{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:VILKRZ7P3TJRKTSBVZVXNHE6CD","short_pith_number":"pith:VILKRZ7P","canonical_record":{"source":{"id":"1811.12716","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-11-30T10:51:47Z","cross_cats_sorted":["math.DG","math.MP"],"title_canon_sha256":"e4368c0c196a5a69da4bcddbe5dffcd00fd1417cdf1fd8e6c054bddea4edec42","abstract_canon_sha256":"89ac9a756f99dbf9367a2d6997b7ec9619c3ace1cb8cf33b63371adbda91496a"},"schema_version":"1.0"},"canonical_sha256":"aa16a8e7efdcd3154e41ae6b769c9e10e19f5de4d03096d8c8358397cdc052b9","source":{"kind":"arxiv","id":"1811.12716","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.12716","created_at":"2026-05-17T23:59:28Z"},{"alias_kind":"arxiv_version","alias_value":"1811.12716v1","created_at":"2026-05-17T23:59:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.12716","created_at":"2026-05-17T23:59:28Z"},{"alias_kind":"pith_short_12","alias_value":"VILKRZ7P3TJR","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"VILKRZ7P3TJRKTSB","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"VILKRZ7P","created_at":"2026-05-18T12:32:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:VILKRZ7P3TJRKTSBVZVXNHE6CD","target":"record","payload":{"canonical_record":{"source":{"id":"1811.12716","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-11-30T10:51:47Z","cross_cats_sorted":["math.DG","math.MP"],"title_canon_sha256":"e4368c0c196a5a69da4bcddbe5dffcd00fd1417cdf1fd8e6c054bddea4edec42","abstract_canon_sha256":"89ac9a756f99dbf9367a2d6997b7ec9619c3ace1cb8cf33b63371adbda91496a"},"schema_version":"1.0"},"canonical_sha256":"aa16a8e7efdcd3154e41ae6b769c9e10e19f5de4d03096d8c8358397cdc052b9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:59:28.746186Z","signature_b64":"AdZ1I/I+7O+clNJUsinQcwqffoeMxZeJOHgAbIIZHwIZArefL+D6u3Ev9nBbjNaBrAVfLEMLDG5xdJmiZTjOCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aa16a8e7efdcd3154e41ae6b769c9e10e19f5de4d03096d8c8358397cdc052b9","last_reissued_at":"2026-05-17T23:59:28.745675Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:59:28.745675Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1811.12716","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":"2026-05-17T23:59:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M78+QwpLVPTXX9p4Z4BKhNoZc6DWtCNqztQqd10/hgb5C99vbEt3LAlxUN12JhCjsIjZ7HQfJfmJqlvIXfpjAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T23:03:40.441623Z"},"content_sha256":"189a81215a49e3244a56c2e22434c290d6109e910ba753b969acfdbfef62feee","schema_version":"1.0","event_id":"sha256:189a81215a49e3244a56c2e22434c290d6109e910ba753b969acfdbfef62feee"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:VILKRZ7P3TJRKTSBVZVXNHE6CD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Finsler connection in moving frame formalism","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.MP"],"primary_cat":"math-ph","authors_text":"Muneyuki Ishida, Ryoko Yahagi, Takayoshi Ootsuka","submitted_at":"2018-11-30T10:51:47Z","abstract_excerpt":"In our previous work, we have defined a nonlinear connection of Finsler manifold which preserves the Finsler metric $L=L(x,dx)$. To make the method easier and more useful in applications, moving frame (vielbein) $\\theta^a={e^a}_\\mu dx^\\mu$ formalism for the nonlinear connection is newly considered. We derive formulae to calculate the Finsler connection in the specific case that the Finsler metric depends not on coordinates $x^\\mu$, but only on moving frame $\\theta^a$: $L=L(\\theta)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.12716","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":"2026-05-17T23:59:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bvl1Eppl503hyR/31pwRs0ctai6ox+Ef4g3H4tp8f3M5wJMWX1jv8UikiBduRnSzWCmxwizanoNHRPcxfBJJBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T23:03:40.442350Z"},"content_sha256":"cda70ec7d35aec34a59f7d27168c82998698804fc1f6496244efc18f4494a4dd","schema_version":"1.0","event_id":"sha256:cda70ec7d35aec34a59f7d27168c82998698804fc1f6496244efc18f4494a4dd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VILKRZ7P3TJRKTSBVZVXNHE6CD/bundle.json","state_url":"https://pith