{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:NI6C4H4XDJHIBUOIXQMK7UUY7O","short_pith_number":"pith:NI6C4H4X","canonical_record":{"source":{"id":"1807.09799","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2018-07-25T18:01:21Z","cross_cats_sorted":["cond-mat.stat-mech","cond-mat.str-el","quant-ph"],"title_canon_sha256":"97ee9e559a73befee6515ffbf2c7d7c06ac43e205d580cd204b3e0573acd6d37","abstract_canon_sha256":"a997342e18235e1c3acca2b7ab0331374a479da50c77da62547b54712fe52413"},"schema_version":"1.0"},"canonical_sha256":"6a3c2e1f971a4e80d1c8bc18afd298fb923b527f3f763c71e07abc7cf90db137","source":{"kind":"arxiv","id":"1807.09799","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.09799","created_at":"2026-05-18T00:00:39Z"},{"alias_kind":"arxiv_version","alias_value":"1807.09799v3","created_at":"2026-05-18T00:00:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.09799","created_at":"2026-05-18T00:00:39Z"},{"alias_kind":"pith_short_12","alias_value":"NI6C4H4XDJHI","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"NI6C4H4XDJHIBUOI","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"NI6C4H4X","created_at":"2026-05-18T12:32:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:NI6C4H4XDJHIBUOIXQMK7UUY7O","target":"record","payload":{"canonical_record":{"source":{"id":"1807.09799","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2018-07-25T18:01:21Z","cross_cats_sorted":["cond-mat.stat-mech","cond-mat.str-el","quant-ph"],"title_canon_sha256":"97ee9e559a73befee6515ffbf2c7d7c06ac43e205d580cd204b3e0573acd6d37","abstract_canon_sha256":"a997342e18235e1c3acca2b7ab0331374a479da50c77da62547b54712fe52413"},"schema_version":"1.0"},"canonical_sha256":"6a3c2e1f971a4e80d1c8bc18afd298fb923b527f3f763c71e07abc7cf90db137","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:00:39.370625Z","signature_b64":"r2/km8gzDqPf+NqTV5lVWvbsVx4lFXGvNFui/l8sYKrTikPv6ds5mlHxvj28slCUp99OZyBl9DnSSB53d4heCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6a3c2e1f971a4e80d1c8bc18afd298fb923b527f3f763c71e07abc7cf90db137","last_reissued_at":"2026-05-18T00:00:39.370083Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:00:39.370083Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1807.09799","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":"2026-05-18T00:00:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M2d730/G9NtjKvzCfqkzEuq4/VC96T44NjjvFd/OaMwKAMfGbaMEAULcMxoP88h1EHc+lfkpWCsf6dokee6NDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-23T12:45:24.568250Z"},"content_sha256":"8a5e6add8e0840c91eed7cc9d6badd3580523a192ef6e2f04759033af3563daa","schema_version":"1.0","event_id":"sha256:8a5e6add8e0840c91eed7cc9d6badd3580523a192ef6e2f04759033af3563daa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:NI6C4H4XDJHIBUOIXQMK7UUY7O","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nonlinear sigma model approach to many-body quantum chaos: Regularized and unregularized out-of-time-ordered correlators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","cond-mat.str-el","quant-ph"],"primary_cat":"cond-mat.dis-nn","authors_text":"Victor Galitski, Yunxiang Liao","submitted_at":"2018-07-25T18:01:21Z","abstract_excerpt":"The out-of-time-ordered correlators (OTOCs) have been proposed and widely used recently as a tool to define and describe many-body quantum chaos. Here, we develop the Keldysh non-linear sigma model technique to calculate these correlators in interacting disordered metals. In particular, we focus on the regularized and unregularized OTOCs, defined as $Tr[\\sqrt{\\rho} A(t) \\sqrt{\\rho} A^\\dagger(t)]$ and $Tr[\\rho A(t)A^\\dagger(t)]$ respectively (where $A(t)$ is the anti-commutator of fermion field operators and $\\rho$ is the thermal density matrix). The calculation of the rate of OTOCs' exponentia"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.09799","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":"2026-05-18T00:00:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1VO8IlK7aHWEK1C2rbk5Qkmxb1GQ+IWnGykTtWP/bqAmrBT+rTJu/XNbDGSKZ20n1w+4s4i7yi0E4iyEI3ZVAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-23T12:45:24.568703Z"},"content_sha256":"2740f7b8eb5b08c9435772eccdcc81148e6ddc8374423b1c48eefcea5293aca3","schema_version":"1.0","event_id":"sha256:2740f7b8eb5b08c9435772eccdcc81148e6ddc8374423b1c48eefcea5293aca3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NI6C4H4XDJHIBUOIXQMK7UUY7O/bundle.json","state_url":"https://pith.science