{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:3TCMZ2O266G2SW532U3GPTDCNE","short_pith_number":"pith:3TCMZ2O2","canonical_record":{"source":{"id":"1411.4741","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-11-18T06:12:51Z","cross_cats_sorted":[],"title_canon_sha256":"cf45cab2ed8ae40dbde769dab2c2b9a37589fc04875035391bcb3738ab9a496b","abstract_canon_sha256":"5c896e78f7ddd15156000a93697df1f4149f1eadd39a7a4608ca4eae4259aef3"},"schema_version":"1.0"},"canonical_sha256":"dcc4cce9daf78da95bbbd53667cc626908bcce46ec6135ea3eec6b2ff02fa8bc","source":{"kind":"arxiv","id":"1411.4741","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.4741","created_at":"2026-05-18T02:34:51Z"},{"alias_kind":"arxiv_version","alias_value":"1411.4741v1","created_at":"2026-05-18T02:34:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.4741","created_at":"2026-05-18T02:34:51Z"},{"alias_kind":"pith_short_12","alias_value":"3TCMZ2O266G2","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3TCMZ2O266G2SW53","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3TCMZ2O2","created_at":"2026-05-18T12:28:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:3TCMZ2O266G2SW532U3GPTDCNE","target":"record","payload":{"canonical_record":{"source":{"id":"1411.4741","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-11-18T06:12:51Z","cross_cats_sorted":[],"title_canon_sha256":"cf45cab2ed8ae40dbde769dab2c2b9a37589fc04875035391bcb3738ab9a496b","abstract_canon_sha256":"5c896e78f7ddd15156000a93697df1f4149f1eadd39a7a4608ca4eae4259aef3"},"schema_version":"1.0"},"canonical_sha256":"dcc4cce9daf78da95bbbd53667cc626908bcce46ec6135ea3eec6b2ff02fa8bc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:34:51.285727Z","signature_b64":"e57cLLTKCVT6FI7TT22fio2N9BqQ1c+VgjsD36DTM2IGpm5/ryVfy347TGbcnmF6MZWBKVBOjQpEtnXNdHoFBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dcc4cce9daf78da95bbbd53667cc626908bcce46ec6135ea3eec6b2ff02fa8bc","last_reissued_at":"2026-05-18T02:34:51.285345Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:34:51.285345Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1411.4741","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":"2026-05-18T02:34:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2Qhwy4U4dqQUw3q5uuhG3dhbrCSxpVYhEWKo4lKdSsyQGzartiD6grfyiuu/EE6KFtXKgbHVC+7gwK75Z38pDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T05:51:38.683993Z"},"content_sha256":"c8cf7ecb03a99ac3a74718c0146fae7fe0d28a3c582af0fa60742e9feeb81d6a","schema_version":"1.0","event_id":"sha256:c8cf7ecb03a99ac3a74718c0146fae7fe0d28a3c582af0fa60742e9feeb81d6a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:3TCMZ2O266G2SW532U3GPTDCNE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Killing tensor fields on the 2-torus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Vladimir Sharafutdinov","submitted_at":"2014-11-18T06:12:51Z","abstract_excerpt":"A symmetric tensor field on a Riemannian manifold is called Killing field if the symmetric part of its covariant derivative is equal to zero. There is a one to one correspondence between Killing tensor fields and first integrals of the geodesic flow which depend polynomially on the velocity. Therefore Killing tensor fields closely relate to the problem of integrability of geodesic flows. In particular, the following question is still open: does there exist a Riemannian metric on the 2-torus which admits an irreducible Killing tensor field of rank $\\geq 3$? We obtain two necessary conditions on"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.4741","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":"2026-05-18T02:34:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FMeyLJocmdOD03q4CMAJxDCIMHygVtCf49P1MX6zUWhKIv4srEh17G12NKKWEx1trQUWFee4JVT0xchthDD8DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T05:51:38.684387Z"},"content_sha256":"a4db8c8480164575cac2960f01b8516fb3c31ed185077c5075002955c6573911","schema_version":"1.0","event_id":"sha256:a4db8c8480164575cac2960f01b8516fb3c31ed185077c5075002955c6573911"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3TCMZ2O266G2SW532U3GPTDCNE/bundle.json","state_url