{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:6NIPSMX472NTLM53DRELLJPVPR","short_pith_number":"pith:6NIPSMX4","canonical_record":{"source":{"id":"0802.1551","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2008-02-12T01:22:13Z","cross_cats_sorted":["math.SG"],"title_canon_sha256":"9f952d37df816a84474e7fe7621136c3b6d11f1398e929f852203aab24bce37a","abstract_canon_sha256":"a4129143070e27138f7eebd368d95e6923850789efdc5c1ada0df4d7a60cba80"},"schema_version":"1.0"},"canonical_sha256":"f350f932fcfe9b35b3bb1c48b5a5f57c598c3b2fdf584307e9a23aee9af68e56","source":{"kind":"arxiv","id":"0802.1551","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0802.1551","created_at":"2026-07-04T15:10:09Z"},{"alias_kind":"arxiv_version","alias_value":"0802.1551v2","created_at":"2026-07-04T15:10:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0802.1551","created_at":"2026-07-04T15:10:09Z"},{"alias_kind":"pith_short_12","alias_value":"6NIPSMX472NT","created_at":"2026-07-04T15:10:09Z"},{"alias_kind":"pith_short_16","alias_value":"6NIPSMX472NTLM53","created_at":"2026-07-04T15:10:09Z"},{"alias_kind":"pith_short_8","alias_value":"6NIPSMX4","created_at":"2026-07-04T15:10:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:6NIPSMX472NTLM53DRELLJPVPR","target":"record","payload":{"canonical_record":{"source":{"id":"0802.1551","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2008-02-12T01:22:13Z","cross_cats_sorted":["math.SG"],"title_canon_sha256":"9f952d37df816a84474e7fe7621136c3b6d11f1398e929f852203aab24bce37a","abstract_canon_sha256":"a4129143070e27138f7eebd368d95e6923850789efdc5c1ada0df4d7a60cba80"},"schema_version":"1.0"},"canonical_sha256":"f350f932fcfe9b35b3bb1c48b5a5f57c598c3b2fdf584307e9a23aee9af68e56","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:10:09.369072Z","signature_b64":"+tMiXTygHc+G9Acja/GPrIA2r5T/IsPEpHcqLb54b/Nrl/zyiPsx2CS5U8iHljBDsDHqxN9ufaQ6H9xuvnWFBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f350f932fcfe9b35b3bb1c48b5a5f57c598c3b2fdf584307e9a23aee9af68e56","last_reissued_at":"2026-07-04T15:10:09.368639Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:10:09.368639Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0802.1551","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":"2026-07-04T15:10:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jRQ1C5klJ0IPQRwK2JdMApn49pkK+GDenepbH8evFwISBcVoZ4GgxwEWOPB9pKWI8K1S22yF8tmUbybAaP5vCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T20:52:24.041245Z"},"content_sha256":"631ac021910984813b881d702069629bbdb8000987cb13dbc850292bf29cc454","schema_version":"1.0","event_id":"sha256:631ac021910984813b881d702069629bbdb8000987cb13dbc850292bf29cc454"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:6NIPSMX472NTLM53DRELLJPVPR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A nonholonomic Moser theorem and optimal transport","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SG"],"primary_cat":"math.DG","authors_text":"Boris Khesin, Paul Lee","submitted_at":"2008-02-12T01:22:13Z","abstract_excerpt":"We prove the following nonholonomic version of the classical Moser theorem: given a bracket-generating distribution on a connected compact manifold (possibly with boundary), two volume forms of equal total volume can be isotoped by the flow of a vector field tangent to this distribution. We describe formal solutions of the corresponding nonholonomic mass transport problem and present the Hamiltonian framework for both the Otto calculus and its nonholonomic counterpart as infinite-dimensional Hamiltonian reductions on diffeomorphism groups.\n  Finally, we define a nonholonomic analog of the Wass"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0802.1551","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/0802.1551/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T15:10:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zzNa+3CwCmKdYRSgTYDkDvmR3FqmxzqWnjRGMT3RFv0WIGUD4MZHvBi1V31LSWEIMzTxDbWPgp0UbphqPzIBBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T20:52:24.041619Z"},"content_sha256":"3eef761a5407ad2c8cfcf811647aed1603f48ee65928a79cd0f5efc5c062baf9","schema_version":"1.0","event_id":"sha256:3eef761a5407ad2c8cfcf811647aed1603f48ee65928a79cd0f5efc5c062baf9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6NIPSMX472NTLM53DRELLJPVPR/bundle.json","state_url":"https://