{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:ZESDPELFNKO453HHLFC4VLPDGN","short_pith_number":"pith:ZESDPELF","canonical_record":{"source":{"id":"2607.17046","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2026-07-19T03:22:26Z","cross_cats_sorted":[],"title_canon_sha256":"81d063fb71796e77343eb5b6dac8886e02d782884274d6325461c49bd27b043c","abstract_canon_sha256":"5f54a55ee44b08b2dead3cc17792b4bb0a14138ed9f023e6b0751c3406a62583"},"schema_version":"1.0"},"canonical_sha256":"c9243791656a9dceece75945caade33356a43e95aabdf1f6ae26e9da953104c7","source":{"kind":"arxiv","id":"2607.17046","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.17046","created_at":"2026-07-21T01:21:12Z"},{"alias_kind":"arxiv_version","alias_value":"2607.17046v1","created_at":"2026-07-21T01:21:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.17046","created_at":"2026-07-21T01:21:12Z"},{"alias_kind":"pith_short_12","alias_value":"ZESDPELFNKO4","created_at":"2026-07-21T01:21:12Z"},{"alias_kind":"pith_short_16","alias_value":"ZESDPELFNKO453HH","created_at":"2026-07-21T01:21:12Z"},{"alias_kind":"pith_short_8","alias_value":"ZESDPELF","created_at":"2026-07-21T01:21:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:ZESDPELFNKO453HHLFC4VLPDGN","target":"record","payload":{"canonical_record":{"source":{"id":"2607.17046","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2026-07-19T03:22:26Z","cross_cats_sorted":[],"title_canon_sha256":"81d063fb71796e77343eb5b6dac8886e02d782884274d6325461c49bd27b043c","abstract_canon_sha256":"5f54a55ee44b08b2dead3cc17792b4bb0a14138ed9f023e6b0751c3406a62583"},"schema_version":"1.0"},"canonical_sha256":"c9243791656a9dceece75945caade33356a43e95aabdf1f6ae26e9da953104c7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-21T01:21:12.110492Z","signature_b64":"U8Z6ZdNPTtxkF3j20oQIhI40JIrAXqlU3bzl1AJ1ghW00etkl+hB7x3uJ6jaIJLhK1AaCAmcabChwdMUaMQoDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c9243791656a9dceece75945caade33356a43e95aabdf1f6ae26e9da953104c7","last_reissued_at":"2026-07-21T01:21:12.109661Z","signature_status":"signed_v1","first_computed_at":"2026-07-21T01:21:12.109661Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.17046","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":"2026-07-21T01:21:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jZLARPPt4AbflE+W3vn/CFqahmeGplO/+TY/b7QN/v3afjtmvfyjdAd7GGyJDkgG6sQBBrHsp/J2tg6iVqJRBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T13:10:56.063580Z"},"content_sha256":"30ade09674974042ddad6140c8ac99e42789191d6c835737fc9c0ae49a03f852","schema_version":"1.0","event_id":"sha256:30ade09674974042ddad6140c8ac99e42789191d6c835737fc9c0ae49a03f852"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:ZESDPELFNKO453HHLFC4VLPDGN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Perturbations of black holes in mass-varying massive gravity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"De-Jun Wu","submitted_at":"2026-07-19T03:22:26Z","abstract_excerpt":"Based on eigendecomposition and matrix perturbation theory, we propose an alternative method for analyzing perturbations in massive gravity that is applicable to both the base theory and its various modifications. We demonstrate the validity of this approach even in seemingly singular regimes. Applying this framework to mass-varying massive gravity, we compute perturbations for all constant-scalar Schwarzschild-(A)dS black hole solutions. We show that, under the condition $\\beta = \\alpha^2$, the tensor sector of these black holes reduces to that of general relativity, while the scalar sector r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.17046","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/2607.17046/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":"2026-07-21T01:21:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EA6qLQRSEEk/Loo+T4VMMI6fT+Vo0W0yfRs2okcNut7hTE50VtX55NKl7d5oJ1BuD6l7cFZ4FFuS8EvmITjjCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T13:10:56.064305Z"},"content_sha256":"96926ed09341cce282ccc7e5fc2c44ca5a054ec494ef216dbcff0dda5f696d35","schema_version":"1.0","event_id":"sha256:96926ed09341cce282ccc7e5fc2c44ca5a054ec494ef216dbcff0dda5f696d35"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZESDPELFNKO453HHLFC4VLPDGN/bundle.json","state_url":"https://pith.science