{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:VXVUYGQIULV2252GKC32OGOJXO","short_pith_number":"pith:VXVUYGQI","canonical_record":{"source":{"id":"2008.11429","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2020-08-26T07:52:34Z","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"title_canon_sha256":"c23d4e00741b2bb9b7ce5ee51c158d2955b3ac52b69a239cee87e50f2f2375b4","abstract_canon_sha256":"41bcf9845f62fe9ad14f72b0e5c54675354ac28315bc0c9c4edf5f904ae758c9"},"schema_version":"1.0"},"canonical_sha256":"adeb4c1a08a2ebad774650b7a719c9bbaf79d754f503fcb582f538701788a440","source":{"kind":"arxiv","id":"2008.11429","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:VXVUYGQIULV2252GKC32OGOJXO","target":"record","payload":{"canonical_record":{"source":{"id":"2008.11429","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2020-08-26T07:52:34Z","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"title_canon_sha256":"c23d4e00741b2bb9b7ce5ee51c158d2955b3ac52b69a239cee87e50f2f2375b4","abstract_canon_sha256":"41bcf9845f62fe9ad14f72b0e5c54675354ac28315bc0c9c4edf5f904ae758c9"},"schema_version":"1.0"},"canonical_sha256":"adeb4c1a08a2ebad774650b7a719c9bbaf79d754f503fcb582f538701788a440","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:55:24.779782Z","signature_b64":"NsVU0E2NOTDw2sfaEznt4vQX7e2vFPysDarbO+xQmgWslRx/mkP9MR3zYYPj0kRVcINHV3OlaISTnYQdrDwtCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"adeb4c1a08a2ebad774650b7a719c9bbaf79d754f503fcb582f538701788a440","last_reissued_at":"2026-07-05T03:55:24.779295Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:55:24.779295Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2008.11429","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":"2026-07-05T03:55:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4i60KP092BWixcFNAtmDkBc7bHWVzCGfHvIsGmjieFd/PZ34AnXxut2pMm2+CdwkKJbi8QfeM7GePpvM0TuWBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T11:45:52.717860Z"},"content_sha256":"7a4a83aa3de6aed0135a3f1393451a6e2f2e6591180bcf48af614e171dd670e5","schema_version":"1.0","event_id":"sha256:7a4a83aa3de6aed0135a3f1393451a6e2f2e6591180bcf48af614e171dd670e5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:VXVUYGQIULV2252GKC32OGOJXO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sharp decay estimates for massless Dirac fields on a Schwarzschild background","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Lin Zhang, Siyuan Ma","submitted_at":"2020-08-26T07:52:34Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2008.11429","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/2008.11429/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":"2026-07-05T03:55:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"00Abv2AQIkKQjuc0Jhiyde3onGGLyX5UBC7mqVVMQAvBLIZoGqPeQeFX6X7dImZpqhbJ2C48n7GuMMIQrl5CAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T11:45:52.718399Z"},"content_sha256":"7303c703d6b35f219faf359c674c271261f5a8a0d9e1fc5586d3840aaaeea5bf","schema_version":"1.0","event_id":"sha256:7303c703d6b35f219faf359c674c271261f5a8a0d9e1fc5586d3840aaaeea5bf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VXVUYGQIULV2252GKC32OGOJXO/bundle.json","state_url":"https://pith.science/pith/VXVUYGQIULV2252GKC32OGOJXO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VXVUYGQIULV2252GKC32OGOJXO/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":"2026-08-11T11:45:52Z","links":{"resolver":"https://pith.science/pith/VXVUYGQIULV2252GKC32OGOJXO","bundle":"https://pith.science/pith/VXVUYGQIULV2252GKC32OGOJXO/bundle.json","state":"https://pith.science/pith/VXVUYGQIULV2252GKC32OGOJXO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VXVUYGQIULV2252GKC32OGOJXO/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jTpMJuEY0GXGfL4ID0pU1UjMMeuQ5nRyrOLni+5IpO58J5MmmiNsWar6YAWbIGqw7t3JPIyr1CZvNp/OPTU/Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T11:45:52.723464Z","bundle_sha256":"17961211d530fd5732f692a5624af59e3ac977ee8c28418680cfe402f2b9444d"}}