{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:Q5KQX6EZB7KY7BR4G374UNR3IO","short_pith_number":"pith:Q5KQX6EZ","canonical_record":{"source":{"id":"1301.1813","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-01-09T11:10:32Z","cross_cats_sorted":[],"title_canon_sha256":"84518f126607761005bfc90bfda6d391629c182a5722e8dcc0c75abbaa4a9676","abstract_canon_sha256":"9cbfe153424f71df7971297003f5ec277390e545b24603f5d5843d7d55703e01"},"schema_version":"1.0"},"canonical_sha256":"87550bf8990fd58f863c36ffca363b4382101eb1562e737a29682ec0a487f2b0","source":{"kind":"arxiv","id":"1301.1813","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.1813","created_at":"2026-05-18T03:05:44Z"},{"alias_kind":"arxiv_version","alias_value":"1301.1813v2","created_at":"2026-05-18T03:05:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.1813","created_at":"2026-05-18T03:05:44Z"},{"alias_kind":"pith_short_12","alias_value":"Q5KQX6EZB7KY","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"Q5KQX6EZB7KY7BR4","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"Q5KQX6EZ","created_at":"2026-05-18T12:27:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:Q5KQX6EZB7KY7BR4G374UNR3IO","target":"record","payload":{"canonical_record":{"source":{"id":"1301.1813","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-01-09T11:10:32Z","cross_cats_sorted":[],"title_canon_sha256":"84518f126607761005bfc90bfda6d391629c182a5722e8dcc0c75abbaa4a9676","abstract_canon_sha256":"9cbfe153424f71df7971297003f5ec277390e545b24603f5d5843d7d55703e01"},"schema_version":"1.0"},"canonical_sha256":"87550bf8990fd58f863c36ffca363b4382101eb1562e737a29682ec0a487f2b0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:05:44.625465Z","signature_b64":"dmxA6DpjIncO5SVDzAkk0DDwTEmtR/jiWFon+BpTgas2CnoMmWpfHestt9mwBLaqjtlgPfmzRDlmhdcxJYztDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"87550bf8990fd58f863c36ffca363b4382101eb1562e737a29682ec0a487f2b0","last_reissued_at":"2026-05-18T03:05:44.624871Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:05:44.624871Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.1813","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":"2026-05-18T03:05:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wAwoyKAgxYvB49YKPAAu4g7Iw8cO54VfQHK2nll1UMYPudLvGGb5n+nwMC065HNaGl+jsUnDvIS+SkMJYpMDDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T04:37:08.841729Z"},"content_sha256":"de6a42c562ae5be3a84d24b1810e1ce3912a950870d1f3fdd9396fb71196e813","schema_version":"1.0","event_id":"sha256:de6a42c562ae5be3a84d24b1810e1ce3912a950870d1f3fdd9396fb71196e813"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:Q5KQX6EZB7KY7BR4G374UNR3IO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Clifford-Wolf homogeneous left invariant $(\\alpha,\\beta)$-metrics on compact semi-simple Lie groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Ming Xu, ShaoQiang Deng","submitted_at":"2013-01-09T11:10:32Z","abstract_excerpt":"Let $(M,F)$ be a connected Finsler space. An isometry of $(M,F)$ is called a Clifford-Wolf translation (or simply CW-translation) if it moves all points the same distance. The compact Finsler space $(M,F)$ is called restrictively Clifford-Wolf homogeneous (restrictively CW-homogeneous) if for any two sufficiently close points $x_1,x_2\\in M$, there exists a CW-translation $\\sigma$ such that $\\sigma(x_1)=x_2$. In this paper, we define the good normalized datum for a homogeneous non-Riemannian $(\\alpha,\\beta)$-space, and use it to study the restrictive CW-homogeneity of left invariant $(\\alpha,\\b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.1813","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":"2026-05-18T03:05:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0sid4xGJk2XotkOgnnjAknMZuY30vl7CGNRooDwAAPqPsBLAemA0kxDf0Ph/VZ/immVeJIQk6YwAUElOfoslCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T04:37:08.842073Z"},"content_sha256":"228eb16be57af64e9c5af2955322a31fb78678b4d71182a5878a69c948593e1b","schema_version":"1.0","event_id":"sha256:228eb16be57af64e9c5af2955322a31fb78678b4d71182a5878a69c948593e1b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Q5KQX6EZB7KY7BR4G374UNR3IO/bundle.json","state_url":"https