{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:PBWIJGQTJEGWH46LMCIQ6IK4OH","short_pith_number":"pith:PBWIJGQT","canonical_record":{"source":{"id":"1402.0113","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-02-01T19:11:00Z","cross_cats_sorted":[],"title_canon_sha256":"6bf262e204119fab915f97c9b37bd8784603e6231cb845ccc85b674b69c1bfab","abstract_canon_sha256":"06b3cdb272ce93836de03effca5674c0a8e31e8f68e3e39a91ff87232284ff7e"},"schema_version":"1.0"},"canonical_sha256":"786c849a13490d63f3cb60910f215c71d5473f5658be4c9853db7541c9a27cd7","source":{"kind":"arxiv","id":"1402.0113","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.0113","created_at":"2026-05-18T03:00:24Z"},{"alias_kind":"arxiv_version","alias_value":"1402.0113v1","created_at":"2026-05-18T03:00:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.0113","created_at":"2026-05-18T03:00:24Z"},{"alias_kind":"pith_short_12","alias_value":"PBWIJGQTJEGW","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"PBWIJGQTJEGWH46L","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"PBWIJGQT","created_at":"2026-05-18T12:28:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:PBWIJGQTJEGWH46LMCIQ6IK4OH","target":"record","payload":{"canonical_record":{"source":{"id":"1402.0113","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-02-01T19:11:00Z","cross_cats_sorted":[],"title_canon_sha256":"6bf262e204119fab915f97c9b37bd8784603e6231cb845ccc85b674b69c1bfab","abstract_canon_sha256":"06b3cdb272ce93836de03effca5674c0a8e31e8f68e3e39a91ff87232284ff7e"},"schema_version":"1.0"},"canonical_sha256":"786c849a13490d63f3cb60910f215c71d5473f5658be4c9853db7541c9a27cd7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:00:24.708400Z","signature_b64":"N1QUGrPvlCxfrUUT/s65QSrTnd2HqpVI7SOohXe9N5H+dF4vIThV9dEabJ+pD8f6x0VsvGID4ZSfBjQOi0o8CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"786c849a13490d63f3cb60910f215c71d5473f5658be4c9853db7541c9a27cd7","last_reissued_at":"2026-05-18T03:00:24.707531Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:00:24.707531Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1402.0113","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":"2026-05-18T03:00:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DJF7P61lxp/UCULfWcoVdcDEbKDJ9OAXd6mgl6VvZSZDb9+QEZStMLfhwLMfobUr2K66qOyLyEgp51/uKodACg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T06:52:20.803596Z"},"content_sha256":"7852fefbc6fc310a0a37a7f07a97b80680c2435b7434f382a7af7f34f09f54cb","schema_version":"1.0","event_id":"sha256:7852fefbc6fc310a0a37a7f07a97b80680c2435b7434f382a7af7f34f09f54cb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:PBWIJGQTJEGWH46LMCIQ6IK4OH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Pointwise Bounds and Blow-up for Systems of Semilinear Elliptic Inequalities at an Isolated Singularity via Nonlinear Potential Estimates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Igor E. Verbitsky, Marius Ghergu, Steven D. Taliaferro","submitted_at":"2014-02-01T19:11:00Z","abstract_excerpt":"We study the behavior near the origin of $C^2$ positive solutions $u(x)$ and $v(x)$ of the system\n  $0\\leq -\\Delta u\\leq f(v)$\n  $0\\leq -\\Delta v\\leq g(u)$ in $B_1(0)\\backslash\\{0\\}$ where $f,g:(0,\\infty)\\to (0,\\infty)$ are continuous functions. We provide optimal conditions on $f$ and $g$ at $\\infty$ such that solutions of this system satisfy pointwise bounds near the origin. In dimension $n=2$ we show that this property holds if $\\log^+ f$ or $\\log^+g$ grow at most linearly at infinity. In dimension $n\\geq 3$ and under the assumption $f(t)=O(t^\\lambda)$, $g(t)=O(t^\\sigma)$ as $t\\to \\infty$, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.0113","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":"2026-05-18T03:00:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IAdAcKYpRm1V9LtHxmj6l13am+AcebEQ+DkBDL0GRMwH0HkNH9u9nTAu2Fa85uXDcczTeZjs1qCjraBeX4JBAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T06:52:20.804255Z"},"content_sha256":"e1c2a0a6bf7fe5d7120afb7586c5f4fd0b8495727bad6ef04b79e38d462a330b","schema_version":"1.0","event_id":"sha256:e1c2a0a6bf7fe5d7120afb7586c5f4fd0b8495727bad6ef04b79e38d462a330b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PBWIJGQTJEGWH46LMCIQ6IK4OH/bundle.json","state_url":"https://