{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:EAXQ4ILJA6EMMMEO3LKJQ4AW35","short_pith_number":"pith:EAXQ4ILJ","canonical_record":{"source":{"id":"1406.5883","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2014-06-23T12:18:10Z","cross_cats_sorted":[],"title_canon_sha256":"bcc934cbdc004390365b2750f335579b97eaf158b53155355ff076454de0dbc3","abstract_canon_sha256":"dc64f85fef75c08fbc2d0aab2d1acef41216aeb0a56434683709c00de51bc45f"},"schema_version":"1.0"},"canonical_sha256":"202f0e21690788c6308edad4987016df7bda59d1ea6c53f1d211facd6adea0a5","source":{"kind":"arxiv","id":"1406.5883","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.5883","created_at":"2026-05-18T02:44:16Z"},{"alias_kind":"arxiv_version","alias_value":"1406.5883v2","created_at":"2026-05-18T02:44:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.5883","created_at":"2026-05-18T02:44:16Z"},{"alias_kind":"pith_short_12","alias_value":"EAXQ4ILJA6EM","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"EAXQ4ILJA6EMMMEO","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"EAXQ4ILJ","created_at":"2026-05-18T12:28:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:EAXQ4ILJA6EMMMEO3LKJQ4AW35","target":"record","payload":{"canonical_record":{"source":{"id":"1406.5883","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2014-06-23T12:18:10Z","cross_cats_sorted":[],"title_canon_sha256":"bcc934cbdc004390365b2750f335579b97eaf158b53155355ff076454de0dbc3","abstract_canon_sha256":"dc64f85fef75c08fbc2d0aab2d1acef41216aeb0a56434683709c00de51bc45f"},"schema_version":"1.0"},"canonical_sha256":"202f0e21690788c6308edad4987016df7bda59d1ea6c53f1d211facd6adea0a5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:44:16.272502Z","signature_b64":"O+3HmXvbBmoAuticeNBoIa4p/tGlmroZclBoMB1lItrFrAXTVJwgwIBr23D7X46z9Ovq69wGD/AWhChjfmfNCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"202f0e21690788c6308edad4987016df7bda59d1ea6c53f1d211facd6adea0a5","last_reissued_at":"2026-05-18T02:44:16.272072Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:44:16.272072Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1406.5883","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":"2026-05-18T02:44:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PeYywxXrm3QPhCxD1VyElR9i0JxLc18c1mowWnQfiLWExA7MvjgtK0kuyNhSgYemeA9QWUd7mn10i5SblPhUDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T22:26:23.958310Z"},"content_sha256":"96bdf62859f8d3bba9383348bc012548002c9694ca4487fb35fb4e946a580479","schema_version":"1.0","event_id":"sha256:96bdf62859f8d3bba9383348bc012548002c9694ca4487fb35fb4e946a580479"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:EAXQ4ILJA6EMMMEO3LKJQ4AW35","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"New approach to study gravitational stability of the solutions to the Einstein equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Janusz Garecki","submitted_at":"2014-06-23T12:18:10Z","abstract_excerpt":"Here we propose a new method to study gravitational stability of the solutions to the Einstein equations. This method uses the canonical superenergy density and it is different from approaches already used (Lyapunov's stability, dynamical systems). Our method is very alike to the procedure of finding the stable minima of the interior energy U for a dynamical system."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.5883","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":"2026-05-18T02:44:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mwp96K+wtBAl+cQGGqdgXoDXrg+VHyZ6okBLe/AA2U/y43BWVbcBWD0xM0pErMTCLd6nw8Wr+xpN11w41zZfAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T22:26:23.958662Z"},"content_sha256":"c624dcbc67836f65f6ce0e8028a2798d5b38738f3d1fb031f1389ce90b8d76f1","schema_version":"1.0","event_id":"sha256:c624dcbc67836f65f6ce0e8028a2798d5b38738f3d1fb031f1389ce90b8d76f1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EAXQ4ILJA6EMMMEO3LKJQ4AW35/bundle.json","state_url":"https