{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:E3TEPWWBVRCSOAFPGZ76ZGVBG2","short_pith_number":"pith:E3TEPWWB","canonical_record":{"source":{"id":"2110.08356","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2021-10-15T20:37:36Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"5960233b3e8b3b438d069cb91b0189831732878adf88241817fb6a1dc1759f6a","abstract_canon_sha256":"d0c27c0c340eb7305599031c2bce9438fdd8f92928b30a2bec2daf92ff46b34f"},"schema_version":"1.0"},"canonical_sha256":"26e647dac1ac452700af367fec9aa1369ff40b51b2c6efab5596f213673093c9","source":{"kind":"arxiv","id":"2110.08356","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2110.08356","created_at":"2026-07-05T04:38:45Z"},{"alias_kind":"arxiv_version","alias_value":"2110.08356v3","created_at":"2026-07-05T04:38:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.08356","created_at":"2026-07-05T04:38:45Z"},{"alias_kind":"pith_short_12","alias_value":"E3TEPWWBVRCS","created_at":"2026-07-05T04:38:45Z"},{"alias_kind":"pith_short_16","alias_value":"E3TEPWWBVRCSOAFP","created_at":"2026-07-05T04:38:45Z"},{"alias_kind":"pith_short_8","alias_value":"E3TEPWWB","created_at":"2026-07-05T04:38:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:E3TEPWWBVRCSOAFPGZ76ZGVBG2","target":"record","payload":{"canonical_record":{"source":{"id":"2110.08356","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2021-10-15T20:37:36Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"5960233b3e8b3b438d069cb91b0189831732878adf88241817fb6a1dc1759f6a","abstract_canon_sha256":"d0c27c0c340eb7305599031c2bce9438fdd8f92928b30a2bec2daf92ff46b34f"},"schema_version":"1.0"},"canonical_sha256":"26e647dac1ac452700af367fec9aa1369ff40b51b2c6efab5596f213673093c9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:38:45.409981Z","signature_b64":"82fjkJy5Xu90FJRQkGcFRlBN2fFJTGLZxFMioMftWbgibjQLfbhiQNuIMlWGAu1SGKgHk4jLyDbfzdgJgUAJDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"26e647dac1ac452700af367fec9aa1369ff40b51b2c6efab5596f213673093c9","last_reissued_at":"2026-07-05T04:38:45.409451Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:38:45.409451Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2110.08356","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":"2026-07-05T04:38:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r0N9AxohQJ/FSqAxsf7vMy1ELegfnjHl+sLpgiT669wRSsgkj5DZYpvS9wSsd7w1PXanQQoSxElIj2vVD3BXBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T19:36:05.077522Z"},"content_sha256":"aca18aabc367a374c10f7e50232d9b41f6566a34a6e287b96ab341a6df92487d","schema_version":"1.0","event_id":"sha256:aca18aabc367a374c10f7e50232d9b41f6566a34a6e287b96ab341a6df92487d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:E3TEPWWBVRCSOAFPGZ76ZGVBG2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Operator Complexity for Quantum Scalar Fields and Cosmological Perturbations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"hep-th","authors_text":"Bret Underwood, Chandan Jana, S. Shajidul Haque","submitted_at":"2021-10-15T20:37:36Z","abstract_excerpt":"We calculate the operator complexity for the displacement, squeeze and rotation operators of a quantum harmonic oscillator. The complexity of the time-dependent displacement operator is constant, equal to the magnitude of the coherent state parameter, while the complexity of unitary evolution by a generic quadratic Hamiltonian is proportional to the amount of squeezing and is sensitive to the time-dependent phase of the unitary operator. We apply these results to study the complexity of a free massive scalar field, finding that the complexity has a period of rapid linear growth followed by a s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.08356","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2110.08356/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":"2026-07-05T04:38:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GuRDzU0UKTIOf2qRzpSEcvees938WBMYLgjfFgcPrx8o7jBuSPRywErz7Cr4gsj9bvy6kPFo66+rrMw1/fXtCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T19:36:05.078138Z"},"content_sha256":"e5ee95225a29e7de90b712ea928dab366c6a462009b7cf7fe74c0a03860c6246","schema_version":"1.0","event_id":"sha256:e5ee95225a29e7de90b712ea928dab366c6a462009b7cf7fe74c0a03860c6246"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/E3TEPWWBVRCSOAFPGZ76ZGVBG2/bundle.json","state_url":"https://pith.science/pith/E3TEPWWBVRCSOAFPGZ76ZGVBG2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/E3TEPWWBVRCSOAFPGZ76ZGVBG2/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":"2026-08-08T19:36:05Z","links":{"resolver":"https://pith.science/pith/E3TEPWWBVRCSOAFPGZ76ZGVBG2","bundle":"https://pith.science/pith/E3TEPWWBVRCSOAFPGZ76ZGVBG2/bundle.json","state":"https://pith.science/pith/E3TEPWWBVRCSOAFPGZ76ZGVBG2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/E3TEPWWBVRCSOAFPGZ76ZGVBG2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:E3TEPWWBVRCSOAFPGZ76ZGVBG2","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":"d0c27c0c340eb7305599031c2bce9438fdd8f92928b30a2bec2daf92ff46b34f","cross_cats_sorted":["quant-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2021-10-15T20:37:36Z","title_canon_sha256":"5960233b3e8b3b438d069cb91b0189831732878adf88241817fb6a1dc1759f6a"},"schema_version":"1.0","source":{"id":"2110.08356","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2110.08356","created_at":"2026-07-05T04:38:45Z"},{"alias_kind":"arxiv_version","alias_value":"2110.08356v3","created_at":"2026-07-05T04:38:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.08356","created_at":"2026-07-05T04:38:45Z"},{"alias_kind":"pith_short_12","alias_value":"E3TEPWWBVRCS","created_at":"2026-07-05T04:38:45Z"},{"alias_kind":"pith_short_16","alias_value":"E3TEPWWBVRCSOAFP","created_at":"2026-07-05T04:38:45Z"},{"alias_kind":"pith_short_8","alias_value":"E3TEPWWB","created_at":"2026-07-05T04:38:45Z"}],"graph_snapshots":[{"event_id":"sha256:e5ee95225a29e7de90b712ea928dab366c6a462009b7cf7fe74c0a03860c6246","target":"graph","created_at":"2026-07-05T04:38:45Z","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/2110.08356/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We calculate the operator complexity for the displacement, squeeze and rotation operators of a quantum harmonic oscillator. The complexity of the time-dependent displacement operator is constant, equal to the magnitude of the coherent state parameter, while the complexity of unitary evolution by a generic quadratic Hamiltonian is proportional to the amount of squeezing and is sensitive to the time-dependent phase of the unitary operator. We apply these results to study the complexity of a free massive scalar field, finding that the complexity has a period of rapid linear growth followed by a s","authors_text":"Bret Underwood, Chandan Jana, S. Shajidul Haque","cross_cats":["quant-ph"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2021-10-15T20:37:36Z","title":"Operator Complexity for Quantum Scalar Fields and Cosmological Perturbations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.08356","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:aca18aabc367a374c10f7e50232d9b41f6566a34a6e287b96ab341a6df92487d","target":"record","created_at":"2026-07-05T04:38:45Z","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":"d0c27c0c340eb7305599031c2bce9438fdd8f92928b30a2bec2daf92ff46b34f","cross_cats_sorted":["quant-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2021-10-15T20:37:36Z","title_canon_sha256":"5960233b3e8b3b438d069cb91b0189831732878adf88241817fb6a1dc1759f6a"},"schema_version":"1.0","source":{"id":"2110.08356","kind":"arxiv","version":3}},"canonical_sha256":"26e647dac1ac452700af367fec9aa1369ff40b51b2c6efab5596f213673093c9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"26e647dac1ac452700af367fec9aa1369ff40b51b2c6efab5596f213673093c9","first_computed_at":"2026-07-05T04:38:45.409451Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:38:45.409451Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"82fjkJy5Xu90FJRQkGcFRlBN2fFJTGLZxFMioMftWbgibjQLfbhiQNuIMlWGAu1SGKgHk4jLyDbfzdgJgUAJDA==","signature_status":"signed_v1","signed_at":"2026-07-05T04:38:45.409981Z","signed_message":"canonical_sha256_bytes"},"source_id":"2110.08356","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aca18aabc367a374c10f7e50232d9b41f6566a34a6e287b96ab341a6df92487d","sha256:e5ee95225a29e7de90b712ea928dab366c6a462009b7cf7fe74c0a03860c6246"],"state_sha256":"7776aac14d4878637d3af48a4ede45f69838d42b37bb78e65988f60ee0e470a5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G1fBOyNvufStf8Y4W6XpoUsteboZFJNc4ufXPPHHRzM9hLVc9YK1i99CM2zsAQI0/IzLkYcqnMBetc2E3NZ7CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T19:36:05.083916Z","bundle_sha256":"032db227c10c735917e796c7e75394a2b8558dad1626f617c7b697515bd8f1f0"}}