{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:THN3AGWU5S6ZRJZ2OAZAWLSN4H","short_pith_number":"pith:THN3AGWU","canonical_record":{"source":{"id":"1401.0326","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-01-01T20:22:48Z","cross_cats_sorted":["math-ph","math.MP","math.PR"],"title_canon_sha256":"79de6f8c7b36b34a9e4f8f6481ab3da7da156000246d5fb378e7cb82a22fcafd","abstract_canon_sha256":"cbbd3147c215e5d2668d6e3e8ea6af936e146ce7c06f74330622f428cf8edeb3"},"schema_version":"1.0"},"canonical_sha256":"99dbb01ad4ecbd98a73a70320b2e4de1c7687e173bb3ec1d0b4901fc1ff4da22","source":{"kind":"arxiv","id":"1401.0326","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.0326","created_at":"2026-05-18T01:16:26Z"},{"alias_kind":"arxiv_version","alias_value":"1401.0326v2","created_at":"2026-05-18T01:16:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.0326","created_at":"2026-05-18T01:16:26Z"},{"alias_kind":"pith_short_12","alias_value":"THN3AGWU5S6Z","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"THN3AGWU5S6ZRJZ2","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"THN3AGWU","created_at":"2026-05-18T12:28:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:THN3AGWU5S6ZRJZ2OAZAWLSN4H","target":"record","payload":{"canonical_record":{"source":{"id":"1401.0326","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-01-01T20:22:48Z","cross_cats_sorted":["math-ph","math.MP","math.PR"],"title_canon_sha256":"79de6f8c7b36b34a9e4f8f6481ab3da7da156000246d5fb378e7cb82a22fcafd","abstract_canon_sha256":"cbbd3147c215e5d2668d6e3e8ea6af936e146ce7c06f74330622f428cf8edeb3"},"schema_version":"1.0"},"canonical_sha256":"99dbb01ad4ecbd98a73a70320b2e4de1c7687e173bb3ec1d0b4901fc1ff4da22","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:16:26.841589Z","signature_b64":"rSzVj5QPNjrcuU6DVeMOV5H9fZjdvoyZMPNbP5k82lrGvBLquRvWU1ha0FEEim1PLqJhN9uq9f8PPMenRuxZBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"99dbb01ad4ecbd98a73a70320b2e4de1c7687e173bb3ec1d0b4901fc1ff4da22","last_reissued_at":"2026-05-18T01:16:26.841061Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:16:26.841061Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1401.0326","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":"2026-05-18T01:16:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ME57pOGe7Vta3Do8nGaELGm5sMDmdZLQpKDUaopwP9jno2wHUcchOjCeV0mhizUikhaYWQ2vIQki3H6PVsTUAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T19:32:10.452021Z"},"content_sha256":"e236845a29a0db6874122ccbee37614da1b694bae6c27c90bd2039eeb1d0fbac","schema_version":"1.0","event_id":"sha256:e236845a29a0db6874122ccbee37614da1b694bae6c27c90bd2039eeb1d0fbac"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:THN3AGWU5S6ZRJZ2OAZAWLSN4H","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Local existence of solutions to Randomized Gross-Pitaevskii hierarchies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.PR"],"primary_cat":"math.AP","authors_text":"Vedran Sohinger","submitted_at":"2014-01-01T20:22:48Z","abstract_excerpt":"In this paper, we study the local-in-time existence of solutions to randomized forms of the Gross-Pitaevskii hierarchy on periodic domains. In particular, we study the independently randomized Gross-Pitaevskii hierarchy and the dependently randomized Gross-Pitaevskii hierarchy, which were first introduced in the author's joint work with Staffilani \\cite{SoSt}. For these hierarchies, we construct local-in-time low-regularity solutions in spaces which contain a random component. The constructed density matrices will solve the full randomized hierarchies, thus extending the results from \\cite{SoS"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.0326","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":""},"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":"2026-05-18T01:16:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"luyUPhh6G+CZiUsTVHmOBA9PnxZSOdL2ja4GqYXcD/xKO+yIATtXyfVEpLMd4hTwovhg51pICC28DvlRZZq2AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T19:32:10.452381Z"},"content_sha256":"13c277ad8a369ce2d0de5f3a53131671a0f0537d5829da1d76eee164a3af4026","schema_version":"1.0","event_id":"sha256:13c277ad8a369ce2d0de5f3a53131671a0f0537d5829da1d76eee164a3af4026"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/THN3AGWU5S6ZRJZ2OAZAWLSN4H/bundle.json