{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:KW3SKBKMSSMMYURDDWAWG4UTSG","short_pith_number":"pith:KW3SKBKM","canonical_record":{"source":{"id":"2105.08936","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2021-05-19T05:54:40Z","cross_cats_sorted":[],"title_canon_sha256":"f5c109f7a0de8df90d354e3c05d5015b9f534ccbd35ae2fdc650134ca5fd7c77","abstract_canon_sha256":"8050d8d1551ada81c8f05c4024014f2de8d8b750411e4591e576982bda09c46c"},"schema_version":"1.0"},"canonical_sha256":"55b725054c9498cc52231d8163729391b92420e59b9f563d62594dbe80af1d5e","source":{"kind":"arxiv","id":"2105.08936","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2105.08936","created_at":"2026-07-05T02:41:35Z"},{"alias_kind":"arxiv_version","alias_value":"2105.08936v1","created_at":"2026-07-05T02:41:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2105.08936","created_at":"2026-07-05T02:41:35Z"},{"alias_kind":"pith_short_12","alias_value":"KW3SKBKMSSMM","created_at":"2026-07-05T02:41:35Z"},{"alias_kind":"pith_short_16","alias_value":"KW3SKBKMSSMMYURD","created_at":"2026-07-05T02:41:35Z"},{"alias_kind":"pith_short_8","alias_value":"KW3SKBKM","created_at":"2026-07-05T02:41:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:KW3SKBKMSSMMYURDDWAWG4UTSG","target":"record","payload":{"canonical_record":{"source":{"id":"2105.08936","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2021-05-19T05:54:40Z","cross_cats_sorted":[],"title_canon_sha256":"f5c109f7a0de8df90d354e3c05d5015b9f534ccbd35ae2fdc650134ca5fd7c77","abstract_canon_sha256":"8050d8d1551ada81c8f05c4024014f2de8d8b750411e4591e576982bda09c46c"},"schema_version":"1.0"},"canonical_sha256":"55b725054c9498cc52231d8163729391b92420e59b9f563d62594dbe80af1d5e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:41:35.435075Z","signature_b64":"/PUkkR337k12FXJsAArGtUd8G34DSEMThxa5kXAFNJLr8RthGZBFzDneN7pD4TNC56HGtXf/7pmcKzn8KhotAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"55b725054c9498cc52231d8163729391b92420e59b9f563d62594dbe80af1d5e","last_reissued_at":"2026-07-05T02:41:35.434659Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:41:35.434659Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2105.08936","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":"2026-07-05T02:41:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XkKi/uOnKIO+K8T57hdggcULJf5igdaJoiGGhlVF7Lt+x+tH+p7MU6R68eGHFTcFzNzHPJLKhVbuqh7TAjd8CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T09:33:08.340285Z"},"content_sha256":"8e9fc9efa4dba02723810d22819d97c919d653baa9723bbae60c8e3ea504d866","schema_version":"1.0","event_id":"sha256:8e9fc9efa4dba02723810d22819d97c919d653baa9723bbae60c8e3ea504d866"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:KW3SKBKMSSMMYURDDWAWG4UTSG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Black holes in the quadratic-order extended vector-tensor theories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Masato Minamitsuji","submitted_at":"2021-05-19T05:54:40Z","abstract_excerpt":"We investigate the static and spherically black hole solutions in the quadratic-order extended vector-tensor theories without suffering from the Ostrogradsky instabilities, which include the quartic-order (beyond-)generalized Proca theories as the subclass. We start from the most general action of the vector-tensor theories constructed with up to the quadratic-order terms of the first-order covariant derivatives of the vector field, and derive the Euler-Lagrange equations for the metric and vector field variables in the static and spherically symmetric backgrounds. We then substitute the space"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2105.08936","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/2105.08936/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":"2026-07-05T02:41:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s3fEZz2p41YbdeNjzIryGT6F+tPfEdRphpSC231RDubAVf+pQQxE8msSyBUOauxbCuEHdwGF97tcmAVI+tS7Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T09:33:08.340770Z"},"content_sha256":"19317fda6dcd33b8a2cf69a2d617bbe860c9cfc2f877b46c516ade51f5a98f2a","schema_version":"1.0","event_id":"sha256:19317fda6dcd33b8a2cf69a2d617bbe860c9cfc2f877b46c516ade51f5a98f2a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KW3SKBKMSSMMYURDDWAWG4UTSG/bundle.json","state_url":"https://pith.science