{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:AZUJ7E2IUSRRCYJNTDB2PQJ6QH","short_pith_number":"pith:AZUJ7E2I","canonical_record":{"source":{"id":"1309.5157","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2013-09-20T02:25:21Z","cross_cats_sorted":[],"title_canon_sha256":"dff6b9d29e8dd2807bccab86d1f20d2e15042fb34fac13f0798a1085926e3858","abstract_canon_sha256":"ad786a597f9bfc5feba4e22e2f242ab38bca4428937c6ec773791fef246029d6"},"schema_version":"1.0"},"canonical_sha256":"06689f9348a4a311612d98c3a7c13e81f6b85f416a48dfe026c903f184850898","source":{"kind":"arxiv","id":"1309.5157","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.5157","created_at":"2026-05-18T01:39:55Z"},{"alias_kind":"arxiv_version","alias_value":"1309.5157v3","created_at":"2026-05-18T01:39:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.5157","created_at":"2026-05-18T01:39:55Z"},{"alias_kind":"pith_short_12","alias_value":"AZUJ7E2IUSRR","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"AZUJ7E2IUSRRCYJN","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"AZUJ7E2I","created_at":"2026-05-18T12:27:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:AZUJ7E2IUSRRCYJNTDB2PQJ6QH","target":"record","payload":{"canonical_record":{"source":{"id":"1309.5157","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2013-09-20T02:25:21Z","cross_cats_sorted":[],"title_canon_sha256":"dff6b9d29e8dd2807bccab86d1f20d2e15042fb34fac13f0798a1085926e3858","abstract_canon_sha256":"ad786a597f9bfc5feba4e22e2f242ab38bca4428937c6ec773791fef246029d6"},"schema_version":"1.0"},"canonical_sha256":"06689f9348a4a311612d98c3a7c13e81f6b85f416a48dfe026c903f184850898","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:39:55.404211Z","signature_b64":"8NSeaFQjWNTPyVI2o+PYFnvwkTk5Eg1ieJc8RkKTyrQoWX5hRE+OKZTGUvssngSEmoaTicwlNVZVUMi+wWwFAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"06689f9348a4a311612d98c3a7c13e81f6b85f416a48dfe026c903f184850898","last_reissued_at":"2026-05-18T01:39:55.403792Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:39:55.403792Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.5157","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":"2026-05-18T01:39:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JwrCP6DPCLi0jKus3FJmmxOF93m/4tVVljQKeb2tuiPDTl7TqzL3XmK5kN7aISfgDM/yH8jnng/sHkw+R7DsBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T15:41:05.808383Z"},"content_sha256":"83e8460da0f0744285eaee5bf444cebfa1d7adf6bc6958a6af279d79a83f9b53","schema_version":"1.0","event_id":"sha256:83e8460da0f0744285eaee5bf444cebfa1d7adf6bc6958a6af279d79a83f9b53"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:AZUJ7E2IUSRRCYJNTDB2PQJ6QH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Level sets of the lapse function in static GR","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Carla Cederbaum","submitted_at":"2013-09-20T02:25:21Z","abstract_excerpt":"We present a novel physical interpretation of the level sets of the (canonical) lapse function in static isolated general relativistic space-times. Our interpretation uses a notion of 'constrained test particles'. It leads to a definition of gravitational force on test particles and to a previously unknown uniqueness result for the lapse function.\n  In Section 5, we discuss 'photon spheres' in static isolated relativistic space-times and relate them to the level sets of the lapse function."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.5157","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":"2026-05-18T01:39:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ldgCVMNKs5nZQKYSDxwya691JdMskN5MGWQu4mZ1YmhZojAIJR4iPQkLyAKg1Byvo76skPgcwGsbkz27VRDhDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T15:41:05.809134Z"},"content_sha256":"d97fa5cef3cbaee0d23b636c0d1a82d32b70b77aad5c30f25c2135f8706972b1","schema_version":"1.0","event_id":"sha256:d97fa5cef3cbaee0d23b636c0d1a82d32b70b77aad5c30f25c2135f8706972b1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AZUJ7E2IUSRRCYJNTDB2PQJ6QH/bundle.json","state_url":"https