{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:S24OHQ6VADYSW2SRRYLOHEPDOO","short_pith_number":"pith:S24OHQ6V","canonical_record":{"source":{"id":"1612.06285","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-12-16T15:37:12Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"afae5480e5e00610e7e03ec45da5de94466028700358c5844304234817455305","abstract_canon_sha256":"5bf470d1e970a4d5bad5d5e679eed263046eeb0a1f764b5f6494897f874e06ad"},"schema_version":"1.0"},"canonical_sha256":"96b8e3c3d500f12b6a518e16e391e3738c55587f8467f1bf09f503062a83ed39","source":{"kind":"arxiv","id":"1612.06285","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.06285","created_at":"2026-05-18T00:54:42Z"},{"alias_kind":"arxiv_version","alias_value":"1612.06285v1","created_at":"2026-05-18T00:54:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.06285","created_at":"2026-05-18T00:54:42Z"},{"alias_kind":"pith_short_12","alias_value":"S24OHQ6VADYS","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"S24OHQ6VADYSW2SR","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"S24OHQ6V","created_at":"2026-05-18T12:30:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:S24OHQ6VADYSW2SRRYLOHEPDOO","target":"record","payload":{"canonical_record":{"source":{"id":"1612.06285","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-12-16T15:37:12Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"afae5480e5e00610e7e03ec45da5de94466028700358c5844304234817455305","abstract_canon_sha256":"5bf470d1e970a4d5bad5d5e679eed263046eeb0a1f764b5f6494897f874e06ad"},"schema_version":"1.0"},"canonical_sha256":"96b8e3c3d500f12b6a518e16e391e3738c55587f8467f1bf09f503062a83ed39","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:54:42.562300Z","signature_b64":"iZLorSg6dnAZN0ZSAeVC5/stYJCAKGwLD+CXTW9hV6lSJzQMLkfZarrtzLta1YFpYpvXsuoTIUhIB/Ah2qygBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"96b8e3c3d500f12b6a518e16e391e3738c55587f8467f1bf09f503062a83ed39","last_reissued_at":"2026-05-18T00:54:42.561947Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:54:42.561947Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.06285","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":"2026-05-18T00:54:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xw17WDyWPAN+D2qDjJ/rMaXWuJGJQzBGR90NmNZWfuNgQ/JRwNS2YYbGen4LkN0B2hEQUJA+tPYYNNOhanU+BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T16:49:14.331471Z"},"content_sha256":"1a90752805ecb564bb2bde68575dee4775f7bc408a31a43b625fbdcddfd30836","schema_version":"1.0","event_id":"sha256:1a90752805ecb564bb2bde68575dee4775f7bc408a31a43b625fbdcddfd30836"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:S24OHQ6VADYSW2SRRYLOHEPDOO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Chaotic motions for a version of the Vlasov equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.AP","authors_text":"Ugo Bessi","submitted_at":"2016-12-16T15:37:12Z","abstract_excerpt":"We consider a version of the Vlasov equation on the circle under a periodic potential $V(x,t)$ and a repulsing smooth interaction $W$. We suppose that the Lagrangian for the single particle has chaotic orbits; using Aubry-Mather theory and ideas of W. Gangbo, A. Tudorascu and P. Bernard, we prove that, for any initial distribution of particles, it is possible to choose their initial speed in such a way to get a chaotic orbit on $[0,+\\infty)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.06285","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":"2026-05-18T00:54:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D/I/345RHoIeHz8OzjrWp/yaJ1Uk4kg671lbW2UpZXE+0g0HbHLSkyl1rBKXo8W0mbj+tM51EdQfKj6OQ27NCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T16:49:14.332328Z"},"content_sha256":"f211a44cbda61a34a73eb5a632824212a5ab920dd0e355177218d1ba49e41f2d","schema_version":"1.0","event_id":"sha256:f211a44cbda61a34a73eb5a632824212a5ab920dd0e355177218d1ba49e41f2d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/S24OHQ6VADYSW2SRRYLOHEPDOO/bundle.json","state