{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:OG34CU76PWY2DJSHL3ATIFRTUV","short_pith_number":"pith:OG34CU76","canonical_record":{"source":{"id":"1401.4549","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-01-18T15:45:38Z","cross_cats_sorted":[],"title_canon_sha256":"38edc53bf49ee5a97b5fe6fba4abf9f11985b2a05ad92e79fe442893488275f0","abstract_canon_sha256":"80e853742dac8d9765a0be92a1d49a590390ab7fb3715b989bd81afe7473d20c"},"schema_version":"1.0"},"canonical_sha256":"71b7c153fe7db1a1a6475ec1341633a55ca21f20af0250bb4304012c0a3c980c","source":{"kind":"arxiv","id":"1401.4549","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.4549","created_at":"2026-05-18T03:01:45Z"},{"alias_kind":"arxiv_version","alias_value":"1401.4549v1","created_at":"2026-05-18T03:01:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.4549","created_at":"2026-05-18T03:01:45Z"},{"alias_kind":"pith_short_12","alias_value":"OG34CU76PWY2","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"OG34CU76PWY2DJSH","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"OG34CU76","created_at":"2026-05-18T12:28:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:OG34CU76PWY2DJSHL3ATIFRTUV","target":"record","payload":{"canonical_record":{"source":{"id":"1401.4549","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-01-18T15:45:38Z","cross_cats_sorted":[],"title_canon_sha256":"38edc53bf49ee5a97b5fe6fba4abf9f11985b2a05ad92e79fe442893488275f0","abstract_canon_sha256":"80e853742dac8d9765a0be92a1d49a590390ab7fb3715b989bd81afe7473d20c"},"schema_version":"1.0"},"canonical_sha256":"71b7c153fe7db1a1a6475ec1341633a55ca21f20af0250bb4304012c0a3c980c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:01:45.477624Z","signature_b64":"25VupSvJu/kuYiwsfbj4ymAbRvSz1k5UsFK2GKIVmcgKyeG2XIWA0/iqkNSTrC4hoA4AgdafX3/aAWyx1jBwCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"71b7c153fe7db1a1a6475ec1341633a55ca21f20af0250bb4304012c0a3c980c","last_reissued_at":"2026-05-18T03:01:45.477100Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:01:45.477100Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1401.4549","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":"2026-05-18T03:01:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jb6O1nJQqCd++t1E4szwftDBf7wMK+AUlmsg/DOlaOn/LpTwBN4H0Pu9xgM/t/KIuKeuHDdoaqM8oK+nHGrTBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T01:25:27.957523Z"},"content_sha256":"cbdafdae834104b5c43933aa48fabaf818eca50f7eb917bda2533d34f2aba344","schema_version":"1.0","event_id":"sha256:cbdafdae834104b5c43933aa48fabaf818eca50f7eb917bda2533d34f2aba344"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:OG34CU76PWY2DJSHL3ATIFRTUV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Non-stability of Paneitz-Branson equations in arbitrary dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jean-Baptiste Cast\\'eras, Laurent Bakri","submitted_at":"2014-01-18T15:45:38Z","abstract_excerpt":"Let $(M,g)$ be a compact riemannian manifold of dimension $n\\geq 5$. We are interested in the stability of a slighly subcritical Paneitz-Branson type equation on $M$. Assuming that there exists a positive nondegenerate solution of the critical equation and under suitable conditions, we prove that this equation is not stable for all $n\\geq 5$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.4549","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":"2026-05-18T03:01:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PQsjOJnqNETEkqYMnZ0urKhGZxP7wXDRjwTMWEhT1b8em3PqH6e5Du9UATCb6pRARgqxZstFDJpgb7kTwA/OCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T01:25:27.958281Z"},"content_sha256":"d16cf097396e4a31b0bd9afdf07db7e113660f6f8ba3eeedb24092a5218faa91","schema_version":"1.0","event_id":"sha256:d16cf097396e4a31b0bd9afdf07db7e113660f6f8ba3eeedb24092a5218faa91"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OG34CU76PWY2DJSHL3ATIFRTUV/bundle.json","state_url":