{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:AXB5U7MRKBNAKIFKKPJZH55ZX6","short_pith_number":"pith:AXB5U7MR","canonical_record":{"source":{"id":"1712.00047","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-11-30T19:43:40Z","cross_cats_sorted":[],"title_canon_sha256":"1a6754165dd07114e81f18d8a3cb438b05957c9126a4f4cec81c8f5cf6e49549","abstract_canon_sha256":"7d7f6b8037af2e74a7c8e87347b0a0e66b5a162817d5ab95131a5ed739fc74ee"},"schema_version":"1.0"},"canonical_sha256":"05c3da7d91505a0520aa53d393f7b9bfa19997508a8e0571646bd528d126bff2","source":{"kind":"arxiv","id":"1712.00047","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.00047","created_at":"2026-05-18T00:29:07Z"},{"alias_kind":"arxiv_version","alias_value":"1712.00047v1","created_at":"2026-05-18T00:29:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.00047","created_at":"2026-05-18T00:29:07Z"},{"alias_kind":"pith_short_12","alias_value":"AXB5U7MRKBNA","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"AXB5U7MRKBNAKIFK","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"AXB5U7MR","created_at":"2026-05-18T12:31:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:AXB5U7MRKBNAKIFKKPJZH55ZX6","target":"record","payload":{"canonical_record":{"source":{"id":"1712.00047","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-11-30T19:43:40Z","cross_cats_sorted":[],"title_canon_sha256":"1a6754165dd07114e81f18d8a3cb438b05957c9126a4f4cec81c8f5cf6e49549","abstract_canon_sha256":"7d7f6b8037af2e74a7c8e87347b0a0e66b5a162817d5ab95131a5ed739fc74ee"},"schema_version":"1.0"},"canonical_sha256":"05c3da7d91505a0520aa53d393f7b9bfa19997508a8e0571646bd528d126bff2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:07.557577Z","signature_b64":"jgrTy2eHXG+Xovn6T/jrPae4XjGAicM8fpvQ5mqffOeelmq40AKVGwouCd7avsB//d6HNXRHTy6oHMh7slbqBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"05c3da7d91505a0520aa53d393f7b9bfa19997508a8e0571646bd528d126bff2","last_reissued_at":"2026-05-18T00:29:07.556883Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:07.556883Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1712.00047","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":"2026-05-18T00:29:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RcCoCzfFdsjbgq0aGNut+gyOlLuvukKw31+O1lIGwH2ppYHXvdLNzhGO6pqzBcHUpjHPf+KWwUtbc4dVn1AEDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T21:19:41.538159Z"},"content_sha256":"99921239726dbfab2cb8bf5713cf357eb8ebc5e58b84887e14e7923a3dcde78a","schema_version":"1.0","event_id":"sha256:99921239726dbfab2cb8bf5713cf357eb8ebc5e58b84887e14e7923a3dcde78a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:AXB5U7MRKBNAKIFKKPJZH55ZX6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Optimal Stochastic Ballistic Transports","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alistair Barton, Nassif Ghoussoub","submitted_at":"2017-11-30T19:43:40Z","abstract_excerpt":"For a given Lagrangian $L:[0,T]\\times M\\times M^\\ast\\rightarrow \\mathbb{R}_+$ and probability measures $\\mu\\in\\mathcal{P}(M^\\ast)$, $\\nu\\in \\mathcal{P}(M)$, we introduce the stochastic ballistic transportation problems \\begin{align}\\tag{$\\star$}\n  \\underline{B}(\\mu,\\nu):=\\inf\\left\\{\\mathbb{E}\\left[\\langle V,X_0\\rangle +\\int_0^T L(t,X,\\beta(t,X))\\,dt\\right]\\middle\\rvert V\\sim\\mu,X_T\\sim \\nu\\right\\}\\\\\\tag{$\\star\\star$}\n  \\overline{B}(\\nu,\\mu):=\\sup\\left\\{\\mathbb{E}\\left[\\langle V,X_T\\rangle -\\int_0^T L(t,X,\\beta(t,X))\\,dt\\right]\\middle\\rvert V\\sim\\mu,X_0\\sim \\nu\\right\\} \\end{align} where $X$ is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.00047","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":"2026-05-18T00:29:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QeEcbhIXEyZ1PBlFn9sdlov5ZfdDX95ASBv0up/hBB0Ntv/hKa/yebod9m2rD+0cur9nhg7esY9b6qDWK7FxBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T21:19:41.538530Z"},"content_sha256":"a61a17cb0909d3e97d0990c66cf43d95377b604117509138557b96fca4c03cf2","schema_version":"1.0","event_id":"sha256:a61a17cb0909d3e97d0990c66cf43d95377b604117509138557b96fca4c03cf2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AXB5U7MRKBNAKIFKKPJZH55ZX6/bundle.json","state_url":"https://pith.science