{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:E3Q3AORS7IBBQVBJNMBVREBKND","short_pith_number":"pith:E3Q3AORS","canonical_record":{"source":{"id":"1506.06225","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-06-20T10:25:06Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"340d6f90214f3d49e77857012d3fb3b981f8d6b67281c98e99ec58e5af5a1446","abstract_canon_sha256":"57744e1790e5637b7ddb2be17a8305c8ea8d37afc54b0307082f544e59616add"},"schema_version":"1.0"},"canonical_sha256":"26e1b03a32fa021854296b0358902a68c59f554d16838ab58a94e9eaf133d625","source":{"kind":"arxiv","id":"1506.06225","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.06225","created_at":"2026-05-18T01:35:26Z"},{"alias_kind":"arxiv_version","alias_value":"1506.06225v1","created_at":"2026-05-18T01:35:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.06225","created_at":"2026-05-18T01:35:26Z"},{"alias_kind":"pith_short_12","alias_value":"E3Q3AORS7IBB","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"E3Q3AORS7IBBQVBJ","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"E3Q3AORS","created_at":"2026-05-18T12:29:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:E3Q3AORS7IBBQVBJNMBVREBKND","target":"record","payload":{"canonical_record":{"source":{"id":"1506.06225","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-06-20T10:25:06Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"340d6f90214f3d49e77857012d3fb3b981f8d6b67281c98e99ec58e5af5a1446","abstract_canon_sha256":"57744e1790e5637b7ddb2be17a8305c8ea8d37afc54b0307082f544e59616add"},"schema_version":"1.0"},"canonical_sha256":"26e1b03a32fa021854296b0358902a68c59f554d16838ab58a94e9eaf133d625","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:35:26.534920Z","signature_b64":"1yVn872pARW2G8BqkEik5KnUiIgxaM8S5YW3R+Mevev9JvLDvdlTnD788ofZ3n1nUzqy2LeWUACeYF4x6WutAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"26e1b03a32fa021854296b0358902a68c59f554d16838ab58a94e9eaf133d625","last_reissued_at":"2026-05-18T01:35:26.534224Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:35:26.534224Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.06225","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":"2026-05-18T01:35:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DzRrKhGki3nFNeAe7IhqyQ+lfxifln4KhZTDufNLHsNkHFTW48VV50E+/oeWN9RmRIWzUk59AVKID+x/mCZPBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T23:55:43.998068Z"},"content_sha256":"f3660d83db77cd383f60c76a3611a3b86f0197e75767e374977190e777e4bea7","schema_version":"1.0","event_id":"sha256:f3660d83db77cd383f60c76a3611a3b86f0197e75767e374977190e777e4bea7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:E3Q3AORS7IBBQVBJNMBVREBKND","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On algebraic endomorphisms of the Einstein gyrogroup","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"D\\'aniel Virosztek, Lajos Moln\\'ar","submitted_at":"2015-06-20T10:25:06Z","abstract_excerpt":"We describe the structure of all continuous algebraic endomorphisms of the open unit ball $\\mathbf{B}$ of $\\mathbb{R}^3$ equipped with the Einstein velocity addition. We show that any nonzero such transformation originates from an orthogonal linear transformation on $\\mathbb{R}^3$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.06225","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":"2026-05-18T01:35:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iewzmNKW4GIcM3DEDQGqY+FQ0IuMzqOJyaxP7fNDLE580Q8Pmtz+h7DAhAjsV0RxOWy3dESxig1mEmcX6L2LAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T23:55:43.998484Z"},"content_sha256":"c37f07746006632051a8c8d48602c6cdd1df79aeffef6c40d4a9f5a0820349e6","schema_version":"1.0","event_id":"sha256:c37f07746006632051a8c8d48602c6cdd1df79aeffef6c40d4a9f5a0820349e6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/E3Q3AORS7IBBQVBJNMBVREBKND/bundle.json","state_url":"https