{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:GSYKFPEH5HAFYH3JDAXJQROU63","short_pith_number":"pith:GSYKFPEH","canonical_record":{"source":{"id":"1911.09672","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2019-11-21T18:57:32Z","cross_cats_sorted":["hep-th","quant-ph"],"title_canon_sha256":"75b4f2e6c1863bde11383a029ce81717f1b3cb01ba14e3b7bb2ac43491ce710f","abstract_canon_sha256":"882113d7bb3816f8f5dfc79bab295ffa8ee9727c6c069c4d7529ca53965e4e6f"},"schema_version":"1.0"},"canonical_sha256":"34b0a2bc87e9c05c1f69182e9845d4f6eccd4d28d7e6491d9adc5237c8f0940a","source":{"kind":"arxiv","id":"1911.09672","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1911.09672","created_at":"2026-07-05T01:52:15Z"},{"alias_kind":"arxiv_version","alias_value":"1911.09672v2","created_at":"2026-07-05T01:52:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1911.09672","created_at":"2026-07-05T01:52:15Z"},{"alias_kind":"pith_short_12","alias_value":"GSYKFPEH5HAF","created_at":"2026-07-05T01:52:15Z"},{"alias_kind":"pith_short_16","alias_value":"GSYKFPEH5HAFYH3J","created_at":"2026-07-05T01:52:15Z"},{"alias_kind":"pith_short_8","alias_value":"GSYKFPEH","created_at":"2026-07-05T01:52:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:GSYKFPEH5HAFYH3JDAXJQROU63","target":"record","payload":{"canonical_record":{"source":{"id":"1911.09672","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2019-11-21T18:57:32Z","cross_cats_sorted":["hep-th","quant-ph"],"title_canon_sha256":"75b4f2e6c1863bde11383a029ce81717f1b3cb01ba14e3b7bb2ac43491ce710f","abstract_canon_sha256":"882113d7bb3816f8f5dfc79bab295ffa8ee9727c6c069c4d7529ca53965e4e6f"},"schema_version":"1.0"},"canonical_sha256":"34b0a2bc87e9c05c1f69182e9845d4f6eccd4d28d7e6491d9adc5237c8f0940a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:52:15.408453Z","signature_b64":"83mtBoVM/gsWdgj3u2CjQfL15GJZfhKS2v4++EonuHYQwJnuFqcbiXk5P25RvL1JsmoJSY+79ONQIelVcLX5AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"34b0a2bc87e9c05c1f69182e9845d4f6eccd4d28d7e6491d9adc5237c8f0940a","last_reissued_at":"2026-07-05T01:52:15.408018Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:52:15.408018Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1911.09672","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":"2026-07-05T01:52:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0cGjRN1kuzEIuPSI6N+RbPGQa+0JWI5qz/clHv+yr4xCDWpnhWUMxoVgMoss371JFJL4fq4Mrl6mFj30UwSpCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T12:14:28.287772Z"},"content_sha256":"686f2cce7fb0802f35c92822fee83bb9fbeafe607e8b513369494480f3e93214","schema_version":"1.0","event_id":"sha256:686f2cce7fb0802f35c92822fee83bb9fbeafe607e8b513369494480f3e93214"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:GSYKFPEH5HAFYH3JDAXJQROU63","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Euclidean operator growth and quantum chaos","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","quant-ph"],"primary_cat":"cond-mat.stat-mech","authors_text":"Alexander Avdoshkin, Anatoly Dymarsky","submitted_at":"2019-11-21T18:57:32Z","abstract_excerpt":"We consider growth of local operators under Euclidean time evolution in lattice systems with local interactions. We derive rigorous bounds on the operator norm growth and then proceed to establish an analog of the Lieb-Robinson bound for the spatial growth. In contrast to the Minkowski case when ballistic spreading of operators is universal, in the Euclidean case spatial growth is system-dependent and indicates if the system is integrable or chaotic. In the integrable case, the Euclidean spatial growth is at most polynomial. In the chaotic case, it is the fastest possible: exponential in 1D, w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1911.09672","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1911.09672/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":"2026-07-05T01:52:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r7DLXmMhDdOzi7bjEpq3uwkZoyfoE9iTdGjvge3SRbRJefs6iLmBK6j6Np2HvwmABzBL+EoZjaCf0FKKEirnBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T12:14:28.288473Z"},"content_sha256":"273c2c642e9cb633b632176fa6bf8241283255f118d27339f2043231803ac2ea","schema_version":"1.0","event_id":"sha256:273c2c642e9cb633b632176fa6bf8241283255f118d27339f2043231803ac2ea"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GSYKFPEH5HAFYH3JDAXJQROU63/bundle.json","state_url":"https://pith.science