{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:W6IOYNGVW77AP6LEMMYZM65JMG","short_pith_number":"pith:W6IOYNGV","canonical_record":{"source":{"id":"1607.08470","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-07-28T14:22:01Z","cross_cats_sorted":[],"title_canon_sha256":"353febb423c518a65631c8655e55d94a50fe07c7858fe84a24a5372df9e323c3","abstract_canon_sha256":"41b0d6775b2a0c8d8f9a1a1b414d9ee4ff93647f2e0444759116c53e98e97666"},"schema_version":"1.0"},"canonical_sha256":"b790ec34d5b7fe07f9646331967ba961b10bcd531a3fd7e5f8dc12e177b2e730","source":{"kind":"arxiv","id":"1607.08470","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.08470","created_at":"2026-05-18T01:10:19Z"},{"alias_kind":"arxiv_version","alias_value":"1607.08470v1","created_at":"2026-05-18T01:10:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.08470","created_at":"2026-05-18T01:10:19Z"},{"alias_kind":"pith_short_12","alias_value":"W6IOYNGVW77A","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"W6IOYNGVW77AP6LE","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"W6IOYNGV","created_at":"2026-05-18T12:30:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:W6IOYNGVW77AP6LEMMYZM65JMG","target":"record","payload":{"canonical_record":{"source":{"id":"1607.08470","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-07-28T14:22:01Z","cross_cats_sorted":[],"title_canon_sha256":"353febb423c518a65631c8655e55d94a50fe07c7858fe84a24a5372df9e323c3","abstract_canon_sha256":"41b0d6775b2a0c8d8f9a1a1b414d9ee4ff93647f2e0444759116c53e98e97666"},"schema_version":"1.0"},"canonical_sha256":"b790ec34d5b7fe07f9646331967ba961b10bcd531a3fd7e5f8dc12e177b2e730","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:19.087392Z","signature_b64":"7T7MaAe7xeD+EhhO8lYbao3yb8eV9HUIVK6WxWeTUu1Ow0cMb3M5Fh1JoMTp1sAtbaP7g2nVOTsFtZZs3fnXDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b790ec34d5b7fe07f9646331967ba961b10bcd531a3fd7e5f8dc12e177b2e730","last_reissued_at":"2026-05-18T01:10:19.086704Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:19.086704Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1607.08470","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":"2026-05-18T01:10:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AQGYinAaIskWl96BYcHfJDdaqJCjH6+U0ktdIV2tNTpoB730bX9PBDiOI8DXipigEWzSswLRkZUpw9g412L2AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T23:58:35.627847Z"},"content_sha256":"5b0bf0a28c726c5b16510d46e18e9cabf22406c59ec0ad72e61b376e11356ee9","schema_version":"1.0","event_id":"sha256:5b0bf0a28c726c5b16510d46e18e9cabf22406c59ec0ad72e61b376e11356ee9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:W6IOYNGVW77AP6LEMMYZM65JMG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nonexistence of stable solutions to quasilinear elliptic equations on Riemannian manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Berardino Sciunzi, Dario D. Monticelli, Fabio Punzo","submitted_at":"2016-07-28T14:22:01Z","abstract_excerpt":"We prove nonexistence of nontrivial, possibly sign changing, stable solutions to a class of quasilinear elliptic equations with a potential on Riemannian manifolds, under suitable weighted volume growth conditions on geodesic balls."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.08470","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":"2026-05-18T01:10:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CPKRcONqC+4pejVQy7XfFC7hSCQRQozZi+73qbY+x5/kKQyn5q69c6eqzJLQElxdfDutfstLm9Q2a3hYbhBUCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T23:58:35.628340Z"},"content_sha256":"6825d65e4aed5bda0e2245527bd762ee191e575bdfe0d121ca9b8cde77802546","schema_version":"1.0","event_id":"sha256:6825d65e4aed5bda0e2245527bd762ee191e575bdfe0d121ca9b8cde77802546"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/W6IOYNGVW77AP6LEMMYZM65JMG/bundle.json","state_url":"https://pith.science