{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:GQLWYFVCAA43THWG2BJTO356LN","short_pith_number":"pith:GQLWYFVC","canonical_record":{"source":{"id":"1512.05018","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-12-16T01:02:09Z","cross_cats_sorted":[],"title_canon_sha256":"8491fa44ece97f2cf3f296e8227e68fb003f489cdc3bb96f788490d035751cb7","abstract_canon_sha256":"4b605baa1e759cff26b570e5de4e0a8f3efd427522d1ddc22d65f0d62942b117"},"schema_version":"1.0"},"canonical_sha256":"34176c16a20039b99ec6d053376fbe5b7b51989675f3bbc78a2af6c3c78efd9a","source":{"kind":"arxiv","id":"1512.05018","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.05018","created_at":"2026-05-18T01:24:13Z"},{"alias_kind":"arxiv_version","alias_value":"1512.05018v1","created_at":"2026-05-18T01:24:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.05018","created_at":"2026-05-18T01:24:13Z"},{"alias_kind":"pith_short_12","alias_value":"GQLWYFVCAA43","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"GQLWYFVCAA43THWG","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"GQLWYFVC","created_at":"2026-05-18T12:29:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:GQLWYFVCAA43THWG2BJTO356LN","target":"record","payload":{"canonical_record":{"source":{"id":"1512.05018","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-12-16T01:02:09Z","cross_cats_sorted":[],"title_canon_sha256":"8491fa44ece97f2cf3f296e8227e68fb003f489cdc3bb96f788490d035751cb7","abstract_canon_sha256":"4b605baa1e759cff26b570e5de4e0a8f3efd427522d1ddc22d65f0d62942b117"},"schema_version":"1.0"},"canonical_sha256":"34176c16a20039b99ec6d053376fbe5b7b51989675f3bbc78a2af6c3c78efd9a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:24:13.726009Z","signature_b64":"PpMDOdh+hQJWXRdUwXMORligFhNWP616XQlvVfXJtIPNhZeqsj0/PUGc+j5okvRbwJPy842uTkAMyAhgGvlvDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"34176c16a20039b99ec6d053376fbe5b7b51989675f3bbc78a2af6c3c78efd9a","last_reissued_at":"2026-05-18T01:24:13.725415Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:24:13.725415Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.05018","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":"2026-05-18T01:24:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OfHhoBYf/ct8OCi1ul5o0c2TPmjNcKTV6+7qJFfzKqqVG8bG6K7mxV3Dz5eFNWn6Cjn7cbNJ0meqZjLujz6GCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T06:18:19.848701Z"},"content_sha256":"5f42abdb420fc680eb782c8a73014f89baf0a3860101e8855713393b412a0e5c","schema_version":"1.0","event_id":"sha256:5f42abdb420fc680eb782c8a73014f89baf0a3860101e8855713393b412a0e5c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:GQLWYFVCAA43THWG2BJTO356LN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Greybody factors for Schwarzschild black holes: Path-ordered exponentials and product integrals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Finnian Gray (Victoria University of Wellington), Matt Visser (Victoria University of Wellington)","submitted_at":"2015-12-16T01:02:09Z","abstract_excerpt":"In recent work concerning the sparsity of the Hawking flux [arXiv:1506.03975v2], we found it necessary to re-examine what is known regarding the greybody factors of black holes, with a view to extending and expanding on some old results from the 1970s. Focussing specifically on Schwarzschild black holes, we re-calculated and re-assessed the greybody factors using a path-ordered-exponential approach, a technique which has the virtue of providing a semi-explicit formula for the relevant Bogoliubov coefficients. These path-ordered-exponentials, (being based on a \"transfer matrix\" formalism), are "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.05018","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":""},"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":"2026-05-18T01:24:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tOehXGYxp7yLkr3ka3Lr6uV3bLdtP9/IlxSvvQd3LOnobvpg725tJMOENz7LnZwOCRKRjPZiijnykE5ci5lbDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T06:18:19.849296Z"},"content_sha256":"7b126d6e1432ee1b5978f583db75fc66832ccb4a538fbcd741c003848e41d4c0","schema_version":"1.0","event_id":"sha256:7b126d6e1432ee1b5978f583db75fc66832ccb4a538fbcd741c003848e41d4c0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GQLWYFVCAA43THWG2BJTO356LN/bundle.json","state