url":"https://pith.science/pith/CCR4NQR5IGU6LR4FCYM6R3UZMP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CCR4NQR5IGU6LR4FCYM6R3UZMP/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":"2026-06-05T02:25:34Z","links":{"resolver":"https://pith.science/pith/CCR4NQR5IGU6LR4FCYM6R3UZMP","bundle":"https://pith.science/pith/CCR4NQR5IGU6LR4FCYM6R3UZMP/bundle.json","state":"https://pith.science/pith/CCR4NQR5IGU6LR4FCYM6R3UZMP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CCR4NQR5IGU6LR4FCYM6R3UZMP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:CCR4NQR5IGU6LR4FCYM6R3UZMP","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":"c25c8ed962aabc950b1f823ee010616f8d951ec4eafe44ed30560716c2208589","cross_cats_sorted":["math.MP","math.RA","math.RT","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-06-27T18:04:29Z","title_canon_sha256":"b491106a79f495b14420a989b6af129834d4254c3bad0b93b5bd4bcdc4200abd"},"schema_version":"1.0","source":{"id":"1306.6589","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.6589","created_at":"2026-05-18T01:24:11Z"},{"alias_kind":"arxiv_version","alias_value":"1306.6589v3","created_at":"2026-05-18T01:24:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.6589","created_at":"2026-05-18T01:24:11Z"},{"alias_kind":"pith_short_12","alias_value":"CCR4NQR5IGU6","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"CCR4NQR5IGU6LR4F","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"CCR4NQR5","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:2172dd92c8722ccddeae3d136897e35cebc182a2454e391ce8e4c41a2e816cd0","target":"graph","created_at":"2026-05-18T01:24:11Z","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 an analogue of Dirac's reduction for an arbitrary local or non-local Poisson bracket in the general setup of non-local Poisson vertex algebras. This leads to Dirac's reduction of an arbitrary non-local Poisson structure. We apply this construction to an example of a generalized Drinfeld-Sokolov hierarchy.","authors_text":"Alberto De Sole, Daniele Valeri, Victor G. Kac","cross_cats":["math.MP","math.RA","math.RT","nlin.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-06-27T18:04:29Z","title":"Dirac reduction for Poisson vertex algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.6589","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:e4d55dad55c5777859e3b911a77ec158af2b3ac52a5820ad72fcc00df7c34819","target":"record","created_at":"2026-05-18T01:24:11Z","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":"c25c8ed962aabc950b1f823ee010616f8d951ec4eafe44ed30560716c2208589","cross_cats_sorted":["math.MP","math.RA","math.RT","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-06-27T18:04:29Z","title_canon_sha256":"b491106a79f495b14420a989b6af129834d4254c3bad0b93b5bd4bcdc4200abd"},"schema_version":"1.0","source":{"id":"1306.6589","kind":"arxiv","version":3}},"canonical_sha256":"10a3c6c23d41a9e5c7851619e8ee9963fbb140d0f9cbef697142a289f1ce6c31","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"10a3c6c23d41a9e5c7851619e8ee9963fbb140d0f9cbef697142a289f1ce6c31","first_computed_at":"2026-05-18T01:24:11.415239Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:24:11.415239Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qdUbtQDG+c5bP6fwxLT2B3bV7uEkCgvNVs7hqQUPwibgV6jDxuV4A/2q5A68b+l42Nt4wfyvIdR6Q1xNibUlBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:24:11.415889Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.6589","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e4d55dad55c5777859e3b911a77ec158af2b3ac52a5820ad72fcc00df7c34819","sha256:2172dd92c8722ccddeae3d136897e35cebc182a2454e391ce8e4c41a2e816cd0"],"state_sha256":"e6c50b867f751751d057e8b5ce31fc6cbc21916d639811a4fa1ee5399bcbac93"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YpnVlDNT0inEZe/fDewH9JM9mhA/xzVehQZKsrvtezffPRQ+ayAKLXjRRT0RMp5O0cFMBYQW78+SaxiM2po+Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T02:25:34.055200Z","bundle_sha256":"84c05560891780f64406ee805ba68e6650d330f5cda9e860d0f5d6eec79f7a50"}}