/pith/NI6C4H4XDJHIBUOIXQMK7UUY7O/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NI6C4H4XDJHIBUOIXQMK7UUY7O/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":"2026-08-23T12:45:24Z","links":{"resolver":"https://pith.science/pith/NI6C4H4XDJHIBUOIXQMK7UUY7O","bundle":"https://pith.science/pith/NI6C4H4XDJHIBUOIXQMK7UUY7O/bundle.json","state":"https://pith.science/pith/NI6C4H4XDJHIBUOIXQMK7UUY7O/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NI6C4H4XDJHIBUOIXQMK7UUY7O/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:NI6C4H4XDJHIBUOIXQMK7UUY7O","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":"a997342e18235e1c3acca2b7ab0331374a479da50c77da62547b54712fe52413","cross_cats_sorted":["cond-mat.stat-mech","cond-mat.str-el","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2018-07-25T18:01:21Z","title_canon_sha256":"97ee9e559a73befee6515ffbf2c7d7c06ac43e205d580cd204b3e0573acd6d37"},"schema_version":"1.0","source":{"id":"1807.09799","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.09799","created_at":"2026-05-18T00:00:39Z"},{"alias_kind":"arxiv_version","alias_value":"1807.09799v3","created_at":"2026-05-18T00:00:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.09799","created_at":"2026-05-18T00:00:39Z"},{"alias_kind":"pith_short_12","alias_value":"NI6C4H4XDJHI","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"NI6C4H4XDJHIBUOI","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"NI6C4H4X","created_at":"2026-05-18T12:32:40Z"}],"graph_snapshots":[{"event_id":"sha256:2740f7b8eb5b08c9435772eccdcc81148e6ddc8374423b1c48eefcea5293aca3","target":"graph","created_at":"2026-05-18T00:00:39Z","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":"The out-of-time-ordered correlators (OTOCs) have been proposed and widely used recently as a tool to define and describe many-body quantum chaos. Here, we develop the Keldysh non-linear sigma model technique to calculate these correlators in interacting disordered metals. In particular, we focus on the regularized and unregularized OTOCs, defined as $Tr[\\sqrt{\\rho} A(t) \\sqrt{\\rho} A^\\dagger(t)]$ and $Tr[\\rho A(t)A^\\dagger(t)]$ respectively (where $A(t)$ is the anti-commutator of fermion field operators and $\\rho$ is the thermal density matrix). The calculation of the rate of OTOCs' exponentia","authors_text":"Victor Galitski, Yunxiang Liao","cross_cats":["cond-mat.stat-mech","cond-mat.str-el","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2018-07-25T18:01:21Z","title":"Nonlinear sigma model approach to many-body quantum chaos: Regularized and unregularized out-of-time-ordered correlators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.09799","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":"sha256:8a5e6add8e0840c91eed7cc9d6badd3580523a192ef6e2f04759033af3563daa","target":"record","created_at":"2026-05-18T00:00:39Z","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":"a997342e18235e1c3acca2b7ab0331374a479da50c77da62547b54712fe52413","cross_cats_sorted":["cond-mat.stat-mech","cond-mat.str-el","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2018-07-25T18:01:21Z","title_canon_sha256":"97ee9e559a73befee6515ffbf2c7d7c06ac43e205d580cd204b3e0573acd6d37"},"schema_version":"1.0","source":{"id":"1807.09799","kind":"arxiv","version":3}},"canonical_sha256":"6a3c2e1f971a4e80d1c8bc18afd298fb923b527f3f763c71e07abc7cf90db137","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6a3c2e1f971a4e80d1c8bc18afd298fb923b527f3f763c71e07abc7cf90db137","first_computed_at":"2026-05-18T00:00:39.370083Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:00:39.370083Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"r2/km8gzDqPf+NqTV5lVWvbsVx4lFXGvNFui/l8sYKrTikPv6ds5mlHxvj28slCUp99OZyBl9DnSSB53d4heCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:00:39.370625Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.09799","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8a5e6add8e0840c91eed7cc9d6badd3580523a192ef6e2f04759033af3563daa","sha256:2740f7b8eb5b08c9435772eccdcc81148e6ddc8374423b1c48eefcea5293aca3"],"state_sha256":"2f6dc8f94f5ea9b5fe10c689f6f9330625c92454c72aa3d8d800bca8794be8ea"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KRP4oN40Mx6rfdg09IDeEPoIK2q/J0uGcbLl++PR1Y5VRNwPfdOE7vD5em6Uou5UQfhyewrS8TbuNvxwdJO5Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-23T12:45:24.573121Z","bundle_sha256":"2f3179640623482b8a26d917015c3244543cc7eb04ddcf9872ab5285c28d6fb9"}}