/pith/W6IOYNGVW77AP6LEMMYZM65JMG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/W6IOYNGVW77AP6LEMMYZM65JMG/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":"2026-05-22T23:58:35Z","links":{"resolver":"https://pith.science/pith/W6IOYNGVW77AP6LEMMYZM65JMG","bundle":"https://pith.science/pith/W6IOYNGVW77AP6LEMMYZM65JMG/bundle.json","state":"https://pith.science/pith/W6IOYNGVW77AP6LEMMYZM65JMG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/W6IOYNGVW77AP6LEMMYZM65JMG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:W6IOYNGVW77AP6LEMMYZM65JMG","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":"41b0d6775b2a0c8d8f9a1a1b414d9ee4ff93647f2e0444759116c53e98e97666","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-07-28T14:22:01Z","title_canon_sha256":"353febb423c518a65631c8655e55d94a50fe07c7858fe84a24a5372df9e323c3"},"schema_version":"1.0","source":{"id":"1607.08470","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.08470","created_at":"2026-05-18T01:10:19Z"},{"alias_kind":"arxiv_version","alias_value":"1607.08470v1","created_at":"2026-05-18T01:10:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.08470","created_at":"2026-05-18T01:10:19Z"},{"alias_kind":"pith_short_12","alias_value":"W6IOYNGVW77A","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"W6IOYNGVW77AP6LE","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"W6IOYNGV","created_at":"2026-05-18T12:30:48Z"}],"graph_snapshots":[{"event_id":"sha256:6825d65e4aed5bda0e2245527bd762ee191e575bdfe0d121ca9b8cde77802546","target":"graph","created_at":"2026-05-18T01:10:19Z","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 prove nonexistence of nontrivial, possibly sign changing, stable solutions to a class of quasilinear elliptic equations with a potential on Riemannian manifolds, under suitable weighted volume growth conditions on geodesic balls.","authors_text":"Berardino Sciunzi, Dario D. Monticelli, Fabio Punzo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-07-28T14:22:01Z","title":"Nonexistence of stable solutions to quasilinear elliptic equations on Riemannian manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.08470","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":"sha256:5b0bf0a28c726c5b16510d46e18e9cabf22406c59ec0ad72e61b376e11356ee9","target":"record","created_at":"2026-05-18T01:10:19Z","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":"41b0d6775b2a0c8d8f9a1a1b414d9ee4ff93647f2e0444759116c53e98e97666","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-07-28T14:22:01Z","title_canon_sha256":"353febb423c518a65631c8655e55d94a50fe07c7858fe84a24a5372df9e323c3"},"schema_version":"1.0","source":{"id":"1607.08470","kind":"arxiv","version":1}},"canonical_sha256":"b790ec34d5b7fe07f9646331967ba961b10bcd531a3fd7e5f8dc12e177b2e730","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b790ec34d5b7fe07f9646331967ba961b10bcd531a3fd7e5f8dc12e177b2e730","first_computed_at":"2026-05-18T01:10:19.086704Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:10:19.086704Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7T7MaAe7xeD+EhhO8lYbao3yb8eV9HUIVK6WxWeTUu1Ow0cMb3M5Fh1JoMTp1sAtbaP7g2nVOTsFtZZs3fnXDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:10:19.087392Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.08470","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5b0bf0a28c726c5b16510d46e18e9cabf22406c59ec0ad72e61b376e11356ee9","sha256:6825d65e4aed5bda0e2245527bd762ee191e575bdfe0d121ca9b8cde77802546"],"state_sha256":"035ef8be478111495e2224bf2708ee50f42c3d5f76e3f2935391f2effd9663bc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mRL7bqP4oOI1vDFRCP4jQbV2F59pQRpxEm2BWEVR93u+uUxBNGMzYZXB7pGODWcvE73wvrTosubU+AmnCxt2BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T23:58:35.631739Z","bundle_sha256":"ba2787a9ba052770d5c113bbab831302c104b940e1d4084f81af232472c56a93"}}