{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:OK7KDQTCUROPI2RABVXOLVF7SK","short_pith_number":"pith:OK7KDQTC","canonical_record":{"source":{"id":"1211.6534","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2012-11-28T07:53:12Z","cross_cats_sorted":[],"title_canon_sha256":"369db8510e6eac75e15501fe9b38b97d51daf296589db7f3e30ace3b25edae4f","abstract_canon_sha256":"82371da57578cd730dc05f2702bc3ab7480a628ee30128ca3013b4c377112bb1"},"schema_version":"1.0"},"canonical_sha256":"72bea1c262a45cf46a200d6ee5d4bf92ad45e8553c4a4985e3099d899d3a66a2","source":{"kind":"arxiv","id":"1211.6534","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.6534","created_at":"2026-05-18T02:32:54Z"},{"alias_kind":"arxiv_version","alias_value":"1211.6534v2","created_at":"2026-05-18T02:32:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.6534","created_at":"2026-05-18T02:32:54Z"},{"alias_kind":"pith_short_12","alias_value":"OK7KDQTCUROP","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"OK7KDQTCUROPI2RA","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"OK7KDQTC","created_at":"2026-05-18T12:27:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:OK7KDQTCUROPI2RABVXOLVF7SK","target":"record","payload":{"canonical_record":{"source":{"id":"1211.6534","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2012-11-28T07:53:12Z","cross_cats_sorted":[],"title_canon_sha256":"369db8510e6eac75e15501fe9b38b97d51daf296589db7f3e30ace3b25edae4f","abstract_canon_sha256":"82371da57578cd730dc05f2702bc3ab7480a628ee30128ca3013b4c377112bb1"},"schema_version":"1.0"},"canonical_sha256":"72bea1c262a45cf46a200d6ee5d4bf92ad45e8553c4a4985e3099d899d3a66a2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:32:54.590128Z","signature_b64":"qCiRSuzTW7V/TR8DD7PdUg37eaw3Zr5V4r7M0ZHNaalniSJ9Y5+wgO6INJDVQaZy9m4W1NSkjBOiz7isbubeBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"72bea1c262a45cf46a200d6ee5d4bf92ad45e8553c4a4985e3099d899d3a66a2","last_reissued_at":"2026-05-18T02:32:54.589712Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:32:54.589712Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1211.6534","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":"2026-05-18T02:32:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Bb8dA9GkurF0OJ2/oLSZn+fYIXR1jYNVjfiyEa0cJ1zao81UDNzI16/m9nv5n/bGLOo3s7spuAsYH0zpCVc3Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T06:05:26.869302Z"},"content_sha256":"741b240458a28aae9a5c99ca5bab85d5ed03bd8188af7919933a8dcfe07f522a","schema_version":"1.0","event_id":"sha256:741b240458a28aae9a5c99ca5bab85d5ed03bd8188af7919933a8dcfe07f522a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:OK7KDQTCUROPI2RABVXOLVF7SK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stability Analysis in N dimensional Gravitational collapse with equation of state","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"R. V. Saraykar, Sanjay Sarwe","submitted_at":"2012-11-28T07:53:12Z","abstract_excerpt":"We study stability of occurrence of black holes and naked singularities that arise as a final state for a complete gravitational collapse of type I matter field in a spherically symmetric $N$ dimensional spacetime with equation of state $p = k \\rho$, $0 \\leq k \\leq 1$. We prove that for a regular initial data comprising of pressure (or density) profiles at an initial surface $t = t_{i}$, from which the collapse evolves, there exists a large class of the velocity functions and classes of solutions of Einstein equations, such that the spacetime evolution goes to a final state which is either a b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.6534","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":""},"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":"2026-05-18T02:32:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CO6EhX5d3uxsuk6uq5gf54TUzYOXb3VD8T0RmSPOAVenlnOnj/VUHM2W6PPBGJ5K5A4KpLOW04oQEn6fWDJmCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T06:05:26.870239Z"},"content_sha256":"83238aa4c1f393601fd585a37609b1e77e4ae81e63d0ae9b954d47532871bb40","schema_version":"1.0","event_id":"sha256:83238aa4c1f393601fd585a37609b1e77e4ae81e63d0ae9b954d47532871bb40"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OK7KDQTCUROPI2RABVXOLVF7SK/bundle.json","state_url":"https://pith.science/pith/OK7KDQTCUROPI2RABVXOLVF7SK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OK7KDQTCUROPI2RABVXOLVF7SK/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":"2026-08-04T06:05:26Z","links":{"resolver":"https://pith.science/pith/OK7KDQTCUROPI2RABVXOLVF7SK","bundle":"https://pith.science/pith/OK7KDQTCUROPI2RABVXOLVF7SK/bundle.json","state":"https://pith.science/pith/OK7KDQTCUROPI2RABVXOLVF7SK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OK7KDQTCUROPI2RABVXOLVF7SK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:OK7KDQTCUROPI2RABVXOLVF7SK","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":"82371da57578cd730dc05f2702bc3ab7480a628ee30128ca3013b4c377112bb1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2012-11-28T07:53:12Z","title_canon_sha256":"369db8510e6eac75e15501fe9b38b97d51daf296589db7f3e30ace3b25edae4f"},"schema_version":"1.0","source":{"id":"1211.6534","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.6534","created_at":"2026-05-18T02:32:54Z"},{"alias_kind":"arxiv_version","alias_value":"1211.6534v2","created_at":"2026-05-18T02:32:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.6534","created_at":"2026-05-18T02:32:54Z"},{"alias_kind":"pith_short_12","alias_value":"OK7KDQTCUROP","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"OK7KDQTCUROPI2RA","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"OK7KDQTC","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:83238aa4c1f393601fd585a37609b1e77e4ae81e63d0ae9b954d47532871bb40","target":"graph","created_at":"2026-05-18T02:32:54Z","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 stability of occurrence of black holes and naked singularities that arise as a final state for a complete gravitational collapse of type I matter field in a spherically symmetric $N$ dimensional spacetime with equation of state $p = k \\rho$, $0 \\leq k \\leq 1$. We prove that for a regular initial data comprising of pressure (or density) profiles at an initial surface $t = t_{i}$, from which the collapse evolves, there exists a large class of the velocity functions and classes of solutions of Einstein equations, such that the spacetime evolution goes to a final state which is either a b","authors_text":"R. V. Saraykar, Sanjay Sarwe","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2012-11-28T07:53:12Z","title":"Stability Analysis in N dimensional Gravitational collapse with equation of state"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.6534","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":"sha256:741b240458a28aae9a5c99ca5bab85d5ed03bd8188af7919933a8dcfe07f522a","target":"record","created_at":"2026-05-18T02:32:54Z","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":"82371da57578cd730dc05f2702bc3ab7480a628ee30128ca3013b4c377112bb1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2012-11-28T07:53:12Z","title_canon_sha256":"369db8510e6eac75e15501fe9b38b97d51daf296589db7f3e30ace3b25edae4f"},"schema_version":"1.0","source":{"id":"1211.6534","kind":"arxiv","version":2}},"canonical_sha256":"72bea1c262a45cf46a200d6ee5d4bf92ad45e8553c4a4985e3099d899d3a66a2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"72bea1c262a45cf46a200d6ee5d4bf92ad45e8553c4a4985e3099d899d3a66a2","first_computed_at":"2026-05-18T02:32:54.589712Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:32:54.589712Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qCiRSuzTW7V/TR8DD7PdUg37eaw3Zr5V4r7M0ZHNaalniSJ9Y5+wgO6INJDVQaZy9m4W1NSkjBOiz7isbubeBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:32:54.590128Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.6534","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:741b240458a28aae9a5c99ca5bab85d5ed03bd8188af7919933a8dcfe07f522a","sha256:83238aa4c1f393601fd585a37609b1e77e4ae81e63d0ae9b954d47532871bb40"],"state_sha256":"bb9e5f22a0cc9497fcc463c9e4c36e61f8e45784c9842ea3eeda7f4d95dd4570"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Uz7J0M2X7OpoRUUYnk9bj3OMH67wKWGf5DIBjgwFbIxke8pbHgQNZmA8mbEILzORESgCMSqPsHe9aOHRgAx1Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T06:05:26.877185Z","bundle_sha256":"e6c983be9370b6a060001595d1602c812d1c6312158f1a309dfab7fea2ed23ba"}}