{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:NYX4J3HQXVABGMIW3D4WUXIOKI","short_pith_number":"pith:NYX4J3HQ","canonical_record":{"source":{"id":"1107.5168","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.gen-ph","submitted_at":"2011-07-26T11:11:35Z","cross_cats_sorted":[],"title_canon_sha256":"5dc128a753313e1d5749da0d38dbeb1710f62278c3a902d85f31361dd89a8c66","abstract_canon_sha256":"53734b5d4d36b2ac3c900880c816614afb4dabb9d3524236701ddc8a6b7b434a"},"schema_version":"1.0"},"canonical_sha256":"6e2fc4ecf0bd40133116d8f96a5d0e520fd06ca7b06c9c479c6a47b62a9fa5fb","source":{"kind":"arxiv","id":"1107.5168","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.5168","created_at":"2026-05-18T03:46:03Z"},{"alias_kind":"arxiv_version","alias_value":"1107.5168v1","created_at":"2026-05-18T03:46:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.5168","created_at":"2026-05-18T03:46:03Z"},{"alias_kind":"pith_short_12","alias_value":"NYX4J3HQXVAB","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"NYX4J3HQXVABGMIW","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"NYX4J3HQ","created_at":"2026-05-18T12:26:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:NYX4J3HQXVABGMIW3D4WUXIOKI","target":"record","payload":{"canonical_record":{"source":{"id":"1107.5168","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.gen-ph","submitted_at":"2011-07-26T11:11:35Z","cross_cats_sorted":[],"title_canon_sha256":"5dc128a753313e1d5749da0d38dbeb1710f62278c3a902d85f31361dd89a8c66","abstract_canon_sha256":"53734b5d4d36b2ac3c900880c816614afb4dabb9d3524236701ddc8a6b7b434a"},"schema_version":"1.0"},"canonical_sha256":"6e2fc4ecf0bd40133116d8f96a5d0e520fd06ca7b06c9c479c6a47b62a9fa5fb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:46:03.899937Z","signature_b64":"jU1kkyK1Qsw1jTncOQvHL6zXNSZ+SY3rwb8H2Xqi/sznsqlKAsIdKz03gXNSvEiLsYh4nYJJQqkZcuuskr+kDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6e2fc4ecf0bd40133116d8f96a5d0e520fd06ca7b06c9c479c6a47b62a9fa5fb","last_reissued_at":"2026-05-18T03:46:03.899349Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:46:03.899349Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1107.5168","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:46:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zRfIrTBinwGeVOSTGnW23HmsQaKRCD4hyq0iL6PcMyae/ihxx7g489W+2eGRsZDi+8n2j84qpOiYh5MbabLmAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T05:41:56.348247Z"},"content_sha256":"1ed5d63375b9ba6db9487538ff1c69837df26a511972a01be0eee920b7943c8e","schema_version":"1.0","event_id":"sha256:1ed5d63375b9ba6db9487538ff1c69837df26a511972a01be0eee920b7943c8e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:NYX4J3HQXVABGMIW3D4WUXIOKI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hubble's law and faster than light expansion speeds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.gen-ph","authors_text":"Ali Kaya","submitted_at":"2011-07-26T11:11:35Z","abstract_excerpt":"Naively applying Hubble's law to a sufficiently distant object gives a receding velocity larger than the speed of light. By discussing a very similar situation in special relativity, we argue that Hubble's law is meaningful only for nearby objects with non-relativistic receding speeds. To support this claim, we note that in a curved spacetime manifold it is not possible to directly compare tangent vectors at different points, and thus there is no natural definition of relative velocity between two spatially separated objects in cosmology. We clarify the geometrical meaning of the Hubble's rece"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.5168","kind":"arxiv","version":1},"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":"2026-05-18T03:46:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vWeZcKK2ERacJOyiv8Uw7ohnHdUacNRTQyvv3oi9O5U5/iHoYN8MjiYZeqU0N7FVBTID2rJHwMM0wb5PGa5aBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T05:41:56.349007Z"},"content_sha256":"942fd61e4a0f42b1902e43f08e2dabd831502d4f98f2fe4d377994f86e9473d7","schema_version":"1.0","event_id":"sha256:942fd61e4a0f42b1902e43f08e2dabd831502d4f98f2fe4d377994f86e9473d7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NYX4J3HQXVABGMIW3D4WUXIOKI/bundle.json","state_url":"https://pith.