{"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"}