{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:PLXLLXVAH33TZ2JDS5R6IOVMV4","short_pith_number":"pith:PLXLLXVA","canonical_record":{"source":{"id":"1308.2159","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2013-08-09T15:30:07Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"2a92db3a073f1c6f4f0be41d558c4d8646b5cbf7b9f64fcf09461298e012d9d4","abstract_canon_sha256":"e50f84fe5fd6b0c623e3886b5a9393f13315a2d19e08f4540da5a47bbec4d7b2"},"schema_version":"1.0"},"canonical_sha256":"7aeeb5dea03ef73ce9239763e43aacaf27ed2ad70273017fc640a84101d66ad6","source":{"kind":"arxiv","id":"1308.2159","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.2159","created_at":"2026-05-18T01:48:21Z"},{"alias_kind":"arxiv_version","alias_value":"1308.2159v1","created_at":"2026-05-18T01:48:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.2159","created_at":"2026-05-18T01:48:21Z"},{"alias_kind":"pith_short_12","alias_value":"PLXLLXVAH33T","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"PLXLLXVAH33TZ2JD","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"PLXLLXVA","created_at":"2026-05-18T12:27:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:PLXLLXVAH33TZ2JDS5R6IOVMV4","target":"record","payload":{"canonical_record":{"source":{"id":"1308.2159","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2013-08-09T15:30:07Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"2a92db3a073f1c6f4f0be41d558c4d8646b5cbf7b9f64fcf09461298e012d9d4","abstract_canon_sha256":"e50f84fe5fd6b0c623e3886b5a9393f13315a2d19e08f4540da5a47bbec4d7b2"},"schema_version":"1.0"},"canonical_sha256":"7aeeb5dea03ef73ce9239763e43aacaf27ed2ad70273017fc640a84101d66ad6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:48:21.673704Z","signature_b64":"TSagT95/KbkODrnocMC3So03gq3lXD0IyN6eP9WlW7l63j5RNzlCBqgdmnXSIMX/K1zRB/oTUX40u+XUDYicCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7aeeb5dea03ef73ce9239763e43aacaf27ed2ad70273017fc640a84101d66ad6","last_reissued_at":"2026-05-18T01:48:21.673029Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:48:21.673029Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1308.2159","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":"2026-05-18T01:48:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ix5srtZU1eNryyo8oB4+42s8udImm60zeLsYtTSK6njDBXBdtCSrY/Xu8zAXW2OCXvzVdMqf0H11YNKeIh0gAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T03:45:31.913482Z"},"content_sha256":"9fe5ff6c239ffbe7ff716586c1974ec4b0938ea9e805112c41ff0b8747110496","schema_version":"1.0","event_id":"sha256:9fe5ff6c239ffbe7ff716586c1974ec4b0938ea9e805112c41ff0b8747110496"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:PLXLLXVAH33TZ2JDS5R6IOVMV4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hawking radiation with dispersion versus breakdown of WKB","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"gr-qc","authors_text":"R. Sch\\\"utzhold, W. G. Unruh","submitted_at":"2013-08-09T15:30:07Z","abstract_excerpt":"Inspired by the condensed matter analogues of black holes (a.k.a. dumb holes), we study Hawking radiation in the presence of a modified dispersion relation which becomes super-luminal at large wave-numbers. In the usual stationary coordinates $(t,x)$, one can describe the asymptotic evolution of the wave-packets in WKB, but this WKB approximation breaks down in the vicinity of the horizon, thereby allowing for a mixing between initial and final creation and annihilation operators. Thus, one might be tempted to identify this point where WKB breaks down with the moment of particle creation. Howe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.2159","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":"2026-05-18T01:48:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b4nSBamo3EgB15s2qvTOdqXP3DzuRLaUeGi/QqXtpkrCSBzcmuvb09FPrYiFtXRm9pztPev7Fb0R2uGxpT++Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T03:45:31.914129Z"},"content_sha256":"8efd9d991e6e0d1eaae3f54e0540f28b65c58b40c5019c52396d58b7bc27ca70","schema_version":"1.0","event_id":"sha256:8efd9d991e6e0d1eaae3f54e0540f28b65c58b40c5019c52396d58b7bc27ca70"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PLXLLXVAH33TZ2JDS5R6IOVMV4/bundle.json","state_url":"https://pith.science