{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:GQAM2OPKGEFGT5W2WQGZEBPZR5","short_pith_number":"pith:GQAM2OPK","canonical_record":{"source":{"id":"1410.3325","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-10-13T14:28:16Z","cross_cats_sorted":["math.MP","math.RA","math.RT","nlin.SI"],"title_canon_sha256":"14502ab237a8fd6397f515825167f9a4e7d435739df2dc0c4bfb78008cbafacb","abstract_canon_sha256":"aa579aa2a56c0d76d7ad6ea858a88e5651bbe9e5924c2659d7f654c92ed27eac"},"schema_version":"1.0"},"canonical_sha256":"3400cd39ea310a69f6dab40d9205f98f6d7c92c7bccaf79a1588792c01181073","source":{"kind":"arxiv","id":"1410.3325","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.3325","created_at":"2026-05-18T01:24:11Z"},{"alias_kind":"arxiv_version","alias_value":"1410.3325v2","created_at":"2026-05-18T01:24:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.3325","created_at":"2026-05-18T01:24:11Z"},{"alias_kind":"pith_short_12","alias_value":"GQAM2OPKGEFG","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"GQAM2OPKGEFGT5W2","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"GQAM2OPK","created_at":"2026-05-18T12:28:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:GQAM2OPKGEFGT5W2WQGZEBPZR5","target":"record","payload":{"canonical_record":{"source":{"id":"1410.3325","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-10-13T14:28:16Z","cross_cats_sorted":["math.MP","math.RA","math.RT","nlin.SI"],"title_canon_sha256":"14502ab237a8fd6397f515825167f9a4e7d435739df2dc0c4bfb78008cbafacb","abstract_canon_sha256":"aa579aa2a56c0d76d7ad6ea858a88e5651bbe9e5924c2659d7f654c92ed27eac"},"schema_version":"1.0"},"canonical_sha256":"3400cd39ea310a69f6dab40d9205f98f6d7c92c7bccaf79a1588792c01181073","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:24:11.102097Z","signature_b64":"ywHXNiBndPzN+vc6qhH9VOs7f/rhxcLc/5KDL0eEmMM8FXu5605wl3MVBTbhO6HPXPxFAGcc3EFFLb+AiewBAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3400cd39ea310a69f6dab40d9205f98f6d7c92c7bccaf79a1588792c01181073","last_reissued_at":"2026-05-18T01:24:11.101571Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:24:11.101571Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1410.3325","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":"2026-05-18T01:24:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bdeNcFWMxJrn5XCvzumffV4jw5D8fqHRtN5juvfVtaibs24xo6hQvhOWYec2atqPRz2/hRaFEXcIj+6v2ygGDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T13:52:56.134992Z"},"content_sha256":"e7b72bf8a3e643322286b25e3a8b456a81abb4ffd4af458a673741f6e331f391","schema_version":"1.0","event_id":"sha256:e7b72bf8a3e643322286b25e3a8b456a81abb4ffd4af458a673741f6e331f391"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:GQAM2OPKGEFGT5W2WQGZEBPZR5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Double Poisson vertex algebras and non-commutative Hamiltonian equations","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":"2014-10-13T14:28:16Z","abstract_excerpt":"We develop the formalism of double Poisson vertex algebras (local and non-local) aimed at the study of non-commutative Hamiltionan PDEs. This is a generalization of the theory of double Poisson algebras, developed by Van den Bergh, which is used in the study of Hamiltonian ODEs. We apply our theory of double Poisson vertex algebras to non-commutative KP and Gelfand-Dickey hierarchies. We also construct the related non-commutative de Rham and variational