{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:PGSMISGMCXOJ2ZQZCM6HQZRMLA","short_pith_number":"pith:PGSMISGM","canonical_record":{"source":{"id":"1512.04427","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"physics.gen-ph","submitted_at":"2015-11-24T15:07:19Z","cross_cats_sorted":[],"title_canon_sha256":"40807e32a8465b5f20b529fab54a3f7b6dc9c0929739fcee5f86d10398bb4f7b","abstract_canon_sha256":"47f3515276f7d6c2a6622a6cde05f975b7655939391377574209058ccecbb68a"},"schema_version":"1.0"},"canonical_sha256":"79a4c448cc15dc9d6619133c78662c582e5bf6c1381e23598f2400dc29cd9103","source":{"kind":"arxiv","id":"1512.04427","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.04427","created_at":"2026-05-18T00:56:04Z"},{"alias_kind":"arxiv_version","alias_value":"1512.04427v2","created_at":"2026-05-18T00:56:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.04427","created_at":"2026-05-18T00:56:04Z"},{"alias_kind":"pith_short_12","alias_value":"PGSMISGMCXOJ","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"PGSMISGMCXOJ2ZQZ","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"PGSMISGM","created_at":"2026-05-18T12:29:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:PGSMISGMCXOJ2ZQZCM6HQZRMLA","target":"record","payload":{"canonical_record":{"source":{"id":"1512.04427","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"physics.gen-ph","submitted_at":"2015-11-24T15:07:19Z","cross_cats_sorted":[],"title_canon_sha256":"40807e32a8465b5f20b529fab54a3f7b6dc9c0929739fcee5f86d10398bb4f7b","abstract_canon_sha256":"47f3515276f7d6c2a6622a6cde05f975b7655939391377574209058ccecbb68a"},"schema_version":"1.0"},"canonical_sha256":"79a4c448cc15dc9d6619133c78662c582e5bf6c1381e23598f2400dc29cd9103","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:56:04.543919Z","signature_b64":"4/MJ8VbTK459nYRjZ8XVpVvn2bWR5VxzQOYuMLeYEwUUPYLhOiFL5+iTdTzOO90ADq3g8kENaHUHmyDMPXEiBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"79a4c448cc15dc9d6619133c78662c582e5bf6c1381e23598f2400dc29cd9103","last_reissued_at":"2026-05-18T00:56:04.543361Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:56:04.543361Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.04427","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":"2026-05-18T00:56:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W4KC3KaIltiFU5miHJJlzTF/3AE039eim3la4Mx+DGG29iktRSueAgIPBup9PLD5VPIq1370RefWpUv9tKSzDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T22:03:08.822863Z"},"content_sha256":"fa72efc849f1e7df023a18f2d6b445f7296bed05fb274a5c5ccf06367959fcaa","schema_version":"1.0","event_id":"sha256:fa72efc849f1e7df023a18f2d6b445f7296bed05fb274a5c5ccf06367959fcaa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:PGSMISGMCXOJ2ZQZCM6HQZRMLA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Homothetic Vectors of Bianchi Type I Spacetimes in Lyra Geometry and General Relativity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"physics.gen-ph","authors_text":"Ahmad T Ali, Azeb Alghanemi, Suhail Khan","submitted_at":"2015-11-24T15:07:19Z","abstract_excerpt":"In this paper Bianchi type I spacetimes are completely classified by their homothetic vectors in the context of Lyra geometry. The non-linear coupled Lyra homothetic equations are obtained and solved completely for different cases. In some cases, Bianchi type I spacetimes admit proper Lyra homothetic vectors (LHVs) for special choices of the metric functions, while there exist other cases where the spacetime under consideration admits only Lyra Killing vectors (LKVs). In all the possible cases where Bianchi type I spacetimes admit proper LHVs or LKVs, we obtained homothetic and Killing vectors"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.04427","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":"2026-05-18T00:56:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i9A5BKxZVAF44Qp7hhIK96zRyMJapVcK7z25RsR1eSZrsMg7bw0IDqAp/PmseaxJk9tHYKUvI2UBAZ+sz0tmBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T22:03:08.823208Z"},"content_sha256":"983e0d3970e9708c272c192adb09ea376b1b25d1f909644d3eaeb187590d5ee6","schema_version":"1.0","event_id":"sha256:983e0d3970e9708c272c192adb09ea376b1b25d1f909644d3eaeb187590d5ee6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PGSMISGMCXOJ2ZQZCM6HQZRMLA/bundle.json","state_url":"https