/pith/KW3SKBKMSSMMYURDDWAWG4UTSG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KW3SKBKMSSMMYURDDWAWG4UTSG/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":"2026-08-09T09:33:08Z","links":{"resolver":"https://pith.science/pith/KW3SKBKMSSMMYURDDWAWG4UTSG","bundle":"https://pith.science/pith/KW3SKBKMSSMMYURDDWAWG4UTSG/bundle.json","state":"https://pith.science/pith/KW3SKBKMSSMMYURDDWAWG4UTSG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KW3SKBKMSSMMYURDDWAWG4UTSG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:KW3SKBKMSSMMYURDDWAWG4UTSG","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":"8050d8d1551ada81c8f05c4024014f2de8d8b750411e4591e576982bda09c46c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2021-05-19T05:54:40Z","title_canon_sha256":"f5c109f7a0de8df90d354e3c05d5015b9f534ccbd35ae2fdc650134ca5fd7c77"},"schema_version":"1.0","source":{"id":"2105.08936","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2105.08936","created_at":"2026-07-05T02:41:35Z"},{"alias_kind":"arxiv_version","alias_value":"2105.08936v1","created_at":"2026-07-05T02:41:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2105.08936","created_at":"2026-07-05T02:41:35Z"},{"alias_kind":"pith_short_12","alias_value":"KW3SKBKMSSMM","created_at":"2026-07-05T02:41:35Z"},{"alias_kind":"pith_short_16","alias_value":"KW3SKBKMSSMMYURD","created_at":"2026-07-05T02:41:35Z"},{"alias_kind":"pith_short_8","alias_value":"KW3SKBKM","created_at":"2026-07-05T02:41:35Z"}],"graph_snapshots":[{"event_id":"sha256:19317fda6dcd33b8a2cf69a2d617bbe860c9cfc2f877b46c516ade51f5a98f2a","target":"graph","created_at":"2026-07-05T02:41:35Z","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/2105.08936/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We investigate the static and spherically black hole solutions in the quadratic-order extended vector-tensor theories without suffering from the Ostrogradsky instabilities, which include the quartic-order (beyond-)generalized Proca theories as the subclass. We start from the most general action of the vector-tensor theories constructed with up to the quadratic-order terms of the first-order covariant derivatives of the vector field, and derive the Euler-Lagrange equations for the metric and vector field variables in the static and spherically symmetric backgrounds. We then substitute the space","authors_text":"Masato Minamitsuji","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2021-05-19T05:54:40Z","title":"Black holes in the quadratic-order extended vector-tensor theories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2105.08936","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":"sha256:8e9fc9efa4dba02723810d22819d97c919d653baa9723bbae60c8e3ea504d866","target":"record","created_at":"2026-07-05T02:41:35Z","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":"8050d8d1551ada81c8f05c4024014f2de8d8b750411e4591e576982bda09c46c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2021-05-19T05:54:40Z","title_canon_sha256":"f5c109f7a0de8df90d354e3c05d5015b9f534ccbd35ae2fdc650134ca5fd7c77"},"schema_version":"1.0","source":{"id":"2105.08936","kind":"arxiv","version":1}},"canonical_sha256":"55b725054c9498cc52231d8163729391b92420e59b9f563d62594dbe80af1d5e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"55b725054c9498cc52231d8163729391b92420e59b9f563d62594dbe80af1d5e","first_computed_at":"2026-07-05T02:41:35.434659Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:41:35.434659Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/PUkkR337k12FXJsAArGtUd8G34DSEMThxa5kXAFNJLr8RthGZBFzDneN7pD4TNC56HGtXf/7pmcKzn8KhotAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T02:41:35.435075Z","signed_message":"canonical_sha256_bytes"},"source_id":"2105.08936","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8e9fc9efa4dba02723810d22819d97c919d653baa9723bbae60c8e3ea504d866","sha256:19317fda6dcd33b8a2cf69a2d617bbe860c9cfc2f877b46c516ade51f5a98f2a"],"state_sha256":"4641382ac3bb04ba728e4a7114bc644fdbb308221ddd12a865849307a4a6039e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0tXncRn3NcIdb0FpqWtu8mO5IcQ0T/FwCQrZ0c8/2xTA7QItQQHnrsAeSKCp0cx4iNdJVMJ/MosN6D4MY/pCDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T09:33:08.343898Z","bundle_sha256":"ff01277b7fb25a814d1c8e62a6f005ab219dc484a8e043491b35ca481ecdc0e4"}}