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(68)) ϕ(p) ℓ(t,r) = 1 2πRe [∫ +∞+ic 0+ic e−iωuD(p) ℓ(ω)dω","work_id":"cda971f8-3601-4a70-8031-abb51817c9c3","year":null},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":5,"title":"This contribution is defined as the discontinuity between the two lips of the cut, as in Eq","work_id":"a7054e5e-03f3-4d5a-9ce1-b851690ab550","year":null}],"snapshot_sha256":"578b7b57e8985c11175e0163d91ab6e4e9aca9bd77e8c19c9189437110212224"},"source":{"id":"2605.15429","kind":"arxiv","version":1},"verdict":{"created_at":"2026-05-19T14:25:02.594549Z","id":"bcff5153-f879-4e82-9601-d9a1f6bd7578","model_set":{"reader":"grok-4.3"},"one_line_summary":"Introduces Debye series and Debye-QNMs to decompose waveforms from Schwarzschild-star models, achieving early-time convergence and organizing ringdown plus echo packets into individual propagation channels.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"A Debye series decomposition of waveforms from compact horizonless bodies converges at early times and reconstructs the full signal including prompt response and echoes.","strongest_claim":"We show that the Debye reconstruction matches well with the exact waveform, and that (unlike the standard QNM reconstruction) it converges even at early times, giving an accurate description of all waveform features including the prompt response.","weakest_assumption":"The assumption that the interior of the compact body permits well-defined successive transmissions and that the quasinormal-mode content of each individual Debye term can be extracted and summed independently without significant cross-channel interference (abstract, paragraph describing the Debye decomposition and its application to Schwarzschild-star spacetimes)."}},"verdict_id":"bcff5153-f879-4e82-9601-d9a1f6bd7578"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:00f5f35b6c247e67724b1998d88171b37b39779d17e1df85994c607ac5655d0a","target":"record","created_at":"2026-05-20T00:00:58Z","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":"fe4f54ac1613fc196e47b2d5b6c7126f1903c7b14bf261b13a97de2e8a6f41c3","cross_cats_sorted":["astro-ph.HE"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2026-05-14T21:23:29Z","title_canon_sha256":"b5b234e05d858ec7a23bcb4179a382db2c95d86a3a6190ecd71c0e4afddff860"},"schema_version":"1.0","source":{"id":"2605.15429","kind":"arxiv","version":1}},"canonical_sha256":"21f35dd47dbd7b76ba252f01a61f5425036a9c023fad3767c00efb120154fc9e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"21f35dd47dbd7b76ba252f01a61f5425036a9c023fad3767c00efb120154fc9e","first_computed_at":"2026-05-20T00:00:58.193610Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:00:58.193610Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DMx0pArGfdAdh0LtZpGINWh5jWIL2JmMLn/J6B91cKf0z7JiMCXRkXjX1C7W4bLTTnhZhQsGKkV1aocynPaxBw==","signature_status":"signed_v1","signed_at":"2026-05-20T00:00:58.194404Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.15429","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:00f5f35b6c247e67724b1998d88171b37b39779d17e1df85994c607ac5655d0a","sha256:0e537caf211c03ec2776cdec184cf663a8e48d1bef88ba316a4980f253819887"],"state_sha256":"8f23be581e208fffa7320efd441b24bd95639b229c69048f6a047a5796923e00"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g3kyQ7yyCytcyhEQjQkJwTfppRZoBlyImpX2HdTbIyzEUSoG3fU8bpI76KYInyyV5MB4qeaIdUlYuZ34O4q/AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-21T13:38:22.137362Z","bundle_sha256":"a023f61ab66bce778cba3c1021acdfcee4bfc2d04470c9bf354df8a99f333833"}}