{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:Z4AEPPZTG5GAFFULUYKROHNXK2","short_pith_number":"pith:Z4AEPPZT","canonical_record":{"source":{"id":"2503.21385","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2025-03-27T11:33:35Z","cross_cats_sorted":["math-ph","math.MP","math.OA","quant-ph"],"title_canon_sha256":"30218fa4f95c6bdb25b1eeac8b79ea0138f5e03e4237f89e41799b389aff70fb","abstract_canon_sha256":"10de747f15ad0de7cc2341b41a8efa37b618388eaf3bda4d3cfbe31b2d73216a"},"schema_version":"1.0"},"canonical_sha256":"cf0047bf33374c02968ba615171db7568c09c386f73bf0e5088ee5addc6cb655","source":{"kind":"arxiv","id":"2503.21385","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.21385","created_at":"2026-07-05T10:40:24Z"},{"alias_kind":"arxiv_version","alias_value":"2503.21385v1","created_at":"2026-07-05T10:40:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.21385","created_at":"2026-07-05T10:40:24Z"},{"alias_kind":"pith_short_12","alias_value":"Z4AEPPZTG5GA","created_at":"2026-07-05T10:40:24Z"},{"alias_kind":"pith_short_16","alias_value":"Z4AEPPZTG5GAFFUL","created_at":"2026-07-05T10:40:24Z"},{"alias_kind":"pith_short_8","alias_value":"Z4AEPPZT","created_at":"2026-07-05T10:40:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:Z4AEPPZTG5GAFFULUYKROHNXK2","target":"record","payload":{"canonical_record":{"source":{"id":"2503.21385","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2025-03-27T11:33:35Z","cross_cats_sorted":["math-ph","math.MP","math.OA","quant-ph"],"title_canon_sha256":"30218fa4f95c6bdb25b1eeac8b79ea0138f5e03e4237f89e41799b389aff70fb","abstract_canon_sha256":"10de747f15ad0de7cc2341b41a8efa37b618388eaf3bda4d3cfbe31b2d73216a"},"schema_version":"1.0"},"canonical_sha256":"cf0047bf33374c02968ba615171db7568c09c386f73bf0e5088ee5addc6cb655","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:40:24.603529Z","signature_b64":"UABcHlhHw6gG0cwb6IZ7a28OwYvOCJ2Mb60DTGch2nLOB8txsocFoBtAzC0DGm1vZYOjsX81wOquh+VTWeUWCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cf0047bf33374c02968ba615171db7568c09c386f73bf0e5088ee5addc6cb655","last_reissued_at":"2026-07-05T10:40:24.602997Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:40:24.602997Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2503.21385","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":"2026-07-05T10:40:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fk0eEUhcWmVN3On4OBg5TeaPq6jGKY49UItOfSDoaX8beNNWAksp8c1zTwgY3WfHPMlJ/06nJBIzx+78xiyvCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T12:23:54.072149Z"},"content_sha256":"31460615616b0a18242a1e1976434b54738ab380b46bced8384c7ae614ba38c6","schema_version":"1.0","event_id":"sha256:31460615616b0a18242a1e1976434b54738ab380b46bced8384c7ae614ba38c6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:Z4AEPPZTG5GAFFULUYKROHNXK2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Modular Time Evolution and the QNEC","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.OA","quant-ph"],"primary_cat":"hep-th","authors_text":"Stefan Hollands","submitted_at":"2025-03-27T11:33:35Z","abstract_excerpt":"We establish an inequality restricting the evolution of states in quantum field theory with respect to the modular flow of a wedge, $\\Delta^{is}$, for large $|s|$. Our bound is related to the quantum null energy condition, QNEC. In one interpretation, it can be seen as providing a ``chaos-bound'' $\\le 2\\pi$ on the Lyapunov exponent with respect to Rindler time, $s$. Mathematically, our inequality is a statement about half-sided modular inclusions of von Neumann algebras."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.21385","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2503.21385/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":"2026-07-05T10:40:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Jk1qYMHrK/8IRqn9n5671EU82Xc4AMaCugDGcbchymgzzsPa8oUDwi7LMha/XvuqBd7IXl8+74N7rEcOzEGsBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T12:23:54.072659Z"},"content_sha256":"d54bfcaf50e2fda6817fcc77fb5dc98dc490a664d6e95ef60a7ddecb413796f7","schema_version":"1.0","event_id":"sha256:d54bfcaf50e2fda6817fcc77fb5dc98dc490a664d6e95ef60a7ddecb413796f7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z4AEPPZTG5GAFFULUYKROHNXK2/bundle.json","state_url":"https://pith.science/pith/Z