/pith/GSYKFPEH5HAFYH3JDAXJQROU63/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GSYKFPEH5HAFYH3JDAXJQROU63/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":"2026-07-05T12:14:28Z","links":{"resolver":"https://pith.science/pith/GSYKFPEH5HAFYH3JDAXJQROU63","bundle":"https://pith.science/pith/GSYKFPEH5HAFYH3JDAXJQROU63/bundle.json","state":"https://pith.science/pith/GSYKFPEH5HAFYH3JDAXJQROU63/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GSYKFPEH5HAFYH3JDAXJQROU63/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:GSYKFPEH5HAFYH3JDAXJQROU63","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":"882113d7bb3816f8f5dfc79bab295ffa8ee9727c6c069c4d7529ca53965e4e6f","cross_cats_sorted":["hep-th","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2019-11-21T18:57:32Z","title_canon_sha256":"75b4f2e6c1863bde11383a029ce81717f1b3cb01ba14e3b7bb2ac43491ce710f"},"schema_version":"1.0","source":{"id":"1911.09672","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1911.09672","created_at":"2026-07-05T01:52:15Z"},{"alias_kind":"arxiv_version","alias_value":"1911.09672v2","created_at":"2026-07-05T01:52:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1911.09672","created_at":"2026-07-05T01:52:15Z"},{"alias_kind":"pith_short_12","alias_value":"GSYKFPEH5HAF","created_at":"2026-07-05T01:52:15Z"},{"alias_kind":"pith_short_16","alias_value":"GSYKFPEH5HAFYH3J","created_at":"2026-07-05T01:52:15Z"},{"alias_kind":"pith_short_8","alias_value":"GSYKFPEH","created_at":"2026-07-05T01:52:15Z"}],"graph_snapshots":[{"event_id":"sha256:273c2c642e9cb633b632176fa6bf8241283255f118d27339f2043231803ac2ea","target":"graph","created_at":"2026-07-05T01:52:15Z","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/1911.09672/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider growth of local operators under Euclidean time evolution in lattice systems with local interactions. We derive rigorous bounds on the operator norm growth and then proceed to establish an analog of the Lieb-Robinson bound for the spatial growth. In contrast to the Minkowski case when ballistic spreading of operators is universal, in the Euclidean case spatial growth is system-dependent and indicates if the system is integrable or chaotic. In the integrable case, the Euclidean spatial growth is at most polynomial. In the chaotic case, it is the fastest possible: exponential in 1D, w","authors_text":"Alexander Avdoshkin, Anatoly Dymarsky","cross_cats":["hep-th","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2019-11-21T18:57:32Z","title":"Euclidean operator growth and quantum chaos"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1911.09672","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":"sha256:686f2cce7fb0802f35c92822fee83bb9fbeafe607e8b513369494480f3e93214","target":"record","created_at":"2026-07-05T01:52:15Z","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":"882113d7bb3816f8f5dfc79bab295ffa8ee9727c6c069c4d7529ca53965e4e6f","cross_cats_sorted":["hep-th","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2019-11-21T18:57:32Z","title_canon_sha256":"75b4f2e6c1863bde11383a029ce81717f1b3cb01ba14e3b7bb2ac43491ce710f"},"schema_version":"1.0","source":{"id":"1911.09672","kind":"arxiv","version":2}},"canonical_sha256":"34b0a2bc87e9c05c1f69182e9845d4f6eccd4d28d7e6491d9adc5237c8f0940a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"34b0a2bc87e9c05c1f69182e9845d4f6eccd4d28d7e6491d9adc5237c8f0940a","first_computed_at":"2026-07-05T01:52:15.408018Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:52:15.408018Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"83mtBoVM/gsWdgj3u2CjQfL15GJZfhKS2v4++EonuHYQwJnuFqcbiXk5P25RvL1JsmoJSY+79ONQIelVcLX5AQ==","signature_status":"signed_v1","signed_at":"2026-07-05T01:52:15.408453Z","signed_message":"canonical_sha256_bytes"},"source_id":"1911.09672","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:686f2cce7fb0802f35c92822fee83bb9fbeafe607e8b513369494480f3e93214","sha256:273c2c642e9cb633b632176fa6bf8241283255f118d27339f2043231803ac2ea"],"state_sha256":"66fe21a2f2589f2a53ede4ab43060bb6e6cf28a7235ebb9bfe0b99f1a7bc1b9c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tyMEjXo8Lppdeo4PCh8oEho/dOVh69B+wJqiE53X0UjV479CUzf7pBT+N5j/7YQaYWLS09CjsmP4kf539qtJCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-05T12:14:28.291795Z","bundle_sha256":"171e80e0a834c46411b82e6a53db7406826240a800c84ca4d8085a90c9d2044a"}}