{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:JKOTNRBZQEIO5SYQJPCNTBJYA4","short_pith_number":"pith:JKOTNRBZ","canonical_record":{"source":{"id":"1609.00705","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-09-02T19:22:43Z","cross_cats_sorted":[],"title_canon_sha256":"d9c1604af4004941b72b227b661677237890f8af57d678631484e846e2be9b92","abstract_canon_sha256":"39f0285236b2c04717f15da332748029245aac611f1a674dfceeeb58b8fb0949"},"schema_version":"1.0"},"canonical_sha256":"4a9d36c4398110eecb104bc4d985380737a5c63578adf23b99985eed9b8ca1a4","source":{"kind":"arxiv","id":"1609.00705","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.00705","created_at":"2026-05-18T01:06:23Z"},{"alias_kind":"arxiv_version","alias_value":"1609.00705v1","created_at":"2026-05-18T01:06:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.00705","created_at":"2026-05-18T01:06:23Z"},{"alias_kind":"pith_short_12","alias_value":"JKOTNRBZQEIO","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"JKOTNRBZQEIO5SYQ","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"JKOTNRBZ","created_at":"2026-05-18T12:30:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:JKOTNRBZQEIO5SYQJPCNTBJYA4","target":"record","payload":{"canonical_record":{"source":{"id":"1609.00705","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-09-02T19:22:43Z","cross_cats_sorted":[],"title_canon_sha256":"d9c1604af4004941b72b227b661677237890f8af57d678631484e846e2be9b92","abstract_canon_sha256":"39f0285236b2c04717f15da332748029245aac611f1a674dfceeeb58b8fb0949"},"schema_version":"1.0"},"canonical_sha256":"4a9d36c4398110eecb104bc4d985380737a5c63578adf23b99985eed9b8ca1a4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:06:23.401791Z","signature_b64":"DXUo4h7WLU9E8c4Gf886ququWCpR6OmN7Z+MNMJiZG1KHCzgLuJE9y9XznI697t4llK3kahk4+trvGg03TLnAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4a9d36c4398110eecb104bc4d985380737a5c63578adf23b99985eed9b8ca1a4","last_reissued_at":"2026-05-18T01:06:23.401172Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:06:23.401172Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.00705","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":"2026-05-18T01:06:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5JCF+fdwt0Lv9gipvCm/GZNUnN1HwbKoYG0hzVJs0Wm9w0XmbPepUwbvI/ADLXQKXXroIZg+GPc1Hxanj5gOBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T06:04:07.466955Z"},"content_sha256":"66494fed972d03fc393a40437aea393da6a49000dc8ccc04f58c6f0a49ff8e8a","schema_version":"1.0","event_id":"sha256:66494fed972d03fc393a40437aea393da6a49000dc8ccc04f58c6f0a49ff8e8a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:JKOTNRBZQEIO5SYQJPCNTBJYA4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Classification of the stable solution to the fractional $2<s<3$ Lane-Emden equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Juncheng Wei, Senping Luo, Wenming Zou","submitted_at":"2016-09-02T19:22:43Z","abstract_excerpt":"We classify the stable solutions (positive or sign-changing, radial or not) to the following nonlocal Lane-Emden equation: $(-\\Delta)^s u=|u|^{p-1}u$ in $\\mathbb{R}^n$ for $2<s<3$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.00705","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":"2026-05-18T01:06:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"boQum5VUhg0xPf9ewYpA9DpWdnYCGUJ8g65cOw7g0BttD+tv8KYExp7iHzQzKIFX+EvZmmwb15vlLC1KUQU7Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T06:04:07.467723Z"},"content_sha256":"4b302a692c76de1f7fcbb6dba52b7f46785acb210ca2a59b2fb3142be81b6568","schema_version":"1.0","event_id":"sha256:4b302a692c76de1f7fcbb6dba52b7f46785acb210ca2a59b2fb3142be81b6568"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JKOTNRBZQEIO5SYQJPCNTBJYA4/bundle.json","state_url":"https://pith.science