{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:ZEMOSZIF4FT2VAXVQKBA4W6727","short_pith_number":"pith:ZEMOSZIF","canonical_record":{"source":{"id":"1807.10365","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-07-26T21:06:29Z","cross_cats_sorted":[],"title_canon_sha256":"015c9d2c4cf6cd4a48b90a117172405ccb16b86323a79aeac69c0975b78020bf","abstract_canon_sha256":"a12b1fc5d81d2f69ba4e84da1c9e9cedbc8a8e4062afe71be650a0f783ee2796"},"schema_version":"1.0"},"canonical_sha256":"c918e96505e167aa82f582820e5bdfd7d32b506db02dc94132b1c36b55c04854","source":{"kind":"arxiv","id":"1807.10365","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.10365","created_at":"2026-05-17T23:46:30Z"},{"alias_kind":"arxiv_version","alias_value":"1807.10365v2","created_at":"2026-05-17T23:46:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.10365","created_at":"2026-05-17T23:46:30Z"},{"alias_kind":"pith_short_12","alias_value":"ZEMOSZIF4FT2","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"ZEMOSZIF4FT2VAXV","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"ZEMOSZIF","created_at":"2026-05-18T12:33:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:ZEMOSZIF4FT2VAXVQKBA4W6727","target":"record","payload":{"canonical_record":{"source":{"id":"1807.10365","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-07-26T21:06:29Z","cross_cats_sorted":[],"title_canon_sha256":"015c9d2c4cf6cd4a48b90a117172405ccb16b86323a79aeac69c0975b78020bf","abstract_canon_sha256":"a12b1fc5d81d2f69ba4e84da1c9e9cedbc8a8e4062afe71be650a0f783ee2796"},"schema_version":"1.0"},"canonical_sha256":"c918e96505e167aa82f582820e5bdfd7d32b506db02dc94132b1c36b55c04854","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:46:30.156079Z","signature_b64":"DefKsUseggip3k1MASkBEsjrsuXuqjiilI6saWr3cvLo9UL5JfdfgdornksY85VEeQM7+L+GhcIDt77J80IqDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c918e96505e167aa82f582820e5bdfd7d32b506db02dc94132b1c36b55c04854","last_reissued_at":"2026-05-17T23:46:30.155454Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:46:30.155454Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1807.10365","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":"2026-05-17T23:46:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S4kZhVLE7BJt6/a4SDi2fpwcCKCDpxdWK0VwZ9HaFQwBe+MuyuyMVv9XoMipFb4avVDuJaXcxX2kE8BTFni0Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T15:22:25.029905Z"},"content_sha256":"3154ad5dfeaac9e6454134401b48fc8675a7f7af90a10a39108d59b647a12062","schema_version":"1.0","event_id":"sha256:3154ad5dfeaac9e6454134401b48fc8675a7f7af90a10a39108d59b647a12062"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:ZEMOSZIF4FT2VAXVQKBA4W6727","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Groundstate asymptotics for a class of singularly perturbed $p$-Laplacian problems in $\\mathbb {R}^N$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Carlo Mercuri, Vitaly Moroz, Wedad Albalawi","submitted_at":"2018-07-26T21:06:29Z","abstract_excerpt":"We study the asymptotic behavior of positive groundstate solutions to the quasilinear elliptic equation \\begin{equation} -\\Delta_{p} u + \\varepsilon u^{p-1} - u^{q-1} +u^{\\mathit{l}-1} = 0 \\qquad \\text{in} \\quad \\mathbb{R}^{N}, \\end{equation} where $1<p<N $, $p<q<l<+\\infty$ and $\\varepsilon> 0 $ is a small parameter. For $\\varepsilon\\rightarrow 0$, we give a characterisation of asymptotic regimes as a function of the parameters $q$, $l$ and $N$. In particular, we show that the behavior of the groundstates is sensitive to whether $q$ is less than, equal to, or greater than the critical Sobolev "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.10365","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":"2026-05-17T23:46:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fC/8UhmokIRyLLMwV2Wk1aJTqk28xi/mmAl7Fisz/t4PBZ2Y9vdXN1lC/XkFbCGWgJAtfWDVO3TYawvxk9tzBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T15:22:25.030534Z"},"content_sha256":"69691b8888725b59a7f1414481bf11fd7d5e1d867a41e8c582e64ba927f2db5f","schema_version":"1.0","event_id":"sha256:69691b8888725b59a7f1414481bf11fd7d5e1d867a41e8c582e64ba927f2db5f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZEMOSZIF4FT2VAXVQKBA4W6727/bundle.json","state_url":"https://pith