{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:O7SKYYH3IRPCMTTXFW76NPJEUZ","short_pith_number":"pith:O7SKYYH3","canonical_record":{"source":{"id":"2512.09689","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2025-12-10T14:36:42Z","cross_cats_sorted":[],"title_canon_sha256":"abcea3253cb21e885f578ff353f1c67de3360e877715f44803c2c756b19289d3","abstract_canon_sha256":"5aa2dcd6ad510107f150977ce9f2eb5dde4cc5bfc032adcfac118444440b84b6"},"schema_version":"1.0"},"canonical_sha256":"77e4ac60fb445e264e772dbfe6bd24a672061446900431df86cb2e46c056f43a","source":{"kind":"arxiv","id":"2512.09689","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2512.09689","created_at":"2026-06-26T01:15:47Z"},{"alias_kind":"arxiv_version","alias_value":"2512.09689v2","created_at":"2026-06-26T01:15:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2512.09689","created_at":"2026-06-26T01:15:47Z"},{"alias_kind":"pith_short_12","alias_value":"O7SKYYH3IRPC","created_at":"2026-06-26T01:15:47Z"},{"alias_kind":"pith_short_16","alias_value":"O7SKYYH3IRPCMTTX","created_at":"2026-06-26T01:15:47Z"},{"alias_kind":"pith_short_8","alias_value":"O7SKYYH3","created_at":"2026-06-26T01:15:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:O7SKYYH3IRPCMTTXFW76NPJEUZ","target":"record","payload":{"canonical_record":{"source":{"id":"2512.09689","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2025-12-10T14:36:42Z","cross_cats_sorted":[],"title_canon_sha256":"abcea3253cb21e885f578ff353f1c67de3360e877715f44803c2c756b19289d3","abstract_canon_sha256":"5aa2dcd6ad510107f150977ce9f2eb5dde4cc5bfc032adcfac118444440b84b6"},"schema_version":"1.0"},"canonical_sha256":"77e4ac60fb445e264e772dbfe6bd24a672061446900431df86cb2e46c056f43a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-26T01:15:47.911351Z","signature_b64":"OUmVRXf7IWC6nQycJYldIk/o8bPkL6YaeI8tAadSp4AQCZZMuinVizY2WDjJdP397BzTV2rDKHjH2663f4AwBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"77e4ac60fb445e264e772dbfe6bd24a672061446900431df86cb2e46c056f43a","last_reissued_at":"2026-06-26T01:15:47.910885Z","signature_status":"signed_v1","first_computed_at":"2026-06-26T01:15:47.910885Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2512.09689","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-26T01:15:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hHXN8WJkA0MHvEJZB+y6kQwK6VT5v8Sbmko9LLXjmfcnKDK6dMPp7I7HMdsmwcuWVdcQdv+KxleXwOslaDjiCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T05:37:55.249303Z"},"content_sha256":"89720325614de789072a2fa88ed2e2ef067f85680085f7ffc5d4c4d41f02c11c","schema_version":"1.0","event_id":"sha256:89720325614de789072a2fa88ed2e2ef067f85680085f7ffc5d4c4d41f02c11c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:O7SKYYH3IRPCMTTXFW76NPJEUZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Regularity and pointwise convergence for dispersive equations on Riemannian symmetric spaces of compact type","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Sanjoy Pusti, Utsav Dewan","submitted_at":"2025-12-10T14:36:42Z","abstract_excerpt":"In this article, we first prove that for general dispersive equations on Riemannian symmetric spaces of compact type $\\mathbb{X}=U/K$, of rank $1$ and $2$ respectively, the Sobolev regularity thresholds for the initial data, $\\alpha >1/2$ and $\\alpha >1$ respectively, are sufficient to obtain pointwise convergence of the solution a.e. on $\\mathbb{X}$. We next focus on $K$-biinvariant initial data for certain special cases of rank $1$, depending on geometric considerations, and prove that the sufficiency of the regularity threshold can be improved down to $\\alpha>1/3$, whereas the phenomenon fa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.09689","kind":"arxiv","version":2},"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/2512.09689/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":"2026-06-26T01:15:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sUAA2Qmyk+W3f8UAa6zWruu621HbQLbxH/1ftvB4Sn8ByOfGNcQA7IaVn0pxtCA5jFqxl85O3WYPQi5pCCeXDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T05:37:55.249716Z"},"content_sha256":"3c36f4ef82407d26af12cabfbe6e3200531fa42ab25b6513aa1c20846630ef44","schema_version":"1.0","event_id":"sha256:3c36f4ef82407d26af12cabfbe6e3200531fa42ab25b6513aa1c20846630ef44"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/O7SKYYH3IRPCMTTXFW76NPJEUZ/bundle.json","state_url":"https://pith.science/pith