4AEPPZTG5GAFFULUYKROHNXK2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z4AEPPZTG5GAFFULUYKROHNXK2/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":"2026-08-04T12:23:54Z","links":{"resolver":"https://pith.science/pith/Z4AEPPZTG5GAFFULUYKROHNXK2","bundle":"https://pith.science/pith/Z4AEPPZTG5GAFFULUYKROHNXK2/bundle.json","state":"https://pith.science/pith/Z4AEPPZTG5GAFFULUYKROHNXK2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z4AEPPZTG5GAFFULUYKROHNXK2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:Z4AEPPZTG5GAFFULUYKROHNXK2","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":"10de747f15ad0de7cc2341b41a8efa37b618388eaf3bda4d3cfbe31b2d73216a","cross_cats_sorted":["math-ph","math.MP","math.OA","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2025-03-27T11:33:35Z","title_canon_sha256":"30218fa4f95c6bdb25b1eeac8b79ea0138f5e03e4237f89e41799b389aff70fb"},"schema_version":"1.0","source":{"id":"2503.21385","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.21385","created_at":"2026-07-05T10:40:24Z"},{"alias_kind":"arxiv_version","alias_value":"2503.21385v1","created_at":"2026-07-05T10:40:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.21385","created_at":"2026-07-05T10:40:24Z"},{"alias_kind":"pith_short_12","alias_value":"Z4AEPPZTG5GA","created_at":"2026-07-05T10:40:24Z"},{"alias_kind":"pith_short_16","alias_value":"Z4AEPPZTG5GAFFUL","created_at":"2026-07-05T10:40:24Z"},{"alias_kind":"pith_short_8","alias_value":"Z4AEPPZT","created_at":"2026-07-05T10:40:24Z"}],"graph_snapshots":[{"event_id":"sha256:d54bfcaf50e2fda6817fcc77fb5dc98dc490a664d6e95ef60a7ddecb413796f7","target":"graph","created_at":"2026-07-05T10:40:24Z","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/2503.21385/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We establish an inequality restricting the evolution of states in quantum field theory with respect to the modular flow of a wedge, $\\Delta^{is}$, for large $|s|$. Our bound is related to the quantum null energy condition, QNEC. In one interpretation, it can be seen as providing a ``chaos-bound'' $\\le 2\\pi$ on the Lyapunov exponent with respect to Rindler time, $s$. Mathematically, our inequality is a statement about half-sided modular inclusions of von Neumann algebras.","authors_text":"Stefan Hollands","cross_cats":["math-ph","math.MP","math.OA","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2025-03-27T11:33:35Z","title":"Modular Time Evolution and the QNEC"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.21385","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":"sha256:31460615616b0a18242a1e1976434b54738ab380b46bced8384c7ae614ba38c6","target":"record","created_at":"2026-07-05T10:40:24Z","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":"10de747f15ad0de7cc2341b41a8efa37b618388eaf3bda4d3cfbe31b2d73216a","cross_cats_sorted":["math-ph","math.MP","math.OA","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2025-03-27T11:33:35Z","title_canon_sha256":"30218fa4f95c6bdb25b1eeac8b79ea0138f5e03e4237f89e41799b389aff70fb"},"schema_version":"1.0","source":{"id":"2503.21385","kind":"arxiv","version":1}},"canonical_sha256":"cf0047bf33374c02968ba615171db7568c09c386f73bf0e5088ee5addc6cb655","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cf0047bf33374c02968ba615171db7568c09c386f73bf0e5088ee5addc6cb655","first_computed_at":"2026-07-05T10:40:24.602997Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:40:24.602997Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UABcHlhHw6gG0cwb6IZ7a28OwYvOCJ2Mb60DTGch2nLOB8txsocFoBtAzC0DGm1vZYOjsX81wOquh+VTWeUWCA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:40:24.603529Z","signed_message":"canonical_sha256_bytes"},"source_id":"2503.21385","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:31460615616b0a18242a1e1976434b54738ab380b46bced8384c7ae614ba38c6","sha256:d54bfcaf50e2fda6817fcc77fb5dc98dc490a664d6e95ef60a7ddecb413796f7"],"state_sha256":"03a2266e0d498b1e8c9539f6cb255a447073f2a5adc2b27b0c4e3493673dc8d9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bfUA6XhqbI/Z6Hp+scxwT+3LL3szX9+ncvAUMzAFSUU3rIgZHQYICfx4cpvN1yKPplqyfC/gF91djv/woZllDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T12:23:54.076505Z","bundle_sha256":"d68bbbfe4a7e1a970febd5162f8cdf4396520dbc20efbee31cc305e89ded89b5"}}