{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:LRD7V4OHT6NTEUQELSG6IINFLK","short_pith_number":"pith:LRD7V4OH","canonical_record":{"source":{"id":"1308.1169","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-08-06T03:18:24Z","cross_cats_sorted":[],"title_canon_sha256":"f94ea3a06b7857d838d4401a5c3af048ef521114c664a47aded8bcd56737c91e","abstract_canon_sha256":"67998af1499a917cb910e63c89cb853fde27cb83208312ac076413f25a924e7a"},"schema_version":"1.0"},"canonical_sha256":"5c47faf1c79f9b3252045c8de421a55ab39c7b9bb8700a61c04e9bc2d9f3d413","source":{"kind":"arxiv","id":"1308.1169","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.1169","created_at":"2026-05-18T03:16:39Z"},{"alias_kind":"arxiv_version","alias_value":"1308.1169v1","created_at":"2026-05-18T03:16:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.1169","created_at":"2026-05-18T03:16:39Z"},{"alias_kind":"pith_short_12","alias_value":"LRD7V4OHT6NT","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"LRD7V4OHT6NTEUQE","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"LRD7V4OH","created_at":"2026-05-18T12:27:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:LRD7V4OHT6NTEUQELSG6IINFLK","target":"record","payload":{"canonical_record":{"source":{"id":"1308.1169","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-08-06T03:18:24Z","cross_cats_sorted":[],"title_canon_sha256":"f94ea3a06b7857d838d4401a5c3af048ef521114c664a47aded8bcd56737c91e","abstract_canon_sha256":"67998af1499a917cb910e63c89cb853fde27cb83208312ac076413f25a924e7a"},"schema_version":"1.0"},"canonical_sha256":"5c47faf1c79f9b3252045c8de421a55ab39c7b9bb8700a61c04e9bc2d9f3d413","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:16:39.650593Z","signature_b64":"tvW6ngfflN3jiNsMEuydOAFEaLwGxIOjer5eOdmluuUQ5IqYtdJIi23C3Y70VJrjoZYKVfSSRuBchyMt7OkFBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5c47faf1c79f9b3252045c8de421a55ab39c7b9bb8700a61c04e9bc2d9f3d413","last_reissued_at":"2026-05-18T03:16:39.649979Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:16:39.649979Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1308.1169","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":"2026-05-18T03:16:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SxtoALLISxQ6nuMfQHY26WyubBsROYH7fi0UDVSBDgyXqKYz7eL91qfYHS3DwFnGetUJzoGkdxU16WF7a6aEDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T22:09:57.250522Z"},"content_sha256":"7a251727f7f25040d9e78ef6cb38222c9c247c8f1b42f4442bb7d01c999cb979","schema_version":"1.0","event_id":"sha256:7a251727f7f25040d9e78ef6cb38222c9c247c8f1b42f4442bb7d01c999cb979"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:LRD7V4OHT6NTEUQELSG6IINFLK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Almost sure well-posedness for the periodic 3D quintic nonlinear Schr\\\"odinger equation below the energy space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Andrea Nahmod, Gigliola Staffilani","submitted_at":"2013-08-06T03:18:24Z","abstract_excerpt":"In this paper we prove an almost sure local well-posedness result for the periodic 3D quintic nonlinear Schr\\\"odinger equation in the supercritical regime, that is below the critical space $H^1(\\mathbb T^3)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.1169","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":"2026-05-18T03:16:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0j6NUGw+gE7fU+c/b3DkuU+AkHRwxVEvRSqZrUen0DuUjQ7vKXTz7oicPJUTK8bng0HvQQ/XX24IvKy9teapDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T22:09:57.250871Z"},"content_sha256":"0653b52191193c29435aa4e3b893b8c130fff7c7f2740a1552a313fee3c38a85","schema_version":"1.0","event_id":"sha256:0653b52191193c29435aa4e3b893b8c130fff7c7f2740a1552a313fee3c38a85"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LRD7V4OHT6NTEUQELSG6IINFLK/bundle.json","state_