{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:EFGVE5PSVAMU7ZHZHIW2ZQWSUU","short_pith_number":"pith:EFGVE5PS","canonical_record":{"source":{"id":"2411.06104","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-11-09T07:42:20Z","cross_cats_sorted":[],"title_canon_sha256":"889e6970b8c4eca8e01dc8e823fd87d1d5dc18bd8c5da7e16408a9fe35691703","abstract_canon_sha256":"b25da883620119fb278e7f3fae64161ef4493d3bd7d7b20660d95150dc78d10c"},"schema_version":"1.0"},"canonical_sha256":"214d5275f2a8194fe4f93a2dacc2d2a51a249b102747088d815d552acca4dba2","source":{"kind":"arxiv","id":"2411.06104","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.06104","created_at":"2026-07-05T09:33:17Z"},{"alias_kind":"arxiv_version","alias_value":"2411.06104v1","created_at":"2026-07-05T09:33:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.06104","created_at":"2026-07-05T09:33:17Z"},{"alias_kind":"pith_short_12","alias_value":"EFGVE5PSVAMU","created_at":"2026-07-05T09:33:17Z"},{"alias_kind":"pith_short_16","alias_value":"EFGVE5PSVAMU7ZHZ","created_at":"2026-07-05T09:33:17Z"},{"alias_kind":"pith_short_8","alias_value":"EFGVE5PS","created_at":"2026-07-05T09:33:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:EFGVE5PSVAMU7ZHZHIW2ZQWSUU","target":"record","payload":{"canonical_record":{"source":{"id":"2411.06104","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-11-09T07:42:20Z","cross_cats_sorted":[],"title_canon_sha256":"889e6970b8c4eca8e01dc8e823fd87d1d5dc18bd8c5da7e16408a9fe35691703","abstract_canon_sha256":"b25da883620119fb278e7f3fae64161ef4493d3bd7d7b20660d95150dc78d10c"},"schema_version":"1.0"},"canonical_sha256":"214d5275f2a8194fe4f93a2dacc2d2a51a249b102747088d815d552acca4dba2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:33:17.162292Z","signature_b64":"B4LFwHG6ARygr2SLdrTSSTvHxogt+TyOQkFTWF7IzVwev/vVRpZdLSsOgTVy9J9s0revCmEGcY3F/ZlLGL69BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"214d5275f2a8194fe4f93a2dacc2d2a51a249b102747088d815d552acca4dba2","last_reissued_at":"2026-07-05T09:33:17.161818Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:33:17.161818Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2411.06104","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":"2026-07-05T09:33:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bV+i4VgOzvFSWW1RvhtZVdjQq6rh7Wg2kFJOKpfUGPX3vm+Lo0fvmiVJIQCReZ/xOsa5I3JHuZcV3pXnC6o/Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T23:21:05.830954Z"},"content_sha256":"96d3dc81175f927ee1da4a3c49fbdd67784004409828d845a5395940c6a07fbb","schema_version":"1.0","event_id":"sha256:96d3dc81175f927ee1da4a3c49fbdd67784004409828d845a5395940c6a07fbb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:EFGVE5PSVAMU7ZHZHIW2ZQWSUU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Regularity of Solution of the Schr\\\"odinger Equation on Symmetric Space","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Manali Sajjan, Pratyoosh Kumar","submitted_at":"2024-11-09T07:42:20Z","abstract_excerpt":"In this article, we investigate the behavior of solutions \\( u(x,t) \\) to the fractional Schr\\\"odinger equation on rank symmetric spaces of non-compact type. We proved that as time \\( t \\) approaches $0$, then $u(x,t)$ converges pointwise almost everywhere to the initial radial data \\( f \\), provided that \\( f \\in H^s(\\mathbb{X}) \\) with \\( s > \\frac{1}{2} \\). This result extends Sj\\\"olin's results in this setting."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.06104","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/2411.06104/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":"2026-07-05T09:33:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pIQsHIW9pAxj5j5uX9Y8rvT5euCPpEukXHp1M2rPRpPKC9nI7YjYxEH5N2fHZ9NxJwkYsXZKdUu3OY/q+uvgDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T23:21:05.831469Z"},"content_sha256":"bcac6dbaf434a1fba40041eb1fc07d41b9813d5b14750bb15b2012bf69a09428","schema_version":"1.0","event_id":"sha256:bcac6dbaf434a1fba40041eb1fc07d41b9813d5b14750bb15b2012bf69a09428"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EFGVE5PSVAMU7ZHZHIW2ZQWSUU/bundle.json","state_url":"https://pith.science