/pith/AXB5U7MRKBNAKIFKKPJZH55ZX6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AXB5U7MRKBNAKIFKKPJZH55ZX6/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":"2026-07-01T21:19:41Z","links":{"resolver":"https://pith.science/pith/AXB5U7MRKBNAKIFKKPJZH55ZX6","bundle":"https://pith.science/pith/AXB5U7MRKBNAKIFKKPJZH55ZX6/bundle.json","state":"https://pith.science/pith/AXB5U7MRKBNAKIFKKPJZH55ZX6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AXB5U7MRKBNAKIFKKPJZH55ZX6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:AXB5U7MRKBNAKIFKKPJZH55ZX6","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":"7d7f6b8037af2e74a7c8e87347b0a0e66b5a162817d5ab95131a5ed739fc74ee","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-11-30T19:43:40Z","title_canon_sha256":"1a6754165dd07114e81f18d8a3cb438b05957c9126a4f4cec81c8f5cf6e49549"},"schema_version":"1.0","source":{"id":"1712.00047","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.00047","created_at":"2026-05-18T00:29:07Z"},{"alias_kind":"arxiv_version","alias_value":"1712.00047v1","created_at":"2026-05-18T00:29:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.00047","created_at":"2026-05-18T00:29:07Z"},{"alias_kind":"pith_short_12","alias_value":"AXB5U7MRKBNA","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"AXB5U7MRKBNAKIFK","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"AXB5U7MR","created_at":"2026-05-18T12:31:08Z"}],"graph_snapshots":[{"event_id":"sha256:a61a17cb0909d3e97d0990c66cf43d95377b604117509138557b96fca4c03cf2","target":"graph","created_at":"2026-05-18T00:29:07Z","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":"For a given Lagrangian $L:[0,T]\\times M\\times M^\\ast\\rightarrow \\mathbb{R}_+$ and probability measures $\\mu\\in\\mathcal{P}(M^\\ast)$, $\\nu\\in \\mathcal{P}(M)$, we introduce the stochastic ballistic transportation problems \\begin{align}\\tag{$\\star$}\n  \\underline{B}(\\mu,\\nu):=\\inf\\left\\{\\mathbb{E}\\left[\\langle V,X_0\\rangle +\\int_0^T L(t,X,\\beta(t,X))\\,dt\\right]\\middle\\rvert V\\sim\\mu,X_T\\sim \\nu\\right\\}\\\\\\tag{$\\star\\star$}\n  \\overline{B}(\\nu,\\mu):=\\sup\\left\\{\\mathbb{E}\\left[\\langle V,X_T\\rangle -\\int_0^T L(t,X,\\beta(t,X))\\,dt\\right]\\middle\\rvert V\\sim\\mu,X_0\\sim \\nu\\right\\} \\end{align} where $X$ is ","authors_text":"Alistair Barton, Nassif Ghoussoub","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-11-30T19:43:40Z","title":"On Optimal Stochastic Ballistic Transports"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.00047","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":"sha256:99921239726dbfab2cb8bf5713cf357eb8ebc5e58b84887e14e7923a3dcde78a","target":"record","created_at":"2026-05-18T00:29:07Z","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":"7d7f6b8037af2e74a7c8e87347b0a0e66b5a162817d5ab95131a5ed739fc74ee","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-11-30T19:43:40Z","title_canon_sha256":"1a6754165dd07114e81f18d8a3cb438b05957c9126a4f4cec81c8f5cf6e49549"},"schema_version":"1.0","source":{"id":"1712.00047","kind":"arxiv","version":1}},"canonical_sha256":"05c3da7d91505a0520aa53d393f7b9bfa19997508a8e0571646bd528d126bff2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"05c3da7d91505a0520aa53d393f7b9bfa19997508a8e0571646bd528d126bff2","first_computed_at":"2026-05-18T00:29:07.556883Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:07.556883Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jgrTy2eHXG+Xovn6T/jrPae4XjGAicM8fpvQ5mqffOeelmq40AKVGwouCd7avsB//d6HNXRHTy6oHMh7slbqBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:07.557577Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.00047","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:99921239726dbfab2cb8bf5713cf357eb8ebc5e58b84887e14e7923a3dcde78a","sha256:a61a17cb0909d3e97d0990c66cf43d95377b604117509138557b96fca4c03cf2"],"state_sha256":"a8815b582aebf9ad10a9ad0fd92d421faecb78ea5a831ee4ee679dc825b4e57d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y+kC1QfJ0m7V8Lj6wGxbi8YxfaN32+ofXV0p0+KBFdHsDBDQn82dwE7ZY+AHNpQ6aJNc3hyETO12HEH+CBYLBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T21:19:41.540711Z","bundle_sha256":"0e6bc45daedef33b3586b1a65e6ea81e77910a49b10f568fa60dcad40a964763"}}