{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:H36GQRERUEG6H35E4W27ASIB4C","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":"6b313c25ce057737088a6d5860235338a2b908dcd1d010cf1ed248eefadb1c3d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-08-27T09:14:30Z","title_canon_sha256":"9a0478e6317cb64e2c10366e0bb27560813336d63ebc7b0b9adce87d8ca682bb"},"schema_version":"1.0","source":{"id":"1408.6359","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.6359","created_at":"2026-05-18T02:44:07Z"},{"alias_kind":"arxiv_version","alias_value":"1408.6359v1","created_at":"2026-05-18T02:44:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.6359","created_at":"2026-05-18T02:44:07Z"},{"alias_kind":"pith_short_12","alias_value":"H36GQRERUEG6","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"H36GQRERUEG6H35E","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"H36GQRER","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:b4674f161552fff180dd4cdc8ff8b1a089db6fdfd3d0b32da3eadea46a48e822","target":"graph","created_at":"2026-05-18T02:44:07Z","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 study solutions and supersolutions of homogeneous and nonhomogeneous $\\mathcal{A}$-harmonic equations with nonstandard growth in $\\mathbb{R}^n$. Various Liouville-type theorems and nonexistence results are proved. The discussion is illustrated by a number of examples.","authors_text":"Przemys{\\l}aw G\\'orka, Tomasz Adamowicz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-08-27T09:14:30Z","title":"The Liouville theorems for elliptic equations with nonstandard growth"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.6359","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":"sha256:4569e26a9abc17e2ab8ff7293c9df41b9b4271717b3648966d8d34982d1a1246","target":"record","created_at":"2026-05-18T02:44:07Z","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":"6b313c25ce057737088a6d5860235338a2b908dcd1d010cf1ed248eefadb1c3d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-08-27T09:14:30Z","title_canon_sha256":"9a0478e6317cb64e2c10366e0bb27560813336d63ebc7b0b9adce87d8ca682bb"},"schema_version":"1.0","source":{"id":"1408.6359","kind":"arxiv","version":1}},"canonical_sha256":"3efc684491a10de3efa4e5b5f04901e0ae603c3026fe9e0c67deb2d08bb99671","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3efc684491a10de3efa4e5b5f04901e0ae603c3026fe9e0c67deb2d08bb99671","first_computed_at":"2026-05-18T02:44:07.660235Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:44:07.660235Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VcdOONGGbufFBENEYxBQwDCXqQ+pRK+yvo5kxP1/1rKMAGexgZLH4AZmqLY8zzGBcDrkWVcovTs6WtfbyojzDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:44:07.660699Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.6359","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4569e26a9abc17e2ab8ff7293c9df41b9b4271717b3648966d8d34982d1a1246","sha256:b4674f161552fff180dd4cdc8ff8b1a089db6fdfd3d0b32da3eadea46a48e822"],"state_sha256":"063eab0006e4647f9aac94a993295a2115d765fb01886fba441fb096627d2fde"}