","state_url":"https://pith.science/pith/THN3AGWU5S6ZRJZ2OAZAWLSN4H/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/THN3AGWU5S6ZRJZ2OAZAWLSN4H/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":"2026-06-29T19:32:10Z","links":{"resolver":"https://pith.science/pith/THN3AGWU5S6ZRJZ2OAZAWLSN4H","bundle":"https://pith.science/pith/THN3AGWU5S6ZRJZ2OAZAWLSN4H/bundle.json","state":"https://pith.science/pith/THN3AGWU5S6ZRJZ2OAZAWLSN4H/state.json","well_known_bundle":"https://pith.science/.well-known/pith/THN3AGWU5S6ZRJZ2OAZAWLSN4H/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:THN3AGWU5S6ZRJZ2OAZAWLSN4H","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":"cbbd3147c215e5d2668d6e3e8ea6af936e146ce7c06f74330622f428cf8edeb3","cross_cats_sorted":["math-ph","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-01-01T20:22:48Z","title_canon_sha256":"79de6f8c7b36b34a9e4f8f6481ab3da7da156000246d5fb378e7cb82a22fcafd"},"schema_version":"1.0","source":{"id":"1401.0326","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.0326","created_at":"2026-05-18T01:16:26Z"},{"alias_kind":"arxiv_version","alias_value":"1401.0326v2","created_at":"2026-05-18T01:16:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.0326","created_at":"2026-05-18T01:16:26Z"},{"alias_kind":"pith_short_12","alias_value":"THN3AGWU5S6Z","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"THN3AGWU5S6ZRJZ2","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"THN3AGWU","created_at":"2026-05-18T12:28:49Z"}],"graph_snapshots":[{"event_id":"sha256:13c277ad8a369ce2d0de5f3a53131671a0f0537d5829da1d76eee164a3af4026","target":"graph","created_at":"2026-05-18T01:16:26Z","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":"In this paper, we study the local-in-time existence of solutions to randomized forms of the Gross-Pitaevskii hierarchy on periodic domains. In particular, we study the independently randomized Gross-Pitaevskii hierarchy and the dependently randomized Gross-Pitaevskii hierarchy, which were first introduced in the author's joint work with Staffilani \\cite{SoSt}. For these hierarchies, we construct local-in-time low-regularity solutions in spaces which contain a random component. The constructed density matrices will solve the full randomized hierarchies, thus extending the results from \\cite{SoS","authors_text":"Vedran Sohinger","cross_cats":["math-ph","math.MP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-01-01T20:22:48Z","title":"Local existence of solutions to Randomized Gross-Pitaevskii hierarchies"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.0326","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:e236845a29a0db6874122ccbee37614da1b694bae6c27c90bd2039eeb1d0fbac","target":"record","created_at":"2026-05-18T01:16:26Z","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":"cbbd3147c215e5d2668d6e3e8ea6af936e146ce7c06f74330622f428cf8edeb3","cross_cats_sorted":["math-ph","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-01-01T20:22:48Z","title_canon_sha256":"79de6f8c7b36b34a9e4f8f6481ab3da7da156000246d5fb378e7cb82a22fcafd"},"schema_version":"1.0","source":{"id":"1401.0326","kind":"arxiv","version":2}},"canonical_sha256":"99dbb01ad4ecbd98a73a70320b2e4de1c7687e173bb3ec1d0b4901fc1ff4da22","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"99dbb01ad4ecbd98a73a70320b2e4de1c7687e173bb3ec1d0b4901fc1ff4da22","first_computed_at":"2026-05-18T01:16:26.841061Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:16:26.841061Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rSzVj5QPNjrcuU6DVeMOV5H9fZjdvoyZMPNbP5k82lrGvBLquRvWU1ha0FEEim1PLqJhN9uq9f8PPMenRuxZBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:16:26.841589Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.0326","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e236845a29a0db6874122ccbee37614da1b694bae6c27c90bd2039eeb1d0fbac","sha256:13c277ad8a369ce2d0de5f3a53131671a0f0537d5829da1d76eee164a3af4026"],"state_sha256":"154adcfdd51923e0b1377a655fa45fd918b69d35c2494404fb8770c9d6c8d4a9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i16eDMmh//NoSKQ5haPBAVaoYU/aSx6JVdy5DWrzi3fIXgqK/uZoycK2GaBnSIEXgngmX6sdyS324z45N9VZCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T19:32:10.454206Z","bundle_sha256":"55db145ca5f0872b283523a788155c9559743a12778dfe5575c50328c7ca1677"}}