/pith/EFGVE5PSVAMU7ZHZHIW2ZQWSUU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EFGVE5PSVAMU7ZHZHIW2ZQWSUU/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":"2026-08-19T23:21:05Z","links":{"resolver":"https://pith.science/pith/EFGVE5PSVAMU7ZHZHIW2ZQWSUU","bundle":"https://pith.science/pith/EFGVE5PSVAMU7ZHZHIW2ZQWSUU/bundle.json","state":"https://pith.science/pith/EFGVE5PSVAMU7ZHZHIW2ZQWSUU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EFGVE5PSVAMU7ZHZHIW2ZQWSUU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:EFGVE5PSVAMU7ZHZHIW2ZQWSUU","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":"b25da883620119fb278e7f3fae64161ef4493d3bd7d7b20660d95150dc78d10c","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-11-09T07:42:20Z","title_canon_sha256":"889e6970b8c4eca8e01dc8e823fd87d1d5dc18bd8c5da7e16408a9fe35691703"},"schema_version":"1.0","source":{"id":"2411.06104","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.06104","created_at":"2026-07-05T09:33:17Z"},{"alias_kind":"arxiv_version","alias_value":"2411.06104v1","created_at":"2026-07-05T09:33:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.06104","created_at":"2026-07-05T09:33:17Z"},{"alias_kind":"pith_short_12","alias_value":"EFGVE5PSVAMU","created_at":"2026-07-05T09:33:17Z"},{"alias_kind":"pith_short_16","alias_value":"EFGVE5PSVAMU7ZHZ","created_at":"2026-07-05T09:33:17Z"},{"alias_kind":"pith_short_8","alias_value":"EFGVE5PS","created_at":"2026-07-05T09:33:17Z"}],"graph_snapshots":[{"event_id":"sha256:bcac6dbaf434a1fba40041eb1fc07d41b9813d5b14750bb15b2012bf69a09428","target":"graph","created_at":"2026-07-05T09:33:17Z","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/2411.06104/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this article, we investigate the behavior of solutions \\( u(x,t) \\) to the fractional Schr\\\"odinger equation on rank symmetric spaces of non-compact type. We proved that as time \\( t \\) approaches $0$, then $u(x,t)$ converges pointwise almost everywhere to the initial radial data \\( f \\), provided that \\( f \\in H^s(\\mathbb{X}) \\) with \\( s > \\frac{1}{2} \\). This result extends Sj\\\"olin's results in this setting.","authors_text":"Manali Sajjan, Pratyoosh Kumar","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-11-09T07:42:20Z","title":"Regularity of Solution of the Schr\\\"odinger Equation on Symmetric Space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.06104","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":"sha256:96d3dc81175f927ee1da4a3c49fbdd67784004409828d845a5395940c6a07fbb","target":"record","created_at":"2026-07-05T09:33:17Z","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":"b25da883620119fb278e7f3fae64161ef4493d3bd7d7b20660d95150dc78d10c","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-11-09T07:42:20Z","title_canon_sha256":"889e6970b8c4eca8e01dc8e823fd87d1d5dc18bd8c5da7e16408a9fe35691703"},"schema_version":"1.0","source":{"id":"2411.06104","kind":"arxiv","version":1}},"canonical_sha256":"214d5275f2a8194fe4f93a2dacc2d2a51a249b102747088d815d552acca4dba2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"214d5275f2a8194fe4f93a2dacc2d2a51a249b102747088d815d552acca4dba2","first_computed_at":"2026-07-05T09:33:17.161818Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:33:17.161818Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"B4LFwHG6ARygr2SLdrTSSTvHxogt+TyOQkFTWF7IzVwev/vVRpZdLSsOgTVy9J9s0revCmEGcY3F/ZlLGL69BA==","signature_status":"signed_v1","signed_at":"2026-07-05T09:33:17.162292Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.06104","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:96d3dc81175f927ee1da4a3c49fbdd67784004409828d845a5395940c6a07fbb","sha256:bcac6dbaf434a1fba40041eb1fc07d41b9813d5b14750bb15b2012bf69a09428"],"state_sha256":"f0a236069c529dd8c7dd7e4538918be2ed8471c335b540521575284f635df2ea"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hj/eYg3E95q10o+eHJqhngu/aDuS1ojhdSWN4+aVYsAmh0h1QgfWbhy0FunUpSoV2Nw8/iLj7Q7B8qqu/4e+BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-19T23:21:05.835680Z","bundle_sha256":"5cd20165a5942a29ff1ba69b0c9f1b399ccf9f56e59e9fdd638ae0d6dbb504bc"}}