{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:AQ3W4FT3PRGPVMTDE3EJURCFCT","short_pith_number":"pith:AQ3W4FT3","canonical_record":{"source":{"id":"2404.01528","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2024-04-01T23:22:41Z","cross_cats_sorted":[],"title_canon_sha256":"585d4edb14ea735dd30499318cf2a5160d94f1f15a727222f3a40bee13ced1c8","abstract_canon_sha256":"09d3502f2c70d0fde48b781c9f6de85fcb9ab368438a6b16e438bbb04161c929"},"schema_version":"1.0"},"canonical_sha256":"04376e167b7c4cfab26326c89a444514d4746c779aeac12cb67ea3597ef0d152","source":{"kind":"arxiv","id":"2404.01528","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.01528","created_at":"2026-07-05T09:39:05Z"},{"alias_kind":"arxiv_version","alias_value":"2404.01528v2","created_at":"2026-07-05T09:39:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.01528","created_at":"2026-07-05T09:39:05Z"},{"alias_kind":"pith_short_12","alias_value":"AQ3W4FT3PRGP","created_at":"2026-07-05T09:39:05Z"},{"alias_kind":"pith_short_16","alias_value":"AQ3W4FT3PRGPVMTD","created_at":"2026-07-05T09:39:05Z"},{"alias_kind":"pith_short_8","alias_value":"AQ3W4FT3","created_at":"2026-07-05T09:39:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:AQ3W4FT3PRGPVMTDE3EJURCFCT","target":"record","payload":{"canonical_record":{"source":{"id":"2404.01528","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2024-04-01T23:22:41Z","cross_cats_sorted":[],"title_canon_sha256":"585d4edb14ea735dd30499318cf2a5160d94f1f15a727222f3a40bee13ced1c8","abstract_canon_sha256":"09d3502f2c70d0fde48b781c9f6de85fcb9ab368438a6b16e438bbb04161c929"},"schema_version":"1.0"},"canonical_sha256":"04376e167b7c4cfab26326c89a444514d4746c779aeac12cb67ea3597ef0d152","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:39:05.978024Z","signature_b64":"xvcYiHgGt+h5v7Ng5aDecdsibcz7IDCJZoWrdO95/TBlNlmHw37wB4aVTFvWIr5325P7UzR9V4iC1DnXPQdUBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"04376e167b7c4cfab26326c89a444514d4746c779aeac12cb67ea3597ef0d152","last_reissued_at":"2026-07-05T09:39:05.977552Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:39:05.977552Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2404.01528","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":"2026-07-05T09:39:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8+P7dwuvR5wvV3mLM8krBGhXU40AIc8stSsP2KA7bZX8x8GD/Y6IuSLcWh9RG9QAdwdinbXEt2hvOipW4UNDAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T21:27:34.892988Z"},"content_sha256":"93cfb07f42a1b0e62ebe84ffb381c3f86593201e0967b6d1f7cacbfd86a74e22","schema_version":"1.0","event_id":"sha256:93cfb07f42a1b0e62ebe84ffb381c3f86593201e0967b6d1f7cacbfd86a74e22"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:AQ3W4FT3PRGPVMTDE3EJURCFCT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hyperbolic times in Minkowski space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"An{\\i}l Zengino\\u{g}lu","submitted_at":"2024-04-01T23:22:41Z","abstract_excerpt":"Time functions with asymptotically hyperbolic geometry play an increasingly important role in many areas of relativity, from computing black-hole perturbations to analyzing wave equations. Despite their significance, many of their properties remain underexplored. In this expository article, I discuss hyperbolic time functions by considering the hyperbola as the relativistic analog of a circle in two-dimensional Minkowski space and argue that suitably defined hyperboloidal coordinates are as natural in Lorentzian manifolds as spherical coordinates are in Riemannian manifolds."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.01528","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2404.01528/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T09:39:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RqneHVvcrgPZIbSIUZ01svnRpW86H0iOd56fY/AbdvFMYmXBczl781tA4fj3311aI8SIjEWXWFUvnqcdPWqOBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T21:27:34.893359Z"},"content_sha256":"a907f3c760bef7c920fd6410c136983119766f299fb971a20d1b925efb650357","schema_version":"1.0","event_id":"sha256:a907f3c760bef7c920fd6410c136983119766f299fb971a20d1b925efb650357"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AQ3W4FT3PRGPVMTDE3EJURCFCT/bundle.json","state_url":"https://pith.science/pith/AQ3W4FT3PRGPVMTDE3EJURCFCT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AQ3W4FT3PRGPVMTDE3EJURCFCT/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":"2026-08-11T21:27:34Z","links":{"resolver":"https://pith.science/pith/AQ3W4FT3PRGPVMTDE3EJURCFCT","bundle":"https://pith.science/pith/AQ3W4FT3PRGPVMTDE3EJURCFCT/bundle.json","state":"https://pith.science/pith/AQ3W4FT3PRGPVMTDE3EJURCFCT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AQ3W4FT3PRGPVMTDE3EJURCFCT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:AQ3W4FT3PRGPVMTDE3EJURCFCT","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":"09d3502f2c70d0fde48b781c9f6de85fcb9ab368438a6b16e438bbb04161c929","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2024-04-01T23:22:41Z","title_canon_sha256":"585d4edb14ea735dd30499318cf2a5160d94f1f15a727222f3a40bee13ced1c8"},"schema_version":"1.0","source":{"id":"2404.01528","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.01528","created_at":"2026-07-05T09:39:05Z"},{"alias_kind":"arxiv_version","alias_value":"2404.01528v2","created_at":"2026-07-05T09:39:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.01528","created_at":"2026-07-05T09:39:05Z"},{"alias_kind":"pith_short_12","alias_value":"AQ3W4FT3PRGP","created_at":"2026-07-05T09:39:05Z"},{"alias_kind":"pith_short_16","alias_value":"AQ3W4FT3PRGPVMTD","created_at":"2026-07-05T09:39:05Z"},{"alias_kind":"pith_short_8","alias_value":"AQ3W4FT3","created_at":"2026-07-05T09:39:05Z"}],"graph_snapshots":[{"event_id":"sha256:a907f3c760bef7c920fd6410c136983119766f299fb971a20d1b925efb650357","target":"graph","created_at":"2026-07-05T09:39:05Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2404.01528/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Time functions with asymptotically hyperbolic geometry play an increasingly important role in many areas of relativity, from computing black-hole perturbations to analyzing wave equations. Despite their significance, many of their properties remain underexplored. In this expository article, I discuss hyperbolic time functions by considering the hyperbola as the relativistic analog of a circle in two-dimensional Minkowski space and argue that suitably defined hyperboloidal coordinates are as natural in Lorentzian manifolds as spherical coordinates are in Riemannian manifolds.","authors_text":"An{\\i}l Zengino\\u{g}lu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2024-04-01T23:22:41Z","title":"Hyperbolic times in Minkowski space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.01528","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":"sha256:93cfb07f42a1b0e62ebe84ffb381c3f86593201e0967b6d1f7cacbfd86a74e22","target":"record","created_at":"2026-07-05T09:39:05Z","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":"09d3502f2c70d0fde48b781c9f6de85fcb9ab368438a6b16e438bbb04161c929","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2024-04-01T23:22:41Z","title_canon_sha256":"585d4edb14ea735dd30499318cf2a5160d94f1f15a727222f3a40bee13ced1c8"},"schema_version":"1.0","source":{"id":"2404.01528","kind":"arxiv","version":2}},"canonical_sha256":"04376e167b7c4cfab26326c89a444514d4746c779aeac12cb67ea3597ef0d152","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"04376e167b7c4cfab26326c89a444514d4746c779aeac12cb67ea3597ef0d152","first_computed_at":"2026-07-05T09:39:05.977552Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:39:05.977552Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xvcYiHgGt+h5v7Ng5aDecdsibcz7IDCJZoWrdO95/TBlNlmHw37wB4aVTFvWIr5325P7UzR9V4iC1DnXPQdUBA==","signature_status":"signed_v1","signed_at":"2026-07-05T09:39:05.978024Z","signed_message":"canonical_sha256_bytes"},"source_id":"2404.01528","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:93cfb07f42a1b0e62ebe84ffb381c3f86593201e0967b6d1f7cacbfd86a74e22","sha256:a907f3c760bef7c920fd6410c136983119766f299fb971a20d1b925efb650357"],"state_sha256":"4e5f919ceee84fb9f0b7fd93cfa0ec06342dac3c82801306876329601bcb00bd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7yPchp7kY4jlZybo+DKqtErMoIoswH3pYlI72EevMQ4/n15IqNJ3JKN9CMr5vqFEx6UB16S/lDxKMHqs5xp3CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T21:27:34.895784Z","bundle_sha256":"d6bcb01c5c3afbbe2a2bf2645f6d1572836fd7ba227e85237febb9532a88058c"}}