/pith/ZESDPELFNKO453HHLFC4VLPDGN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZESDPELFNKO453HHLFC4VLPDGN/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":"2026-08-04T13:10:56Z","links":{"resolver":"https://pith.science/pith/ZESDPELFNKO453HHLFC4VLPDGN","bundle":"https://pith.science/pith/ZESDPELFNKO453HHLFC4VLPDGN/bundle.json","state":"https://pith.science/pith/ZESDPELFNKO453HHLFC4VLPDGN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZESDPELFNKO453HHLFC4VLPDGN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:ZESDPELFNKO453HHLFC4VLPDGN","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":"5f54a55ee44b08b2dead3cc17792b4bb0a14138ed9f023e6b0751c3406a62583","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2026-07-19T03:22:26Z","title_canon_sha256":"81d063fb71796e77343eb5b6dac8886e02d782884274d6325461c49bd27b043c"},"schema_version":"1.0","source":{"id":"2607.17046","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.17046","created_at":"2026-07-21T01:21:12Z"},{"alias_kind":"arxiv_version","alias_value":"2607.17046v1","created_at":"2026-07-21T01:21:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.17046","created_at":"2026-07-21T01:21:12Z"},{"alias_kind":"pith_short_12","alias_value":"ZESDPELFNKO4","created_at":"2026-07-21T01:21:12Z"},{"alias_kind":"pith_short_16","alias_value":"ZESDPELFNKO453HH","created_at":"2026-07-21T01:21:12Z"},{"alias_kind":"pith_short_8","alias_value":"ZESDPELF","created_at":"2026-07-21T01:21:12Z"}],"graph_snapshots":[{"event_id":"sha256:96926ed09341cce282ccc7e5fc2c44ca5a054ec494ef216dbcff0dda5f696d35","target":"graph","created_at":"2026-07-21T01:21:12Z","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/2607.17046/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Based on eigendecomposition and matrix perturbation theory, we propose an alternative method for analyzing perturbations in massive gravity that is applicable to both the base theory and its various modifications. We demonstrate the validity of this approach even in seemingly singular regimes. Applying this framework to mass-varying massive gravity, we compute perturbations for all constant-scalar Schwarzschild-(A)dS black hole solutions. We show that, under the condition $\\beta = \\alpha^2$, the tensor sector of these black holes reduces to that of general relativity, while the scalar sector r","authors_text":"De-Jun Wu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2026-07-19T03:22:26Z","title":"Perturbations of black holes in mass-varying massive gravity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.17046","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":"sha256:30ade09674974042ddad6140c8ac99e42789191d6c835737fc9c0ae49a03f852","target":"record","created_at":"2026-07-21T01:21:12Z","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":"5f54a55ee44b08b2dead3cc17792b4bb0a14138ed9f023e6b0751c3406a62583","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2026-07-19T03:22:26Z","title_canon_sha256":"81d063fb71796e77343eb5b6dac8886e02d782884274d6325461c49bd27b043c"},"schema_version":"1.0","source":{"id":"2607.17046","kind":"arxiv","version":1}},"canonical_sha256":"c9243791656a9dceece75945caade33356a43e95aabdf1f6ae26e9da953104c7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c9243791656a9dceece75945caade33356a43e95aabdf1f6ae26e9da953104c7","first_computed_at":"2026-07-21T01:21:12.109661Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-21T01:21:12.109661Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"U8Z6ZdNPTtxkF3j20oQIhI40JIrAXqlU3bzl1AJ1ghW00etkl+hB7x3uJ6jaIJLhK1AaCAmcabChwdMUaMQoDw==","signature_status":"signed_v1","signed_at":"2026-07-21T01:21:12.110492Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.17046","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:30ade09674974042ddad6140c8ac99e42789191d6c835737fc9c0ae49a03f852","sha256:96926ed09341cce282ccc7e5fc2c44ca5a054ec494ef216dbcff0dda5f696d35"],"state_sha256":"125b2d2463a786d7e4e59a34634fffafab97cd7c0f56498fd8d692a1b51f1b0b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yrqamCpu1dvwztaKvdKzsPrkMkMcwDWR+NRn6Pm4Fl/GatM51Bpjs7OhrkF9NjAWYtUhvmWBSJtPMorzK9ewDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T13:10:56.070396Z","bundle_sha256":"fcb5653a1d9900b8763f420169d674dd0504d08be856c4a04cb54ec7e94ec650"}}