pith.science/pith/PBWIJGQTJEGWH46LMCIQ6IK4OH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PBWIJGQTJEGWH46LMCIQ6IK4OH/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":"2026-05-27T06:52:20Z","links":{"resolver":"https://pith.science/pith/PBWIJGQTJEGWH46LMCIQ6IK4OH","bundle":"https://pith.science/pith/PBWIJGQTJEGWH46LMCIQ6IK4OH/bundle.json","state":"https://pith.science/pith/PBWIJGQTJEGWH46LMCIQ6IK4OH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PBWIJGQTJEGWH46LMCIQ6IK4OH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:PBWIJGQTJEGWH46LMCIQ6IK4OH","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":"06b3cdb272ce93836de03effca5674c0a8e31e8f68e3e39a91ff87232284ff7e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-02-01T19:11:00Z","title_canon_sha256":"6bf262e204119fab915f97c9b37bd8784603e6231cb845ccc85b674b69c1bfab"},"schema_version":"1.0","source":{"id":"1402.0113","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.0113","created_at":"2026-05-18T03:00:24Z"},{"alias_kind":"arxiv_version","alias_value":"1402.0113v1","created_at":"2026-05-18T03:00:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.0113","created_at":"2026-05-18T03:00:24Z"},{"alias_kind":"pith_short_12","alias_value":"PBWIJGQTJEGW","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"PBWIJGQTJEGWH46L","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"PBWIJGQT","created_at":"2026-05-18T12:28:43Z"}],"graph_snapshots":[{"event_id":"sha256:e1c2a0a6bf7fe5d7120afb7586c5f4fd0b8495727bad6ef04b79e38d462a330b","target":"graph","created_at":"2026-05-18T03:00:24Z","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 behavior near the origin of $C^2$ positive solutions $u(x)$ and $v(x)$ of the system\n  $0\\leq -\\Delta u\\leq f(v)$\n  $0\\leq -\\Delta v\\leq g(u)$ in $B_1(0)\\backslash\\{0\\}$ where $f,g:(0,\\infty)\\to (0,\\infty)$ are continuous functions. We provide optimal conditions on $f$ and $g$ at $\\infty$ such that solutions of this system satisfy pointwise bounds near the origin. In dimension $n=2$ we show that this property holds if $\\log^+ f$ or $\\log^+g$ grow at most linearly at infinity. In dimension $n\\geq 3$ and under the assumption $f(t)=O(t^\\lambda)$, $g(t)=O(t^\\sigma)$ as $t\\to \\infty$, ","authors_text":"Igor E. Verbitsky, Marius Ghergu, Steven D. Taliaferro","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-02-01T19:11:00Z","title":"Pointwise Bounds and Blow-up for Systems of Semilinear Elliptic Inequalities at an Isolated Singularity via Nonlinear Potential Estimates"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.0113","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":"sha256:7852fefbc6fc310a0a37a7f07a97b80680c2435b7434f382a7af7f34f09f54cb","target":"record","created_at":"2026-05-18T03:00:24Z","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":"06b3cdb272ce93836de03effca5674c0a8e31e8f68e3e39a91ff87232284ff7e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-02-01T19:11:00Z","title_canon_sha256":"6bf262e204119fab915f97c9b37bd8784603e6231cb845ccc85b674b69c1bfab"},"schema_version":"1.0","source":{"id":"1402.0113","kind":"arxiv","version":1}},"canonical_sha256":"786c849a13490d63f3cb60910f215c71d5473f5658be4c9853db7541c9a27cd7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"786c849a13490d63f3cb60910f215c71d5473f5658be4c9853db7541c9a27cd7","first_computed_at":"2026-05-18T03:00:24.707531Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:00:24.707531Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"N1QUGrPvlCxfrUUT/s65QSrTnd2HqpVI7SOohXe9N5H+dF4vIThV9dEabJ+pD8f6x0VsvGID4ZSfBjQOi0o8CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:00:24.708400Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.0113","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7852fefbc6fc310a0a37a7f07a97b80680c2435b7434f382a7af7f34f09f54cb","sha256:e1c2a0a6bf7fe5d7120afb7586c5f4fd0b8495727bad6ef04b79e38d462a330b"],"state_sha256":"139ccbfdc74d7c49bd937751eaf03545e4c11e7cf293139504ac8c5b96800dc9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hhMZtxx5gRSMQtOY9qR8EaboyaQ29jkUXmxrXvaTNqnEN2HVCky6ghDR1zpiXXkcDTu3KmHGavt47rZRQcB3DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T06:52:20.807808Z","bundle_sha256":"9ddc973fc78077786649b2a4c3a96fc923bd0bf5de676a4002cc610cd2b14967"}}