{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:CHACC2SSHRHUYTNESV2XTW2M4D","short_pith_number":"pith:CHACC2SS","canonical_record":{"source":{"id":"1109.1234","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"hep-th","submitted_at":"2011-09-06T17:16:22Z","cross_cats_sorted":["nlin.CD"],"title_canon_sha256":"58ecb392cd102414c543093cf5984858fdda17272def0516597c1200f22d7da9","abstract_canon_sha256":"6a80d7323eded2f3f05b4a65ee4494e8d4250753098547c2c523fa2eeea40d89"},"schema_version":"1.0"},"canonical_sha256":"11c0216a523c4f4c4da4957579db4ce0c118673bef9a7e068fbe0de789a1f336","source":{"kind":"arxiv","id":"1109.1234","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.1234","created_at":"2026-05-18T00:54:42Z"},{"alias_kind":"arxiv_version","alias_value":"1109.1234v1","created_at":"2026-05-18T00:54:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.1234","created_at":"2026-05-18T00:54:42Z"},{"alias_kind":"pith_short_12","alias_value":"CHACC2SSHRHU","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"CHACC2SSHRHUYTNE","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"CHACC2SS","created_at":"2026-05-18T12:26:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:CHACC2SSHRHUYTNESV2XTW2M4D","target":"record","payload":{"canonical_record":{"source":{"id":"1109.1234","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"hep-th","submitted_at":"2011-09-06T17:16:22Z","cross_cats_sorted":["nlin.CD"],"title_canon_sha256":"58ecb392cd102414c543093cf5984858fdda17272def0516597c1200f22d7da9","abstract_canon_sha256":"6a80d7323eded2f3f05b4a65ee4494e8d4250753098547c2c523fa2eeea40d89"},"schema_version":"1.0"},"canonical_sha256":"11c0216a523c4f4c4da4957579db4ce0c118673bef9a7e068fbe0de789a1f336","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:54:42.075530Z","signature_b64":"x+gsNaT2Tplbw3eio762gA3EBVnEB6Ni0bbTvxCWoTzIqrvWHb+V3MUzvrN8LwZb6wsOtg16tbPxF8uxEHbpBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"11c0216a523c4f4c4da4957579db4ce0c118673bef9a7e068fbe0de789a1f336","last_reissued_at":"2026-05-18T00:54:42.075016Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:54:42.075016Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1109.1234","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":"2026-05-18T00:54:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YTKH3vFyhKGpo9FVMH1GmoBSp4PPG415fmpNimWqELuCZNsZbqZeDxLC2bmUUBl7WIJJaPl+L/GpQztSfkeIAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T10:09:12.159846Z"},"content_sha256":"98a4c90004c3d9f94d19bdd34aefc6c40cd4c643657cb0b0f6d76f0fec9b8d2e","schema_version":"1.0","event_id":"sha256:98a4c90004c3d9f94d19bdd34aefc6c40cd4c643657cb0b0f6d76f0fec9b8d2e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:CHACC2SSHRHUYTNESV2XTW2M4D","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Matrix Quantization of Turbulence","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["nlin.CD"],"primary_cat":"hep-th","authors_text":"Emmanuel Floratos","submitted_at":"2011-09-06T17:16:22Z","abstract_excerpt":"Based on our recent work on Quantum Nambu Mechanics $\\cite{af2}$, we provide an explicit quantization of the Lorenz chaotic attractor through the introduction of Non-commutative phase space coordinates as Hermitian $ N \\times N $ matrices in $ R^{3}$. For the volume preserving part, they satisfy the commutation relations induced by one of the two Nambu Hamiltonians, the second one generating a unique time evolution. Dissipation is incorporated quantum mechanically in a self-consistent way having the correct classical limit without the introduction of external degrees of freedom. Due to its vol"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.1234","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":"2026-05-18T00:54:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6MhsBG4Y/HYE+QATP47JkG3iLrKNVvxJuP1ZyM8oICr6t/4a9J6UgphratvufrRZVns5lSlwQvpJYXrPIashDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T10:09:12.160189Z"},"content_sha256":"19fb371c053ff9c8a4193b0720d099459b56dada4a8d3612cfd5cf52e24d59eb","schema_version":"1.0","event_id":"sha256:19fb371c053ff9c8a4193b0720d099459b56dada4a8d3612cfd5cf52e24d59eb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CHACC2SSHRHUYTNESV2XTW2M4D/bundle.json","state_url":"https://pith.science/pith/CHACC2SSHRHUYTNESV2XTW2M4D/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CHACC2SSHRHUYTNESV2XTW2M4D/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":"2026-06-12T10:09:12Z","links":{"resolver":"https://pith.science/pith/CHACC2SSHRHUYTNESV2XTW2M4D","bundle":"https://pith.science/pith/CHACC2SSHRHUYTNESV2XTW2M4D/bundle.json","state":"https://pith.science/pith/CHACC2SSHRHUYTNESV2XTW2M4D/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CHACC2SSHRHUYTNESV2XTW2M4D/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:CHACC2SSHRHUYTNESV2XTW2M4D","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":"6a80d7323eded2f3f05b4a65ee4494e8d4250753098547c2c523fa2eeea40d89","cross_cats_sorted":["nlin.CD"],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"hep-th","submitted_at":"2011-09-06T17:16:22Z","title_canon_sha256":"58ecb392cd102414c543093cf5984858fdda17272def0516597c1200f22d7da9"},"schema_version":"1.0","source":{"id":"1109.1234","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.1234","created_at":"2026-05-18T00:54:42Z"},{"alias_kind":"arxiv_version","alias_value":"1109.1234v1","created_at":"2026-05-18T00:54:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.1234","created_at":"2026-05-18T00:54:42Z"},{"alias_kind":"pith_short_12","alias_value":"CHACC2SSHRHU","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"CHACC2SSHRHUYTNE","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"CHACC2SS","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:19fb371c053ff9c8a4193b0720d099459b56dada4a8d3612cfd5cf52e24d59eb","target":"graph","created_at":"2026-05-18T00:54:42Z","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":"Based on our recent work on Quantum Nambu Mechanics $\\cite{af2}$, we provide an explicit quantization of the Lorenz chaotic attractor through the introduction of Non-commutative phase space coordinates as Hermitian $ N \\times N $ matrices in $ R^{3}$. For the volume preserving part, they satisfy the commutation relations induced by one of the two Nambu Hamiltonians, the second one generating a unique time evolution. Dissipation is incorporated quantum mechanically in a self-consistent way having the correct classical limit without the introduction of external degrees of freedom. Due to its vol","authors_text":"Emmanuel Floratos","cross_cats":["nlin.CD"],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"hep-th","submitted_at":"2011-09-06T17:16:22Z","title":"Matrix Quantization of Turbulence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.1234","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":"sha256:98a4c90004c3d9f94d19bdd34aefc6c40cd4c643657cb0b0f6d76f0fec9b8d2e","target":"record","created_at":"2026-05-18T00:54:42Z","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":"6a80d7323eded2f3f05b4a65ee4494e8d4250753098547c2c523fa2eeea40d89","cross_cats_sorted":["nlin.CD"],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"hep-th","submitted_at":"2011-09-06T17:16:22Z","title_canon_sha256":"58ecb392cd102414c543093cf5984858fdda17272def0516597c1200f22d7da9"},"schema_version":"1.0","source":{"id":"1109.1234","kind":"arxiv","version":1}},"canonical_sha256":"11c0216a523c4f4c4da4957579db4ce0c118673bef9a7e068fbe0de789a1f336","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"11c0216a523c4f4c4da4957579db4ce0c118673bef9a7e068fbe0de789a1f336","first_computed_at":"2026-05-18T00:54:42.075016Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:54:42.075016Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"x+gsNaT2Tplbw3eio762gA3EBVnEB6Ni0bbTvxCWoTzIqrvWHb+V3MUzvrN8LwZb6wsOtg16tbPxF8uxEHbpBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:54:42.075530Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.1234","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:98a4c90004c3d9f94d19bdd34aefc6c40cd4c643657cb0b0f6d76f0fec9b8d2e","sha256:19fb371c053ff9c8a4193b0720d099459b56dada4a8d3612cfd5cf52e24d59eb"],"state_sha256":"ed379fe234d358714a3e5c39460deb7d7c31a2328e2040814e331d8600c49673"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JU3nOHAMIK3SryCE6h9ud4QPc3/AzXCizyUmfnaMuyoMP+azkNUcltOTSuw9SGz/a8m+0GJOyX7jzfXn/jnRDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T10:09:12.162347Z","bundle_sha256":"135e4ea422acdb1a7ccc8064721aa3e569f6c5e9190cda8b06f2d491698ffdb9"}}