://pith.science/pith/E3Q3AORS7IBBQVBJNMBVREBKND/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/E3Q3AORS7IBBQVBJNMBVREBKND/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":"2026-05-30T23:55:44Z","links":{"resolver":"https://pith.science/pith/E3Q3AORS7IBBQVBJNMBVREBKND","bundle":"https://pith.science/pith/E3Q3AORS7IBBQVBJNMBVREBKND/bundle.json","state":"https://pith.science/pith/E3Q3AORS7IBBQVBJNMBVREBKND/state.json","well_known_bundle":"https://pith.science/.well-known/pith/E3Q3AORS7IBBQVBJNMBVREBKND/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:E3Q3AORS7IBBQVBJNMBVREBKND","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":"57744e1790e5637b7ddb2be17a8305c8ea8d37afc54b0307082f544e59616add","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-06-20T10:25:06Z","title_canon_sha256":"340d6f90214f3d49e77857012d3fb3b981f8d6b67281c98e99ec58e5af5a1446"},"schema_version":"1.0","source":{"id":"1506.06225","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.06225","created_at":"2026-05-18T01:35:26Z"},{"alias_kind":"arxiv_version","alias_value":"1506.06225v1","created_at":"2026-05-18T01:35:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.06225","created_at":"2026-05-18T01:35:26Z"},{"alias_kind":"pith_short_12","alias_value":"E3Q3AORS7IBB","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"E3Q3AORS7IBBQVBJ","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"E3Q3AORS","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:c37f07746006632051a8c8d48602c6cdd1df79aeffef6c40d4a9f5a0820349e6","target":"graph","created_at":"2026-05-18T01:35:26Z","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":"We describe the structure of all continuous algebraic endomorphisms of the open unit ball $\\mathbf{B}$ of $\\mathbb{R}^3$ equipped with the Einstein velocity addition. We show that any nonzero such transformation originates from an orthogonal linear transformation on $\\mathbb{R}^3$.","authors_text":"D\\'aniel Virosztek, Lajos Moln\\'ar","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-06-20T10:25:06Z","title":"On algebraic endomorphisms of the Einstein gyrogroup"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.06225","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:f3660d83db77cd383f60c76a3611a3b86f0197e75767e374977190e777e4bea7","target":"record","created_at":"2026-05-18T01:35:26Z","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":"57744e1790e5637b7ddb2be17a8305c8ea8d37afc54b0307082f544e59616add","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-06-20T10:25:06Z","title_canon_sha256":"340d6f90214f3d49e77857012d3fb3b981f8d6b67281c98e99ec58e5af5a1446"},"schema_version":"1.0","source":{"id":"1506.06225","kind":"arxiv","version":1}},"canonical_sha256":"26e1b03a32fa021854296b0358902a68c59f554d16838ab58a94e9eaf133d625","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"26e1b03a32fa021854296b0358902a68c59f554d16838ab58a94e9eaf133d625","first_computed_at":"2026-05-18T01:35:26.534224Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:35:26.534224Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1yVn872pARW2G8BqkEik5KnUiIgxaM8S5YW3R+Mevev9JvLDvdlTnD788ofZ3n1nUzqy2LeWUACeYF4x6WutAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:35:26.534920Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.06225","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f3660d83db77cd383f60c76a3611a3b86f0197e75767e374977190e777e4bea7","sha256:c37f07746006632051a8c8d48602c6cdd1df79aeffef6c40d4a9f5a0820349e6"],"state_sha256":"48d0b3c5f3272e893d2bc0c75923b32a6c3e70518e83c29a0ac47e82763844e5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lpZGBGPu6OAu9jD/bAKUsAWRsa++UvnzrLJsV1HUPE4VmL1HwEGz6AGLvQsTNnZwMlPgh6GBcDUQaTjdvdliAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T23:55:44.001764Z","bundle_sha256":"e987d9328e88b9432291150f34c3b6a4f0c5208a4fc2ef0bd896e5a542959ce6"}}