/pith/JKOTNRBZQEIO5SYQJPCNTBJYA4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JKOTNRBZQEIO5SYQJPCNTBJYA4/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":"2026-06-07T06:04:07Z","links":{"resolver":"https://pith.science/pith/JKOTNRBZQEIO5SYQJPCNTBJYA4","bundle":"https://pith.science/pith/JKOTNRBZQEIO5SYQJPCNTBJYA4/bundle.json","state":"https://pith.science/pith/JKOTNRBZQEIO5SYQJPCNTBJYA4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JKOTNRBZQEIO5SYQJPCNTBJYA4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:JKOTNRBZQEIO5SYQJPCNTBJYA4","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":"39f0285236b2c04717f15da332748029245aac611f1a674dfceeeb58b8fb0949","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-09-02T19:22:43Z","title_canon_sha256":"d9c1604af4004941b72b227b661677237890f8af57d678631484e846e2be9b92"},"schema_version":"1.0","source":{"id":"1609.00705","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.00705","created_at":"2026-05-18T01:06:23Z"},{"alias_kind":"arxiv_version","alias_value":"1609.00705v1","created_at":"2026-05-18T01:06:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.00705","created_at":"2026-05-18T01:06:23Z"},{"alias_kind":"pith_short_12","alias_value":"JKOTNRBZQEIO","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"JKOTNRBZQEIO5SYQ","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"JKOTNRBZ","created_at":"2026-05-18T12:30:25Z"}],"graph_snapshots":[{"event_id":"sha256:4b302a692c76de1f7fcbb6dba52b7f46785acb210ca2a59b2fb3142be81b6568","target":"graph","created_at":"2026-05-18T01:06:23Z","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 classify the stable solutions (positive or sign-changing, radial or not) to the following nonlocal Lane-Emden equation: $(-\\Delta)^s u=|u|^{p-1}u$ in $\\mathbb{R}^n$ for $2<s<3$.","authors_text":"Juncheng Wei, Senping Luo, Wenming Zou","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-09-02T19:22:43Z","title":"Classification of the stable solution to the fractional $2<s<3$ Lane-Emden equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.00705","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":"sha256:66494fed972d03fc393a40437aea393da6a49000dc8ccc04f58c6f0a49ff8e8a","target":"record","created_at":"2026-05-18T01:06:23Z","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":"39f0285236b2c04717f15da332748029245aac611f1a674dfceeeb58b8fb0949","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-09-02T19:22:43Z","title_canon_sha256":"d9c1604af4004941b72b227b661677237890f8af57d678631484e846e2be9b92"},"schema_version":"1.0","source":{"id":"1609.00705","kind":"arxiv","version":1}},"canonical_sha256":"4a9d36c4398110eecb104bc4d985380737a5c63578adf23b99985eed9b8ca1a4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4a9d36c4398110eecb104bc4d985380737a5c63578adf23b99985eed9b8ca1a4","first_computed_at":"2026-05-18T01:06:23.401172Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:06:23.401172Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DXUo4h7WLU9E8c4Gf886ququWCpR6OmN7Z+MNMJiZG1KHCzgLuJE9y9XznI697t4llK3kahk4+trvGg03TLnAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:06:23.401791Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.00705","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:66494fed972d03fc393a40437aea393da6a49000dc8ccc04f58c6f0a49ff8e8a","sha256:4b302a692c76de1f7fcbb6dba52b7f46785acb210ca2a59b2fb3142be81b6568"],"state_sha256":"6fb09a483e092f2b18fbef0642e00eb7302d6e0f5a33b51eb201eebd80f13b84"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q+Bm44q1vqK5fhYtikEkAw1XMuncPZ4VCndD4/dkO+wLk/IlF0nBtNsuVN3u1OMVCbZvZi/7ZH2/4bVMfeX8Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T06:04:07.471763Z","bundle_sha256":"81d74f9b48788effb3a62c93e03bd33544f9d793ac3458f95936337beeb48896"}}