_url":"https://pith.science/pith/GQLWYFVCAA43THWG2BJTO356LN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GQLWYFVCAA43THWG2BJTO356LN/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":"2026-07-01T06:18:19Z","links":{"resolver":"https://pith.science/pith/GQLWYFVCAA43THWG2BJTO356LN","bundle":"https://pith.science/pith/GQLWYFVCAA43THWG2BJTO356LN/bundle.json","state":"https://pith.science/pith/GQLWYFVCAA43THWG2BJTO356LN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GQLWYFVCAA43THWG2BJTO356LN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:GQLWYFVCAA43THWG2BJTO356LN","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":"4b605baa1e759cff26b570e5de4e0a8f3efd427522d1ddc22d65f0d62942b117","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-12-16T01:02:09Z","title_canon_sha256":"8491fa44ece97f2cf3f296e8227e68fb003f489cdc3bb96f788490d035751cb7"},"schema_version":"1.0","source":{"id":"1512.05018","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.05018","created_at":"2026-05-18T01:24:13Z"},{"alias_kind":"arxiv_version","alias_value":"1512.05018v1","created_at":"2026-05-18T01:24:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.05018","created_at":"2026-05-18T01:24:13Z"},{"alias_kind":"pith_short_12","alias_value":"GQLWYFVCAA43","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"GQLWYFVCAA43THWG","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"GQLWYFVC","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:7b126d6e1432ee1b5978f583db75fc66832ccb4a538fbcd741c003848e41d4c0","target":"graph","created_at":"2026-05-18T01:24:13Z","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"},"paper":{"abstract_excerpt":"In recent work concerning the sparsity of the Hawking flux [arXiv:1506.03975v2], we found it necessary to re-examine what is known regarding the greybody factors of black holes, with a view to extending and expanding on some old results from the 1970s. Focussing specifically on Schwarzschild black holes, we re-calculated and re-assessed the greybody factors using a path-ordered-exponential approach, a technique which has the virtue of providing a semi-explicit formula for the relevant Bogoliubov coefficients. These path-ordered-exponentials, (being based on a \"transfer matrix\" formalism), are ","authors_text":"Finnian Gray (Victoria University of Wellington), Matt Visser (Victoria University of Wellington)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-12-16T01:02:09Z","title":"Greybody factors for Schwarzschild black holes: Path-ordered exponentials and product integrals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.05018","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":"sha256:5f42abdb420fc680eb782c8a73014f89baf0a3860101e8855713393b412a0e5c","target":"record","created_at":"2026-05-18T01:24:13Z","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":"4b605baa1e759cff26b570e5de4e0a8f3efd427522d1ddc22d65f0d62942b117","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-12-16T01:02:09Z","title_canon_sha256":"8491fa44ece97f2cf3f296e8227e68fb003f489cdc3bb96f788490d035751cb7"},"schema_version":"1.0","source":{"id":"1512.05018","kind":"arxiv","version":1}},"canonical_sha256":"34176c16a20039b99ec6d053376fbe5b7b51989675f3bbc78a2af6c3c78efd9a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"34176c16a20039b99ec6d053376fbe5b7b51989675f3bbc78a2af6c3c78efd9a","first_computed_at":"2026-05-18T01:24:13.725415Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:24:13.725415Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PpMDOdh+hQJWXRdUwXMORligFhNWP616XQlvVfXJtIPNhZeqsj0/PUGc+j5okvRbwJPy842uTkAMyAhgGvlvDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:24:13.726009Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.05018","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5f42abdb420fc680eb782c8a73014f89baf0a3860101e8855713393b412a0e5c","sha256:7b126d6e1432ee1b5978f583db75fc66832ccb4a538fbcd741c003848e41d4c0"],"state_sha256":"1c9e9440fde0bd8c54debd46073692218cfd6ea40bc6dd1fbd4f19175ddd929c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C/ynKIJx75/noyaTvVSlDKUtRLJjlMbBdFr6jKC0Cq0mr2k7gNJ3dp5tNNwOb0NYGOVbFxId0oq+dAGMtTUADg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T06:18:19.852966Z","bundle_sha256":"fb3428db2f3f2fd95bbab97ce38c12bea63a1cf73134dcb30b100cc6e4ce351d"}}