{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:GKXIYQJG7OVZHW7HTCV2YMMCI3","short_pith_number":"pith:GKXIYQJG","canonical_record":{"source":{"id":"1610.00964","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-04T13:01:03Z","cross_cats_sorted":[],"title_canon_sha256":"c9816f7c1d9ea15e1f25c2ca467de52a1b8aab6e79a032b01adc948ed2e45637","abstract_canon_sha256":"16ffb06439705f6d6b3509c2a565641460b3c5849b3688b046f1824f5d9af672"},"schema_version":"1.0"},"canonical_sha256":"32ae8c4126fbab93dbe798abac318246c8bfb8b79bd172bcb67ff6ac079258e2","source":{"kind":"arxiv","id":"1610.00964","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.00964","created_at":"2026-05-18T00:21:57Z"},{"alias_kind":"arxiv_version","alias_value":"1610.00964v3","created_at":"2026-05-18T00:21:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.00964","created_at":"2026-05-18T00:21:57Z"},{"alias_kind":"pith_short_12","alias_value":"GKXIYQJG7OVZ","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"GKXIYQJG7OVZHW7H","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"GKXIYQJG","created_at":"2026-05-18T12:30:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:GKXIYQJG7OVZHW7HTCV2YMMCI3","target":"record","payload":{"canonical_record":{"source":{"id":"1610.00964","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-04T13:01:03Z","cross_cats_sorted":[],"title_canon_sha256":"c9816f7c1d9ea15e1f25c2ca467de52a1b8aab6e79a032b01adc948ed2e45637","abstract_canon_sha256":"16ffb06439705f6d6b3509c2a565641460b3c5849b3688b046f1824f5d9af672"},"schema_version":"1.0"},"canonical_sha256":"32ae8c4126fbab93dbe798abac318246c8bfb8b79bd172bcb67ff6ac079258e2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:21:57.194768Z","signature_b64":"uX7h1O25iXyIZBkAwslZaiKkVyXSVFEpr9UWeU2zNxfn1F4Uw0074fcORZ1kWLWKwOSZcC7YjJSZBFlfWgIlBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"32ae8c4126fbab93dbe798abac318246c8bfb8b79bd172bcb67ff6ac079258e2","last_reissued_at":"2026-05-18T00:21:57.194074Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:21:57.194074Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.00964","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:21:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gbU3xhWuQ78rCpdYLEB84//Cu+9uszF4Bluy+4VBdKonl1PXf+PoTa5vQ80ZevLZx9a1DMDknZS4qHcEAdMJDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T23:48:12.001948Z"},"content_sha256":"0259742ddd1e45e8c03d63b39bb11920e9a8a048164b463098413dc880274cd1","schema_version":"1.0","event_id":"sha256:0259742ddd1e45e8c03d63b39bb11920e9a8a048164b463098413dc880274cd1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:GKXIYQJG7OVZHW7HTCV2YMMCI3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A loop type component in the non-negative solutions set of an indefinite elliptic problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Humberto Ramos Quoirin, Kenichiro Umezu","submitted_at":"2016-10-04T13:01:03Z","abstract_excerpt":"We prove the existence of a loop type component of non-negative solutions for an indefinite elliptic equation with homogeneous Neumann boundary conditions. This result complements our previous results obtained in [12], where the existence of another loop type component was established in a different situation. Our proof combines local and global bifurcation theory, rescaling and regularizing arguments, a priori bounds, and Whyburn's topological method. A further investigation of the loop type component established in [12] is also provided."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.00964","kind":"arxiv","version":3},"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":"2026-05-18T00:21:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l3AfbHa/loYaXPZTLlVva1GpXhcAR05s8XedppaS/PrD7fqicXxGksh/KFsDMjFoOgbSpT/ZY/ncaD71WP4FAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T23:48:12.002277Z"},"content_sha256":"c6ceb92d1d3c8feb3d1323947be7fdc08e8108c4c39b96f08b06d48054643746","schema_version":"1.0","event_id":"sha256:c6ceb92d1d3c8feb3d1323947be7fdc08e8108c4c39b96f08b06d48054643746"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GKXIYQJG7OVZHW7HTCV2YMMCI3/bundle.json","state_url":"https://