":"https://pith.science/pith/3TCMZ2O266G2SW532U3GPTDCNE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3TCMZ2O266G2SW532U3GPTDCNE/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":"2026-06-22T05:51:38Z","links":{"resolver":"https://pith.science/pith/3TCMZ2O266G2SW532U3GPTDCNE","bundle":"https://pith.science/pith/3TCMZ2O266G2SW532U3GPTDCNE/bundle.json","state":"https://pith.science/pith/3TCMZ2O266G2SW532U3GPTDCNE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3TCMZ2O266G2SW532U3GPTDCNE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:3TCMZ2O266G2SW532U3GPTDCNE","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":"5c896e78f7ddd15156000a93697df1f4149f1eadd39a7a4608ca4eae4259aef3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-11-18T06:12:51Z","title_canon_sha256":"cf45cab2ed8ae40dbde769dab2c2b9a37589fc04875035391bcb3738ab9a496b"},"schema_version":"1.0","source":{"id":"1411.4741","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.4741","created_at":"2026-05-18T02:34:51Z"},{"alias_kind":"arxiv_version","alias_value":"1411.4741v1","created_at":"2026-05-18T02:34:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.4741","created_at":"2026-05-18T02:34:51Z"},{"alias_kind":"pith_short_12","alias_value":"3TCMZ2O266G2","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3TCMZ2O266G2SW53","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3TCMZ2O2","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:a4db8c8480164575cac2960f01b8516fb3c31ed185077c5075002955c6573911","target":"graph","created_at":"2026-05-18T02:34:51Z","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":"A symmetric tensor field on a Riemannian manifold is called Killing field if the symmetric part of its covariant derivative is equal to zero. There is a one to one correspondence between Killing tensor fields and first integrals of the geodesic flow which depend polynomially on the velocity. Therefore Killing tensor fields closely relate to the problem of integrability of geodesic flows. In particular, the following question is still open: does there exist a Riemannian metric on the 2-torus which admits an irreducible Killing tensor field of rank $\\geq 3$? We obtain two necessary conditions on","authors_text":"Vladimir Sharafutdinov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-11-18T06:12:51Z","title":"Killing tensor fields on the 2-torus"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.4741","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:c8cf7ecb03a99ac3a74718c0146fae7fe0d28a3c582af0fa60742e9feeb81d6a","target":"record","created_at":"2026-05-18T02:34:51Z","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":"5c896e78f7ddd15156000a93697df1f4149f1eadd39a7a4608ca4eae4259aef3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-11-18T06:12:51Z","title_canon_sha256":"cf45cab2ed8ae40dbde769dab2c2b9a37589fc04875035391bcb3738ab9a496b"},"schema_version":"1.0","source":{"id":"1411.4741","kind":"arxiv","version":1}},"canonical_sha256":"dcc4cce9daf78da95bbbd53667cc626908bcce46ec6135ea3eec6b2ff02fa8bc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dcc4cce9daf78da95bbbd53667cc626908bcce46ec6135ea3eec6b2ff02fa8bc","first_computed_at":"2026-05-18T02:34:51.285345Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:34:51.285345Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"e57cLLTKCVT6FI7TT22fio2N9BqQ1c+VgjsD36DTM2IGpm5/ryVfy347TGbcnmF6MZWBKVBOjQpEtnXNdHoFBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:34:51.285727Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.4741","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c8cf7ecb03a99ac3a74718c0146fae7fe0d28a3c582af0fa60742e9feeb81d6a","sha256:a4db8c8480164575cac2960f01b8516fb3c31ed185077c5075002955c6573911"],"state_sha256":"0dad4053a933aada60107433b433fc1c24a5545184b3637e02231c4f53383d69"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L5CsSCYAGfv9NLxEqqtJUQGWqD2yRwVkPQ9d5JJZn24xokZuKf/r0wqUhgBxYG2lBtXP6dJPZuu/kI3beZIUDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T05:51:38.686328Z","bundle_sha256":"a4cc9555f5ec86749ff962bf2f120ce4bcf542fac8e77e1f99200ba9a47fe008"}}