{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:AGMC4DG6K7TZDPQMWER44EQKT7","short_pith_number":"pith:AGMC4DG6","canonical_record":{"source":{"id":"1511.08577","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-11-27T07:53:47Z","cross_cats_sorted":[],"title_canon_sha256":"fe1e5617551eebc8fb8c88e3106f0502aa8c172fcc966e1aaa2ec275e4df41d8","abstract_canon_sha256":"f0c1010b480aa030596f6d73660bc9db2f7499d9de1a19ca5c1e77ef16fa2fc4"},"schema_version":"1.0"},"canonical_sha256":"01982e0cde57e791be0cb123ce120a9fd67763f3dd38d0f95deac8324af15b06","source":{"kind":"arxiv","id":"1511.08577","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.08577","created_at":"2026-05-18T01:03:06Z"},{"alias_kind":"arxiv_version","alias_value":"1511.08577v1","created_at":"2026-05-18T01:03:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.08577","created_at":"2026-05-18T01:03:06Z"},{"alias_kind":"pith_short_12","alias_value":"AGMC4DG6K7TZ","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"AGMC4DG6K7TZDPQM","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"AGMC4DG6","created_at":"2026-05-18T12:29:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:AGMC4DG6K7TZDPQMWER44EQKT7","target":"record","payload":{"canonical_record":{"source":{"id":"1511.08577","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-11-27T07:53:47Z","cross_cats_sorted":[],"title_canon_sha256":"fe1e5617551eebc8fb8c88e3106f0502aa8c172fcc966e1aaa2ec275e4df41d8","abstract_canon_sha256":"f0c1010b480aa030596f6d73660bc9db2f7499d9de1a19ca5c1e77ef16fa2fc4"},"schema_version":"1.0"},"canonical_sha256":"01982e0cde57e791be0cb123ce120a9fd67763f3dd38d0f95deac8324af15b06","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:03:06.299348Z","signature_b64":"EHyR1VsgMFa0SA+OUFkzedBnIrtClQTsPQT2O/i6r5n3vFzqDjtuRmuNw1atbaisxXsSLYLSlha5wtx2Hc7kBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"01982e0cde57e791be0cb123ce120a9fd67763f3dd38d0f95deac8324af15b06","last_reissued_at":"2026-05-18T01:03:06.298794Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:03:06.298794Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.08577","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":"2026-05-18T01:03:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"APYaCf3XQHHGL2zyj+NA4gXGRX2kZNemtn3Ih4mcCgcplu5SWfqb2A5cPyXmYA7QVVU65zuhhOl6QevGB+evBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T07:24:44.937841Z"},"content_sha256":"fb9c6e343be7c5d55ba609aced2da003bd5e4ca1ada553afc115b28ae91ca4c9","schema_version":"1.0","event_id":"sha256:fb9c6e343be7c5d55ba609aced2da003bd5e4ca1ada553afc115b28ae91ca4c9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:AGMC4DG6K7TZDPQMWER44EQKT7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Some remarks on the nonlinear Schr\\\"odinger equation with fractional dissipation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Luc Molinet, Mohamad Darwich","submitted_at":"2015-11-27T07:53:47Z","abstract_excerpt":"We consider the Cauchy problem for the $L^2$-critical nonlinear Schr\\\"odinger equation with a fractional dissipation. According to the order of the fractional dissipation, we prove the global existence or the existence of finite time blowup dynamics with the log-log blow-up speed for $\\|\\nabla u(t)\\|_{L^2}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.08577","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":"2026-05-18T01:03:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YEFz/3kil+FdTummXou1K8sXY1h1q4e4kcUgLLFjq/yM7650jiMtnY/WImxsBGWMuan8dun3uRqdEMv0baNIBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T07:24:44.938190Z"},"content_sha256":"37468e06f2113a9890aa5595c4657015a14d777cfc5b6af5ac63e19d09abaf45","schema_version":"1.0","event_id":"sha256:37468e06f2113a9890aa5595c4657015a14d777cfc5b6af5ac63e19d09abaf45"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AGMC4DG6K7TZDPQMWER44EQKT7/bundle.json","state_url":