{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:DAUOUKU2SKZBYY65RZ7VGKU2VA","short_pith_number":"pith:DAUOUKU2","canonical_record":{"source":{"id":"1811.08474","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-11-20T20:39:08Z","cross_cats_sorted":[],"title_canon_sha256":"72670ff08e6ded86c87e8c9842210ffaa3a01e69bab895dcd2cae21f2b4d73e3","abstract_canon_sha256":"5486ad06e5ecf374095a263e7a6761ecaa1c67edd177cfdf1efa45848ba824e6"},"schema_version":"1.0"},"canonical_sha256":"1828ea2a9a92b21c63dd8e7f532a9aa8184751d46e812b05f4f2816cfd34df92","source":{"kind":"arxiv","id":"1811.08474","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.08474","created_at":"2026-05-18T00:00:12Z"},{"alias_kind":"arxiv_version","alias_value":"1811.08474v1","created_at":"2026-05-18T00:00:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.08474","created_at":"2026-05-18T00:00:12Z"},{"alias_kind":"pith_short_12","alias_value":"DAUOUKU2SKZB","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"DAUOUKU2SKZBYY65","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"DAUOUKU2","created_at":"2026-05-18T12:32:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:DAUOUKU2SKZBYY65RZ7VGKU2VA","target":"record","payload":{"canonical_record":{"source":{"id":"1811.08474","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-11-20T20:39:08Z","cross_cats_sorted":[],"title_canon_sha256":"72670ff08e6ded86c87e8c9842210ffaa3a01e69bab895dcd2cae21f2b4d73e3","abstract_canon_sha256":"5486ad06e5ecf374095a263e7a6761ecaa1c67edd177cfdf1efa45848ba824e6"},"schema_version":"1.0"},"canonical_sha256":"1828ea2a9a92b21c63dd8e7f532a9aa8184751d46e812b05f4f2816cfd34df92","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:00:12.435483Z","signature_b64":"Jf2g/kVkeK9ch4/x5ew92RU5l1oJ/jaTpy+S4i/w9JJyDJS0fTTpO3dTsmP8mqmWn2anafM4m32NLrHyD/uNDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1828ea2a9a92b21c63dd8e7f532a9aa8184751d46e812b05f4f2816cfd34df92","last_reissued_at":"2026-05-18T00:00:12.434969Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:00:12.434969Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1811.08474","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":"2026-05-18T00:00:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Quj2KInQdT4Oyvmzg5kOM2EjT5M1UInGsPR8rRsnan3IPNsy3JRy1O33IkY3VF6JhOFzfRF+bDiOGqigPlp8BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T16:56:47.468411Z"},"content_sha256":"6d76e6ab2b884c6a8309a763e748355f2132d90feb6936dbc511370021baa6d8","schema_version":"1.0","event_id":"sha256:6d76e6ab2b884c6a8309a763e748355f2132d90feb6936dbc511370021baa6d8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:DAUOUKU2SKZBYY65RZ7VGKU2VA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Log-optimal and rapid paths in von Neumann-Gale dynamical systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Esmaeil Babaei, Igor V. Evstigneev, Klaus R. Schenk-Hopp\\'e","submitted_at":"2018-11-20T20:39:08Z","abstract_excerpt":"Von Neumann-Gale dynamical systems are defined in terms of multivalued operators in spaces of random vectors, possessing certain properties of convexity and homogeneity. A central role in the theory of such systems is played by a special class of paths (trajectories) called rapid: they grow over each time period t-1,t in a sense faster than others. The paper establishes existence and characterization theorems for such paths showing, in particular, that any trajectory maximizing a logarithmic functional over a finite time horizon is rapid. The proof of this result is based on the methods of con"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.08474","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":"2026-05-18T00:00:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+paSqkd+Gfjr9Bg2vgrJ35SNr8mAldCJ4sUG3foPf0Flr2VFmcDJF1/Bu38iHlxmQGNiZTRvpSolRZBR9aHcDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T16:56:47.468770Z"},"content_sha256":"af52aa96c25b3b2101f35fae3158d5646dc78a48b278ee625a5a8272f008068f","schema_version":"1.0","event_id":"sha256:af52aa96c25b3b2101f35fae3158d5646dc78a48b278ee625a5a8272f008068f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DAUOUKU2SKZBYY65RZ7VGKU2VA/bundle.json","state_url":"https://pith