_url":"https://pith.science/pith/S24OHQ6VADYSW2SRRYLOHEPDOO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/S24OHQ6VADYSW2SRRYLOHEPDOO/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":"2026-06-07T16:49:14Z","links":{"resolver":"https://pith.science/pith/S24OHQ6VADYSW2SRRYLOHEPDOO","bundle":"https://pith.science/pith/S24OHQ6VADYSW2SRRYLOHEPDOO/bundle.json","state":"https://pith.science/pith/S24OHQ6VADYSW2SRRYLOHEPDOO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/S24OHQ6VADYSW2SRRYLOHEPDOO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:S24OHQ6VADYSW2SRRYLOHEPDOO","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":"5bf470d1e970a4d5bad5d5e679eed263046eeb0a1f764b5f6494897f874e06ad","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-12-16T15:37:12Z","title_canon_sha256":"afae5480e5e00610e7e03ec45da5de94466028700358c5844304234817455305"},"schema_version":"1.0","source":{"id":"1612.06285","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.06285","created_at":"2026-05-18T00:54:42Z"},{"alias_kind":"arxiv_version","alias_value":"1612.06285v1","created_at":"2026-05-18T00:54:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.06285","created_at":"2026-05-18T00:54:42Z"},{"alias_kind":"pith_short_12","alias_value":"S24OHQ6VADYS","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"S24OHQ6VADYSW2SR","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"S24OHQ6V","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:f211a44cbda61a34a73eb5a632824212a5ab920dd0e355177218d1ba49e41f2d","target":"graph","created_at":"2026-05-18T00:54:42Z","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 consider a version of the Vlasov equation on the circle under a periodic potential $V(x,t)$ and a repulsing smooth interaction $W$. We suppose that the Lagrangian for the single particle has chaotic orbits; using Aubry-Mather theory and ideas of W. Gangbo, A. Tudorascu and P. Bernard, we prove that, for any initial distribution of particles, it is possible to choose their initial speed in such a way to get a chaotic orbit on $[0,+\\infty)$.","authors_text":"Ugo Bessi","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-12-16T15:37:12Z","title":"Chaotic motions for a version of the Vlasov equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.06285","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":"sha256:1a90752805ecb564bb2bde68575dee4775f7bc408a31a43b625fbdcddfd30836","target":"record","created_at":"2026-05-18T00:54:42Z","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":"5bf470d1e970a4d5bad5d5e679eed263046eeb0a1f764b5f6494897f874e06ad","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-12-16T15:37:12Z","title_canon_sha256":"afae5480e5e00610e7e03ec45da5de94466028700358c5844304234817455305"},"schema_version":"1.0","source":{"id":"1612.06285","kind":"arxiv","version":1}},"canonical_sha256":"96b8e3c3d500f12b6a518e16e391e3738c55587f8467f1bf09f503062a83ed39","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"96b8e3c3d500f12b6a518e16e391e3738c55587f8467f1bf09f503062a83ed39","first_computed_at":"2026-05-18T00:54:42.561947Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:54:42.561947Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iZLorSg6dnAZN0ZSAeVC5/stYJCAKGwLD+CXTW9hV6lSJzQMLkfZarrtzLta1YFpYpvXsuoTIUhIB/Ah2qygBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:54:42.562300Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.06285","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1a90752805ecb564bb2bde68575dee4775f7bc408a31a43b625fbdcddfd30836","sha256:f211a44cbda61a34a73eb5a632824212a5ab920dd0e355177218d1ba49e41f2d"],"state_sha256":"885954d1d0fcf4220eddfd3811ae6db2d6bdd904cd76c075400133deff9e2a97"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BwDUGdqVygWtBHY93L91ryCjP1euG+lbCjAgAPrtnPKf+vhtyIKMYgzC13fol6dpcuVnnQ8I6jtLMu4e+K7/AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T16:49:14.336164Z","bundle_sha256":"2a5da39d4b8fd2e613213517e1249810915cc9e6096cd6ff8d3a9daae1ff9fdd"}}