{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:ITAMX2Z6XCI6EQRHNB5XGBVGUL","short_pith_number":"pith:ITAMX2Z6","canonical_record":{"source":{"id":"1508.07872","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-08-31T15:29:36Z","cross_cats_sorted":[],"title_canon_sha256":"feda0d9d8b9e3a1f125df572b074aa9c2443d1347c17218adf3b903c45b4f2ac","abstract_canon_sha256":"40dd0e6f8138e52da7d922a0f8c47ebdef3ac1e3d9f51e750c40e75211a596cb"},"schema_version":"1.0"},"canonical_sha256":"44c0cbeb3eb891e24227687b7306a6a2f8c984744e50a9e60ae705a6cbc099cd","source":{"kind":"arxiv","id":"1508.07872","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.07872","created_at":"2026-05-18T01:01:29Z"},{"alias_kind":"arxiv_version","alias_value":"1508.07872v2","created_at":"2026-05-18T01:01:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.07872","created_at":"2026-05-18T01:01:29Z"},{"alias_kind":"pith_short_12","alias_value":"ITAMX2Z6XCI6","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"ITAMX2Z6XCI6EQRH","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"ITAMX2Z6","created_at":"2026-05-18T12:29:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:ITAMX2Z6XCI6EQRHNB5XGBVGUL","target":"record","payload":{"canonical_record":{"source":{"id":"1508.07872","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-08-31T15:29:36Z","cross_cats_sorted":[],"title_canon_sha256":"feda0d9d8b9e3a1f125df572b074aa9c2443d1347c17218adf3b903c45b4f2ac","abstract_canon_sha256":"40dd0e6f8138e52da7d922a0f8c47ebdef3ac1e3d9f51e750c40e75211a596cb"},"schema_version":"1.0"},"canonical_sha256":"44c0cbeb3eb891e24227687b7306a6a2f8c984744e50a9e60ae705a6cbc099cd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:01:29.116058Z","signature_b64":"mL/846TciKOvw0KVI1AkMptiAdJbzePHAXF+Bp9mQRHDNjR/ZP4hg4KgSq4zlRusTbo5LMLhk6ibGLNQi3fIBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"44c0cbeb3eb891e24227687b7306a6a2f8c984744e50a9e60ae705a6cbc099cd","last_reissued_at":"2026-05-18T01:01:29.115617Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:01:29.115617Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.07872","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":"2026-05-18T01:01:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uIfJjecoPHzcPQuMNYehMN8ncnnbR/C+IRg8F+vBpkz7lGv+mIShq9xD1fHdwliaDxiI7AnUrhL6EdA1IofUDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T19:36:21.585162Z"},"content_sha256":"5d3fa35ade7076d6738f64699fdf5921fca7c92ba4c263f59372a08e276dfdb3","schema_version":"1.0","event_id":"sha256:5d3fa35ade7076d6738f64699fdf5921fca7c92ba4c263f59372a08e276dfdb3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:ITAMX2Z6XCI6EQRHNB5XGBVGUL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the existence of rigid spheres in four-dimensional spacetime manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Hans-Peter Gittel, Jacek Jezierski, Jerzy Kijowski","submitted_at":"2015-08-31T15:29:36Z","abstract_excerpt":"This paper deals with the generalization of usual round spheres in the flat Minkowski spacetime to the case of a generic four-dimensional spacetime manifold $M$. We consider geometric properties of sphere-like submanifolds in $M$ and introduce conditions on external curvature and torsion, which lead to a definition of a {\\em rigid sphere}. The main result is a local existence theorem concernig such spheres. For this purpose we apply the surjective implicit function theorem. The proof is based on a detailed analysis of the linearized problem and leads to an eight-parameter family of solutions i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.07872","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":"2026-05-18T01:01:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YK/WKwqMYiRyDQEhp4WoL+6uB0aV4T/G9P/koZiV9iZNI4hWE25jHbWUNAdiCX2YDH7wLhy1l6GusExh+w/FCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T19:36:21.585973Z"},"content_sha256":"5a86b87436ab2338cf659252b610f852294312a9a0880ac4c049b7ce2046f890","schema_version":"1.0","event_id":"sha256:5a86b87436ab2338cf659252b610f852294312a9a0880ac4c049b7ce2046f890"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ITAMX2Z6XCI6EQRHNB5XGBVGUL/bundle.json","state_url":"https