{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:DERNFGG35JPSQDJASNW2VPYWF5","short_pith_number":"pith:DERNFGG3","canonical_record":{"source":{"id":"1708.03909","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-08-13T13:47:36Z","cross_cats_sorted":[],"title_canon_sha256":"a7c2afc1e520a2c18cbdde1a33fcb9dab066ef594162df80375da710a835f332","abstract_canon_sha256":"b43b3b4e2dccaf2d1293d56f18bae904f4eba6a787491ab8e7c2470b0a994a1d"},"schema_version":"1.0"},"canonical_sha256":"1922d298dbea5f280d20936daabf162f550153e53c5bab4bb85db631d98e99d0","source":{"kind":"arxiv","id":"1708.03909","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.03909","created_at":"2026-05-17T23:56:34Z"},{"alias_kind":"arxiv_version","alias_value":"1708.03909v5","created_at":"2026-05-17T23:56:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.03909","created_at":"2026-05-17T23:56:34Z"},{"alias_kind":"pith_short_12","alias_value":"DERNFGG35JPS","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"DERNFGG35JPSQDJA","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"DERNFGG3","created_at":"2026-05-18T12:31:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:DERNFGG35JPSQDJASNW2VPYWF5","target":"record","payload":{"canonical_record":{"source":{"id":"1708.03909","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-08-13T13:47:36Z","cross_cats_sorted":[],"title_canon_sha256":"a7c2afc1e520a2c18cbdde1a33fcb9dab066ef594162df80375da710a835f332","abstract_canon_sha256":"b43b3b4e2dccaf2d1293d56f18bae904f4eba6a787491ab8e7c2470b0a994a1d"},"schema_version":"1.0"},"canonical_sha256":"1922d298dbea5f280d20936daabf162f550153e53c5bab4bb85db631d98e99d0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:34.459122Z","signature_b64":"crspVMDKxV97FucjDz13ZdpR9wjuiNy9UDXT66MW/Ub+vfpPVas9QAdsuBVFtvW6F8QGSKzGd41jVDnI4uHNBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1922d298dbea5f280d20936daabf162f550153e53c5bab4bb85db631d98e99d0","last_reissued_at":"2026-05-17T23:56:34.458298Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:34.458298Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1708.03909","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:56:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0+mJ0ZXVJ+QIZ+e5/ozCKipZ4N7wIhWBD5g1x3w+eK83sY4yWUA6cQqmI8c7sFkKgmgea8QZgFUVmz7y9Lt7DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T20:54:39.036834Z"},"content_sha256":"564bfe121a71dd168997c75d3e6f95bc5690b105278a935d742b69d3467e4c4f","schema_version":"1.0","event_id":"sha256:564bfe121a71dd168997c75d3e6f95bc5690b105278a935d742b69d3467e4c4f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:DERNFGG35JPSQDJASNW2VPYWF5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Martingale solution to stochastic extended Korteweg - de Vries equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Anna Karczewska, Maciej Szczeci\\'nski","submitted_at":"2017-08-13T13:47:36Z","abstract_excerpt":"We study a stochastic extended Korteweg - de Vries equation driven by a multiplicative noise. We prove the existence of a martingale solution to the equation studied. The proof of the solution is based on two approximations of the problem considered and the compactness method."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.03909","kind":"arxiv","version":5},"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":"2026-05-17T23:56:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7oQ0Gl8CokQvRkNhuu8gohCbpgBzfL/XEhNrIELxy4Le/tg/CnL1gtOWVSFErggUcPVy6IpMrMG9h9RATkK8DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T20:54:39.037234Z"},"content_sha256":"c4a02c39a76c61594b2dee854a83ef3844276ad9841759b080706cf9e4b1a267","schema_version":"1.0","event_id":"sha256:c4a02c39a76c61594b2dee854a83ef3844276ad9841759b080706cf9e4b1a267"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DERNFGG35JPSQDJASNW2VPYWF5/bundle.json","state_url":"https://pith.science