complexes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.3325","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":"2026-05-18T01:24:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BHq3cMQOE6HpPmV7PFlWoxBWvp9ogaNleIsiNvoFUz4rvD984BMlcwjoswsBiDzg2hasqIJfUHz4Spuk09EyBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T13:52:56.135364Z"},"content_sha256":"726bcb0f43b719dbfd834fab10129d6a10187b2c5c964ec758a3c47b8f596f2f","schema_version":"1.0","event_id":"sha256:726bcb0f43b719dbfd834fab10129d6a10187b2c5c964ec758a3c47b8f596f2f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GQAM2OPKGEFGT5W2WQGZEBPZR5/bundle.json","state_url":"https://pith.science/pith/GQAM2OPKGEFGT5W2WQGZEBPZR5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GQAM2OPKGEFGT5W2WQGZEBPZR5/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":"2026-06-04T13:52:56Z","links":{"resolver":"https://pith.science/pith/GQAM2OPKGEFGT5W2WQGZEBPZR5","bundle":"https://pith.science/pith/GQAM2OPKGEFGT5W2WQGZEBPZR5/bundle.json","state":"https://pith.science/pith/GQAM2OPKGEFGT5W2WQGZEBPZR5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GQAM2OPKGEFGT5W2WQGZEBPZR5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:GQAM2OPKGEFGT5W2WQGZEBPZR5","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":"aa579aa2a56c0d76d7ad6ea858a88e5651bbe9e5924c2659d7f654c92ed27eac","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":"2014-10-13T14:28:16Z","title_canon_sha256":"14502ab237a8fd6397f515825167f9a4e7d435739df2dc0c4bfb78008cbafacb"},"schema_version":"1.0","source":{"id":"1410.3325","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.3325","created_at":"2026-05-18T01:24:11Z"},{"alias_kind":"arxiv_version","alias_value":"1410.3325v2","created_at":"2026-05-18T01:24:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.3325","created_at":"2026-05-18T01:24:11Z"},{"alias_kind":"pith_short_12","alias_value":"GQAM2OPKGEFG","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"GQAM2OPKGEFGT5W2","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"GQAM2OPK","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:726bcb0f43b719dbfd834fab10129d6a10187b2c5c964ec758a3c47b8f596f2f","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 develop the formalism of double Poisson vertex algebras (local and non-local) aimed at the study of non-commutative Hamiltionan PDEs. This is a generalization of the theory of double Poisson algebras, developed by Van den Bergh, which is used in the study of Hamiltonian ODEs. We apply our theory of double Poisson vertex algebras to non-commutative KP and Gelfand-Dickey hierarchies. We also construct the related non-commutative de Rham and variational complexes.","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":"2014-10-13T14:28:16Z","title":"Double Poisson vertex algebras and non-commutative Hamiltonian equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.3325","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:e7b72bf8a3e643322286b25e3a8b456a81abb4ffd4af458a673741f6e331f391","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":"aa579aa2a56c0d76d7ad6ea858a88e5651bbe9e5924c2659d7f654c92ed27eac","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":"2014-10-13T14:28:16Z","title_canon_sha256":"14502ab237a8fd6397f515825167f9a4e7d435739df2dc0c4bfb78008cbafacb"},"schema_version":"1.0","source":{"id":"1410.3325","kind":"arxiv","version":2}},"canonical_sha256":"3400cd39ea310a69f6dab40d9205f98f6d7c92c7bccaf79a1588792c01181073","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3400cd39ea310a69f6dab40d9205f98f6d7c92c7bccaf79a1588792c01181073","first_computed_at":"2026-05-18T01:24:11.101571Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:24:11.101571Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ywHXNiBndPzN+vc6qhH9VOs7f/rhxcLc/5KDL0eEmMM8FXu5605wl3MVBTbhO6HPXPxFAGcc3EFFLb+AiewBAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:24:11.102097Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.3325","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e7b72bf8a3e643322286b25e3a8b456a81abb4ffd4af458a673741f6e331f391","sha256:726bcb0f43b719dbfd834fab10129d6a10187b2c5c964ec758a3c47b8f596f2f"],"state_sha256":"dcc48ee36fdc176735111d59a1289e8f6b9c382e49498461a90f6a96d027b2d5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4DlSxrrWDwPsRFK0gV6IIllFiUo4NxtipDF7Mg3r0etamEdD5/6AxsrcTPDskUUExFyd/aLtd1Z7nzqSRZ2vBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T13:52:56.137441Z","bundle_sha256":"acf40d2edd3f29be8cdc90af04fa933c975bf542878942d2c72c773b0f91d21f"}}