{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:R7RDSVR2PQZYTAB5QAWY5CIN7T","short_pith_number":"pith:R7RDSVR2","canonical_record":{"source":{"id":"1810.12363","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-10-29T19:11:49Z","cross_cats_sorted":[],"title_canon_sha256":"7dba51d9935b1077072920e3b51b163d3fafbae667790cc7b5078cfa2163a8f4","abstract_canon_sha256":"c84cda09af99aca546606a4bc0b3ff78465869d602a2e4f00b819ee94c5ae83f"},"schema_version":"1.0"},"canonical_sha256":"8fe239563a7c3389803d802d8e890dfcd840bd483ae5a7410948fae504b90d69","source":{"kind":"arxiv","id":"1810.12363","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.12363","created_at":"2026-05-18T00:02:02Z"},{"alias_kind":"arxiv_version","alias_value":"1810.12363v1","created_at":"2026-05-18T00:02:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.12363","created_at":"2026-05-18T00:02:02Z"},{"alias_kind":"pith_short_12","alias_value":"R7RDSVR2PQZY","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"R7RDSVR2PQZYTAB5","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"R7RDSVR2","created_at":"2026-05-18T12:32:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:R7RDSVR2PQZYTAB5QAWY5CIN7T","target":"record","payload":{"canonical_record":{"source":{"id":"1810.12363","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-10-29T19:11:49Z","cross_cats_sorted":[],"title_canon_sha256":"7dba51d9935b1077072920e3b51b163d3fafbae667790cc7b5078cfa2163a8f4","abstract_canon_sha256":"c84cda09af99aca546606a4bc0b3ff78465869d602a2e4f00b819ee94c5ae83f"},"schema_version":"1.0"},"canonical_sha256":"8fe239563a7c3389803d802d8e890dfcd840bd483ae5a7410948fae504b90d69","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:02.911897Z","signature_b64":"cb5cyKBlwmKi2OFAhdEUANuG0UsDoOhVpQFLUcsqD8ZEgLlR30On/k1cXUc6d1YwZMJyfbxcF+iaLlCbNUCiAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8fe239563a7c3389803d802d8e890dfcd840bd483ae5a7410948fae504b90d69","last_reissued_at":"2026-05-18T00:02:02.911356Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:02.911356Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.12363","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":"2026-05-18T00:02:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vQJqbq5WYZK0eRdlbTrGmdQMZiLHZzxKB6aKidaO582mqxy7ybYLDb9q/AvZMkJ59JAdoHe0/eSJO13buEm9BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T21:57:04.911360Z"},"content_sha256":"83de61bd0f32462f455ed99b324fc09f25a5a4a1b7a3fa5f30f2f3d76aa10e9e","schema_version":"1.0","event_id":"sha256:83de61bd0f32462f455ed99b324fc09f25a5a4a1b7a3fa5f30f2f3d76aa10e9e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:R7RDSVR2PQZYTAB5QAWY5CIN7T","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Linear instability and nondegeneracy of ground state for combined power-type nonlinear scalar field equations with the Sobolev critical exponent and large frequency parameter","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hiroaki Kikuchi, Slim Ibrahim, Takafumi Akahori","submitted_at":"2018-10-29T19:11:49Z","abstract_excerpt":"We consider combined power-type nonlinear scalar field equations with the Sobolev critical exponent. In \\cite{AIKN3}, it was shown that if the frequency parameter is sufficiently small, then the positive ground state is nondegenerate and linearly unstable, together with an application to a study of global dynamics for nonlinear Schr\\\"odinger equations. In this paper, we prove the nondegeneracy and linear instability of the ground state frequency for sufficiently large frequency parameters. Moreover, we show that the derivative of the mass of ground state with respect to the frequency is negati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.12363","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":"2026-05-18T00:02:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L29oxwTQC+Oxb3H7C8G0WJIQ3Zx5kZmLSzkHEKzEw8D/I4Hn5pgYvj9UlSbyhEUSBHyjCCjne97tiP6a/yZLBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T21:57:04.911718Z"},"content_sha256":"d4f226e86471a12500c076a10e2d1959003ea4835e787372ce374526c7bb6c9c","schema_version":"1.0","event_id":"sha256:d4f226e86471a12500c076a10e2d1959003ea4835e787372ce374526c7bb6c9c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/R7RDSVR2PQZYTAB5QAWY5CIN7T/bundle.json","state_url":"https://pith.science/pith