pith.science/pith/6NIPSMX472NTLM53DRELLJPVPR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6NIPSMX472NTLM53DRELLJPVPR/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":"2026-08-04T20:52:24Z","links":{"resolver":"https://pith.science/pith/6NIPSMX472NTLM53DRELLJPVPR","bundle":"https://pith.science/pith/6NIPSMX472NTLM53DRELLJPVPR/bundle.json","state":"https://pith.science/pith/6NIPSMX472NTLM53DRELLJPVPR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6NIPSMX472NTLM53DRELLJPVPR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:6NIPSMX472NTLM53DRELLJPVPR","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":"a4129143070e27138f7eebd368d95e6923850789efdc5c1ada0df4d7a60cba80","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2008-02-12T01:22:13Z","title_canon_sha256":"9f952d37df816a84474e7fe7621136c3b6d11f1398e929f852203aab24bce37a"},"schema_version":"1.0","source":{"id":"0802.1551","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0802.1551","created_at":"2026-07-04T15:10:09Z"},{"alias_kind":"arxiv_version","alias_value":"0802.1551v2","created_at":"2026-07-04T15:10:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0802.1551","created_at":"2026-07-04T15:10:09Z"},{"alias_kind":"pith_short_12","alias_value":"6NIPSMX472NT","created_at":"2026-07-04T15:10:09Z"},{"alias_kind":"pith_short_16","alias_value":"6NIPSMX472NTLM53","created_at":"2026-07-04T15:10:09Z"},{"alias_kind":"pith_short_8","alias_value":"6NIPSMX4","created_at":"2026-07-04T15:10:09Z"}],"graph_snapshots":[{"event_id":"sha256:3eef761a5407ad2c8cfcf811647aed1603f48ee65928a79cd0f5efc5c062baf9","target":"graph","created_at":"2026-07-04T15:10:09Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/0802.1551/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove the following nonholonomic version of the classical Moser theorem: given a bracket-generating distribution on a connected compact manifold (possibly with boundary), two volume forms of equal total volume can be isotoped by the flow of a vector field tangent to this distribution. We describe formal solutions of the corresponding nonholonomic mass transport problem and present the Hamiltonian framework for both the Otto calculus and its nonholonomic counterpart as infinite-dimensional Hamiltonian reductions on diffeomorphism groups.\n  Finally, we define a nonholonomic analog of the Wass","authors_text":"Boris Khesin, Paul Lee","cross_cats":["math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2008-02-12T01:22:13Z","title":"A nonholonomic Moser theorem and optimal transport"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0802.1551","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":"sha256:631ac021910984813b881d702069629bbdb8000987cb13dbc850292bf29cc454","target":"record","created_at":"2026-07-04T15:10:09Z","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":"a4129143070e27138f7eebd368d95e6923850789efdc5c1ada0df4d7a60cba80","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2008-02-12T01:22:13Z","title_canon_sha256":"9f952d37df816a84474e7fe7621136c3b6d11f1398e929f852203aab24bce37a"},"schema_version":"1.0","source":{"id":"0802.1551","kind":"arxiv","version":2}},"canonical_sha256":"f350f932fcfe9b35b3bb1c48b5a5f57c598c3b2fdf584307e9a23aee9af68e56","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f350f932fcfe9b35b3bb1c48b5a5f57c598c3b2fdf584307e9a23aee9af68e56","first_computed_at":"2026-07-04T15:10:09.368639Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:10:09.368639Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+tMiXTygHc+G9Acja/GPrIA2r5T/IsPEpHcqLb54b/Nrl/zyiPsx2CS5U8iHljBDsDHqxN9ufaQ6H9xuvnWFBA==","signature_status":"signed_v1","signed_at":"2026-07-04T15:10:09.369072Z","signed_message":"canonical_sha256_bytes"},"source_id":"0802.1551","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:631ac021910984813b881d702069629bbdb8000987cb13dbc850292bf29cc454","sha256:3eef761a5407ad2c8cfcf811647aed1603f48ee65928a79cd0f5efc5c062baf9"],"state_sha256":"f9143061f4d4d10577f401076157c6c13568a922bef9e634cecb303c3ca6e5e4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"meoNQW5H76/+HAH4eVz94Hf5PM4hONUUkxmNz358iWD18RFryDplAho6Cnw9Jyjzl8vcTbhPXIS0iL9ksEJYBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T20:52:24.044401Z","bundle_sha256":"e71bb504de8c5a2f7309718c41ba6a84697fae1f005aba7b4b44c7687bcfdff3"}}