/pith/PLXLLXVAH33TZ2JDS5R6IOVMV4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PLXLLXVAH33TZ2JDS5R6IOVMV4/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":"2026-06-04T03:45:31Z","links":{"resolver":"https://pith.science/pith/PLXLLXVAH33TZ2JDS5R6IOVMV4","bundle":"https://pith.science/pith/PLXLLXVAH33TZ2JDS5R6IOVMV4/bundle.json","state":"https://pith.science/pith/PLXLLXVAH33TZ2JDS5R6IOVMV4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PLXLLXVAH33TZ2JDS5R6IOVMV4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:PLXLLXVAH33TZ2JDS5R6IOVMV4","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":"e50f84fe5fd6b0c623e3886b5a9393f13315a2d19e08f4540da5a47bbec4d7b2","cross_cats_sorted":["quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2013-08-09T15:30:07Z","title_canon_sha256":"2a92db3a073f1c6f4f0be41d558c4d8646b5cbf7b9f64fcf09461298e012d9d4"},"schema_version":"1.0","source":{"id":"1308.2159","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.2159","created_at":"2026-05-18T01:48:21Z"},{"alias_kind":"arxiv_version","alias_value":"1308.2159v1","created_at":"2026-05-18T01:48:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.2159","created_at":"2026-05-18T01:48:21Z"},{"alias_kind":"pith_short_12","alias_value":"PLXLLXVAH33T","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"PLXLLXVAH33TZ2JD","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"PLXLLXVA","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:8efd9d991e6e0d1eaae3f54e0540f28b65c58b40c5019c52396d58b7bc27ca70","target":"graph","created_at":"2026-05-18T01:48:21Z","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":"Inspired by the condensed matter analogues of black holes (a.k.a. dumb holes), we study Hawking radiation in the presence of a modified dispersion relation which becomes super-luminal at large wave-numbers. In the usual stationary coordinates $(t,x)$, one can describe the asymptotic evolution of the wave-packets in WKB, but this WKB approximation breaks down in the vicinity of the horizon, thereby allowing for a mixing between initial and final creation and annihilation operators. Thus, one might be tempted to identify this point where WKB breaks down with the moment of particle creation. Howe","authors_text":"R. Sch\\\"utzhold, W. G. Unruh","cross_cats":["quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2013-08-09T15:30:07Z","title":"Hawking radiation with dispersion versus breakdown of WKB"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.2159","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":"sha256:9fe5ff6c239ffbe7ff716586c1974ec4b0938ea9e805112c41ff0b8747110496","target":"record","created_at":"2026-05-18T01:48:21Z","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":"e50f84fe5fd6b0c623e3886b5a9393f13315a2d19e08f4540da5a47bbec4d7b2","cross_cats_sorted":["quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2013-08-09T15:30:07Z","title_canon_sha256":"2a92db3a073f1c6f4f0be41d558c4d8646b5cbf7b9f64fcf09461298e012d9d4"},"schema_version":"1.0","source":{"id":"1308.2159","kind":"arxiv","version":1}},"canonical_sha256":"7aeeb5dea03ef73ce9239763e43aacaf27ed2ad70273017fc640a84101d66ad6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7aeeb5dea03ef73ce9239763e43aacaf27ed2ad70273017fc640a84101d66ad6","first_computed_at":"2026-05-18T01:48:21.673029Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:48:21.673029Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TSagT95/KbkODrnocMC3So03gq3lXD0IyN6eP9WlW7l63j5RNzlCBqgdmnXSIMX/K1zRB/oTUX40u+XUDYicCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:48:21.673704Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.2159","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9fe5ff6c239ffbe7ff716586c1974ec4b0938ea9e805112c41ff0b8747110496","sha256:8efd9d991e6e0d1eaae3f54e0540f28b65c58b40c5019c52396d58b7bc27ca70"],"state_sha256":"49f3e20d7d6586cf4cf2b12846ef40169e0415719d0dcd235b476127637c6bfb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5JWNfJcZ3OzM1VlHnWpvzJQwkdx4kfud6DvtZ9yzdQo3E40Zt4SNMMWETFZHjDaDGqpN6AgYavPukWtDbEcNBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T03:45:31.917380Z","bundle_sha256":"2fbc7da581262f0a5a13a384d3d67b4f1a2c372e7e5eac87b838b3cb63700c29"}}