.science/pith/DAUOUKU2SKZBYY65RZ7VGKU2VA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DAUOUKU2SKZBYY65RZ7VGKU2VA/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":"2026-06-23T16:56:47Z","links":{"resolver":"https://pith.science/pith/DAUOUKU2SKZBYY65RZ7VGKU2VA","bundle":"https://pith.science/pith/DAUOUKU2SKZBYY65RZ7VGKU2VA/bundle.json","state":"https://pith.science/pith/DAUOUKU2SKZBYY65RZ7VGKU2VA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DAUOUKU2SKZBYY65RZ7VGKU2VA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:DAUOUKU2SKZBYY65RZ7VGKU2VA","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":"5486ad06e5ecf374095a263e7a6761ecaa1c67edd177cfdf1efa45848ba824e6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-11-20T20:39:08Z","title_canon_sha256":"72670ff08e6ded86c87e8c9842210ffaa3a01e69bab895dcd2cae21f2b4d73e3"},"schema_version":"1.0","source":{"id":"1811.08474","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.08474","created_at":"2026-05-18T00:00:12Z"},{"alias_kind":"arxiv_version","alias_value":"1811.08474v1","created_at":"2026-05-18T00:00:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.08474","created_at":"2026-05-18T00:00:12Z"},{"alias_kind":"pith_short_12","alias_value":"DAUOUKU2SKZB","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"DAUOUKU2SKZBYY65","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"DAUOUKU2","created_at":"2026-05-18T12:32:19Z"}],"graph_snapshots":[{"event_id":"sha256:af52aa96c25b3b2101f35fae3158d5646dc78a48b278ee625a5a8272f008068f","target":"graph","created_at":"2026-05-18T00:00:12Z","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":"Von Neumann-Gale dynamical systems are defined in terms of multivalued operators in spaces of random vectors, possessing certain properties of convexity and homogeneity. A central role in the theory of such systems is played by a special class of paths (trajectories) called rapid: they grow over each time period t-1,t in a sense faster than others. The paper establishes existence and characterization theorems for such paths showing, in particular, that any trajectory maximizing a logarithmic functional over a finite time horizon is rapid. The proof of this result is based on the methods of con","authors_text":"Esmaeil Babaei, Igor V. Evstigneev, Klaus R. Schenk-Hopp\\'e","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-11-20T20:39:08Z","title":"Log-optimal and rapid paths in von Neumann-Gale dynamical systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.08474","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":"sha256:6d76e6ab2b884c6a8309a763e748355f2132d90feb6936dbc511370021baa6d8","target":"record","created_at":"2026-05-18T00:00:12Z","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":"5486ad06e5ecf374095a263e7a6761ecaa1c67edd177cfdf1efa45848ba824e6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-11-20T20:39:08Z","title_canon_sha256":"72670ff08e6ded86c87e8c9842210ffaa3a01e69bab895dcd2cae21f2b4d73e3"},"schema_version":"1.0","source":{"id":"1811.08474","kind":"arxiv","version":1}},"canonical_sha256":"1828ea2a9a92b21c63dd8e7f532a9aa8184751d46e812b05f4f2816cfd34df92","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1828ea2a9a92b21c63dd8e7f532a9aa8184751d46e812b05f4f2816cfd34df92","first_computed_at":"2026-05-18T00:00:12.434969Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:00:12.434969Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Jf2g/kVkeK9ch4/x5ew92RU5l1oJ/jaTpy+S4i/w9JJyDJS0fTTpO3dTsmP8mqmWn2anafM4m32NLrHyD/uNDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:00:12.435483Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.08474","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6d76e6ab2b884c6a8309a763e748355f2132d90feb6936dbc511370021baa6d8","sha256:af52aa96c25b3b2101f35fae3158d5646dc78a48b278ee625a5a8272f008068f"],"state_sha256":"81b51ca775d35182e3f0387d7788d454586882e77f5fb56932a970b9d647a8e2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qVTPmeXDDiWb4a7ePLWCCmyLMHyDKRL34ie4rFuy6FWHMdyGplFosHVgKnJmrBYvSKLSDsvyJdg6hCA9hpq2Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T16:56:47.470792Z","bundle_sha256":"b16dc158da318897cca2df41410328c9f2d532bc2f76f3a1830ee1057136a7bb"}}