://pith.science/pith/AZUJ7E2IUSRRCYJNTDB2PQJ6QH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AZUJ7E2IUSRRCYJNTDB2PQJ6QH/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":"2026-06-08T15:41:05Z","links":{"resolver":"https://pith.science/pith/AZUJ7E2IUSRRCYJNTDB2PQJ6QH","bundle":"https://pith.science/pith/AZUJ7E2IUSRRCYJNTDB2PQJ6QH/bundle.json","state":"https://pith.science/pith/AZUJ7E2IUSRRCYJNTDB2PQJ6QH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AZUJ7E2IUSRRCYJNTDB2PQJ6QH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:AZUJ7E2IUSRRCYJNTDB2PQJ6QH","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":"ad786a597f9bfc5feba4e22e2f242ab38bca4428937c6ec773791fef246029d6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2013-09-20T02:25:21Z","title_canon_sha256":"dff6b9d29e8dd2807bccab86d1f20d2e15042fb34fac13f0798a1085926e3858"},"schema_version":"1.0","source":{"id":"1309.5157","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.5157","created_at":"2026-05-18T01:39:55Z"},{"alias_kind":"arxiv_version","alias_value":"1309.5157v3","created_at":"2026-05-18T01:39:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.5157","created_at":"2026-05-18T01:39:55Z"},{"alias_kind":"pith_short_12","alias_value":"AZUJ7E2IUSRR","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"AZUJ7E2IUSRRCYJN","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"AZUJ7E2I","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:d97fa5cef3cbaee0d23b636c0d1a82d32b70b77aad5c30f25c2135f8706972b1","target":"graph","created_at":"2026-05-18T01:39:55Z","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 present a novel physical interpretation of the level sets of the (canonical) lapse function in static isolated general relativistic space-times. Our interpretation uses a notion of 'constrained test particles'. It leads to a definition of gravitational force on test particles and to a previously unknown uniqueness result for the lapse function.\n  In Section 5, we discuss 'photon spheres' in static isolated relativistic space-times and relate them to the level sets of the lapse function.","authors_text":"Carla Cederbaum","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2013-09-20T02:25:21Z","title":"Level sets of the lapse function in static GR"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.5157","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":"sha256:83e8460da0f0744285eaee5bf444cebfa1d7adf6bc6958a6af279d79a83f9b53","target":"record","created_at":"2026-05-18T01:39:55Z","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":"ad786a597f9bfc5feba4e22e2f242ab38bca4428937c6ec773791fef246029d6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2013-09-20T02:25:21Z","title_canon_sha256":"dff6b9d29e8dd2807bccab86d1f20d2e15042fb34fac13f0798a1085926e3858"},"schema_version":"1.0","source":{"id":"1309.5157","kind":"arxiv","version":3}},"canonical_sha256":"06689f9348a4a311612d98c3a7c13e81f6b85f416a48dfe026c903f184850898","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"06689f9348a4a311612d98c3a7c13e81f6b85f416a48dfe026c903f184850898","first_computed_at":"2026-05-18T01:39:55.403792Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:39:55.403792Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8NSeaFQjWNTPyVI2o+PYFnvwkTk5Eg1ieJc8RkKTyrQoWX5hRE+OKZTGUvssngSEmoaTicwlNVZVUMi+wWwFAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:39:55.404211Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.5157","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:83e8460da0f0744285eaee5bf444cebfa1d7adf6bc6958a6af279d79a83f9b53","sha256:d97fa5cef3cbaee0d23b636c0d1a82d32b70b77aad5c30f25c2135f8706972b1"],"state_sha256":"90ec183df90fe5b4823981ae708b4b443a90b84f82d8cc9f296edf2ec68f9126"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YHDpButYT5hKRDr+C0szpLNegqp056gjX78vhDexBhpCEpkZ4ZMQHEHFr7ukllmKLfQXifA2tdHDgtb/sD5KAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T15:41:05.812962Z","bundle_sha256":"6f9aad0031d76c3d9f1c8309aa770023656abf63875375bb869d4ea35072afb2"}}