{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:HNGMMNSW6YHH5FHD6I56EWWR42","short_pith_number":"pith:HNGMMNSW","canonical_record":{"source":{"id":"1108.4628","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-08-23T15:10:55Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"64f60415aa846712019bb3fee6c8de82563202cc3e8a3e361b51c4e0b772e60a","abstract_canon_sha256":"dad1081749c4af70b6ee8e48009b67e0c499f34a619f07e93ba50ef11c13f63a"},"schema_version":"1.0"},"canonical_sha256":"3b4cc63656f60e7e94e3f23be25ad1e6995fc50588d12f15a4248fd02b357dc7","source":{"kind":"arxiv","id":"1108.4628","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.4628","created_at":"2026-05-18T03:49:45Z"},{"alias_kind":"arxiv_version","alias_value":"1108.4628v1","created_at":"2026-05-18T03:49:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.4628","created_at":"2026-05-18T03:49:45Z"},{"alias_kind":"pith_short_12","alias_value":"HNGMMNSW6YHH","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"HNGMMNSW6YHH5FHD","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"HNGMMNSW","created_at":"2026-05-18T12:26:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:HNGMMNSW6YHH5FHD6I56EWWR42","target":"record","payload":{"canonical_record":{"source":{"id":"1108.4628","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-08-23T15:10:55Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"64f60415aa846712019bb3fee6c8de82563202cc3e8a3e361b51c4e0b772e60a","abstract_canon_sha256":"dad1081749c4af70b6ee8e48009b67e0c499f34a619f07e93ba50ef11c13f63a"},"schema_version":"1.0"},"canonical_sha256":"3b4cc63656f60e7e94e3f23be25ad1e6995fc50588d12f15a4248fd02b357dc7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:49:45.815482Z","signature_b64":"Eo7FSpRxWxdbJG6giHOYOfQNTGdnI4G/qdcCPQG8gVJGPZm0LsHQeGUvXrgtQK613N7ug6sIzE/gfGQnk1PxCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3b4cc63656f60e7e94e3f23be25ad1e6995fc50588d12f15a4248fd02b357dc7","last_reissued_at":"2026-05-18T03:49:45.814876Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:49:45.814876Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1108.4628","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":"2026-05-18T03:49:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BAg4rsal3qQwEX5jbLKpshgmsl4RaWNtYWtu697CFENe1Mk/JenVW795LlhmFMnhiddhSmpES0ABNN6sSi/3Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T06:40:25.005309Z"},"content_sha256":"9c8b185f91399693368d85ead8e10117434f15d11d3d1d9e5bc3480688ff2619","schema_version":"1.0","event_id":"sha256:9c8b185f91399693368d85ead8e10117434f15d11d3d1d9e5bc3480688ff2619"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:HNGMMNSW6YHH5FHD6I56EWWR42","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Projective and Finsler metrizability: parameterization-rigidity of the geodesics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.DG","authors_text":"Ioan Bucataru, Zolt\\'an Muzsnay","submitted_at":"2011-08-23T15:10:55Z","abstract_excerpt":"In this work we show that for the geodesic spray $S$ of a Finsler function $F$ the most natural projective deformation $\\widetilde{S}=S -2 \\lambda F\\mathbb C$ leads to a non-Finsler metrizable spray, for almost every value of $\\lambda \\in \\mathbb R$. This result shows how rigid is the metrizablility property with respect to certain reparameterizations of the geodesics. As a consequence we obtain that the projective class of an arbitrary spray contains infinitely many sprays that are not Finsler metrizable."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.4628","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":"2026-05-18T03:49:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Pq3CE5+RTbvzM3QOgoqB/kArW30TT1opWssRcej23cVkcMEhwWEuKwiPjqwpl9MTCCT1kGdFngtc4/V7GrswAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T06:40:25.005688Z"},"content_sha256":"fbd2007074fa13be5e59a80b81a04fcdf3cc003d662d93dd4d664d33302fd08f","schema_version":"1.0","event_id":"sha256:fbd2007074fa13be5e59a80b81a04fcdf3cc003d662d93dd4d664d33302fd08f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HNGMMNSW6YHH5FHD6I56EWWR42/bundle.json