{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:ESPWARMVLFJDCIM2BY4R4HH53F","short_pith_number":"pith:ESPWARMV","canonical_record":{"source":{"id":"1911.04354","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2019-11-11T15:56:53Z","cross_cats_sorted":[],"title_canon_sha256":"9616e20e196f9a876dd6a25d9f025e6214472a74a94f95867190899aebb6b06b","abstract_canon_sha256":"d672762ab50bf4422550240088b1e3fcf44cd60a89cadfe80d13505ca5169c27"},"schema_version":"1.0"},"canonical_sha256":"249f604595595231219a0e391e1cfdd97196268cd3dbb630765eabbe027abcf7","source":{"kind":"arxiv","id":"1911.04354","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1911.04354","created_at":"2026-07-05T00:25:56Z"},{"alias_kind":"arxiv_version","alias_value":"1911.04354v2","created_at":"2026-07-05T00:25:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1911.04354","created_at":"2026-07-05T00:25:56Z"},{"alias_kind":"pith_short_12","alias_value":"ESPWARMVLFJD","created_at":"2026-07-05T00:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"ESPWARMVLFJDCIM2","created_at":"2026-07-05T00:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"ESPWARMV","created_at":"2026-07-05T00:25:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:ESPWARMVLFJDCIM2BY4R4HH53F","target":"record","payload":{"canonical_record":{"source":{"id":"1911.04354","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2019-11-11T15:56:53Z","cross_cats_sorted":[],"title_canon_sha256":"9616e20e196f9a876dd6a25d9f025e6214472a74a94f95867190899aebb6b06b","abstract_canon_sha256":"d672762ab50bf4422550240088b1e3fcf44cd60a89cadfe80d13505ca5169c27"},"schema_version":"1.0"},"canonical_sha256":"249f604595595231219a0e391e1cfdd97196268cd3dbb630765eabbe027abcf7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:25:56.815896Z","signature_b64":"1zTC4UTklTfa13JBD3DMRPdHYMAqtStBD7HgPleMjXLW6LOgHH5x7zAQHG/eDeP9alVAgLnH5OjHVmpSJdZ1Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"249f604595595231219a0e391e1cfdd97196268cd3dbb630765eabbe027abcf7","last_reissued_at":"2026-07-05T00:25:56.815477Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:25:56.815477Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1911.04354","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T00:25:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"40sWPTtgTIUa/fw2a/kcThjP23YCkV9pFr6Un1AL7lsDDQ6701EB1Tf3ucp/6IdJohl3q4ZCyZ50t4z+y+WUDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T17:59:39.642970Z"},"content_sha256":"a3e4f0e91a0f81edc7db0e62ec3a6e17ac8094514085c3cc6315e5d2025e74cb","schema_version":"1.0","event_id":"sha256:a3e4f0e91a0f81edc7db0e62ec3a6e17ac8094514085c3cc6315e5d2025e74cb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:ESPWARMVLFJDCIM2BY4R4HH53F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Almost-Killing equation: Stability, hyperbolicity, and black hole Gauss law","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Edgar Gasper\\'in, Jarrod L. Williams, Justin C. Feng","submitted_at":"2019-11-11T15:56:53Z","abstract_excerpt":"We examine the Hamiltonian formulation and hyperbolicity of the almost-Killing equation (AKE). We find that for all but one parameter choice, the Hamiltonian is unbounded, and in some cases, the AKE has ghost degrees of freedom. We also show the AKE is only strongly hyperbolic for one parameter choice, which corresponds to a case in which the AKE has ghosts. Fortunately, one finds that the AKE reduces to the homogeneous Maxwell equation in a vacuum, so that with the addition of the divergence-free constraint (a \"Lorenz gauge\"), one can still obtain a well-posed problem that is stable in the se"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1911.04354","kind":"arxiv","version":2},"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/1911.04354/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":"2026-07-05T00:25:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y9gyVdjj8gYTXmbIY98iQPyLv0juX+jeCPVAXNSj+KzPRUP6XJtla13xxDcADkxMAaIh+oO8l0KjsBlYcpVNAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T17:59:39.643356Z"},"content_sha256":"0275e4a43a364e08e7b1744b4cd1cd6a05cb406c99a676ecdc38f06c314055e8","schema_version":"1.0","event_id":"sha256:0275e4a43a364e08e7b1744b4cd1cd6a05cb406c99a676ecdc38f06c314055e8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ESPWARMVLFJDCIM2BY4R4HH53F/bundle.json","state_url":"https://pith.science/pith/ESPWARMVLFJDCIM2BY4R4HH53F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ESPWARMVLFJDCIM2BY4R4HH53F/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":"2026-07-06T17:59:39Z","links":{"resolver":"https://pith.science/pith/ESPWARMVLFJDCIM2BY4R4HH53F","bundle":"https://pith.science/pith/ESPWARMVLFJDCIM2BY4R4HH53F/bundle.json","state":"https://pith.science/pith/ESPWARMVLFJDCIM2BY4R4HH53F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ESPWARMVLFJDCIM2BY4R4HH53F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:ESPWARMVLFJDCIM2BY4R4HH53F","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":"d672762ab50bf4422550240088b1e3fcf44cd60a89cadfe80d13505ca5169c27","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2019-11-11T15:56:53Z","title_canon_sha256":"9616e20e196f9a876dd6a25d9f025e6214472a74a94f95867190899aebb6b06b"},"schema_version":"1.0","source":{"id":"1911.04354","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1911.04354","created_at":"2026-07-05T00:25:56Z"},{"alias_kind":"arxiv_version","alias_value":"1911.04354v2","created_at":"2026-07-05T00:25:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1911.04354","created_at":"2026-07-05T00:25:56Z"},{"alias_kind":"pith_short_12","alias_value":"ESPWARMVLFJD","created_at":"2026-07-05T00:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"ESPWARMVLFJDCIM2","created_at":"2026-07-05T00:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"ESPWARMV","created_at":"2026-07-05T00:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:0275e4a43a364e08e7b1744b4cd1cd6a05cb406c99a676ecdc38f06c314055e8","target":"graph","created_at":"2026-07-05T00:25:56Z","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/1911.04354/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We examine the Hamiltonian formulation and hyperbolicity of the almost-Killing equation (AKE). We find that for all but one parameter choice, the Hamiltonian is unbounded, and in some cases, the AKE has ghost degrees of freedom. We also show the AKE is only strongly hyperbolic for one parameter choice, which corresponds to a case in which the AKE has ghosts. Fortunately, one finds that the AKE reduces to the homogeneous Maxwell equation in a vacuum, so that with the addition of the divergence-free constraint (a \"Lorenz gauge\"), one can still obtain a well-posed problem that is stable in the se","authors_text":"Edgar Gasper\\'in, Jarrod L. Williams, Justin C. Feng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2019-11-11T15:56:53Z","title":"Almost-Killing equation: Stability, hyperbolicity, and black hole Gauss law"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1911.04354","kind":"arxiv","version":2},"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:a3e4f0e91a0f81edc7db0e62ec3a6e17ac8094514085c3cc6315e5d2025e74cb","target":"record","created_at":"2026-07-05T00:25:56Z","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":"d672762ab50bf4422550240088b1e3fcf44cd60a89cadfe80d13505ca5169c27","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2019-11-11T15:56:53Z","title_canon_sha256":"9616e20e196f9a876dd6a25d9f025e6214472a74a94f95867190899aebb6b06b"},"schema_version":"1.0","source":{"id":"1911.04354","kind":"arxiv","version":2}},"canonical_sha256":"249f604595595231219a0e391e1cfdd97196268cd3dbb630765eabbe027abcf7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"249f604595595231219a0e391e1cfdd97196268cd3dbb630765eabbe027abcf7","first_computed_at":"2026-07-05T00:25:56.815477Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:25:56.815477Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1zTC4UTklTfa13JBD3DMRPdHYMAqtStBD7HgPleMjXLW6LOgHH5x7zAQHG/eDeP9alVAgLnH5OjHVmpSJdZ1Bg==","signature_status":"signed_v1","signed_at":"2026-07-05T00:25:56.815896Z","signed_message":"canonical_sha256_bytes"},"source_id":"1911.04354","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a3e4f0e91a0f81edc7db0e62ec3a6e17ac8094514085c3cc6315e5d2025e74cb","sha256:0275e4a43a364e08e7b1744b4cd1cd6a05cb406c99a676ecdc38f06c314055e8"],"state_sha256":"057572828262162f6bb4c46b39c4c9a6cc16afa48dd724fa43b1ed856e9e9752"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yusRinugqcJS3+gM1oFMVpsTYnbSKm/N+eC0hyKYoIwPNUh9jhswEHLrf00A+FaXHxvI/99vuGaYCUgRMLZUDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T17:59:39.645248Z","bundle_sha256":"bbf82052cf91319596b7268fe1b75d4995f240a61910520fbcdc1eafdeb9ea2d"}}