{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:TMUJWX7CWPVIJO353KUPZOKUTC","short_pith_number":"pith:TMUJWX7C","canonical_record":{"source":{"id":"2607.09408","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2026-07-10T13:42:33Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"54c83ca614e207feedb8d68a0a4681b7b5b2fa0fb37d46f87d4a75c4390d1c4c","abstract_canon_sha256":"29e6c0f3aef8d36a297a0bc9cbb8da56101ae0525ad4795d94044e2770a9290f"},"schema_version":"1.0"},"canonical_sha256":"9b289b5fe2b3ea84bb7ddaa8fcb9549897e6250abffc1a99c50feaa54b330f90","source":{"kind":"arxiv","id":"2607.09408","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.09408","created_at":"2026-07-13T01:19:11Z"},{"alias_kind":"arxiv_version","alias_value":"2607.09408v1","created_at":"2026-07-13T01:19:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.09408","created_at":"2026-07-13T01:19:11Z"},{"alias_kind":"pith_short_12","alias_value":"TMUJWX7CWPVI","created_at":"2026-07-13T01:19:11Z"},{"alias_kind":"pith_short_16","alias_value":"TMUJWX7CWPVIJO35","created_at":"2026-07-13T01:19:11Z"},{"alias_kind":"pith_short_8","alias_value":"TMUJWX7C","created_at":"2026-07-13T01:19:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:TMUJWX7CWPVIJO353KUPZOKUTC","target":"record","payload":{"canonical_record":{"source":{"id":"2607.09408","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2026-07-10T13:42:33Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"54c83ca614e207feedb8d68a0a4681b7b5b2fa0fb37d46f87d4a75c4390d1c4c","abstract_canon_sha256":"29e6c0f3aef8d36a297a0bc9cbb8da56101ae0525ad4795d94044e2770a9290f"},"schema_version":"1.0"},"canonical_sha256":"9b289b5fe2b3ea84bb7ddaa8fcb9549897e6250abffc1a99c50feaa54b330f90","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-13T01:19:11.034998Z","signature_b64":"rhRWFoS5vCpWZPF5zNK3iVRWIE859y1NJMzOGdHosf+sSUOKPPl+wOXAPF3wgN/FrmT1Uz9iofjcnhxP2vWkDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9b289b5fe2b3ea84bb7ddaa8fcb9549897e6250abffc1a99c50feaa54b330f90","last_reissued_at":"2026-07-13T01:19:11.033917Z","signature_status":"signed_v1","first_computed_at":"2026-07-13T01:19:11.033917Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.09408","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":"2026-07-13T01:19:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E1tNJiq74Wsz6K2HUUSbCjknCIv9GB4zS52uWmmBpmmDZo++v5faqEsitq/ETgRle2q6MA9+4AWC/7Zry4e4Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T08:57:55.888326Z"},"content_sha256":"43f622a74f48e095db9106e55099624c9e2430e9f33be554d622dc2c1b2de26d","schema_version":"1.0","event_id":"sha256:43f622a74f48e095db9106e55099624c9e2430e9f33be554d622dc2c1b2de26d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:TMUJWX7CWPVIJO353KUPZOKUTC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Circuit and Krylov complexity of primordial perturbations of modified gravity in inflation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["gr-qc"],"primary_cat":"hep-th","authors_text":"Hai-Bing Fu, Tao Li","submitted_at":"2026-07-10T13:42:33Z","abstract_excerpt":"In this work, we investigate quantum complexity diagnostics of primordial curvature perturbations within the inflationary paradigm. We compare canonical scalar-field inflation with the modified gravity model $f(\\phi,R)$, focusing on the evolution of the two-mode squeezed state generated by the coupling between the $\\vec{k}$ and $-\\vec{k}$ momentum sectors. Starting from the quadratic action for curvature perturbations, we derive the evolution equations for the squeezed strength $r_k$ and squeezed angle $\\phi_k$, utilizing them to evaluate both circuit complexity and Krylov-space diagnostics. S"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.09408","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/2607.09408/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":"2026-07-13T01:19:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6MCxaxPI9GBTMS1e4FUOQKD9IdxFtzNtJh5ITYY7t5EMyIBh2baMUY4LS/t6XbKNb0/6a4hIFjSTidfk9xHODA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T08:57:55.888834Z"},"content_sha256":"331cd15e0b14f671bb75f3bff9d87ebc2f6243378d5f5b0987a437234acf9913","schema_version":"1.0","event_id":"sha256:331cd15e0b14f671bb75f3bff9d87ebc2f6243378d5f5b0987a437234acf9913"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TMUJWX7CWPVIJO353KUPZOKUTC/bundle.json","state_url":"https://pith.science/