/pith/DERNFGG35JPSQDJASNW2VPYWF5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DERNFGG35JPSQDJASNW2VPYWF5/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":"2026-05-30T20:54:39Z","links":{"resolver":"https://pith.science/pith/DERNFGG35JPSQDJASNW2VPYWF5","bundle":"https://pith.science/pith/DERNFGG35JPSQDJASNW2VPYWF5/bundle.json","state":"https://pith.science/pith/DERNFGG35JPSQDJASNW2VPYWF5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DERNFGG35JPSQDJASNW2VPYWF5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:DERNFGG35JPSQDJASNW2VPYWF5","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":"b43b3b4e2dccaf2d1293d56f18bae904f4eba6a787491ab8e7c2470b0a994a1d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-08-13T13:47:36Z","title_canon_sha256":"a7c2afc1e520a2c18cbdde1a33fcb9dab066ef594162df80375da710a835f332"},"schema_version":"1.0","source":{"id":"1708.03909","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.03909","created_at":"2026-05-17T23:56:34Z"},{"alias_kind":"arxiv_version","alias_value":"1708.03909v5","created_at":"2026-05-17T23:56:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.03909","created_at":"2026-05-17T23:56:34Z"},{"alias_kind":"pith_short_12","alias_value":"DERNFGG35JPS","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"DERNFGG35JPSQDJA","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"DERNFGG3","created_at":"2026-05-18T12:31:10Z"}],"graph_snapshots":[{"event_id":"sha256:c4a02c39a76c61594b2dee854a83ef3844276ad9841759b080706cf9e4b1a267","target":"graph","created_at":"2026-05-17T23:56:34Z","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 study a stochastic extended Korteweg - de Vries equation driven by a multiplicative noise. We prove the existence of a martingale solution to the equation studied. The proof of the solution is based on two approximations of the problem considered and the compactness method.","authors_text":"Anna Karczewska, Maciej Szczeci\\'nski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-08-13T13:47:36Z","title":"Martingale solution to stochastic extended Korteweg - de Vries equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.03909","kind":"arxiv","version":5},"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":"sha256:564bfe121a71dd168997c75d3e6f95bc5690b105278a935d742b69d3467e4c4f","target":"record","created_at":"2026-05-17T23:56:34Z","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":"b43b3b4e2dccaf2d1293d56f18bae904f4eba6a787491ab8e7c2470b0a994a1d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-08-13T13:47:36Z","title_canon_sha256":"a7c2afc1e520a2c18cbdde1a33fcb9dab066ef594162df80375da710a835f332"},"schema_version":"1.0","source":{"id":"1708.03909","kind":"arxiv","version":5}},"canonical_sha256":"1922d298dbea5f280d20936daabf162f550153e53c5bab4bb85db631d98e99d0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1922d298dbea5f280d20936daabf162f550153e53c5bab4bb85db631d98e99d0","first_computed_at":"2026-05-17T23:56:34.458298Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:34.458298Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"crspVMDKxV97FucjDz13ZdpR9wjuiNy9UDXT66MW/Ub+vfpPVas9QAdsuBVFtvW6F8QGSKzGd41jVDnI4uHNBg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:34.459122Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.03909","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:564bfe121a71dd168997c75d3e6f95bc5690b105278a935d742b69d3467e4c4f","sha256:c4a02c39a76c61594b2dee854a83ef3844276ad9841759b080706cf9e4b1a267"],"state_sha256":"860db3c2ec45fd1bacf5cce3bff461d3b5d1981564b3318b403949087717f19b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"as5xEI4OaJG+JD5JsMOHFzD4457hX/HVl6/4hxZF7kct3qGXBZTAsbgFXGbMR3ha5hKCTyavpvNsGnELKz2ECA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T20:54:39.040034Z","bundle_sha256":"f0274a913adefbf426013466e0a78a1eb6f44bfc7ca9fa8773a0e0aa6be337d8"}}