","state_url":"https://pith.science/pith/HNGMMNSW6YHH5FHD6I56EWWR42/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HNGMMNSW6YHH5FHD6I56EWWR42/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":"2026-06-24T06:40:25Z","links":{"resolver":"https://pith.science/pith/HNGMMNSW6YHH5FHD6I56EWWR42","bundle":"https://pith.science/pith/HNGMMNSW6YHH5FHD6I56EWWR42/bundle.json","state":"https://pith.science/pith/HNGMMNSW6YHH5FHD6I56EWWR42/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HNGMMNSW6YHH5FHD6I56EWWR42/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:HNGMMNSW6YHH5FHD6I56EWWR42","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":"dad1081749c4af70b6ee8e48009b67e0c499f34a619f07e93ba50ef11c13f63a","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-08-23T15:10:55Z","title_canon_sha256":"64f60415aa846712019bb3fee6c8de82563202cc3e8a3e361b51c4e0b772e60a"},"schema_version":"1.0","source":{"id":"1108.4628","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.4628","created_at":"2026-05-18T03:49:45Z"},{"alias_kind":"arxiv_version","alias_value":"1108.4628v1","created_at":"2026-05-18T03:49:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.4628","created_at":"2026-05-18T03:49:45Z"},{"alias_kind":"pith_short_12","alias_value":"HNGMMNSW6YHH","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"HNGMMNSW6YHH5FHD","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"HNGMMNSW","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:fbd2007074fa13be5e59a80b81a04fcdf3cc003d662d93dd4d664d33302fd08f","target":"graph","created_at":"2026-05-18T03:49:45Z","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 work we show that for the geodesic spray $S$ of a Finsler function $F$ the most natural projective deformation $\\widetilde{S}=S -2 \\lambda F\\mathbb C$ leads to a non-Finsler metrizable spray, for almost every value of $\\lambda \\in \\mathbb R$. This result shows how rigid is the metrizablility property with respect to certain reparameterizations of the geodesics. As a consequence we obtain that the projective class of an arbitrary spray contains infinitely many sprays that are not Finsler metrizable.","authors_text":"Ioan Bucataru, Zolt\\'an Muzsnay","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-08-23T15:10:55Z","title":"Projective and Finsler metrizability: parameterization-rigidity of the geodesics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.4628","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":"sha256:9c8b185f91399693368d85ead8e10117434f15d11d3d1d9e5bc3480688ff2619","target":"record","created_at":"2026-05-18T03:49:45Z","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":"dad1081749c4af70b6ee8e48009b67e0c499f34a619f07e93ba50ef11c13f63a","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-08-23T15:10:55Z","title_canon_sha256":"64f60415aa846712019bb3fee6c8de82563202cc3e8a3e361b51c4e0b772e60a"},"schema_version":"1.0","source":{"id":"1108.4628","kind":"arxiv","version":1}},"canonical_sha256":"3b4cc63656f60e7e94e3f23be25ad1e6995fc50588d12f15a4248fd02b357dc7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3b4cc63656f60e7e94e3f23be25ad1e6995fc50588d12f15a4248fd02b357dc7","first_computed_at":"2026-05-18T03:49:45.814876Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:49:45.814876Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Eo7FSpRxWxdbJG6giHOYOfQNTGdnI4G/qdcCPQG8gVJGPZm0LsHQeGUvXrgtQK613N7ug6sIzE/gfGQnk1PxCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:49:45.815482Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.4628","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9c8b185f91399693368d85ead8e10117434f15d11d3d1d9e5bc3480688ff2619","sha256:fbd2007074fa13be5e59a80b81a04fcdf3cc003d662d93dd4d664d33302fd08f"],"state_sha256":"b23f705eb60fc1e1b99a3f087e2356c0dff97b6be6ff83e27b025da6858be4d1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pjGCiI/4DXX5kmJJZJuk8meNYI7tlgagSmK+dvV62dM89F1zO1ZXk9rq48AXZo3njpAdLORXOxjvp8m9zsK8AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T06:40:25.007765Z","bundle_sha256":"c34af0dcd865a80b3bfea30772c18ed29eae77d4aff732e58fe20a43897f638a"}}