"https://pith.science/pith/OG34CU76PWY2DJSHL3ATIFRTUV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OG34CU76PWY2DJSHL3ATIFRTUV/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":"2026-06-01T01:25:27Z","links":{"resolver":"https://pith.science/pith/OG34CU76PWY2DJSHL3ATIFRTUV","bundle":"https://pith.science/pith/OG34CU76PWY2DJSHL3ATIFRTUV/bundle.json","state":"https://pith.science/pith/OG34CU76PWY2DJSHL3ATIFRTUV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OG34CU76PWY2DJSHL3ATIFRTUV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:OG34CU76PWY2DJSHL3ATIFRTUV","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":"80e853742dac8d9765a0be92a1d49a590390ab7fb3715b989bd81afe7473d20c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-01-18T15:45:38Z","title_canon_sha256":"38edc53bf49ee5a97b5fe6fba4abf9f11985b2a05ad92e79fe442893488275f0"},"schema_version":"1.0","source":{"id":"1401.4549","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.4549","created_at":"2026-05-18T03:01:45Z"},{"alias_kind":"arxiv_version","alias_value":"1401.4549v1","created_at":"2026-05-18T03:01:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.4549","created_at":"2026-05-18T03:01:45Z"},{"alias_kind":"pith_short_12","alias_value":"OG34CU76PWY2","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"OG34CU76PWY2DJSH","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"OG34CU76","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:d16cf097396e4a31b0bd9afdf07db7e113660f6f8ba3eeedb24092a5218faa91","target":"graph","created_at":"2026-05-18T03:01:45Z","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":"Let $(M,g)$ be a compact riemannian manifold of dimension $n\\geq 5$. We are interested in the stability of a slighly subcritical Paneitz-Branson type equation on $M$. Assuming that there exists a positive nondegenerate solution of the critical equation and under suitable conditions, we prove that this equation is not stable for all $n\\geq 5$.","authors_text":"Jean-Baptiste Cast\\'eras, Laurent Bakri","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-01-18T15:45:38Z","title":"Non-stability of Paneitz-Branson equations in arbitrary dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.4549","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:cbdafdae834104b5c43933aa48fabaf818eca50f7eb917bda2533d34f2aba344","target":"record","created_at":"2026-05-18T03:01:45Z","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":"80e853742dac8d9765a0be92a1d49a590390ab7fb3715b989bd81afe7473d20c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-01-18T15:45:38Z","title_canon_sha256":"38edc53bf49ee5a97b5fe6fba4abf9f11985b2a05ad92e79fe442893488275f0"},"schema_version":"1.0","source":{"id":"1401.4549","kind":"arxiv","version":1}},"canonical_sha256":"71b7c153fe7db1a1a6475ec1341633a55ca21f20af0250bb4304012c0a3c980c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"71b7c153fe7db1a1a6475ec1341633a55ca21f20af0250bb4304012c0a3c980c","first_computed_at":"2026-05-18T03:01:45.477100Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:01:45.477100Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"25VupSvJu/kuYiwsfbj4ymAbRvSz1k5UsFK2GKIVmcgKyeG2XIWA0/iqkNSTrC4hoA4AgdafX3/aAWyx1jBwCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:01:45.477624Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.4549","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cbdafdae834104b5c43933aa48fabaf818eca50f7eb917bda2533d34f2aba344","sha256:d16cf097396e4a31b0bd9afdf07db7e113660f6f8ba3eeedb24092a5218faa91"],"state_sha256":"411a5a0d91f2c3da3d68742cad1aa1742b12aef3618cc12c163173f4d4604409"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5ENzW9rmNGtUFupdTo+UiebvbKn+9rLHKRQQk5AO52qtm4dpMLoT1SDnrTJhq3FKbIjv5Mo2aLRRBMnoHLQ0Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T01:25:27.961835Z","bundle_sha256":"a76180e10074bcd5058f720a1821dc78108a2cdb47abfb0e0bf2f1be75b00a58"}}