/O7SKYYH3IRPCMTTXFW76NPJEUZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/O7SKYYH3IRPCMTTXFW76NPJEUZ/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":"2026-07-04T05:37:55Z","links":{"resolver":"https://pith.science/pith/O7SKYYH3IRPCMTTXFW76NPJEUZ","bundle":"https://pith.science/pith/O7SKYYH3IRPCMTTXFW76NPJEUZ/bundle.json","state":"https://pith.science/pith/O7SKYYH3IRPCMTTXFW76NPJEUZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/O7SKYYH3IRPCMTTXFW76NPJEUZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:O7SKYYH3IRPCMTTXFW76NPJEUZ","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":"5aa2dcd6ad510107f150977ce9f2eb5dde4cc5bfc032adcfac118444440b84b6","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2025-12-10T14:36:42Z","title_canon_sha256":"abcea3253cb21e885f578ff353f1c67de3360e877715f44803c2c756b19289d3"},"schema_version":"1.0","source":{"id":"2512.09689","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2512.09689","created_at":"2026-06-26T01:15:47Z"},{"alias_kind":"arxiv_version","alias_value":"2512.09689v2","created_at":"2026-06-26T01:15:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2512.09689","created_at":"2026-06-26T01:15:47Z"},{"alias_kind":"pith_short_12","alias_value":"O7SKYYH3IRPC","created_at":"2026-06-26T01:15:47Z"},{"alias_kind":"pith_short_16","alias_value":"O7SKYYH3IRPCMTTX","created_at":"2026-06-26T01:15:47Z"},{"alias_kind":"pith_short_8","alias_value":"O7SKYYH3","created_at":"2026-06-26T01:15:47Z"}],"graph_snapshots":[{"event_id":"sha256:3c36f4ef82407d26af12cabfbe6e3200531fa42ab25b6513aa1c20846630ef44","target":"graph","created_at":"2026-06-26T01:15:47Z","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/2512.09689/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this article, we first prove that for general dispersive equations on Riemannian symmetric spaces of compact type $\\mathbb{X}=U/K$, of rank $1$ and $2$ respectively, the Sobolev regularity thresholds for the initial data, $\\alpha >1/2$ and $\\alpha >1$ respectively, are sufficient to obtain pointwise convergence of the solution a.e. on $\\mathbb{X}$. We next focus on $K$-biinvariant initial data for certain special cases of rank $1$, depending on geometric considerations, and prove that the sufficiency of the regularity threshold can be improved down to $\\alpha>1/3$, whereas the phenomenon fa","authors_text":"Sanjoy Pusti, Utsav Dewan","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2025-12-10T14:36:42Z","title":"Regularity and pointwise convergence for dispersive equations on Riemannian symmetric spaces of compact type"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.09689","kind":"arxiv","version":2},"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":"sha256:89720325614de789072a2fa88ed2e2ef067f85680085f7ffc5d4c4d41f02c11c","target":"record","created_at":"2026-06-26T01:15:47Z","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":"5aa2dcd6ad510107f150977ce9f2eb5dde4cc5bfc032adcfac118444440b84b6","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2025-12-10T14:36:42Z","title_canon_sha256":"abcea3253cb21e885f578ff353f1c67de3360e877715f44803c2c756b19289d3"},"schema_version":"1.0","source":{"id":"2512.09689","kind":"arxiv","version":2}},"canonical_sha256":"77e4ac60fb445e264e772dbfe6bd24a672061446900431df86cb2e46c056f43a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"77e4ac60fb445e264e772dbfe6bd24a672061446900431df86cb2e46c056f43a","first_computed_at":"2026-06-26T01:15:47.910885Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-26T01:15:47.910885Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OUmVRXf7IWC6nQycJYldIk/o8bPkL6YaeI8tAadSp4AQCZZMuinVizY2WDjJdP397BzTV2rDKHjH2663f4AwBA==","signature_status":"signed_v1","signed_at":"2026-06-26T01:15:47.911351Z","signed_message":"canonical_sha256_bytes"},"source_id":"2512.09689","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:89720325614de789072a2fa88ed2e2ef067f85680085f7ffc5d4c4d41f02c11c","sha256:3c36f4ef82407d26af12cabfbe6e3200531fa42ab25b6513aa1c20846630ef44"],"state_sha256":"1440b5525e06a802b0f17085a4474a4e71e8c2651460561c62809ec135332e40"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NxhiNhAC06ibpQ8eQsxjDN+w7Zfj7P4GE+2Z/QkNTey5QRET5FaszAGJypkLE2pbNtdiQKJjK7Z5nMygo7A+AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-04T05:37:55.252438Z","bundle_sha256":"be593bf6bd2ce7343190957905ec15822ee70a6a278995ba584e89c483c501a8"}}