/R7RDSVR2PQZYTAB5QAWY5CIN7T/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/R7RDSVR2PQZYTAB5QAWY5CIN7T/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":"2026-06-02T21:57:04Z","links":{"resolver":"https://pith.science/pith/R7RDSVR2PQZYTAB5QAWY5CIN7T","bundle":"https://pith.science/pith/R7RDSVR2PQZYTAB5QAWY5CIN7T/bundle.json","state":"https://pith.science/pith/R7RDSVR2PQZYTAB5QAWY5CIN7T/state.json","well_known_bundle":"https://pith.science/.well-known/pith/R7RDSVR2PQZYTAB5QAWY5CIN7T/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:R7RDSVR2PQZYTAB5QAWY5CIN7T","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":"c84cda09af99aca546606a4bc0b3ff78465869d602a2e4f00b819ee94c5ae83f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-10-29T19:11:49Z","title_canon_sha256":"7dba51d9935b1077072920e3b51b163d3fafbae667790cc7b5078cfa2163a8f4"},"schema_version":"1.0","source":{"id":"1810.12363","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.12363","created_at":"2026-05-18T00:02:02Z"},{"alias_kind":"arxiv_version","alias_value":"1810.12363v1","created_at":"2026-05-18T00:02:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.12363","created_at":"2026-05-18T00:02:02Z"},{"alias_kind":"pith_short_12","alias_value":"R7RDSVR2PQZY","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"R7RDSVR2PQZYTAB5","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"R7RDSVR2","created_at":"2026-05-18T12:32:50Z"}],"graph_snapshots":[{"event_id":"sha256:d4f226e86471a12500c076a10e2d1959003ea4835e787372ce374526c7bb6c9c","target":"graph","created_at":"2026-05-18T00:02:02Z","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 consider combined power-type nonlinear scalar field equations with the Sobolev critical exponent. In \\cite{AIKN3}, it was shown that if the frequency parameter is sufficiently small, then the positive ground state is nondegenerate and linearly unstable, together with an application to a study of global dynamics for nonlinear Schr\\\"odinger equations. In this paper, we prove the nondegeneracy and linear instability of the ground state frequency for sufficiently large frequency parameters. Moreover, we show that the derivative of the mass of ground state with respect to the frequency is negati","authors_text":"Hiroaki Kikuchi, Slim Ibrahim, Takafumi Akahori","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-10-29T19:11:49Z","title":"Linear instability and nondegeneracy of ground state for combined power-type nonlinear scalar field equations with the Sobolev critical exponent and large frequency parameter"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.12363","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":"sha256:83de61bd0f32462f455ed99b324fc09f25a5a4a1b7a3fa5f30f2f3d76aa10e9e","target":"record","created_at":"2026-05-18T00:02:02Z","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":"c84cda09af99aca546606a4bc0b3ff78465869d602a2e4f00b819ee94c5ae83f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-10-29T19:11:49Z","title_canon_sha256":"7dba51d9935b1077072920e3b51b163d3fafbae667790cc7b5078cfa2163a8f4"},"schema_version":"1.0","source":{"id":"1810.12363","kind":"arxiv","version":1}},"canonical_sha256":"8fe239563a7c3389803d802d8e890dfcd840bd483ae5a7410948fae504b90d69","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8fe239563a7c3389803d802d8e890dfcd840bd483ae5a7410948fae504b90d69","first_computed_at":"2026-05-18T00:02:02.911356Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:02:02.911356Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cb5cyKBlwmKi2OFAhdEUANuG0UsDoOhVpQFLUcsqD8ZEgLlR30On/k1cXUc6d1YwZMJyfbxcF+iaLlCbNUCiAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:02:02.911897Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.12363","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:83de61bd0f32462f455ed99b324fc09f25a5a4a1b7a3fa5f30f2f3d76aa10e9e","sha256:d4f226e86471a12500c076a10e2d1959003ea4835e787372ce374526c7bb6c9c"],"state_sha256":"28d49e25af78f7f4b5172a6606891701aea75c581b0bf8a73adabaf40e7d29a9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BBh+l6Lyz8FmDVU+DdVvXkXpNHSEkSdLvwc+c1VH/x9luCeOTRdYG9R87v5szunO7Ao0C1e33XVRyHmyJ02aAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T21:57:04.913673Z","bundle_sha256":"16f74ab1b58ad8192934be089c294813e5a12d645bd32cd74ccfafc740580b71"}}