{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:D2IPH7BCLG2HHD3WW2UPJ6HRZY","short_pith_number":"pith:D2IPH7BC","canonical_record":{"source":{"id":"2008.01085","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2020-08-03T18:00:01Z","cross_cats_sorted":["cond-mat.quant-gas","quant-ph"],"title_canon_sha256":"95439104349b3e9401d1dceec563301d58f713bd495dcba35ae7e8b09afacc8e","abstract_canon_sha256":"54f59e29c6e15b11768d2613f33c89d388d5209bbf64451fe7f735f859137653"},"schema_version":"1.0"},"canonical_sha256":"1e90f3fc2259b4738f76b6a8f4f8f1ce1529f63c7c709b7b7d47c11a1a3864f2","source":{"kind":"arxiv","id":"2008.01085","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2008.01085","created_at":"2026-07-05T01:57:19Z"},{"alias_kind":"arxiv_version","alias_value":"2008.01085v2","created_at":"2026-07-05T01:57:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2008.01085","created_at":"2026-07-05T01:57:19Z"},{"alias_kind":"pith_short_12","alias_value":"D2IPH7BCLG2H","created_at":"2026-07-05T01:57:19Z"},{"alias_kind":"pith_short_16","alias_value":"D2IPH7BCLG2HHD3W","created_at":"2026-07-05T01:57:19Z"},{"alias_kind":"pith_short_8","alias_value":"D2IPH7BC","created_at":"2026-07-05T01:57:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:D2IPH7BCLG2HHD3WW2UPJ6HRZY","target":"record","payload":{"canonical_record":{"source":{"id":"2008.01085","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2020-08-03T18:00:01Z","cross_cats_sorted":["cond-mat.quant-gas","quant-ph"],"title_canon_sha256":"95439104349b3e9401d1dceec563301d58f713bd495dcba35ae7e8b09afacc8e","abstract_canon_sha256":"54f59e29c6e15b11768d2613f33c89d388d5209bbf64451fe7f735f859137653"},"schema_version":"1.0"},"canonical_sha256":"1e90f3fc2259b4738f76b6a8f4f8f1ce1529f63c7c709b7b7d47c11a1a3864f2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:57:19.097504Z","signature_b64":"FhEXtcCLLfrpE/RnU2AOaAoBuuKGlfF8zR9exfvBLE78265eE5zoYzKpJNVST6xb+aevx5OOzbg9C9wqokM+BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1e90f3fc2259b4738f76b6a8f4f8f1ce1529f63c7c709b7b7d47c11a1a3864f2","last_reissued_at":"2026-07-05T01:57:19.097067Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:57:19.097067Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2008.01085","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":"2026-07-05T01:57:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KHe26hGTAf8esXSI6I36lZrRtRqcTs6rK8jfGppmrDiI4lKTe8Rsqhtg7PKolDH9QO7c0jRyq/wGARspWqojDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T21:49:09.292863Z"},"content_sha256":"8afcb50b2071c729f95650a2481f3bb7cbc9c16e11c7ad6daa80c09acd0472e1","schema_version":"1.0","event_id":"sha256:8afcb50b2071c729f95650a2481f3bb7cbc9c16e11c7ad6daa80c09acd0472e1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:D2IPH7BCLG2HHD3WW2UPJ6HRZY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Eigenstate thermalization for observables that break Hamiltonian symmetries and its counterpart in interacting integrable systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.quant-gas","quant-ph"],"primary_cat":"cond-mat.stat-mech","authors_text":"Marcos Rigol, Tyler LeBlond","submitted_at":"2020-08-03T18:00:01Z","abstract_excerpt":"We study the off-diagonal matrix elements of observables that break the translational symmetry of a spin-chain Hamiltonian, and as such connect energy eigenstates from different total quasimomentum sectors. We consider quantum-chaotic and interacting integrable points of the Hamiltonian, and focus on average energies at the center of the spectrum. In the quantum-chaotic model, we find that there is eigenstate thermalization; specifically, the matrix elements are Gaussian distributed with a variance that is a smooth function of $\\omega=E_{\\alpha}-E_{\\beta}$ ({$E_{\\alpha}$} are the eigenenergies"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2008.01085","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/2008.01085/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":"2026-07-05T01:57:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Flzz3kNCKzZ8E/WtXZ1S7r4D1yeGosqwCRqdohISTU1jsjy5O3LSbmA7/G6vWgevyx4qgF18F3zsEMKvGII6Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T21:49:09.293237Z"},"content_sha256":"0f8d27107f4eb7357b50fc4d841a2755b937a171dfc7b6b003fcfa14963c129c","schema_version":"1.0","event_id":"sha256:0f8d27107f4eb7357b50fc4d841a2755b937a171dfc7b6b003fcfa14963c129c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D2IPH7BCLG2HHD3WW2UPJ6HRZY/bundle.json","state_url":"https://pith.