pith.science/pith/GKXIYQJG7OVZHW7HTCV2YMMCI3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GKXIYQJG7OVZHW7HTCV2YMMCI3/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":"2026-06-26T23:48:12Z","links":{"resolver":"https://pith.science/pith/GKXIYQJG7OVZHW7HTCV2YMMCI3","bundle":"https://pith.science/pith/GKXIYQJG7OVZHW7HTCV2YMMCI3/bundle.json","state":"https://pith.science/pith/GKXIYQJG7OVZHW7HTCV2YMMCI3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GKXIYQJG7OVZHW7HTCV2YMMCI3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:GKXIYQJG7OVZHW7HTCV2YMMCI3","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":"16ffb06439705f6d6b3509c2a565641460b3c5849b3688b046f1824f5d9af672","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-04T13:01:03Z","title_canon_sha256":"c9816f7c1d9ea15e1f25c2ca467de52a1b8aab6e79a032b01adc948ed2e45637"},"schema_version":"1.0","source":{"id":"1610.00964","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.00964","created_at":"2026-05-18T00:21:57Z"},{"alias_kind":"arxiv_version","alias_value":"1610.00964v3","created_at":"2026-05-18T00:21:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.00964","created_at":"2026-05-18T00:21:57Z"},{"alias_kind":"pith_short_12","alias_value":"GKXIYQJG7OVZ","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"GKXIYQJG7OVZHW7H","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"GKXIYQJG","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:c6ceb92d1d3c8feb3d1323947be7fdc08e8108c4c39b96f08b06d48054643746","target":"graph","created_at":"2026-05-18T00:21:57Z","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 the existence of a loop type component of non-negative solutions for an indefinite elliptic equation with homogeneous Neumann boundary conditions. This result complements our previous results obtained in [12], where the existence of another loop type component was established in a different situation. Our proof combines local and global bifurcation theory, rescaling and regularizing arguments, a priori bounds, and Whyburn's topological method. A further investigation of the loop type component established in [12] is also provided.","authors_text":"Humberto Ramos Quoirin, Kenichiro Umezu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-04T13:01:03Z","title":"A loop type component in the non-negative solutions set of an indefinite elliptic problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.00964","kind":"arxiv","version":3},"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":"sha256:0259742ddd1e45e8c03d63b39bb11920e9a8a048164b463098413dc880274cd1","target":"record","created_at":"2026-05-18T00:21:57Z","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":"16ffb06439705f6d6b3509c2a565641460b3c5849b3688b046f1824f5d9af672","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-04T13:01:03Z","title_canon_sha256":"c9816f7c1d9ea15e1f25c2ca467de52a1b8aab6e79a032b01adc948ed2e45637"},"schema_version":"1.0","source":{"id":"1610.00964","kind":"arxiv","version":3}},"canonical_sha256":"32ae8c4126fbab93dbe798abac318246c8bfb8b79bd172bcb67ff6ac079258e2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"32ae8c4126fbab93dbe798abac318246c8bfb8b79bd172bcb67ff6ac079258e2","first_computed_at":"2026-05-18T00:21:57.194074Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:21:57.194074Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uX7h1O25iXyIZBkAwslZaiKkVyXSVFEpr9UWeU2zNxfn1F4Uw0074fcORZ1kWLWKwOSZcC7YjJSZBFlfWgIlBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:21:57.194768Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.00964","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0259742ddd1e45e8c03d63b39bb11920e9a8a048164b463098413dc880274cd1","sha256:c6ceb92d1d3c8feb3d1323947be7fdc08e8108c4c39b96f08b06d48054643746"],"state_sha256":"09cfc1aa9934c0040416fc7c44a3acf216e0d1aec729573002db875a1c583c7e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o8uk0hJ2Vukeb+7LjGS9rJ8EcRRU/sZHDI2G2R0H3OaRX6LO+9yAm5q/82ksK7fmInJC5kC2pYQKQHk89sNeAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T23:48:12.004115Z","bundle_sha256":"66829a19bf1de2b26ba2f98a33651389fc7fac0315dd98866ee5ba243c27153f"}}