://pith.science/pith/Q5KQX6EZB7KY7BR4G374UNR3IO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Q5KQX6EZB7KY7BR4G374UNR3IO/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":"2026-06-24T04:37:08Z","links":{"resolver":"https://pith.science/pith/Q5KQX6EZB7KY7BR4G374UNR3IO","bundle":"https://pith.science/pith/Q5KQX6EZB7KY7BR4G374UNR3IO/bundle.json","state":"https://pith.science/pith/Q5KQX6EZB7KY7BR4G374UNR3IO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Q5KQX6EZB7KY7BR4G374UNR3IO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:Q5KQX6EZB7KY7BR4G374UNR3IO","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":"9cbfe153424f71df7971297003f5ec277390e545b24603f5d5843d7d55703e01","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-01-09T11:10:32Z","title_canon_sha256":"84518f126607761005bfc90bfda6d391629c182a5722e8dcc0c75abbaa4a9676"},"schema_version":"1.0","source":{"id":"1301.1813","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.1813","created_at":"2026-05-18T03:05:44Z"},{"alias_kind":"arxiv_version","alias_value":"1301.1813v2","created_at":"2026-05-18T03:05:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.1813","created_at":"2026-05-18T03:05:44Z"},{"alias_kind":"pith_short_12","alias_value":"Q5KQX6EZB7KY","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"Q5KQX6EZB7KY7BR4","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"Q5KQX6EZ","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:228eb16be57af64e9c5af2955322a31fb78678b4d71182a5878a69c948593e1b","target":"graph","created_at":"2026-05-18T03:05:44Z","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":"Let $(M,F)$ be a connected Finsler space. An isometry of $(M,F)$ is called a Clifford-Wolf translation (or simply CW-translation) if it moves all points the same distance. The compact Finsler space $(M,F)$ is called restrictively Clifford-Wolf homogeneous (restrictively CW-homogeneous) if for any two sufficiently close points $x_1,x_2\\in M$, there exists a CW-translation $\\sigma$ such that $\\sigma(x_1)=x_2$. In this paper, we define the good normalized datum for a homogeneous non-Riemannian $(\\alpha,\\beta)$-space, and use it to study the restrictive CW-homogeneity of left invariant $(\\alpha,\\b","authors_text":"Ming Xu, ShaoQiang Deng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-01-09T11:10:32Z","title":"Clifford-Wolf homogeneous left invariant $(\\alpha,\\beta)$-metrics on compact semi-simple Lie groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.1813","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:de6a42c562ae5be3a84d24b1810e1ce3912a950870d1f3fdd9396fb71196e813","target":"record","created_at":"2026-05-18T03:05:44Z","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":"9cbfe153424f71df7971297003f5ec277390e545b24603f5d5843d7d55703e01","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-01-09T11:10:32Z","title_canon_sha256":"84518f126607761005bfc90bfda6d391629c182a5722e8dcc0c75abbaa4a9676"},"schema_version":"1.0","source":{"id":"1301.1813","kind":"arxiv","version":2}},"canonical_sha256":"87550bf8990fd58f863c36ffca363b4382101eb1562e737a29682ec0a487f2b0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"87550bf8990fd58f863c36ffca363b4382101eb1562e737a29682ec0a487f2b0","first_computed_at":"2026-05-18T03:05:44.624871Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:05:44.624871Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dmxA6DpjIncO5SVDzAkk0DDwTEmtR/jiWFon+BpTgas2CnoMmWpfHestt9mwBLaqjtlgPfmzRDlmhdcxJYztDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:05:44.625465Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.1813","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:de6a42c562ae5be3a84d24b1810e1ce3912a950870d1f3fdd9396fb71196e813","sha256:228eb16be57af64e9c5af2955322a31fb78678b4d71182a5878a69c948593e1b"],"state_sha256":"bb0bf160d9c67d34620069d57c5b64421a324f8f8dc4cd068aec55797315bdd1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S90RqVCSsILSeKOgbESsh7K0nYkd5c8dXiu6wj2cKwXDZPHP1+hosR6f3pncEoUP93hg4d5p9YMA2cYlj8z5CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T04:37:08.844157Z","bundle_sha256":"80ff2cd55056a4e1e29e12e92475726bd925c3271d71236c9de14dabee7a77ca"}}