pith/TMUJWX7CWPVIJO353KUPZOKUTC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TMUJWX7CWPVIJO353KUPZOKUTC/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":"2026-08-15T08:57:55Z","links":{"resolver":"https://pith.science/pith/TMUJWX7CWPVIJO353KUPZOKUTC","bundle":"https://pith.science/pith/TMUJWX7CWPVIJO353KUPZOKUTC/bundle.json","state":"https://pith.science/pith/TMUJWX7CWPVIJO353KUPZOKUTC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TMUJWX7CWPVIJO353KUPZOKUTC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:TMUJWX7CWPVIJO353KUPZOKUTC","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":"29e6c0f3aef8d36a297a0bc9cbb8da56101ae0525ad4795d94044e2770a9290f","cross_cats_sorted":["gr-qc"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2026-07-10T13:42:33Z","title_canon_sha256":"54c83ca614e207feedb8d68a0a4681b7b5b2fa0fb37d46f87d4a75c4390d1c4c"},"schema_version":"1.0","source":{"id":"2607.09408","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.09408","created_at":"2026-07-13T01:19:11Z"},{"alias_kind":"arxiv_version","alias_value":"2607.09408v1","created_at":"2026-07-13T01:19:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.09408","created_at":"2026-07-13T01:19:11Z"},{"alias_kind":"pith_short_12","alias_value":"TMUJWX7CWPVI","created_at":"2026-07-13T01:19:11Z"},{"alias_kind":"pith_short_16","alias_value":"TMUJWX7CWPVIJO35","created_at":"2026-07-13T01:19:11Z"},{"alias_kind":"pith_short_8","alias_value":"TMUJWX7C","created_at":"2026-07-13T01:19:11Z"}],"graph_snapshots":[{"event_id":"sha256:331cd15e0b14f671bb75f3bff9d87ebc2f6243378d5f5b0987a437234acf9913","target":"graph","created_at":"2026-07-13T01:19:11Z","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/2607.09408/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this work, we investigate quantum complexity diagnostics of primordial curvature perturbations within the inflationary paradigm. We compare canonical scalar-field inflation with the modified gravity model $f(\\phi,R)$, focusing on the evolution of the two-mode squeezed state generated by the coupling between the $\\vec{k}$ and $-\\vec{k}$ momentum sectors. Starting from the quadratic action for curvature perturbations, we derive the evolution equations for the squeezed strength $r_k$ and squeezed angle $\\phi_k$, utilizing them to evaluate both circuit complexity and Krylov-space diagnostics. S","authors_text":"Hai-Bing Fu, Tao Li","cross_cats":["gr-qc"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2026-07-10T13:42:33Z","title":"Circuit and Krylov complexity of primordial perturbations of modified gravity in inflation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.09408","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":"sha256:43f622a74f48e095db9106e55099624c9e2430e9f33be554d622dc2c1b2de26d","target":"record","created_at":"2026-07-13T01:19:11Z","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":"29e6c0f3aef8d36a297a0bc9cbb8da56101ae0525ad4795d94044e2770a9290f","cross_cats_sorted":["gr-qc"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2026-07-10T13:42:33Z","title_canon_sha256":"54c83ca614e207feedb8d68a0a4681b7b5b2fa0fb37d46f87d4a75c4390d1c4c"},"schema_version":"1.0","source":{"id":"2607.09408","kind":"arxiv","version":1}},"canonical_sha256":"9b289b5fe2b3ea84bb7ddaa8fcb9549897e6250abffc1a99c50feaa54b330f90","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9b289b5fe2b3ea84bb7ddaa8fcb9549897e6250abffc1a99c50feaa54b330f90","first_computed_at":"2026-07-13T01:19:11.033917Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-13T01:19:11.033917Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rhRWFoS5vCpWZPF5zNK3iVRWIE859y1NJMzOGdHosf+sSUOKPPl+wOXAPF3wgN/FrmT1Uz9iofjcnhxP2vWkDA==","signature_status":"signed_v1","signed_at":"2026-07-13T01:19:11.034998Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.09408","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:43f622a74f48e095db9106e55099624c9e2430e9f33be554d622dc2c1b2de26d","sha256:331cd15e0b14f671bb75f3bff9d87ebc2f6243378d5f5b0987a437234acf9913"],"state_sha256":"d3a8d2ae0f8526c07372c4669193e5d818a3f2336e68855be86d3cf1dae81156"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GPPaA9fN6QrfY8Ct4O1N4iQh2IQG9cCFF6W/ZeYQQlb4Rgh4U/+g9N25VJLxlB/AGqtGn3F/KjngvhVI1Y/cCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T08:57:55.894513Z","bundle_sha256":"6795b753d02e81115dd44c229777136e1186e933fe35b4f1627ed4c8d45c8699"}}