{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:JJCJDZZN6PSTGTQSYFV3VZW2ZO","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":"04048d411b0c16f074e731767af0d4a19c611491b5894a49164b21ec5afd1b30","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2017-04-25T14:31:24Z","title_canon_sha256":"3402e57613447a2bc93071df187fc6c8ee16bcffdbd8976ebdfdc2e8a41cf506"},"schema_version":"1.0","source":{"id":"1704.07713","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.07713","created_at":"2026-05-18T00:41:07Z"},{"alias_kind":"arxiv_version","alias_value":"1704.07713v2","created_at":"2026-05-18T00:41:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.07713","created_at":"2026-05-18T00:41:07Z"},{"alias_kind":"pith_short_12","alias_value":"JJCJDZZN6PST","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"JJCJDZZN6PSTGTQS","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"JJCJDZZN","created_at":"2026-05-18T12:31:24Z"}],"graph_snapshots":[{"event_id":"sha256:955af0f663ef007ea5129f0a64f32d0beba4e2e5f934120fc14bd513b0125cb6","target":"graph","created_at":"2026-05-18T00:41:07Z","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":"We study behaviour of gravitational waves in the recently introduced general relativistic polytropic spheres containing a region of trapped null geodesics extended around radius of the stable null circular geodesic that can exist for the polytropic index $N>2.138$ and the relativistic parameter, giving ratio of the central pressure $p_\\mathrm{c}$ to the central energy density $\\rho_\\mathrm{c}$, higher than $\\sigma = 0.677$. In the trapping zones of such polytropes, the effective potential of the axial gravitational wave perturbations resembles those related to the ultracompact uniform density ","authors_text":"Bobir Toshmatov, Jan Hlad\\'ik, Jan Novotn\\'y, Jan Schee, Zden\\v{e}k Stuchl\\'ik","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2017-04-25T14:31:24Z","title":"Gravitational instability of polytropic spheres containing region of trapped null geodesics: a possible explanation of central supermassive black holes in galactic halos"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.07713","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:a5d84d29a1988fab907870bc84204d950126209ad4e010a3c31d728d88fcba53","target":"record","created_at":"2026-05-18T00:41:07Z","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":"04048d411b0c16f074e731767af0d4a19c611491b5894a49164b21ec5afd1b30","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2017-04-25T14:31:24Z","title_canon_sha256":"3402e57613447a2bc93071df187fc6c8ee16bcffdbd8976ebdfdc2e8a41cf506"},"schema_version":"1.0","source":{"id":"1704.07713","kind":"arxiv","version":2}},"canonical_sha256":"4a4491e72df3e5334e12c16bbae6dacb889106f845ecf9466c4b448f944bf88c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4a4491e72df3e5334e12c16bbae6dacb889106f845ecf9466c4b448f944bf88c","first_computed_at":"2026-05-18T00:41:07.051821Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:07.051821Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"x3a8h++asmKZQKcJFZ62ScPcvgAhxWJQgAIpntmAGSBQCianzLv7UO9Moalu0HP7Dp4hQXzmg5lPNrM/wLaMAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:07.052415Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.07713","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a5d84d29a1988fab907870bc84204d950126209ad4e010a3c31d728d88fcba53","sha256:955af0f663ef007ea5129f0a64f32d0beba4e2e5f934120fc14bd513b0125cb6"],"state_sha256":"4cf8f17f1f382c220519bab210255d292ac89c0fb03be0471e289d48af0b3830"}