.science/pith/ZEMOSZIF4FT2VAXVQKBA4W6727/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZEMOSZIF4FT2VAXVQKBA4W6727/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":"2026-05-25T15:22:25Z","links":{"resolver":"https://pith.science/pith/ZEMOSZIF4FT2VAXVQKBA4W6727","bundle":"https://pith.science/pith/ZEMOSZIF4FT2VAXVQKBA4W6727/bundle.json","state":"https://pith.science/pith/ZEMOSZIF4FT2VAXVQKBA4W6727/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZEMOSZIF4FT2VAXVQKBA4W6727/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:ZEMOSZIF4FT2VAXVQKBA4W6727","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":"a12b1fc5d81d2f69ba4e84da1c9e9cedbc8a8e4062afe71be650a0f783ee2796","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-07-26T21:06:29Z","title_canon_sha256":"015c9d2c4cf6cd4a48b90a117172405ccb16b86323a79aeac69c0975b78020bf"},"schema_version":"1.0","source":{"id":"1807.10365","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.10365","created_at":"2026-05-17T23:46:30Z"},{"alias_kind":"arxiv_version","alias_value":"1807.10365v2","created_at":"2026-05-17T23:46:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.10365","created_at":"2026-05-17T23:46:30Z"},{"alias_kind":"pith_short_12","alias_value":"ZEMOSZIF4FT2","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"ZEMOSZIF4FT2VAXV","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"ZEMOSZIF","created_at":"2026-05-18T12:33:07Z"}],"graph_snapshots":[{"event_id":"sha256:69691b8888725b59a7f1414481bf11fd7d5e1d867a41e8c582e64ba927f2db5f","target":"graph","created_at":"2026-05-17T23:46:30Z","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 the asymptotic behavior of positive groundstate solutions to the quasilinear elliptic equation \\begin{equation} -\\Delta_{p} u + \\varepsilon u^{p-1} - u^{q-1} +u^{\\mathit{l}-1} = 0 \\qquad \\text{in} \\quad \\mathbb{R}^{N}, \\end{equation} where $1<p<N $, $p<q<l<+\\infty$ and $\\varepsilon> 0 $ is a small parameter. For $\\varepsilon\\rightarrow 0$, we give a characterisation of asymptotic regimes as a function of the parameters $q$, $l$ and $N$. In particular, we show that the behavior of the groundstates is sensitive to whether $q$ is less than, equal to, or greater than the critical Sobolev ","authors_text":"Carlo Mercuri, Vitaly Moroz, Wedad Albalawi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-07-26T21:06:29Z","title":"Groundstate asymptotics for a class of singularly perturbed $p$-Laplacian problems in $\\mathbb {R}^N$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.10365","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":"sha256:3154ad5dfeaac9e6454134401b48fc8675a7f7af90a10a39108d59b647a12062","target":"record","created_at":"2026-05-17T23:46:30Z","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":"a12b1fc5d81d2f69ba4e84da1c9e9cedbc8a8e4062afe71be650a0f783ee2796","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-07-26T21:06:29Z","title_canon_sha256":"015c9d2c4cf6cd4a48b90a117172405ccb16b86323a79aeac69c0975b78020bf"},"schema_version":"1.0","source":{"id":"1807.10365","kind":"arxiv","version":2}},"canonical_sha256":"c918e96505e167aa82f582820e5bdfd7d32b506db02dc94132b1c36b55c04854","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c918e96505e167aa82f582820e5bdfd7d32b506db02dc94132b1c36b55c04854","first_computed_at":"2026-05-17T23:46:30.155454Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:46:30.155454Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DefKsUseggip3k1MASkBEsjrsuXuqjiilI6saWr3cvLo9UL5JfdfgdornksY85VEeQM7+L+GhcIDt77J80IqDA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:46:30.156079Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.10365","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3154ad5dfeaac9e6454134401b48fc8675a7f7af90a10a39108d59b647a12062","sha256:69691b8888725b59a7f1414481bf11fd7d5e1d867a41e8c582e64ba927f2db5f"],"state_sha256":"da9cbfe27a4acba60da8cf69f629c7b6448b975aca3adfc45a4f419dd3f2b981"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cG+dNy5G1zSHm1yokJISv+MGsrWj72YpKj5lXWeShEEQZjwVJzixboGytxzEBbkQvTYr1U03dByUGju6i+BxCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T15:22:25.033658Z","bundle_sha256":"65de48c49c291e29fe902a763e107f43977e4c336d5571d9f52ccc62ae3264de"}}