{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:HPHBZJTXXKBGBHFXGBL6LTBCSC","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":"b8032efe15ffe566fb8353bb2a8e5c2064f13dcd6c25b310b50a687454cfba42","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"gr-qc","submitted_at":"2026-05-30T00:45:48Z","title_canon_sha256":"127a3a2391852ac90f25c10803ff122d2496359121f308485a69c0ed4b163959"},"schema_version":"1.0","source":{"id":"2606.00456","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.00456","created_at":"2026-06-02T01:03:55Z"},{"alias_kind":"arxiv_version","alias_value":"2606.00456v1","created_at":"2026-06-02T01:03:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.00456","created_at":"2026-06-02T01:03:55Z"},{"alias_kind":"pith_short_12","alias_value":"HPHBZJTXXKBG","created_at":"2026-06-02T01:03:55Z"},{"alias_kind":"pith_short_16","alias_value":"HPHBZJTXXKBGBHFX","created_at":"2026-06-02T01:03:55Z"},{"alias_kind":"pith_short_8","alias_value":"HPHBZJTX","created_at":"2026-06-02T01:03:55Z"}],"graph_snapshots":[{"event_id":"sha256:6a06f584e4117ad0c81245773c6d01651660cc99b933e2f1402958863b274a2d","target":"graph","created_at":"2026-06-02T01:03:55Z","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/2606.00456/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The spacetime behavior at very extreme conditions, such as the regions near a black hole, can be very difficult to modelize. In this work we introduce a new geometric method that allows to calculate the parameters of photon spheres, massive particle surfaces and shadow radius of black holes. We build upon a perturvative approach but bases in intrinsic curvatures, such as the geodesic and Gaussian curvatures. At leading order, the method allows to find the radius of the perturbation in the time-like case, which has not been studied in the literature. In the null case we are able to recover the ","authors_text":"Fernando G. Veloz, Oscar Lasso Andino","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"gr-qc","submitted_at":"2026-05-30T00:45:48Z","title":"A perturbative geometric approach for photon spheres, massive particle surfaces and black hole shadows with mass variations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.00456","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":"sha256:05a0d9f6707fa7b8f426d02295eac73990e2cad5544e8dd3539202f294a8e345","target":"record","created_at":"2026-06-02T01:03:55Z","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":"b8032efe15ffe566fb8353bb2a8e5c2064f13dcd6c25b310b50a687454cfba42","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"gr-qc","submitted_at":"2026-05-30T00:45:48Z","title_canon_sha256":"127a3a2391852ac90f25c10803ff122d2496359121f308485a69c0ed4b163959"},"schema_version":"1.0","source":{"id":"2606.00456","kind":"arxiv","version":1}},"canonical_sha256":"3bce1ca677ba82609cb73057e5cc2290807b9ba503b3b0060d4677eb31a10d2e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3bce1ca677ba82609cb73057e5cc2290807b9ba503b3b0060d4677eb31a10d2e","first_computed_at":"2026-06-02T01:03:55.226381Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-02T01:03:55.226381Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"b2ijSPgZgJDSQNSw04RzJqseXNNqOJgXsiIXeIcq49xdUiy4JqXJRO9zjCJkCrw6AUi9q97kWCgBAsU2cTQ9AQ==","signature_status":"signed_v1","signed_at":"2026-06-02T01:03:55.226761Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.00456","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:05a0d9f6707fa7b8f426d02295eac73990e2cad5544e8dd3539202f294a8e345","sha256:6a06f584e4117ad0c81245773c6d01651660cc99b933e2f1402958863b274a2d"],"state_sha256":"9349775f54e1c016ea381d5569c6f894dc1f8c996a87d8fae7c8c2c745465428"}