url":"https://pith.science/pith/LRD7V4OHT6NTEUQELSG6IINFLK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LRD7V4OHT6NTEUQELSG6IINFLK/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":"2026-06-02T22:09:57Z","links":{"resolver":"https://pith.science/pith/LRD7V4OHT6NTEUQELSG6IINFLK","bundle":"https://pith.science/pith/LRD7V4OHT6NTEUQELSG6IINFLK/bundle.json","state":"https://pith.science/pith/LRD7V4OHT6NTEUQELSG6IINFLK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LRD7V4OHT6NTEUQELSG6IINFLK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:LRD7V4OHT6NTEUQELSG6IINFLK","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":"67998af1499a917cb910e63c89cb853fde27cb83208312ac076413f25a924e7a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-08-06T03:18:24Z","title_canon_sha256":"f94ea3a06b7857d838d4401a5c3af048ef521114c664a47aded8bcd56737c91e"},"schema_version":"1.0","source":{"id":"1308.1169","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.1169","created_at":"2026-05-18T03:16:39Z"},{"alias_kind":"arxiv_version","alias_value":"1308.1169v1","created_at":"2026-05-18T03:16:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.1169","created_at":"2026-05-18T03:16:39Z"},{"alias_kind":"pith_short_12","alias_value":"LRD7V4OHT6NT","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"LRD7V4OHT6NTEUQE","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"LRD7V4OH","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:0653b52191193c29435aa4e3b893b8c130fff7c7f2740a1552a313fee3c38a85","target":"graph","created_at":"2026-05-18T03:16:39Z","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 prove an almost sure local well-posedness result for the periodic 3D quintic nonlinear Schr\\\"odinger equation in the supercritical regime, that is below the critical space $H^1(\\mathbb T^3)$.","authors_text":"Andrea Nahmod, Gigliola Staffilani","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-08-06T03:18:24Z","title":"Almost sure well-posedness for the periodic 3D quintic nonlinear Schr\\\"odinger equation below the energy space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.1169","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":"sha256:7a251727f7f25040d9e78ef6cb38222c9c247c8f1b42f4442bb7d01c999cb979","target":"record","created_at":"2026-05-18T03:16:39Z","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":"67998af1499a917cb910e63c89cb853fde27cb83208312ac076413f25a924e7a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-08-06T03:18:24Z","title_canon_sha256":"f94ea3a06b7857d838d4401a5c3af048ef521114c664a47aded8bcd56737c91e"},"schema_version":"1.0","source":{"id":"1308.1169","kind":"arxiv","version":1}},"canonical_sha256":"5c47faf1c79f9b3252045c8de421a55ab39c7b9bb8700a61c04e9bc2d9f3d413","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5c47faf1c79f9b3252045c8de421a55ab39c7b9bb8700a61c04e9bc2d9f3d413","first_computed_at":"2026-05-18T03:16:39.649979Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:16:39.649979Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tvW6ngfflN3jiNsMEuydOAFEaLwGxIOjer5eOdmluuUQ5IqYtdJIi23C3Y70VJrjoZYKVfSSRuBchyMt7OkFBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:16:39.650593Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.1169","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7a251727f7f25040d9e78ef6cb38222c9c247c8f1b42f4442bb7d01c999cb979","sha256:0653b52191193c29435aa4e3b893b8c130fff7c7f2740a1552a313fee3c38a85"],"state_sha256":"e3d045b0a1010bcc83d09e49eca9351d18e64f6b18ef777e61812964eeadfc3b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UmQS7XtsBKFzhpH9pvg/TTgf5s5k3PVt8CaQRURu8aEwPytzwJjahw2MTTSNI6/wbnEeLvnp+ZzOaywmDP9FBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T22:09:57.252796Z","bundle_sha256":"460e6f8ca7fe22152f219d99f32d2cf05cd6e8ce7a09a0afb43c5a2d36c75495"}}