{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:LNFMGC2UOESGYZUNKVTXSC7RF2","short_pith_number":"pith:LNFMGC2U","canonical_record":{"source":{"id":"1612.04533","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-12-14T08:39:22Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"a0f6583dc420e65ca4d3a17b482c9abbf1372e3dc98238fba28f724ab436042b","abstract_canon_sha256":"d42177f161aef2ff6dfccab57ccedd868df9b416d03311b0a05e523c33de6b43"},"schema_version":"1.0"},"canonical_sha256":"5b4ac30b5471246c668d5567790bf12e8fadbe9b865882a0589149f28ca77c69","source":{"kind":"arxiv","id":"1612.04533","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.04533","created_at":"2026-05-18T00:34:42Z"},{"alias_kind":"arxiv_version","alias_value":"1612.04533v2","created_at":"2026-05-18T00:34:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.04533","created_at":"2026-05-18T00:34:42Z"},{"alias_kind":"pith_short_12","alias_value":"LNFMGC2UOESG","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LNFMGC2UOESGYZUN","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LNFMGC2U","created_at":"2026-05-18T12:30:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:LNFMGC2UOESGYZUNKVTXSC7RF2","target":"record","payload":{"canonical_record":{"source":{"id":"1612.04533","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-12-14T08:39:22Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"a0f6583dc420e65ca4d3a17b482c9abbf1372e3dc98238fba28f724ab436042b","abstract_canon_sha256":"d42177f161aef2ff6dfccab57ccedd868df9b416d03311b0a05e523c33de6b43"},"schema_version":"1.0"},"canonical_sha256":"5b4ac30b5471246c668d5567790bf12e8fadbe9b865882a0589149f28ca77c69","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:34:42.117520Z","signature_b64":"DbgUuT75F4h3lruANWl9LWiM8/4Gx5lgYp+d/2r2UPV8GsSczXVDnZWo3dcW5nh2/1F5CTJbFIWglFgmI5iYBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5b4ac30b5471246c668d5567790bf12e8fadbe9b865882a0589149f28ca77c69","last_reissued_at":"2026-05-18T00:34:42.116801Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:34:42.116801Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.04533","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":"2026-05-18T00:34:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YvfJhSyuFdMNknPEpsaD+f/uPE7kaR1UgEjSM6aa++Vvo9WcjmuNCTnDklwmEAAv4Hvpb7nFoLWPRzOU5qeiDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T06:39:56.537453Z"},"content_sha256":"d0ed71d1eb002b6112e79e56876eb15bde03aa727148d47db19095c8f79fc861","schema_version":"1.0","event_id":"sha256:d0ed71d1eb002b6112e79e56876eb15bde03aa727148d47db19095c8f79fc861"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:LNFMGC2UOESGYZUNKVTXSC7RF2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Some quasilinear elliptic equations involving multiple $p$-Laplacians","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Alessio Pomponio, Tatsuya Watanabe","submitted_at":"2016-12-14T08:39:22Z","abstract_excerpt":"This paper is devoted to the study, with variational technique, of (p,q)-Laplacian equations in presence of general nonlinearities. Especially we obtain the existence result for the zero mass case, which includes a large class of pure power nonlinearities. More general quasilinear problems of Born-Infeld type are also considered."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.04533","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":"2026-05-18T00:34:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8qUoJD7ZXsqZ7BefFvgkE3tSEBkrcv2H0qrjThl69gpdXvsavHqWIgcGF50aILycU6sTvCJdKykrt2gcMuTNDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T06:39:56.537811Z"},"content_sha256":"8af50ae3807cf78c657371b8ddc9b535bb383553dc63f4c0f6eb2289232f9220","schema_version":"1.0","event_id":"sha256:8af50ae3807cf78c657371b8ddc9b535bb383553dc63f4c0f6eb2289232f9220"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LNFMGC2UOESGYZUNKVTXSC7RF2/bundle.json","state_url