://pith.science/pith/PGSMISGMCXOJ2ZQZCM6HQZRMLA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PGSMISGMCXOJ2ZQZCM6HQZRMLA/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":"2026-06-26T22:03:08Z","links":{"resolver":"https://pith.science/pith/PGSMISGMCXOJ2ZQZCM6HQZRMLA","bundle":"https://pith.science/pith/PGSMISGMCXOJ2ZQZCM6HQZRMLA/bundle.json","state":"https://pith.science/pith/PGSMISGMCXOJ2ZQZCM6HQZRMLA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PGSMISGMCXOJ2ZQZCM6HQZRMLA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:PGSMISGMCXOJ2ZQZCM6HQZRMLA","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":"47f3515276f7d6c2a6622a6cde05f975b7655939391377574209058ccecbb68a","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"physics.gen-ph","submitted_at":"2015-11-24T15:07:19Z","title_canon_sha256":"40807e32a8465b5f20b529fab54a3f7b6dc9c0929739fcee5f86d10398bb4f7b"},"schema_version":"1.0","source":{"id":"1512.04427","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.04427","created_at":"2026-05-18T00:56:04Z"},{"alias_kind":"arxiv_version","alias_value":"1512.04427v2","created_at":"2026-05-18T00:56:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.04427","created_at":"2026-05-18T00:56:04Z"},{"alias_kind":"pith_short_12","alias_value":"PGSMISGMCXOJ","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"PGSMISGMCXOJ2ZQZ","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"PGSMISGM","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:983e0d3970e9708c272c192adb09ea376b1b25d1f909644d3eaeb187590d5ee6","target":"graph","created_at":"2026-05-18T00:56:04Z","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":"In this paper Bianchi type I spacetimes are completely classified by their homothetic vectors in the context of Lyra geometry. The non-linear coupled Lyra homothetic equations are obtained and solved completely for different cases. In some cases, Bianchi type I spacetimes admit proper Lyra homothetic vectors (LHVs) for special choices of the metric functions, while there exist other cases where the spacetime under consideration admits only Lyra Killing vectors (LKVs). In all the possible cases where Bianchi type I spacetimes admit proper LHVs or LKVs, we obtained homothetic and Killing vectors","authors_text":"Ahmad T Ali, Azeb Alghanemi, Suhail Khan","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"physics.gen-ph","submitted_at":"2015-11-24T15:07:19Z","title":"Homothetic Vectors of Bianchi Type I Spacetimes in Lyra Geometry and General Relativity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.04427","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:fa72efc849f1e7df023a18f2d6b445f7296bed05fb274a5c5ccf06367959fcaa","target":"record","created_at":"2026-05-18T00:56:04Z","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":"47f3515276f7d6c2a6622a6cde05f975b7655939391377574209058ccecbb68a","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"physics.gen-ph","submitted_at":"2015-11-24T15:07:19Z","title_canon_sha256":"40807e32a8465b5f20b529fab54a3f7b6dc9c0929739fcee5f86d10398bb4f7b"},"schema_version":"1.0","source":{"id":"1512.04427","kind":"arxiv","version":2}},"canonical_sha256":"79a4c448cc15dc9d6619133c78662c582e5bf6c1381e23598f2400dc29cd9103","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"79a4c448cc15dc9d6619133c78662c582e5bf6c1381e23598f2400dc29cd9103","first_computed_at":"2026-05-18T00:56:04.543361Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:56:04.543361Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4/MJ8VbTK459nYRjZ8XVpVvn2bWR5VxzQOYuMLeYEwUUPYLhOiFL5+iTdTzOO90ADq3g8kENaHUHmyDMPXEiBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:56:04.543919Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.04427","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fa72efc849f1e7df023a18f2d6b445f7296bed05fb274a5c5ccf06367959fcaa","sha256:983e0d3970e9708c272c192adb09ea376b1b25d1f909644d3eaeb187590d5ee6"],"state_sha256":"adb80dd34bf5421f71e3a454bec71b5877690723449c2de372cef68c8b6de216"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HY5Alxf5AOnKO8jJ1UGRQqeYkKiH4PtBw7tBCMCM83Ip5Lf7gDdd0xJrli8R4escTKviVkAPF15Un0ae4bB2Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T22:03:08.825167Z","bundle_sha256":"666b704669d68cf51a806672b334b71915f2d3db3d80842bfa86b604e866736c"}}