{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:3NJJJAXDE4FRWW5IFQQZ2MH7RQ","short_pith_number":"pith:3NJJJAXD","canonical_record":{"source":{"id":"1310.7785","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-29T12:37:37Z","cross_cats_sorted":[],"title_canon_sha256":"f900689355059f5c30415f311b7eb9dfb786f4e64dde23b950a3026bbdcf5e2b","abstract_canon_sha256":"b0a21fdc72ddc723d88c16d74c4ea21431f72671a0119aac3fb620f494c9cef7"},"schema_version":"1.0"},"canonical_sha256":"db529482e3270b1b5ba82c219d30ff8c37bae451754b0571f6a7f89e449aa778","source":{"kind":"arxiv","id":"1310.7785","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.7785","created_at":"2026-05-18T03:07:33Z"},{"alias_kind":"arxiv_version","alias_value":"1310.7785v2","created_at":"2026-05-18T03:07:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.7785","created_at":"2026-05-18T03:07:33Z"},{"alias_kind":"pith_short_12","alias_value":"3NJJJAXDE4FR","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"3NJJJAXDE4FRWW5I","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"3NJJJAXD","created_at":"2026-05-18T12:27:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:3NJJJAXDE4FRWW5IFQQZ2MH7RQ","target":"record","payload":{"canonical_record":{"source":{"id":"1310.7785","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-29T12:37:37Z","cross_cats_sorted":[],"title_canon_sha256":"f900689355059f5c30415f311b7eb9dfb786f4e64dde23b950a3026bbdcf5e2b","abstract_canon_sha256":"b0a21fdc72ddc723d88c16d74c4ea21431f72671a0119aac3fb620f494c9cef7"},"schema_version":"1.0"},"canonical_sha256":"db529482e3270b1b5ba82c219d30ff8c37bae451754b0571f6a7f89e449aa778","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:07:33.681280Z","signature_b64":"zs+nIgCIU66f+lFGQ+m3X2Nw6Yj9cSxdZ/w7rAb0lbEvlOnzdS1mh3E0RGfkpEELOXXdyczObqBS83u8U5aIBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"db529482e3270b1b5ba82c219d30ff8c37bae451754b0571f6a7f89e449aa778","last_reissued_at":"2026-05-18T03:07:33.680847Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:07:33.680847Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.7785","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":"2026-05-18T03:07:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sPdMoFVVohGpppKHOz/a5Z/DwAznK8PfDjJqSOXlk9GiQCdDoBZzm2AYetyZMrW1o4g5yFLxThU7HsDKKVUUAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T22:11:20.313586Z"},"content_sha256":"7aeae77217223c608f60d10461a589b8d7ae0c557877429fa2c3dc9408b744e1","schema_version":"1.0","event_id":"sha256:7aeae77217223c608f60d10461a589b8d7ae0c557877429fa2c3dc9408b744e1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:3NJJJAXDE4FRWW5IFQQZ2MH7RQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"1/2-Laplacian problems with exponential nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Antonio Iannizzotto, Marco Squassina","submitted_at":"2013-10-29T12:37:37Z","abstract_excerpt":"By exploiting a suitable Trudinger-Moser inequality for fractional Sobolev spaces, we obtain existence and multiplicity of solutions for a class of one-dimensional nonlocal equations with fractional diffusion and nonlinearity at exponential growth."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.7785","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":"2026-05-18T03:07:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xQ4z5p+y8i12TnliaNyAKBofG8wM+H200TUqzSQJGfawfVbvN64IcfRXG14P0VFTg5DJWvGeRT8hZcaZijAoCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T22:11:20.313922Z"},"content_sha256":"d713887a692f964147de238aff9eb4a5b7530c0082bc30114caf7b7a13881032","schema_version":"1.0","event_id":"sha256:d713887a692f964147de238aff9eb4a5b7530c0082bc30114caf7b7a13881032"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3NJJJAXDE4FRWW5IFQQZ2MH7RQ/bundle.json","state_url":"https://