{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:Y2BOJMOK6T3AT6HU2LOFU2UIBG","short_pith_number":"pith:Y2BOJMOK","canonical_record":{"source":{"id":"2309.01313","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AP","submitted_at":"2023-09-04T02:02:05Z","cross_cats_sorted":[],"title_canon_sha256":"1a95befaafc987050053a345ec74b3de164fc286f2cd47e7d34a0dcffda88044","abstract_canon_sha256":"a19c7d67d4379e5c55de43574ea043cd6f1b483a363a2adcf437db035372d60e"},"schema_version":"1.0"},"canonical_sha256":"c682e4b1caf4f609f8f4d2dc5a6a8809a6af856d98f5091d9e2d52e810b61ec7","source":{"kind":"arxiv","id":"2309.01313","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2309.01313","created_at":"2026-07-05T07:41:42Z"},{"alias_kind":"arxiv_version","alias_value":"2309.01313v2","created_at":"2026-07-05T07:41:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2309.01313","created_at":"2026-07-05T07:41:42Z"},{"alias_kind":"pith_short_12","alias_value":"Y2BOJMOK6T3A","created_at":"2026-07-05T07:41:42Z"},{"alias_kind":"pith_short_16","alias_value":"Y2BOJMOK6T3AT6HU","created_at":"2026-07-05T07:41:42Z"},{"alias_kind":"pith_short_8","alias_value":"Y2BOJMOK","created_at":"2026-07-05T07:41:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:Y2BOJMOK6T3AT6HU2LOFU2UIBG","target":"record","payload":{"canonical_record":{"source":{"id":"2309.01313","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AP","submitted_at":"2023-09-04T02:02:05Z","cross_cats_sorted":[],"title_canon_sha256":"1a95befaafc987050053a345ec74b3de164fc286f2cd47e7d34a0dcffda88044","abstract_canon_sha256":"a19c7d67d4379e5c55de43574ea043cd6f1b483a363a2adcf437db035372d60e"},"schema_version":"1.0"},"canonical_sha256":"c682e4b1caf4f609f8f4d2dc5a6a8809a6af856d98f5091d9e2d52e810b61ec7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:41:42.395008Z","signature_b64":"P/vYBqhsSKLnGbJG7midp0Xy4UEQzCG8maaGxfdSiBEctMx+eCiQLy6+HLhFspVASWXjBXWaihOpnl82bjdZCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c682e4b1caf4f609f8f4d2dc5a6a8809a6af856d98f5091d9e2d52e810b61ec7","last_reissued_at":"2026-07-05T07:41:42.394491Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:41:42.394491Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2309.01313","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":"2026-07-05T07:41:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XexR/QDRDGPUwka5h8IwGqbYuVujiQt0nTqHuKcj4CYhvkCD/BwenrLTwNoBs7yxuz/QBA8atcRiz4AEFSIEAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T21:12:21.446736Z"},"content_sha256":"33f5468be732f2e73ff93ae38f9812d98c1b564ae23faa6a3553b19d49750be6","schema_version":"1.0","event_id":"sha256:33f5468be732f2e73ff93ae38f9812d98c1b564ae23faa6a3553b19d49750be6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:Y2BOJMOK6T3AT6HU2LOFU2UIBG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Pointwise decay for radial solutions of the Schr\\\"odinger equation with a repulsive Coulomb potential","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Adam Black, Bruno Vergara, Ebru Toprak, Jiahua Zou","submitted_at":"2023-09-04T02:02:05Z","abstract_excerpt":"We study the long-time behavior of solutions to the Schr\\\"odinger equation with a repulsive Coulomb potential on $\\mathbb{R}^3$ for spherically symmetric initial data. Our approach involves computing the distorted Fourier transform of the action of the associated Hamiltonian $H=-\\Delta+\\frac{q}{|x|}$ on radial data $f$, which allows us to explicitly write the evolution $e^{itH}f$. A comprehensive analysis of the kernel is then used to establish that, for large times, $\\|e^{i t H}f\\|_{L^{\\infty}} \\leq C t^{-\\frac{3}{2}}\\|f\\|_{L^1}$. Our analysis of the distorted Fourier transform is expected to"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.01313","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/2309.01313/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":"2026-07-05T07:41:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V2hGvtwOxlhG7mNGobCBGrCuKORtAfF9a5WTj8xXcBuY/ImxlFoIAvXhldbKIMXFcJXTOP1OmRVrJzTKItHhDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T21:12:21.447108Z"},"content_sha256":"51d4a35958c426daaf95a1ae7980668d82b6036e74b1917a9b06cf40a21159a3","schema_version":"1.0","event_id":"sha256:51d4a35958c426daaf95a1ae7980668d82b6036e74b1917a9b06cf40a21159a3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Y2BOJMOK6T3AT6HU2LOFU2UIBG/bundle.json","state_url":"https://pith.science/pith/Y2BOJMOK6T3AT6HU2LOFU2UIBG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Y2BOJMOK6T3AT6HU2LOFU2UIBG/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":"2026-07-06T21:12:21Z","links":{"resolver":"https://pith.science/pith/Y2BOJMOK6T3AT6HU2LOFU2UIBG","bundle":"https://pith.science/pith/Y2BOJMOK6T3AT6HU2LOFU2UIBG/bundle.json","state":"https://pith.science/pith/Y2BOJMOK6T3AT6HU2LOFU2UIBG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Y2BOJMOK6T3AT6HU2LOFU2UIBG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:Y2BOJMOK6T3AT6HU2LOFU2UIBG","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":"a19c7d67d4379e5c55de43574ea043cd6f1b483a363a2adcf437db035372d60e","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AP","submitted_at":"2023-09-04T02:02:05Z","title_canon_sha256":"1a95befaafc987050053a345ec74b3de164fc286f2cd47e7d34a0dcffda88044"},"schema_version":"1.0","source":{"id":"2309.01313","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2309.01313","created_at":"2026-07-05T07:41:42Z"},{"alias_kind":"arxiv_version","alias_value":"2309.01313v2","created_at":"2026-07-05T07:41:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2309.01313","created_at":"2026-07-05T07:41:42Z"},{"alias_kind":"pith_short_12","alias_value":"Y2BOJMOK6T3A","created_at":"2026-07-05T07:41:42Z"},{"alias_kind":"pith_short_16","alias_value":"Y2BOJMOK6T3AT6HU","created_at":"2026-07-05T07:41:42Z"},{"alias_kind":"pith_short_8","alias_value":"Y2BOJMOK","created_at":"2026-07-05T07:41:42Z"}],"graph_snapshots":[{"event_id":"sha256:51d4a35958c426daaf95a1ae7980668d82b6036e74b1917a9b06cf40a21159a3","target":"graph","created_at":"2026-07-05T07:41:42Z","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/2309.01313/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the long-time behavior of solutions to the Schr\\\"odinger equation with a repulsive Coulomb potential on $\\mathbb{R}^3$ for spherically symmetric initial data. Our approach involves computing the distorted Fourier transform of the action of the associated Hamiltonian $H=-\\Delta+\\frac{q}{|x|}$ on radial data $f$, which allows us to explicitly write the evolution $e^{itH}f$. A comprehensive analysis of the kernel is then used to establish that, for large times, $\\|e^{i t H}f\\|_{L^{\\infty}} \\leq C t^{-\\frac{3}{2}}\\|f\\|_{L^1}$. Our analysis of the distorted Fourier transform is expected to","authors_text":"Adam Black, Bruno Vergara, Ebru Toprak, Jiahua Zou","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AP","submitted_at":"2023-09-04T02:02:05Z","title":"Pointwise decay for radial solutions of the Schr\\\"odinger equation with a repulsive Coulomb potential"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.01313","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":"sha256:33f5468be732f2e73ff93ae38f9812d98c1b564ae23faa6a3553b19d49750be6","target":"record","created_at":"2026-07-05T07:41:42Z","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":"a19c7d67d4379e5c55de43574ea043cd6f1b483a363a2adcf437db035372d60e","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AP","submitted_at":"2023-09-04T02:02:05Z","title_canon_sha256":"1a95befaafc987050053a345ec74b3de164fc286f2cd47e7d34a0dcffda88044"},"schema_version":"1.0","source":{"id":"2309.01313","kind":"arxiv","version":2}},"canonical_sha256":"c682e4b1caf4f609f8f4d2dc5a6a8809a6af856d98f5091d9e2d52e810b61ec7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c682e4b1caf4f609f8f4d2dc5a6a8809a6af856d98f5091d9e2d52e810b61ec7","first_computed_at":"2026-07-05T07:41:42.394491Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:41:42.394491Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"P/vYBqhsSKLnGbJG7midp0Xy4UEQzCG8maaGxfdSiBEctMx+eCiQLy6+HLhFspVASWXjBXWaihOpnl82bjdZCw==","signature_status":"signed_v1","signed_at":"2026-07-05T07:41:42.395008Z","signed_message":"canonical_sha256_bytes"},"source_id":"2309.01313","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:33f5468be732f2e73ff93ae38f9812d98c1b564ae23faa6a3553b19d49750be6","sha256:51d4a35958c426daaf95a1ae7980668d82b6036e74b1917a9b06cf40a21159a3"],"state_sha256":"1cb8cc4865906c47e078c11889ba74bb1e6cacb5c10d31151ac8bb0a84193a44"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SWrudy1rcjAXpWYe+vcSZTtmdkkE6YNrcPiFkosZkz1Kt73qPC+q4l7vW+XtfT/rI8v1enqkXlUuAZUP1YjlCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T21:12:21.449689Z","bundle_sha256":"9f457bf64684f9ea8cf06b733ec64ae65e5c398995fe77c95e7b960b2e905e5a"}}