{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:TSZK7ZUJDWGJO4UKHKDCUZJI6D","short_pith_number":"pith:TSZK7ZUJ","canonical_record":{"source":{"id":"2504.02592","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2025-04-03T13:55:24Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"7569529cc6cebd17f7878d92159da637f6fc1f3ae60384c3129b3bb38d631b6c","abstract_canon_sha256":"6c7e6ca082cc639c2d8065a7624c8f00fdc773ffdae8ff6e3fa5d415fa0ef9d2"},"schema_version":"1.0"},"canonical_sha256":"9cb2afe6891d8c97728a3a862a6528f0f93733cbcad9bc61747b5ae1eee3477e","source":{"kind":"arxiv","id":"2504.02592","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.02592","created_at":"2026-07-03T00:16:49Z"},{"alias_kind":"arxiv_version","alias_value":"2504.02592v4","created_at":"2026-07-03T00:16:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.02592","created_at":"2026-07-03T00:16:49Z"},{"alias_kind":"pith_short_12","alias_value":"TSZK7ZUJDWGJ","created_at":"2026-07-03T00:16:49Z"},{"alias_kind":"pith_short_16","alias_value":"TSZK7ZUJDWGJO4UK","created_at":"2026-07-03T00:16:49Z"},{"alias_kind":"pith_short_8","alias_value":"TSZK7ZUJ","created_at":"2026-07-03T00:16:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:TSZK7ZUJDWGJO4UKHKDCUZJI6D","target":"record","payload":{"canonical_record":{"source":{"id":"2504.02592","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2025-04-03T13:55:24Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"7569529cc6cebd17f7878d92159da637f6fc1f3ae60384c3129b3bb38d631b6c","abstract_canon_sha256":"6c7e6ca082cc639c2d8065a7624c8f00fdc773ffdae8ff6e3fa5d415fa0ef9d2"},"schema_version":"1.0"},"canonical_sha256":"9cb2afe6891d8c97728a3a862a6528f0f93733cbcad9bc61747b5ae1eee3477e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-03T00:16:49.557675Z","signature_b64":"/H66EqlEXYTjkzhl0U4uUn2q5LzHFW7hCIDGYB+VDMamvHx1BSq9K7Dkp1v5kXs2pEhyICeRrdT+N66AdeUbBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9cb2afe6891d8c97728a3a862a6528f0f93733cbcad9bc61747b5ae1eee3477e","last_reissued_at":"2026-07-03T00:16:49.557168Z","signature_status":"signed_v1","first_computed_at":"2026-07-03T00:16:49.557168Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2504.02592","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-03T00:16:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XiX1gYwOtl6fG9bCFJlCwu6qoX5rHIjtMHSWZ5jYJ42bsFEWvkuIk2PVRtLVdeZCVTByHSjZS0VGOl0vmsr7Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T19:26:22.963860Z"},"content_sha256":"a19301cf0eb9ebbac6ac80ee5041887da0d39d6c192799dc0dd3fec18d5c358f","schema_version":"1.0","event_id":"sha256:a19301cf0eb9ebbac6ac80ee5041887da0d39d6c192799dc0dd3fec18d5c358f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:TSZK7ZUJDWGJO4UKHKDCUZJI6D","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Unified equation for massless spin fields and new definitions of key spin coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc"],"primary_cat":"hep-th","authors_text":"Zhong-Heng Li","submitted_at":"2025-04-03T13:55:24Z","abstract_excerpt":"Whether studying gravitational waves from extreme mass ratio inspirals or exploring the analogy between massless spin-particle waves, black hole perturbation theory proves indispensable. At the heart of developing a universal perturbation framework for such problems lies the challenge of formulating a coordinate-independent, unified wave equation that is universally applicable to any black hole spacetime. This paper resolves this central issue in type-D spacetimes by introducing a generating function $H$ and establishing new definitions for the key spin coefficients. Specifically, the spin coe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.02592","kind":"arxiv","version":4},"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/2504.02592/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":"2026-07-03T00:16:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nyhPeFIghK7GDdKzHaxHkQB787RpB/DZEVVqauzm4F21IuGv5nRWkEuoGLoqvW+Hy7EBKJX65m2EthbfrWzDDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T19:26:22.964225Z"},"content_sha256":"fa20b55976ec5044acbdacc1289cc280aef77ea093ee4ec672d62c51afcc6ac4","schema_version":"1.0","event_id":"sha256:fa20b55976ec5044acbdacc1289cc280aef77ea093ee4ec672d62c51afcc6ac4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TSZK7ZUJDWGJO4UKHKDCUZJI6D/bundle.json","state_url":"https://