://pith.science/pith/EAXQ4ILJA6EMMMEO3LKJQ4AW35/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EAXQ4ILJA6EMMMEO3LKJQ4AW35/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":"2026-06-27T22:26:23Z","links":{"resolver":"https://pith.science/pith/EAXQ4ILJA6EMMMEO3LKJQ4AW35","bundle":"https://pith.science/pith/EAXQ4ILJA6EMMMEO3LKJQ4AW35/bundle.json","state":"https://pith.science/pith/EAXQ4ILJA6EMMMEO3LKJQ4AW35/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EAXQ4ILJA6EMMMEO3LKJQ4AW35/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:EAXQ4ILJA6EMMMEO3LKJQ4AW35","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":"dc64f85fef75c08fbc2d0aab2d1acef41216aeb0a56434683709c00de51bc45f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2014-06-23T12:18:10Z","title_canon_sha256":"bcc934cbdc004390365b2750f335579b97eaf158b53155355ff076454de0dbc3"},"schema_version":"1.0","source":{"id":"1406.5883","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.5883","created_at":"2026-05-18T02:44:16Z"},{"alias_kind":"arxiv_version","alias_value":"1406.5883v2","created_at":"2026-05-18T02:44:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.5883","created_at":"2026-05-18T02:44:16Z"},{"alias_kind":"pith_short_12","alias_value":"EAXQ4ILJA6EM","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"EAXQ4ILJA6EMMMEO","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"EAXQ4ILJ","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:c624dcbc67836f65f6ce0e8028a2798d5b38738f3d1fb031f1389ce90b8d76f1","target":"graph","created_at":"2026-05-18T02:44:16Z","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":"Here we propose a new method to study gravitational stability of the solutions to the Einstein equations. This method uses the canonical superenergy density and it is different from approaches already used (Lyapunov's stability, dynamical systems). Our method is very alike to the procedure of finding the stable minima of the interior energy U for a dynamical system.","authors_text":"Janusz Garecki","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2014-06-23T12:18:10Z","title":"New approach to study gravitational stability of the solutions to the Einstein equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.5883","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":"sha256:96bdf62859f8d3bba9383348bc012548002c9694ca4487fb35fb4e946a580479","target":"record","created_at":"2026-05-18T02:44:16Z","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":"dc64f85fef75c08fbc2d0aab2d1acef41216aeb0a56434683709c00de51bc45f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2014-06-23T12:18:10Z","title_canon_sha256":"bcc934cbdc004390365b2750f335579b97eaf158b53155355ff076454de0dbc3"},"schema_version":"1.0","source":{"id":"1406.5883","kind":"arxiv","version":2}},"canonical_sha256":"202f0e21690788c6308edad4987016df7bda59d1ea6c53f1d211facd6adea0a5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"202f0e21690788c6308edad4987016df7bda59d1ea6c53f1d211facd6adea0a5","first_computed_at":"2026-05-18T02:44:16.272072Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:44:16.272072Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"O+3HmXvbBmoAuticeNBoIa4p/tGlmroZclBoMB1lItrFrAXTVJwgwIBr23D7X46z9Ovq69wGD/AWhChjfmfNCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:44:16.272502Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.5883","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:96bdf62859f8d3bba9383348bc012548002c9694ca4487fb35fb4e946a580479","sha256:c624dcbc67836f65f6ce0e8028a2798d5b38738f3d1fb031f1389ce90b8d76f1"],"state_sha256":"54d784b8676091279c83db2ef03d503b23b2fe972cdde4bc90af757bcd59864a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t7qa+9s0Lgpn3ocEFOHpiatrww66hR+j4F2tQOf61pCzAfdYyF+/NWEGNnjxLlseg1QNk8gTsKLPVt+FX7APDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T22:26:23.960508Z","bundle_sha256":"dd67cf143691e0522dab18b54d173a7949c3c89edb76960bf7d5559021d6794a"}}