.science/pith/VILKRZ7P3TJRKTSBVZVXNHE6CD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VILKRZ7P3TJRKTSBVZVXNHE6CD/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":"2026-06-10T23:03:40Z","links":{"resolver":"https://pith.science/pith/VILKRZ7P3TJRKTSBVZVXNHE6CD","bundle":"https://pith.science/pith/VILKRZ7P3TJRKTSBVZVXNHE6CD/bundle.json","state":"https://pith.science/pith/VILKRZ7P3TJRKTSBVZVXNHE6CD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VILKRZ7P3TJRKTSBVZVXNHE6CD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:VILKRZ7P3TJRKTSBVZVXNHE6CD","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":"89ac9a756f99dbf9367a2d6997b7ec9619c3ace1cb8cf33b63371adbda91496a","cross_cats_sorted":["math.DG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-11-30T10:51:47Z","title_canon_sha256":"e4368c0c196a5a69da4bcddbe5dffcd00fd1417cdf1fd8e6c054bddea4edec42"},"schema_version":"1.0","source":{"id":"1811.12716","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.12716","created_at":"2026-05-17T23:59:28Z"},{"alias_kind":"arxiv_version","alias_value":"1811.12716v1","created_at":"2026-05-17T23:59:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.12716","created_at":"2026-05-17T23:59:28Z"},{"alias_kind":"pith_short_12","alias_value":"VILKRZ7P3TJR","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"VILKRZ7P3TJRKTSB","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"VILKRZ7P","created_at":"2026-05-18T12:32:59Z"}],"graph_snapshots":[{"event_id":"sha256:cda70ec7d35aec34a59f7d27168c82998698804fc1f6496244efc18f4494a4dd","target":"graph","created_at":"2026-05-17T23:59:28Z","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 our previous work, we have defined a nonlinear connection of Finsler manifold which preserves the Finsler metric $L=L(x,dx)$. To make the method easier and more useful in applications, moving frame (vielbein) $\\theta^a={e^a}_\\mu dx^\\mu$ formalism for the nonlinear connection is newly considered. We derive formulae to calculate the Finsler connection in the specific case that the Finsler metric depends not on coordinates $x^\\mu$, but only on moving frame $\\theta^a$: $L=L(\\theta)$.","authors_text":"Muneyuki Ishida, Ryoko Yahagi, Takayoshi Ootsuka","cross_cats":["math.DG","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-11-30T10:51:47Z","title":"Finsler connection in moving frame formalism"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.12716","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":"sha256:189a81215a49e3244a56c2e22434c290d6109e910ba753b969acfdbfef62feee","target":"record","created_at":"2026-05-17T23:59:28Z","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":"89ac9a756f99dbf9367a2d6997b7ec9619c3ace1cb8cf33b63371adbda91496a","cross_cats_sorted":["math.DG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-11-30T10:51:47Z","title_canon_sha256":"e4368c0c196a5a69da4bcddbe5dffcd00fd1417cdf1fd8e6c054bddea4edec42"},"schema_version":"1.0","source":{"id":"1811.12716","kind":"arxiv","version":1}},"canonical_sha256":"aa16a8e7efdcd3154e41ae6b769c9e10e19f5de4d03096d8c8358397cdc052b9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aa16a8e7efdcd3154e41ae6b769c9e10e19f5de4d03096d8c8358397cdc052b9","first_computed_at":"2026-05-17T23:59:28.745675Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:59:28.745675Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AdZ1I/I+7O+clNJUsinQcwqffoeMxZeJOHgAbIIZHwIZArefL+D6u3Ev9nBbjNaBrAVfLEMLDG5xdJmiZTjOCA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:59:28.746186Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.12716","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:189a81215a49e3244a56c2e22434c290d6109e910ba753b969acfdbfef62feee","sha256:cda70ec7d35aec34a59f7d27168c82998698804fc1f6496244efc18f4494a4dd"],"state_sha256":"0c4d85d161bef0475aeea4c864041694121272debb4a38f2dc97df1d177a61d8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PkVuAEFx2HqVEGXClBJ7Z1+55xSunG4s+yQBm8yBz/jb0jwMvb4JqDeL2lu/ltxiax9/Jb07v5nLJ37W8he6Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T23:03:40.446173Z","bundle_sha256":"e2f46a2d71a33220234aeff2d96204e0500daf77bb098b28757bfaeff1f279ac"}}