pith.science/pith/3NJJJAXDE4FRWW5IFQQZ2MH7RQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3NJJJAXDE4FRWW5IFQQZ2MH7RQ/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":"2026-06-08T22:11:20Z","links":{"resolver":"https://pith.science/pith/3NJJJAXDE4FRWW5IFQQZ2MH7RQ","bundle":"https://pith.science/pith/3NJJJAXDE4FRWW5IFQQZ2MH7RQ/bundle.json","state":"https://pith.science/pith/3NJJJAXDE4FRWW5IFQQZ2MH7RQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3NJJJAXDE4FRWW5IFQQZ2MH7RQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:3NJJJAXDE4FRWW5IFQQZ2MH7RQ","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":"b0a21fdc72ddc723d88c16d74c4ea21431f72671a0119aac3fb620f494c9cef7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-29T12:37:37Z","title_canon_sha256":"f900689355059f5c30415f311b7eb9dfb786f4e64dde23b950a3026bbdcf5e2b"},"schema_version":"1.0","source":{"id":"1310.7785","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.7785","created_at":"2026-05-18T03:07:33Z"},{"alias_kind":"arxiv_version","alias_value":"1310.7785v2","created_at":"2026-05-18T03:07:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.7785","created_at":"2026-05-18T03:07:33Z"},{"alias_kind":"pith_short_12","alias_value":"3NJJJAXDE4FR","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"3NJJJAXDE4FRWW5I","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"3NJJJAXD","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:d713887a692f964147de238aff9eb4a5b7530c0082bc30114caf7b7a13881032","target":"graph","created_at":"2026-05-18T03:07:33Z","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":"By exploiting a suitable Trudinger-Moser inequality for fractional Sobolev spaces, we obtain existence and multiplicity of solutions for a class of one-dimensional nonlocal equations with fractional diffusion and nonlinearity at exponential growth.","authors_text":"Antonio Iannizzotto, Marco Squassina","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-29T12:37:37Z","title":"1/2-Laplacian problems with exponential nonlinearity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.7785","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":"sha256:7aeae77217223c608f60d10461a589b8d7ae0c557877429fa2c3dc9408b744e1","target":"record","created_at":"2026-05-18T03:07:33Z","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":"b0a21fdc72ddc723d88c16d74c4ea21431f72671a0119aac3fb620f494c9cef7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-29T12:37:37Z","title_canon_sha256":"f900689355059f5c30415f311b7eb9dfb786f4e64dde23b950a3026bbdcf5e2b"},"schema_version":"1.0","source":{"id":"1310.7785","kind":"arxiv","version":2}},"canonical_sha256":"db529482e3270b1b5ba82c219d30ff8c37bae451754b0571f6a7f89e449aa778","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"db529482e3270b1b5ba82c219d30ff8c37bae451754b0571f6a7f89e449aa778","first_computed_at":"2026-05-18T03:07:33.680847Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:07:33.680847Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zs+nIgCIU66f+lFGQ+m3X2Nw6Yj9cSxdZ/w7rAb0lbEvlOnzdS1mh3E0RGfkpEELOXXdyczObqBS83u8U5aIBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:07:33.681280Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.7785","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7aeae77217223c608f60d10461a589b8d7ae0c557877429fa2c3dc9408b744e1","sha256:d713887a692f964147de238aff9eb4a5b7530c0082bc30114caf7b7a13881032"],"state_sha256":"e58c2847ebf185c207b3932226bdfba3f22160c2651c28019f4190f34e3b8b41"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kJ/FH63x8FHdQ5chPwxr0MwPsJF5NvcRQ71fE0ZaxnSMHM8ZPUZUCnYC2nm61GTOEPaeqCPRz5XxoHzuem6/Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T22:11:20.315720Z","bundle_sha256":"019ce8bed2914027cefdbf76da8aabf61a50b5abc40c7414a79156c9876ecc79"}}