pith.science/pith/TSZK7ZUJDWGJO4UKHKDCUZJI6D/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TSZK7ZUJDWGJO4UKHKDCUZJI6D/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":"2026-07-03T19:26:22Z","links":{"resolver":"https://pith.science/pith/TSZK7ZUJDWGJO4UKHKDCUZJI6D","bundle":"https://pith.science/pith/TSZK7ZUJDWGJO4UKHKDCUZJI6D/bundle.json","state":"https://pith.science/pith/TSZK7ZUJDWGJO4UKHKDCUZJI6D/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TSZK7ZUJDWGJO4UKHKDCUZJI6D/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:TSZK7ZUJDWGJO4UKHKDCUZJI6D","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":"6c7e6ca082cc639c2d8065a7624c8f00fdc773ffdae8ff6e3fa5d415fa0ef9d2","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2025-04-03T13:55:24Z","title_canon_sha256":"7569529cc6cebd17f7878d92159da637f6fc1f3ae60384c3129b3bb38d631b6c"},"schema_version":"1.0","source":{"id":"2504.02592","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.02592","created_at":"2026-07-03T00:16:49Z"},{"alias_kind":"arxiv_version","alias_value":"2504.02592v4","created_at":"2026-07-03T00:16:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.02592","created_at":"2026-07-03T00:16:49Z"},{"alias_kind":"pith_short_12","alias_value":"TSZK7ZUJDWGJ","created_at":"2026-07-03T00:16:49Z"},{"alias_kind":"pith_short_16","alias_value":"TSZK7ZUJDWGJO4UK","created_at":"2026-07-03T00:16:49Z"},{"alias_kind":"pith_short_8","alias_value":"TSZK7ZUJ","created_at":"2026-07-03T00:16:49Z"}],"graph_snapshots":[{"event_id":"sha256:fa20b55976ec5044acbdacc1289cc280aef77ea093ee4ec672d62c51afcc6ac4","target":"graph","created_at":"2026-07-03T00:16:49Z","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/2504.02592/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Whether studying gravitational waves from extreme mass ratio inspirals or exploring the analogy between massless spin-particle waves, black hole perturbation theory proves indispensable. At the heart of developing a universal perturbation framework for such problems lies the challenge of formulating a coordinate-independent, unified wave equation that is universally applicable to any black hole spacetime. This paper resolves this central issue in type-D spacetimes by introducing a generating function $H$ and establishing new definitions for the key spin coefficients. Specifically, the spin coe","authors_text":"Zhong-Heng Li","cross_cats":["gr-qc"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2025-04-03T13:55:24Z","title":"Unified equation for massless spin fields and new definitions of key spin coefficients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.02592","kind":"arxiv","version":4},"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:a19301cf0eb9ebbac6ac80ee5041887da0d39d6c192799dc0dd3fec18d5c358f","target":"record","created_at":"2026-07-03T00:16:49Z","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":"6c7e6ca082cc639c2d8065a7624c8f00fdc773ffdae8ff6e3fa5d415fa0ef9d2","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2025-04-03T13:55:24Z","title_canon_sha256":"7569529cc6cebd17f7878d92159da637f6fc1f3ae60384c3129b3bb38d631b6c"},"schema_version":"1.0","source":{"id":"2504.02592","kind":"arxiv","version":4}},"canonical_sha256":"9cb2afe6891d8c97728a3a862a6528f0f93733cbcad9bc61747b5ae1eee3477e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9cb2afe6891d8c97728a3a862a6528f0f93733cbcad9bc61747b5ae1eee3477e","first_computed_at":"2026-07-03T00:16:49.557168Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-03T00:16:49.557168Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/H66EqlEXYTjkzhl0U4uUn2q5LzHFW7hCIDGYB+VDMamvHx1BSq9K7Dkp1v5kXs2pEhyICeRrdT+N66AdeUbBg==","signature_status":"signed_v1","signed_at":"2026-07-03T00:16:49.557675Z","signed_message":"canonical_sha256_bytes"},"source_id":"2504.02592","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a19301cf0eb9ebbac6ac80ee5041887da0d39d6c192799dc0dd3fec18d5c358f","sha256:fa20b55976ec5044acbdacc1289cc280aef77ea093ee4ec672d62c51afcc6ac4"],"state_sha256":"0e381faf6863c409a1ca1304bfe9d835188b0c19d1b1f88e4568dd71c08c590b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M4/6I364RmdwKIubXLZfVrCnZiHBF27wfjNkACdpwFaloFw/pdJ2qY6Ha8iaD8ns4g9/wsRHF635vGokeHtkCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T19:26:22.966283Z","bundle_sha256":"ed20e5f1c99932db6c17f1fabbf7b2b5661396fb4ec034ca03339c024d5c13c7"}}