{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:5RYJ3FASBJYLMZHUMMOLCPDF3Q","short_pith_number":"pith:5RYJ3FAS","canonical_record":{"source":{"id":"2409.10873","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-09-17T03:58:18Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"e17a8607c25693147f73af047208bd0ab006d31462b50c69e307ece9322c2cae","abstract_canon_sha256":"b0a0013167aaf1ed721d8cb99e5babadd2b8c732ac82601e5774eb4209883998"},"schema_version":"1.0"},"canonical_sha256":"ec709d94120a70b664f4631cb13c65dc00aacd1d5ba141e019e1e9b7d2cfead2","source":{"kind":"arxiv","id":"2409.10873","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.10873","created_at":"2026-07-05T09:07:58Z"},{"alias_kind":"arxiv_version","alias_value":"2409.10873v1","created_at":"2026-07-05T09:07:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.10873","created_at":"2026-07-05T09:07:58Z"},{"alias_kind":"pith_short_12","alias_value":"5RYJ3FASBJYL","created_at":"2026-07-05T09:07:58Z"},{"alias_kind":"pith_short_16","alias_value":"5RYJ3FASBJYLMZHU","created_at":"2026-07-05T09:07:58Z"},{"alias_kind":"pith_short_8","alias_value":"5RYJ3FAS","created_at":"2026-07-05T09:07:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:5RYJ3FASBJYLMZHUMMOLCPDF3Q","target":"record","payload":{"canonical_record":{"source":{"id":"2409.10873","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-09-17T03:58:18Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"e17a8607c25693147f73af047208bd0ab006d31462b50c69e307ece9322c2cae","abstract_canon_sha256":"b0a0013167aaf1ed721d8cb99e5babadd2b8c732ac82601e5774eb4209883998"},"schema_version":"1.0"},"canonical_sha256":"ec709d94120a70b664f4631cb13c65dc00aacd1d5ba141e019e1e9b7d2cfead2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:07:58.324809Z","signature_b64":"aL38slr2a8f0j6AH1UepY+RPVh+xzRmcYyDzqcsRJoOyARAyeLvX1lzr0v9ysiQMJB8eEw92EVyhNYrpEZPVCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ec709d94120a70b664f4631cb13c65dc00aacd1d5ba141e019e1e9b7d2cfead2","last_reissued_at":"2026-07-05T09:07:58.324284Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:07:58.324284Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2409.10873","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":"2026-07-05T09:07:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+n20YIcAfKfR2k3Y3sU0QC9sew7sL0A86pSp79w2QZao5ovF8P4KvUfWxfBggQ7WIWnXxcHxXSggCUaHiHmdDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T20:27:35.612927Z"},"content_sha256":"9e0a835dd2daad0e803d22990174150274af5bce318ce6f413e7ee24e8184cf1","schema_version":"1.0","event_id":"sha256:9e0a835dd2daad0e803d22990174150274af5bce318ce6f413e7ee24e8184cf1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:5RYJ3FASBJYLMZHUMMOLCPDF3Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spectral localization estimates for abstract linear Schr\\\"odinger equations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.AP","authors_text":"Jingxuan Zhang","submitted_at":"2024-09-17T03:58:18Z","abstract_excerpt":"We study the propagation properties of abstract linear Schr\\\"odinger equations of the form $i\\partial_t\\psi = H_0\\psi+V(t)\\psi$, where $H_0$ is a self-adjoint operator and $V(t)$ a time-dependent potential. We present explicit sufficient conditions ensuring that if the initial state $\\psi_0$ has spectral support in $(-\\infty,0]$ with respect to a reference self-adjoint operator $\\phi$, then, for some $c>0$ independent of $\\psi_0$ and all $t\\ne0$, the solution $\\psi_t$ remains spectrally supported in $(-\\infty,c|t|]$ with respect to $\\phi$, up to an $O(|t|^{-n})$ remainder in norm. The main con"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.10873","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/2409.10873/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":"2026-07-05T09:07:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MgH8j6X3yEebAMyuRQcV012TBCUveYpHa723mifE74WgPMtoiGJZlV9NMMDE4r4y23/Hvr4d1QDjzHL3BxrMAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T20:27:35.613457Z"},"content_sha256":"4fcf446f5522df9272e07444cdc13bbd649016b24398b2bbd3edea7b2000beca","schema_version":"1.0","event_id":"sha256:4fcf446f5522df9272e07444cdc13bbd649016b24398b2bbd3edea7b2000beca"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5RYJ3FASBJYLMZHUMMOLCPDF3Q/bundle.json","state_url":"https://pith.science/pith/5RYJ3FASBJYLMZHUMMOLCPDF3Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5RYJ3FASBJYLMZHUMMOLCPDF3Q/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":"2026-08-15T20:27:35Z","links":{"resolver":"https://pith.science/pith/5RYJ3FASBJYLMZHUMMOLCPDF3Q","bundle":"https://pith.science/pith/5RYJ3FASBJYLMZHUMMOLCPDF3Q/bundle.json","state":"https://pith.science/pith/5RYJ3FASBJYLMZHUMMOLCPDF3Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5RYJ3FASBJYLMZHUMMOLCPDF3Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:5RYJ3FASBJYLMZHUMMOLCPDF3Q","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":"b0a0013167aaf1ed721d8cb99e5babadd2b8c732ac82601e5774eb4209883998","cross_cats_sorted":["math.DS"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-09-17T03:58:18Z","title_canon_sha256":"e17a8607c25693147f73af047208bd0ab006d31462b50c69e307ece9322c2cae"},"schema_version":"1.0","source":{"id":"2409.10873","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.10873","created_at":"2026-07-05T09:07:58Z"},{"alias_kind":"arxiv_version","alias_value":"2409.10873v1","created_at":"2026-07-05T09:07:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.10873","created_at":"2026-07-05T09:07:58Z"},{"alias_kind":"pith_short_12","alias_value":"5RYJ3FASBJYL","created_at":"2026-07-05T09:07:58Z"},{"alias_kind":"pith_short_16","alias_value":"5RYJ3FASBJYLMZHU","created_at":"2026-07-05T09:07:58Z"},{"alias_kind":"pith_short_8","alias_value":"5RYJ3FAS","created_at":"2026-07-05T09:07:58Z"}],"graph_snapshots":[{"event_id":"sha256:4fcf446f5522df9272e07444cdc13bbd649016b24398b2bbd3edea7b2000beca","target":"graph","created_at":"2026-07-05T09:07:58Z","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/2409.10873/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the propagation properties of abstract linear Schr\\\"odinger equations of the form $i\\partial_t\\psi = H_0\\psi+V(t)\\psi$, where $H_0$ is a self-adjoint operator and $V(t)$ a time-dependent potential. We present explicit sufficient conditions ensuring that if the initial state $\\psi_0$ has spectral support in $(-\\infty,0]$ with respect to a reference self-adjoint operator $\\phi$, then, for some $c>0$ independent of $\\psi_0$ and all $t\\ne0$, the solution $\\psi_t$ remains spectrally supported in $(-\\infty,c|t|]$ with respect to $\\phi$, up to an $O(|t|^{-n})$ remainder in norm. The main con","authors_text":"Jingxuan Zhang","cross_cats":["math.DS"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-09-17T03:58:18Z","title":"Spectral localization estimates for abstract linear Schr\\\"odinger equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.10873","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":"sha256:9e0a835dd2daad0e803d22990174150274af5bce318ce6f413e7ee24e8184cf1","target":"record","created_at":"2026-07-05T09:07:58Z","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":"b0a0013167aaf1ed721d8cb99e5babadd2b8c732ac82601e5774eb4209883998","cross_cats_sorted":["math.DS"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-09-17T03:58:18Z","title_canon_sha256":"e17a8607c25693147f73af047208bd0ab006d31462b50c69e307ece9322c2cae"},"schema_version":"1.0","source":{"id":"2409.10873","kind":"arxiv","version":1}},"canonical_sha256":"ec709d94120a70b664f4631cb13c65dc00aacd1d5ba141e019e1e9b7d2cfead2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ec709d94120a70b664f4631cb13c65dc00aacd1d5ba141e019e1e9b7d2cfead2","first_computed_at":"2026-07-05T09:07:58.324284Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:07:58.324284Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aL38slr2a8f0j6AH1UepY+RPVh+xzRmcYyDzqcsRJoOyARAyeLvX1lzr0v9ysiQMJB8eEw92EVyhNYrpEZPVCA==","signature_status":"signed_v1","signed_at":"2026-07-05T09:07:58.324809Z","signed_message":"canonical_sha256_bytes"},"source_id":"2409.10873","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9e0a835dd2daad0e803d22990174150274af5bce318ce6f413e7ee24e8184cf1","sha256:4fcf446f5522df9272e07444cdc13bbd649016b24398b2bbd3edea7b2000beca"],"state_sha256":"a528839e9edaa65c896d7b3d7e57ab6987f13c75fe1b58029cab6cfd667ac61a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2amrvuQDzNHGRGsOVhY4cDbxsgir6H8gHrMeEjEGviksTrSri+vRc79DjF/YHXMxmpSy/MbHmPnP8NNk+DgXDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T20:27:35.618542Z","bundle_sha256":"b3228168c2b03fe9e24cdf8c819e714feebd735f2c910225177f40a0b74a951e"}}