{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:Y3S7DVBDYZUAHKGSSX3V4GVXPM","short_pith_number":"pith:Y3S7DVBD","canonical_record":{"source":{"id":"1205.5656","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2012-05-25T10:41:52Z","cross_cats_sorted":["astro-ph.CO"],"title_canon_sha256":"d605a6cf9c1b9f40161407442cfea55680aaddd29fd413f23e054dbb33d4aaf5","abstract_canon_sha256":"879760366184534493a07a4d8a61e9dea7d5a3334f802917df4533d3db7e7094"},"schema_version":"1.0"},"canonical_sha256":"c6e5f1d423c66803a8d295f75e1ab77b3bfeb9155a9e23913b02f39facb5a8ce","source":{"kind":"arxiv","id":"1205.5656","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.5656","created_at":"2026-05-18T01:12:25Z"},{"alias_kind":"arxiv_version","alias_value":"1205.5656v3","created_at":"2026-05-18T01:12:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.5656","created_at":"2026-05-18T01:12:25Z"},{"alias_kind":"pith_short_12","alias_value":"Y3S7DVBDYZUA","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"Y3S7DVBDYZUAHKGS","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"Y3S7DVBD","created_at":"2026-05-18T12:27:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:Y3S7DVBDYZUAHKGSSX3V4GVXPM","target":"record","payload":{"canonical_record":{"source":{"id":"1205.5656","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2012-05-25T10:41:52Z","cross_cats_sorted":["astro-ph.CO"],"title_canon_sha256":"d605a6cf9c1b9f40161407442cfea55680aaddd29fd413f23e054dbb33d4aaf5","abstract_canon_sha256":"879760366184534493a07a4d8a61e9dea7d5a3334f802917df4533d3db7e7094"},"schema_version":"1.0"},"canonical_sha256":"c6e5f1d423c66803a8d295f75e1ab77b3bfeb9155a9e23913b02f39facb5a8ce","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:25.438225Z","signature_b64":"hWojgOUx0dXSByEUL9ZT3CG+2pQ8hzzgO+KynTxFVl88fLNVgsEzsO4//pHZh3zNuYtLOAK50HApiEGHRP/0BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c6e5f1d423c66803a8d295f75e1ab77b3bfeb9155a9e23913b02f39facb5a8ce","last_reissued_at":"2026-05-18T01:12:25.437885Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:25.437885Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.5656","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:12:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"f7EHx/M+ddATGQrJBhuHDnGsltrgFhx/fxsqS90YuwWZW+mUcrXajY08kSVdL9NIFwIS06QgaTPNuGhwQruABQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T00:24:25.201250Z"},"content_sha256":"9b628d953968248f72daa50caa9f9102b72f7c6059b90e19363db7e093473aaf","schema_version":"1.0","event_id":"sha256:9b628d953968248f72daa50caa9f9102b72f7c6059b90e19363db7e093473aaf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:Y3S7DVBDYZUAHKGSSX3V4GVXPM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stability analysis and quasinormal modes of Reissner Nordstr{\\o}m Space-time via Lyapunov exponent","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.CO"],"primary_cat":"gr-qc","authors_text":"Parthapratim Pradhan","submitted_at":"2012-05-25T10:41:52Z","abstract_excerpt":"We explicitly derive the proper time $(\\tau)$ principal Lyapunov exponent ($\\lambda_{p}$) and coordinate time ($t$) principal Lyapunov exponent ($\\lambda_{c}$) for Reissner Nordstr{\\o}m (RN) black hole (BH) . We also compute their ratio. For RN space-time, it is shown that the ratio is $\\frac{\\lambda_{p}}{\\lambda_{c}}=\\frac{r_{0}}{\\sqrt{r_{0}^2-3Mr_{0}+2Q^2}}$ for time-like circular geodesics and for Schwarzschild BH it is $\\frac{\\lambda_{p}}{\\lambda_{c}}=\\frac{\\sqrt{r_{0}}}{\\sqrt{r_{0}-3M}}$. We further show that their ratio $\\frac{\\lambda_{p}}{\\lambda_{c}}$ may vary from orbit to orbit. For "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.5656","kind":"arxiv","version":3},"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":"2026-05-18T01:12:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uns2Ys0GwmUXnTzZO6BkaQTwBO7izlDF3XsrIWGbJVwwirGP5IebTTVIIAyGmL93bwOjSSsfACjVRDV+tduuBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T00:24:25.201924Z"},"content_sha256":"9abb6e3b679101121f89608684966bf14d11f5217072a70f176f341481c57260","schema_version":"1.0","event_id":"sha256:9abb6e3b679101121f89608684966bf14d11f5217072a70f176f341481c57260"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Y3S7DVBDYZUAHKGSSX3V4GVXPM/bundle.json","state_url":"https://pith.science