://pith.science/pith/ITAMX2Z6XCI6EQRHNB5XGBVGUL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ITAMX2Z6XCI6EQRHNB5XGBVGUL/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":"2026-06-09T19:36:21Z","links":{"resolver":"https://pith.science/pith/ITAMX2Z6XCI6EQRHNB5XGBVGUL","bundle":"https://pith.science/pith/ITAMX2Z6XCI6EQRHNB5XGBVGUL/bundle.json","state":"https://pith.science/pith/ITAMX2Z6XCI6EQRHNB5XGBVGUL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ITAMX2Z6XCI6EQRHNB5XGBVGUL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ITAMX2Z6XCI6EQRHNB5XGBVGUL","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":"40dd0e6f8138e52da7d922a0f8c47ebdef3ac1e3d9f51e750c40e75211a596cb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-08-31T15:29:36Z","title_canon_sha256":"feda0d9d8b9e3a1f125df572b074aa9c2443d1347c17218adf3b903c45b4f2ac"},"schema_version":"1.0","source":{"id":"1508.07872","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.07872","created_at":"2026-05-18T01:01:29Z"},{"alias_kind":"arxiv_version","alias_value":"1508.07872v2","created_at":"2026-05-18T01:01:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.07872","created_at":"2026-05-18T01:01:29Z"},{"alias_kind":"pith_short_12","alias_value":"ITAMX2Z6XCI6","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"ITAMX2Z6XCI6EQRH","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"ITAMX2Z6","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:5a86b87436ab2338cf659252b610f852294312a9a0880ac4c049b7ce2046f890","target":"graph","created_at":"2026-05-18T01:01:29Z","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":"This paper deals with the generalization of usual round spheres in the flat Minkowski spacetime to the case of a generic four-dimensional spacetime manifold $M$. We consider geometric properties of sphere-like submanifolds in $M$ and introduce conditions on external curvature and torsion, which lead to a definition of a {\\em rigid sphere}. The main result is a local existence theorem concernig such spheres. For this purpose we apply the surjective implicit function theorem. The proof is based on a detailed analysis of the linearized problem and leads to an eight-parameter family of solutions i","authors_text":"Hans-Peter Gittel, Jacek Jezierski, Jerzy Kijowski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-08-31T15:29:36Z","title":"On the existence of rigid spheres in four-dimensional spacetime manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.07872","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":"sha256:5d3fa35ade7076d6738f64699fdf5921fca7c92ba4c263f59372a08e276dfdb3","target":"record","created_at":"2026-05-18T01:01:29Z","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":"40dd0e6f8138e52da7d922a0f8c47ebdef3ac1e3d9f51e750c40e75211a596cb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-08-31T15:29:36Z","title_canon_sha256":"feda0d9d8b9e3a1f125df572b074aa9c2443d1347c17218adf3b903c45b4f2ac"},"schema_version":"1.0","source":{"id":"1508.07872","kind":"arxiv","version":2}},"canonical_sha256":"44c0cbeb3eb891e24227687b7306a6a2f8c984744e50a9e60ae705a6cbc099cd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"44c0cbeb3eb891e24227687b7306a6a2f8c984744e50a9e60ae705a6cbc099cd","first_computed_at":"2026-05-18T01:01:29.115617Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:01:29.115617Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mL/846TciKOvw0KVI1AkMptiAdJbzePHAXF+Bp9mQRHDNjR/ZP4hg4KgSq4zlRusTbo5LMLhk6ibGLNQi3fIBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:01:29.116058Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.07872","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5d3fa35ade7076d6738f64699fdf5921fca7c92ba4c263f59372a08e276dfdb3","sha256:5a86b87436ab2338cf659252b610f852294312a9a0880ac4c049b7ce2046f890"],"state_sha256":"6867ba51ea1f99adfed4941ef81b5c63f893e939c9e56f384f27c8e5d6c1941f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PJxxoiBrzFSM++x9C83OsenwEZsWZ8CSAvWUOverPCtHBWEv042WZVGQEi9uEWRdcpjY+rzzcXCv6OUntKVjDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T19:36:21.590308Z","bundle_sha256":"ef2ea3a730ebf3393fb19c52232045e9ce28cd9b3c33764d299ad719ad8a2c6c"}}