":"https://pith.science/pith/LNFMGC2UOESGYZUNKVTXSC7RF2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LNFMGC2UOESGYZUNKVTXSC7RF2/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":"2026-06-12T06:39:56Z","links":{"resolver":"https://pith.science/pith/LNFMGC2UOESGYZUNKVTXSC7RF2","bundle":"https://pith.science/pith/LNFMGC2UOESGYZUNKVTXSC7RF2/bundle.json","state":"https://pith.science/pith/LNFMGC2UOESGYZUNKVTXSC7RF2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LNFMGC2UOESGYZUNKVTXSC7RF2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:LNFMGC2UOESGYZUNKVTXSC7RF2","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":"d42177f161aef2ff6dfccab57ccedd868df9b416d03311b0a05e523c33de6b43","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-12-14T08:39:22Z","title_canon_sha256":"a0f6583dc420e65ca4d3a17b482c9abbf1372e3dc98238fba28f724ab436042b"},"schema_version":"1.0","source":{"id":"1612.04533","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.04533","created_at":"2026-05-18T00:34:42Z"},{"alias_kind":"arxiv_version","alias_value":"1612.04533v2","created_at":"2026-05-18T00:34:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.04533","created_at":"2026-05-18T00:34:42Z"},{"alias_kind":"pith_short_12","alias_value":"LNFMGC2UOESG","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LNFMGC2UOESGYZUN","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LNFMGC2U","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:8af50ae3807cf78c657371b8ddc9b535bb383553dc63f4c0f6eb2289232f9220","target":"graph","created_at":"2026-05-18T00:34:42Z","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":"This paper is devoted to the study, with variational technique, of (p,q)-Laplacian equations in presence of general nonlinearities. Especially we obtain the existence result for the zero mass case, which includes a large class of pure power nonlinearities. More general quasilinear problems of Born-Infeld type are also considered.","authors_text":"Alessio Pomponio, Tatsuya Watanabe","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-12-14T08:39:22Z","title":"Some quasilinear elliptic equations involving multiple $p$-Laplacians"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.04533","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:d0ed71d1eb002b6112e79e56876eb15bde03aa727148d47db19095c8f79fc861","target":"record","created_at":"2026-05-18T00:34:42Z","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":"d42177f161aef2ff6dfccab57ccedd868df9b416d03311b0a05e523c33de6b43","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-12-14T08:39:22Z","title_canon_sha256":"a0f6583dc420e65ca4d3a17b482c9abbf1372e3dc98238fba28f724ab436042b"},"schema_version":"1.0","source":{"id":"1612.04533","kind":"arxiv","version":2}},"canonical_sha256":"5b4ac30b5471246c668d5567790bf12e8fadbe9b865882a0589149f28ca77c69","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5b4ac30b5471246c668d5567790bf12e8fadbe9b865882a0589149f28ca77c69","first_computed_at":"2026-05-18T00:34:42.116801Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:34:42.116801Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DbgUuT75F4h3lruANWl9LWiM8/4Gx5lgYp+d/2r2UPV8GsSczXVDnZWo3dcW5nh2/1F5CTJbFIWglFgmI5iYBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:34:42.117520Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.04533","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d0ed71d1eb002b6112e79e56876eb15bde03aa727148d47db19095c8f79fc861","sha256:8af50ae3807cf78c657371b8ddc9b535bb383553dc63f4c0f6eb2289232f9220"],"state_sha256":"ef946afc6e2cca89c67f5cddc87ee697fc2571d3f088bc7e93186086efa18fb9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+4fUeC9JQGt9UESbICTDj3Rm6gL8FHZLWuVr+CnCjU1L9GQPd/kOCqhcLzWRHDBP3WSD/nWwAV097nx/IbNnCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T06:39:56.539850Z","bundle_sha256":"2c87b1c0db55decb4d4b1a002acae4b319c4398602a37f4c0abc4bd692c38d21"}}