/pith/Y3S7DVBDYZUAHKGSSX3V4GVXPM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Y3S7DVBDYZUAHKGSSX3V4GVXPM/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":"2026-05-26T00:24:25Z","links":{"resolver":"https://pith.science/pith/Y3S7DVBDYZUAHKGSSX3V4GVXPM","bundle":"https://pith.science/pith/Y3S7DVBDYZUAHKGSSX3V4GVXPM/bundle.json","state":"https://pith.science/pith/Y3S7DVBDYZUAHKGSSX3V4GVXPM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Y3S7DVBDYZUAHKGSSX3V4GVXPM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:Y3S7DVBDYZUAHKGSSX3V4GVXPM","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":"879760366184534493a07a4d8a61e9dea7d5a3334f802917df4533d3db7e7094","cross_cats_sorted":["astro-ph.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2012-05-25T10:41:52Z","title_canon_sha256":"d605a6cf9c1b9f40161407442cfea55680aaddd29fd413f23e054dbb33d4aaf5"},"schema_version":"1.0","source":{"id":"1205.5656","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.5656","created_at":"2026-05-18T01:12:25Z"},{"alias_kind":"arxiv_version","alias_value":"1205.5656v3","created_at":"2026-05-18T01:12:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.5656","created_at":"2026-05-18T01:12:25Z"},{"alias_kind":"pith_short_12","alias_value":"Y3S7DVBDYZUA","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"Y3S7DVBDYZUAHKGS","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"Y3S7DVBD","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:9abb6e3b679101121f89608684966bf14d11f5217072a70f176f341481c57260","target":"graph","created_at":"2026-05-18T01:12:25Z","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 explicitly derive the proper time $(\\tau)$ principal Lyapunov exponent ($\\lambda_{p}$) and coordinate time ($t$) principal Lyapunov exponent ($\\lambda_{c}$) for Reissner Nordstr{\\o}m (RN) black hole (BH) . We also compute their ratio. For RN space-time, it is shown that the ratio is $\\frac{\\lambda_{p}}{\\lambda_{c}}=\\frac{r_{0}}{\\sqrt{r_{0}^2-3Mr_{0}+2Q^2}}$ for time-like circular geodesics and for Schwarzschild BH it is $\\frac{\\lambda_{p}}{\\lambda_{c}}=\\frac{\\sqrt{r_{0}}}{\\sqrt{r_{0}-3M}}$. We further show that their ratio $\\frac{\\lambda_{p}}{\\lambda_{c}}$ may vary from orbit to orbit. For ","authors_text":"Parthapratim Pradhan","cross_cats":["astro-ph.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2012-05-25T10:41:52Z","title":"Stability analysis and quasinormal modes of Reissner Nordstr{\\o}m Space-time via Lyapunov exponent"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.5656","kind":"arxiv","version":3},"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":"sha256:9b628d953968248f72daa50caa9f9102b72f7c6059b90e19363db7e093473aaf","target":"record","created_at":"2026-05-18T01:12:25Z","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":"879760366184534493a07a4d8a61e9dea7d5a3334f802917df4533d3db7e7094","cross_cats_sorted":["astro-ph.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2012-05-25T10:41:52Z","title_canon_sha256":"d605a6cf9c1b9f40161407442cfea55680aaddd29fd413f23e054dbb33d4aaf5"},"schema_version":"1.0","source":{"id":"1205.5656","kind":"arxiv","version":3}},"canonical_sha256":"c6e5f1d423c66803a8d295f75e1ab77b3bfeb9155a9e23913b02f39facb5a8ce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c6e5f1d423c66803a8d295f75e1ab77b3bfeb9155a9e23913b02f39facb5a8ce","first_computed_at":"2026-05-18T01:12:25.437885Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:25.437885Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hWojgOUx0dXSByEUL9ZT3CG+2pQ8hzzgO+KynTxFVl88fLNVgsEzsO4//pHZh3zNuYtLOAK50HApiEGHRP/0BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:25.438225Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.5656","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9b628d953968248f72daa50caa9f9102b72f7c6059b90e19363db7e093473aaf","sha256:9abb6e3b679101121f89608684966bf14d11f5217072a70f176f341481c57260"],"state_sha256":"d498c00b7aad516dc052e847e48b7cc6c5b1664d97ef88e9cf99032bf8cb2d47"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y90JYRFeB1mKdQxh3ZzTMXoU4cdkuXpzpr1ck4q16226WR+LeA+TDHeIIRqVmLz3Uifub/gAPSr+1uL7NtHoDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T00:24:25.204421Z","bundle_sha256":"7f3cae310df274b2dd9066a41ca0e64ff64206971cd70a904594a29c2f9b0877"}}