{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:D4WYU46QEK6CU2OPVNDQQCPGBV","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":"3903ba124b204fa673369cd3ef148d8f257d05a7cd0c4a51caf666ac624a0c53","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-02-22T11:26:55Z","title_canon_sha256":"f957d8e1a2828cf80806a25f2cd7104b43cb771cc74a6bcf7c5ae8ed0172dac7"},"schema_version":"1.0","source":{"id":"1602.06734","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.06734","created_at":"2026-05-18T01:15:32Z"},{"alias_kind":"arxiv_version","alias_value":"1602.06734v1","created_at":"2026-05-18T01:15:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.06734","created_at":"2026-05-18T01:15:32Z"},{"alias_kind":"pith_short_12","alias_value":"D4WYU46QEK6C","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"D4WYU46QEK6CU2OP","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"D4WYU46Q","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:932f3c3da3da0e134445a27ff093b68077907590d4a1b564ee3d30f8f2513ba5","target":"graph","created_at":"2026-05-18T01:15:32Z","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 his book \"Differential Geometry of Spray and Finsler spaces\", page 177, Zhongmin Shen asks \"wether or not there always exist non-trivial Funk functions on a spray space\". In this note, we will prove that the answer is negative for the geodesic spray of a finslerian function of non-vanishing scalar flag curvature.","authors_text":"Ioan Bucataru, Zolt\\'an Muzsnay","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-02-22T11:26:55Z","title":"Non-existence of Funk functions for Finsler spaces of non-vanishing scalar flag curvature"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.06734","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":"sha256:8c70bf698ac95f6084b4c7049309b2686de6989914db4dc2ec7ff892f7ec7c41","target":"record","created_at":"2026-05-18T01:15:32Z","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":"3903ba124b204fa673369cd3ef148d8f257d05a7cd0c4a51caf666ac624a0c53","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-02-22T11:26:55Z","title_canon_sha256":"f957d8e1a2828cf80806a25f2cd7104b43cb771cc74a6bcf7c5ae8ed0172dac7"},"schema_version":"1.0","source":{"id":"1602.06734","kind":"arxiv","version":1}},"canonical_sha256":"1f2d8a73d022bc2a69cfab470809e60d786ca85a3b0a8feb4d7292d0f76c403b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1f2d8a73d022bc2a69cfab470809e60d786ca85a3b0a8feb4d7292d0f76c403b","first_computed_at":"2026-05-18T01:15:32.009629Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:15:32.009629Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"15YzMfiqeJxJHY+ViO8ySpzWYLLzoWa4kzoNOZzpT0SPW/TP2zH8LygJGRL8qBxSmJtpfXnMBpPCbEYe1Wl8DA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:15:32.010464Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.06734","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8c70bf698ac95f6084b4c7049309b2686de6989914db4dc2ec7ff892f7ec7c41","sha256:932f3c3da3da0e134445a27ff093b68077907590d4a1b564ee3d30f8f2513ba5"],"state_sha256":"32bf06870c23346a6c91e2c61eb8b9bb9e2ebaf9ef67bef5e79032afef0739f6"}