"https://pith.science/pith/AGMC4DG6K7TZDPQMWER44EQKT7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AGMC4DG6K7TZDPQMWER44EQKT7/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":"2026-07-07T07:24:44Z","links":{"resolver":"https://pith.science/pith/AGMC4DG6K7TZDPQMWER44EQKT7","bundle":"https://pith.science/pith/AGMC4DG6K7TZDPQMWER44EQKT7/bundle.json","state":"https://pith.science/pith/AGMC4DG6K7TZDPQMWER44EQKT7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AGMC4DG6K7TZDPQMWER44EQKT7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:AGMC4DG6K7TZDPQMWER44EQKT7","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":"f0c1010b480aa030596f6d73660bc9db2f7499d9de1a19ca5c1e77ef16fa2fc4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-11-27T07:53:47Z","title_canon_sha256":"fe1e5617551eebc8fb8c88e3106f0502aa8c172fcc966e1aaa2ec275e4df41d8"},"schema_version":"1.0","source":{"id":"1511.08577","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.08577","created_at":"2026-05-18T01:03:06Z"},{"alias_kind":"arxiv_version","alias_value":"1511.08577v1","created_at":"2026-05-18T01:03:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.08577","created_at":"2026-05-18T01:03:06Z"},{"alias_kind":"pith_short_12","alias_value":"AGMC4DG6K7TZ","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"AGMC4DG6K7TZDPQM","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"AGMC4DG6","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:37468e06f2113a9890aa5595c4657015a14d777cfc5b6af5ac63e19d09abaf45","target":"graph","created_at":"2026-05-18T01:03:06Z","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 consider the Cauchy problem for the $L^2$-critical nonlinear Schr\\\"odinger equation with a fractional dissipation. According to the order of the fractional dissipation, we prove the global existence or the existence of finite time blowup dynamics with the log-log blow-up speed for $\\|\\nabla u(t)\\|_{L^2}$.","authors_text":"Luc Molinet, Mohamad Darwich","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-11-27T07:53:47Z","title":"Some remarks on the nonlinear Schr\\\"odinger equation with fractional dissipation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.08577","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:fb9c6e343be7c5d55ba609aced2da003bd5e4ca1ada553afc115b28ae91ca4c9","target":"record","created_at":"2026-05-18T01:03:06Z","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":"f0c1010b480aa030596f6d73660bc9db2f7499d9de1a19ca5c1e77ef16fa2fc4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-11-27T07:53:47Z","title_canon_sha256":"fe1e5617551eebc8fb8c88e3106f0502aa8c172fcc966e1aaa2ec275e4df41d8"},"schema_version":"1.0","source":{"id":"1511.08577","kind":"arxiv","version":1}},"canonical_sha256":"01982e0cde57e791be0cb123ce120a9fd67763f3dd38d0f95deac8324af15b06","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"01982e0cde57e791be0cb123ce120a9fd67763f3dd38d0f95deac8324af15b06","first_computed_at":"2026-05-18T01:03:06.298794Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:03:06.298794Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EHyR1VsgMFa0SA+OUFkzedBnIrtClQTsPQT2O/i6r5n3vFzqDjtuRmuNw1atbaisxXsSLYLSlha5wtx2Hc7kBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:03:06.299348Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.08577","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fb9c6e343be7c5d55ba609aced2da003bd5e4ca1ada553afc115b28ae91ca4c9","sha256:37468e06f2113a9890aa5595c4657015a14d777cfc5b6af5ac63e19d09abaf45"],"state_sha256":"57b8a13f20a44bb13c918e3a25f3f3fa0d75e65937ddf65126a56ba171b06089"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8vJqU25/jhGC3BbF2QF69TPaK8uMImL/kfRQ4wnQb2S0KSuM3eVh+m7j5qENkS+EO4ETZVUt7DeYuBy7GuK2Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T07:24:44.940927Z","bundle_sha256":"03827b0f1f997a1887e4d9a9658520648ad8940dd9d1cb38061d0d60a1fbe7a5"}}