science/pith/D2IPH7BCLG2HHD3WW2UPJ6HRZY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D2IPH7BCLG2HHD3WW2UPJ6HRZY/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":"2026-07-06T21:49:09Z","links":{"resolver":"https://pith.science/pith/D2IPH7BCLG2HHD3WW2UPJ6HRZY","bundle":"https://pith.science/pith/D2IPH7BCLG2HHD3WW2UPJ6HRZY/bundle.json","state":"https://pith.science/pith/D2IPH7BCLG2HHD3WW2UPJ6HRZY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D2IPH7BCLG2HHD3WW2UPJ6HRZY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:D2IPH7BCLG2HHD3WW2UPJ6HRZY","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":"54f59e29c6e15b11768d2613f33c89d388d5209bbf64451fe7f735f859137653","cross_cats_sorted":["cond-mat.quant-gas","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2020-08-03T18:00:01Z","title_canon_sha256":"95439104349b3e9401d1dceec563301d58f713bd495dcba35ae7e8b09afacc8e"},"schema_version":"1.0","source":{"id":"2008.01085","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2008.01085","created_at":"2026-07-05T01:57:19Z"},{"alias_kind":"arxiv_version","alias_value":"2008.01085v2","created_at":"2026-07-05T01:57:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2008.01085","created_at":"2026-07-05T01:57:19Z"},{"alias_kind":"pith_short_12","alias_value":"D2IPH7BCLG2H","created_at":"2026-07-05T01:57:19Z"},{"alias_kind":"pith_short_16","alias_value":"D2IPH7BCLG2HHD3W","created_at":"2026-07-05T01:57:19Z"},{"alias_kind":"pith_short_8","alias_value":"D2IPH7BC","created_at":"2026-07-05T01:57:19Z"}],"graph_snapshots":[{"event_id":"sha256:0f8d27107f4eb7357b50fc4d841a2755b937a171dfc7b6b003fcfa14963c129c","target":"graph","created_at":"2026-07-05T01:57:19Z","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/2008.01085/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the off-diagonal matrix elements of observables that break the translational symmetry of a spin-chain Hamiltonian, and as such connect energy eigenstates from different total quasimomentum sectors. We consider quantum-chaotic and interacting integrable points of the Hamiltonian, and focus on average energies at the center of the spectrum. In the quantum-chaotic model, we find that there is eigenstate thermalization; specifically, the matrix elements are Gaussian distributed with a variance that is a smooth function of $\\omega=E_{\\alpha}-E_{\\beta}$ ({$E_{\\alpha}$} are the eigenenergies","authors_text":"Marcos Rigol, Tyler LeBlond","cross_cats":["cond-mat.quant-gas","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2020-08-03T18:00:01Z","title":"Eigenstate thermalization for observables that break Hamiltonian symmetries and its counterpart in interacting integrable systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2008.01085","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":"sha256:8afcb50b2071c729f95650a2481f3bb7cbc9c16e11c7ad6daa80c09acd0472e1","target":"record","created_at":"2026-07-05T01:57:19Z","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":"54f59e29c6e15b11768d2613f33c89d388d5209bbf64451fe7f735f859137653","cross_cats_sorted":["cond-mat.quant-gas","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2020-08-03T18:00:01Z","title_canon_sha256":"95439104349b3e9401d1dceec563301d58f713bd495dcba35ae7e8b09afacc8e"},"schema_version":"1.0","source":{"id":"2008.01085","kind":"arxiv","version":2}},"canonical_sha256":"1e90f3fc2259b4738f76b6a8f4f8f1ce1529f63c7c709b7b7d47c11a1a3864f2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1e90f3fc2259b4738f76b6a8f4f8f1ce1529f63c7c709b7b7d47c11a1a3864f2","first_computed_at":"2026-07-05T01:57:19.097067Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:57:19.097067Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FhEXtcCLLfrpE/RnU2AOaAoBuuKGlfF8zR9exfvBLE78265eE5zoYzKpJNVST6xb+aevx5OOzbg9C9wqokM+BA==","signature_status":"signed_v1","signed_at":"2026-07-05T01:57:19.097504Z","signed_message":"canonical_sha256_bytes"},"source_id":"2008.01085","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8afcb50b2071c729f95650a2481f3bb7cbc9c16e11c7ad6daa80c09acd0472e1","sha256:0f8d27107f4eb7357b50fc4d841a2755b937a171dfc7b6b003fcfa14963c129c"],"state_sha256":"ec28c8bd5f5a6574831180b7c78c3968b46dcd16c657a225de03ce3638f08fb7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Lft+ILvyFLmAPFSmyJN3zqo1l4o4HEi2702AdRCa8NrcgQrU/km3n9SscP8h7uUNyJhjMDH+8HjISqXCv4K+CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T21:49:09.295258Z","bundle_sha256":"4e4674ac870fe4f34f7cae20ccf1cf0e80971bd840e178cb86a43a538f1144b8"}}