science/pith/NYX4J3HQXVABGMIW3D4WUXIOKI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NYX4J3HQXVABGMIW3D4WUXIOKI/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":"2026-06-01T05:41:56Z","links":{"resolver":"https://pith.science/pith/NYX4J3HQXVABGMIW3D4WUXIOKI","bundle":"https://pith.science/pith/NYX4J3HQXVABGMIW3D4WUXIOKI/bundle.json","state":"https://pith.science/pith/NYX4J3HQXVABGMIW3D4WUXIOKI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NYX4J3HQXVABGMIW3D4WUXIOKI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:NYX4J3HQXVABGMIW3D4WUXIOKI","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":"53734b5d4d36b2ac3c900880c816614afb4dabb9d3524236701ddc8a6b7b434a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.gen-ph","submitted_at":"2011-07-26T11:11:35Z","title_canon_sha256":"5dc128a753313e1d5749da0d38dbeb1710f62278c3a902d85f31361dd89a8c66"},"schema_version":"1.0","source":{"id":"1107.5168","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.5168","created_at":"2026-05-18T03:46:03Z"},{"alias_kind":"arxiv_version","alias_value":"1107.5168v1","created_at":"2026-05-18T03:46:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.5168","created_at":"2026-05-18T03:46:03Z"},{"alias_kind":"pith_short_12","alias_value":"NYX4J3HQXVAB","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"NYX4J3HQXVABGMIW","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"NYX4J3HQ","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:942fd61e4a0f42b1902e43f08e2dabd831502d4f98f2fe4d377994f86e9473d7","target":"graph","created_at":"2026-05-18T03:46:03Z","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":"Naively applying Hubble's law to a sufficiently distant object gives a receding velocity larger than the speed of light. By discussing a very similar situation in special relativity, we argue that Hubble's law is meaningful only for nearby objects with non-relativistic receding speeds. To support this claim, we note that in a curved spacetime manifold it is not possible to directly compare tangent vectors at different points, and thus there is no natural definition of relative velocity between two spatially separated objects in cosmology. We clarify the geometrical meaning of the Hubble's rece","authors_text":"Ali Kaya","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.gen-ph","submitted_at":"2011-07-26T11:11:35Z","title":"Hubble's law and faster than light expansion speeds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.5168","kind":"arxiv","version":1},"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":"sha256:1ed5d63375b9ba6db9487538ff1c69837df26a511972a01be0eee920b7943c8e","target":"record","created_at":"2026-05-18T03:46:03Z","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":"53734b5d4d36b2ac3c900880c816614afb4dabb9d3524236701ddc8a6b7b434a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.gen-ph","submitted_at":"2011-07-26T11:11:35Z","title_canon_sha256":"5dc128a753313e1d5749da0d38dbeb1710f62278c3a902d85f31361dd89a8c66"},"schema_version":"1.0","source":{"id":"1107.5168","kind":"arxiv","version":1}},"canonical_sha256":"6e2fc4ecf0bd40133116d8f96a5d0e520fd06ca7b06c9c479c6a47b62a9fa5fb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6e2fc4ecf0bd40133116d8f96a5d0e520fd06ca7b06c9c479c6a47b62a9fa5fb","first_computed_at":"2026-05-18T03:46:03.899349Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:46:03.899349Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jU1kkyK1Qsw1jTncOQvHL6zXNSZ+SY3rwb8H2Xqi/sznsqlKAsIdKz03gXNSvEiLsYh4nYJJQqkZcuuskr+kDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:46:03.899937Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.5168","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1ed5d63375b9ba6db9487538ff1c69837df26a511972a01be0eee920b7943c8e","sha256:942fd61e4a0f42b1902e43f08e2dabd831502d4f98f2fe4d377994f86e9473d7"],"state_sha256":"7dd4f79c66ff02b56c0c748140d9fe5574f5de3453ee7d1a8b83089794b93eef"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lmVYRaVjS8ENqgVK5SpB1Y+wp5Gt/Oo2OxgEdCeSNKmdmNOYUuyCH3Ce4BSNNMNQo1fAb3nGz+lXSsw5XlApBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T05:41:56.352524Z","bundle_sha256":"fcb2a77e5a569bfc5e2db87875387c27d92efb018eeb4a88244a26a63c53b214"}}