{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:VXVUYGQIULV2252GKC32OGOJXO","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":"41bcf9845f62fe9ad14f72b0e5c54675354ac28315bc0c9c4edf5f904ae758c9","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2020-08-26T07:52:34Z","title_canon_sha256":"c23d4e00741b2bb9b7ce5ee51c158d2955b3ac52b69a239cee87e50f2f2375b4"},"schema_version":"1.0","source":{"id":"2008.11429","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2008.11429","created_at":"2026-07-05T03:55:24Z"},{"alias_kind":"arxiv_version","alias_value":"2008.11429v2","created_at":"2026-07-05T03:55:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2008.11429","created_at":"2026-07-05T03:55:24Z"},{"alias_kind":"pith_short_12","alias_value":"VXVUYGQIULV2","created_at":"2026-07-05T03:55:24Z"},{"alias_kind":"pith_short_16","alias_value":"VXVUYGQIULV2252G","created_at":"2026-07-05T03:55:24Z"},{"alias_kind":"pith_short_8","alias_value":"VXVUYGQI","created_at":"2026-07-05T03:55:24Z"}],"graph_snapshots":[{"event_id":"sha256:7303c703d6b35f219faf359c674c271261f5a8a0d9e1fc5586d3840aaaeea5bf","target":"graph","created_at":"2026-07-05T03:55:24Z","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/2008.11429/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider the explicit asymptotic profile of massless Dirac fields on a Schwarzschild background. First, we prove for the spin $s=\\pm \\frac{1}{2}$ components of the Dirac field a uniform bound of a positive definite energy and an integrated local energy decay estimate from a symmetric hyperbolic wave system. Based on these estimates, we further show that these components have globally pointwise decay $fv^{-3/2-s}\\tau^{-5/2+s}$ as both an upper and a lower bound outside the black hole, with function $f$ finite and explicitly expressed in terms of the initial data and the coordinates. This est","authors_text":"Lin Zhang, Siyuan Ma","cross_cats":["gr-qc","math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2020-08-26T07:52:34Z","title":"Sharp decay estimates for massless Dirac fields on a Schwarzschild background"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2008.11429","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":"sha256:7a4a83aa3de6aed0135a3f1393451a6e2f2e6591180bcf48af614e171dd670e5","target":"record","created_at":"2026-07-05T03:55:24Z","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":"41bcf9845f62fe9ad14f72b0e5c54675354ac28315bc0c9c4edf5f904ae758c9","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2020-08-26T07:52:34Z","title_canon_sha256":"c23d4e00741b2bb9b7ce5ee51c158d2955b3ac52b69a239cee87e50f2f2375b4"},"schema_version":"1.0","source":{"id":"2008.11429","kind":"arxiv","version":2}},"canonical_sha256":"adeb4c1a08a2ebad774650b7a719c9bbaf79d754f503fcb582f538701788a440","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"adeb4c1a08a2ebad774650b7a719c9bbaf79d754f503fcb582f538701788a440","first_computed_at":"2026-07-05T03:55:24.779295Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:55:24.779295Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NsVU0E2NOTDw2sfaEznt4vQX7e2vFPysDarbO+xQmgWslRx/mkP9MR3zYYPj0kRVcINHV3OlaISTnYQdrDwtCg==","signature_status":"signed_v1","signed_at":"2026-07-05T03:55:24.779782Z","signed_message":"canonical_sha256_bytes"},"source_id":"2008.11429","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7a4a83aa3de6aed0135a3f1393451a6e2f2e6591180bcf48af614e171dd670e5","sha256:7303c703d6b35f219faf359c674c271261f5a8a0d9e1fc5586d3840aaaeea5bf"],"state_sha256":"9c28f06d5c7c0778cefbdb20e2d83c293b2efbc9b7b3db81bab5cebc6cc85a2b"}