{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:PDUFBN4UI6NN5L5I7ZIKBQAAD3","short_pith_number":"pith:PDUFBN4U","canonical_record":{"source":{"id":"2607.11145","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2026-07-13T06:33:06Z","cross_cats_sorted":["hep-ph"],"title_canon_sha256":"23522dfabbd058255579bd87f9c38e9e56e2f6eb8de89785d32575d6b3b825b3","abstract_canon_sha256":"ae02281db1b72b6acefc62c318efa0f83e85559ac7917801340bdfc0a538d4e8"},"schema_version":"1.0"},"canonical_sha256":"78e850b794479adeafa8fe50a0c0001eedf2d6640f7f75ed1b655909fe4a7b1b","source":{"kind":"arxiv","id":"2607.11145","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.11145","created_at":"2026-07-14T01:22:18Z"},{"alias_kind":"arxiv_version","alias_value":"2607.11145v1","created_at":"2026-07-14T01:22:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.11145","created_at":"2026-07-14T01:22:18Z"},{"alias_kind":"pith_short_12","alias_value":"PDUFBN4UI6NN","created_at":"2026-07-14T01:22:18Z"},{"alias_kind":"pith_short_16","alias_value":"PDUFBN4UI6NN5L5I","created_at":"2026-07-14T01:22:18Z"},{"alias_kind":"pith_short_8","alias_value":"PDUFBN4U","created_at":"2026-07-14T01:22:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:PDUFBN4UI6NN5L5I7ZIKBQAAD3","target":"record","payload":{"canonical_record":{"source":{"id":"2607.11145","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2026-07-13T06:33:06Z","cross_cats_sorted":["hep-ph"],"title_canon_sha256":"23522dfabbd058255579bd87f9c38e9e56e2f6eb8de89785d32575d6b3b825b3","abstract_canon_sha256":"ae02281db1b72b6acefc62c318efa0f83e85559ac7917801340bdfc0a538d4e8"},"schema_version":"1.0"},"canonical_sha256":"78e850b794479adeafa8fe50a0c0001eedf2d6640f7f75ed1b655909fe4a7b1b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-14T01:22:18.857900Z","signature_b64":"/7DG4qMjQDThhOMd7ZN+9I+ha0HLLqW4GXXW9icWxmYfJ/8gCYknIHJjXJpUKsU2ACi1bzp34HlipoaXUifeDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"78e850b794479adeafa8fe50a0c0001eedf2d6640f7f75ed1b655909fe4a7b1b","last_reissued_at":"2026-07-14T01:22:18.857046Z","signature_status":"signed_v1","first_computed_at":"2026-07-14T01:22:18.857046Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.11145","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-14T01:22:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8mQCdrOay8Rncy6dAlmNj/g7FyvoSyJFVTVrgdGzjdYkiVAnXRpaC1unjDAKwu/PmH3MPO0ro7ocJJH5jXgkAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T16:13:32.386802Z"},"content_sha256":"4ad3d1ff0a2b9061a696723e5219f0644ea23b2c30c96eda6d58d92e1bd537c8","schema_version":"1.0","event_id":"sha256:4ad3d1ff0a2b9061a696723e5219f0644ea23b2c30c96eda6d58d92e1bd537c8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:PDUFBN4UI6NN5L5I7ZIKBQAAD3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Reconstruction of Primordial Power Spectrum from Gravitational Waves of High-Redshift Black Hole Binaries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-ph"],"primary_cat":"astro-ph.CO","authors_text":"Masahide Yamaguchi, Qianhang Ding, Xinpeng Wang, Ying-li Zhang","submitted_at":"2026-07-13T06:33:06Z","abstract_excerpt":"High-redshift binary black hole (BBH) events are promising candidates for primordial black holes (PBHs) detectable by next-generation gravitational wave (GW) detectors. A redshifted mass distribution of detected PBH candidates can be obtained from GW observations, from which the underlying PBH mass function can be reconstructed. In this work, we develop a framework that applies the gradient-descent method to the observed redshifted mass distribution and reconstructs the PBH mass function and, subsequently, the primordial power spectrum (PPS) on small scales. As an illustrative application, we "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.11145","kind":"arxiv","version":1},"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/2607.11145/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":"2026-07-14T01:22:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8IgwjGa6Gq1G2OCL7+MXZcBiczjGP5b+J3mRFol8pY/wAbxEDUTRYskIuQLP3Jnhad5rPgZuiK6VYI2WxaRaCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T16:13:32.387817Z"},"content_sha256":"0bc17585763ce7b84da0eccb1537f60f93fbc2840f4e00e7e0416e4f29e7f995","schema_version":"1.0","event_id":"sha256:0bc17585763ce7b84da0eccb1537f60f93fbc2840f4e00e7e0416e4f29e7f995"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PDUFBN4UI6NN5L5I7ZIKBQAAD3/bundle.json","state_url":"https://pith.science/pith/PDUFBN4UI6NN5L5I7ZIKBQAAD3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PDUFBN4UI6NN5L5I7ZIKBQAAD3/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":"2026-08-03T16:13:32Z","links":{"resolver":"https://pith.science/pith/PDUFBN4UI6NN5L5I7ZIKBQAAD3","bundle":"https://pith.science/pith/PDUFBN4UI6NN5L5I7ZIKBQAAD3/bundle.json","state":"https://pith.science/pith/PDUFBN4UI6NN5L5I7ZIKBQAAD3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PDUFBN4UI6NN5L5I7ZIKBQAAD3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:PDUFBN4UI6NN5L5I7ZIKBQAAD3","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":"ae02281db1b72b6acefc62c318efa0f83e85559ac7917801340bdfc0a538d4e8","cross_cats_sorted":["hep-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2026-07-13T06:33:06Z","title_canon_sha256":"23522dfabbd058255579bd87f9c38e9e56e2f6eb8de89785d32575d6b3b825b3"},"schema_version":"1.0","source":{"id":"2607.11145","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.11145","created_at":"2026-07-14T01:22:18Z"},{"alias_kind":"arxiv_version","alias_value":"2607.11145v1","created_at":"2026-07-14T01:22:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.11145","created_at":"2026-07-14T01:22:18Z"},{"alias_kind":"pith_short_12","alias_value":"PDUFBN4UI6NN","created_at":"2026-07-14T01:22:18Z"},{"alias_kind":"pith_short_16","alias_value":"PDUFBN4UI6NN5L5I","created_at":"2026-07-14T01:22:18Z"},{"alias_kind":"pith_short_8","alias_value":"PDUFBN4U","created_at":"2026-07-14T01:22:18Z"}],"graph_snapshots":[{"event_id":"sha256:0bc17585763ce7b84da0eccb1537f60f93fbc2840f4e00e7e0416e4f29e7f995","target":"graph","created_at":"2026-07-14T01:22:18Z","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/2607.11145/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"High-redshift binary black hole (BBH) events are promising candidates for primordial black holes (PBHs) detectable by next-generation gravitational wave (GW) detectors. A redshifted mass distribution of detected PBH candidates can be obtained from GW observations, from which the underlying PBH mass function can be reconstructed. In this work, we develop a framework that applies the gradient-descent method to the observed redshifted mass distribution and reconstructs the PBH mass function and, subsequently, the primordial power spectrum (PPS) on small scales. As an illustrative application, we ","authors_text":"Masahide Yamaguchi, Qianhang Ding, Xinpeng Wang, Ying-li Zhang","cross_cats":["hep-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2026-07-13T06:33:06Z","title":"Reconstruction of Primordial Power Spectrum from Gravitational Waves of High-Redshift Black Hole Binaries"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.11145","kind":"arxiv","version":1},"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":"sha256:4ad3d1ff0a2b9061a696723e5219f0644ea23b2c30c96eda6d58d92e1bd537c8","target":"record","created_at":"2026-07-14T01:22:18Z","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":"ae02281db1b72b6acefc62c318efa0f83e85559ac7917801340bdfc0a538d4e8","cross_cats_sorted":["hep-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2026-07-13T06:33:06Z","title_canon_sha256":"23522dfabbd058255579bd87f9c38e9e56e2f6eb8de89785d32575d6b3b825b3"},"schema_version":"1.0","source":{"id":"2607.11145","kind":"arxiv","version":1}},"canonical_sha256":"78e850b794479adeafa8fe50a0c0001eedf2d6640f7f75ed1b655909fe4a7b1b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"78e850b794479adeafa8fe50a0c0001eedf2d6640f7f75ed1b655909fe4a7b1b","first_computed_at":"2026-07-14T01:22:18.857046Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-14T01:22:18.857046Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/7DG4qMjQDThhOMd7ZN+9I+ha0HLLqW4GXXW9icWxmYfJ/8gCYknIHJjXJpUKsU2ACi1bzp34HlipoaXUifeDQ==","signature_status":"signed_v1","signed_at":"2026-07-14T01:22:18.857900Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.11145","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4ad3d1ff0a2b9061a696723e5219f0644ea23b2c30c96eda6d58d92e1bd537c8","sha256:0bc17585763ce7b84da0eccb1537f60f93fbc2840f4e00e7e0416e4f29e7f995"],"state_sha256":"9ea9f09de0d12aa3628740cc3d99f61a567e40afc4adf03f1641f22999f18d3b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MJZ/Aj+0EYdhagxHjmvk9uPJatGGvrEbQ69auWMEjuUeiPPRPgJSCvMrA6J4yufUSViZdQUDtA61uibzVqtJDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T16:13:32.397644Z","bundle_sha256":"4ee3cd1c7b14718ee776ec497a825b684c1b64f8e0731de255132a3e8e76c4ca"}}