{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:ZTMOTBI6ZH47MLMMZQYDBUOQ5I","short_pith_number":"pith:ZTMOTBI6","canonical_record":{"source":{"id":"2105.09879","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2021-05-20T16:25:47Z","cross_cats_sorted":[],"title_canon_sha256":"6fe86a61e262c015c8becb0f51869cad67f94eb6c2b74876e2ae1ea6f5f196db","abstract_canon_sha256":"d0929b3ff08e3ae63d949525097e8201aaa88cc5a131b65cbd7e04226b26881e"},"schema_version":"1.0"},"canonical_sha256":"ccd8e9851ec9f9f62d8ccc3030d1d0ea1fb092de4a88cdb7ef26ea78227c89ca","source":{"kind":"arxiv","id":"2105.09879","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2105.09879","created_at":"2026-07-05T10:50:39Z"},{"alias_kind":"arxiv_version","alias_value":"2105.09879v2","created_at":"2026-07-05T10:50:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2105.09879","created_at":"2026-07-05T10:50:39Z"},{"alias_kind":"pith_short_12","alias_value":"ZTMOTBI6ZH47","created_at":"2026-07-05T10:50:39Z"},{"alias_kind":"pith_short_16","alias_value":"ZTMOTBI6ZH47MLMM","created_at":"2026-07-05T10:50:39Z"},{"alias_kind":"pith_short_8","alias_value":"ZTMOTBI6","created_at":"2026-07-05T10:50:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:ZTMOTBI6ZH47MLMMZQYDBUOQ5I","target":"record","payload":{"canonical_record":{"source":{"id":"2105.09879","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2021-05-20T16:25:47Z","cross_cats_sorted":[],"title_canon_sha256":"6fe86a61e262c015c8becb0f51869cad67f94eb6c2b74876e2ae1ea6f5f196db","abstract_canon_sha256":"d0929b3ff08e3ae63d949525097e8201aaa88cc5a131b65cbd7e04226b26881e"},"schema_version":"1.0"},"canonical_sha256":"ccd8e9851ec9f9f62d8ccc3030d1d0ea1fb092de4a88cdb7ef26ea78227c89ca","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:50:39.297968Z","signature_b64":"l6Qglj1OJXPpGaXPht1P7kp/kA3JYyonbxeLsQxLtwIsHp27BQv0KmgDeG08rRZL4LFRYBfGf8RbwZhz6K1bBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ccd8e9851ec9f9f62d8ccc3030d1d0ea1fb092de4a88cdb7ef26ea78227c89ca","last_reissued_at":"2026-07-05T10:50:39.297482Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:50:39.297482Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2105.09879","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:50:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1v5imF/xhRk5lR3mFM5+Rg9nUex+4W1myytkZid2iryoC1KswKKRy79lBItWu/CPOU21t4cJ6+4qZgzyOxGbCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T08:04:01.094818Z"},"content_sha256":"802c70aced264db52a9c4a7f847f28b6e5ad65f08699583ed5b0ed9ec7c494da","schema_version":"1.0","event_id":"sha256:802c70aced264db52a9c4a7f847f28b6e5ad65f08699583ed5b0ed9ec7c494da"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:ZTMOTBI6ZH47MLMMZQYDBUOQ5I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the the critical exponent for the semilinear Euler-Poisson-Darboux-Tricomi equation with power nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alessandro Palmieri","submitted_at":"2021-05-20T16:25:47Z","abstract_excerpt":"In this note, we derive a blow-up result for a semilinear generalized Tricomi equation with damping and mass terms having time-dependent coefficients. We consider these coefficients with critical decay rates. Due to this threshold nature of the time-dependent coefficients (both for the damping and for the mass), the multiplicative constants appearing in these lower-order terms strongly influence the value of the critical exponent, determining a competition between a Fujita-type exponent and a Strauss-type exponent."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2105.09879","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2105.09879/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T10:50:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/xMK0+KW3TjfYYo4eFDS8a2PkqCGZvrVAQKM8icx9N2T6Y9fSXUCndfasEr9vz9X0PMo+pO4ubtmN+ctRCLyDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T08:04:01.095307Z"},"content_sha256":"ee0b5b123ec272cf1ac1faab4b461384f943b739f091501526cc9bcf7eea9a91","schema_version":"1.0","event_id":"sha256:ee0b5b123ec272cf1ac1faab4b461384f943b739f091501526cc9bcf7eea9a91"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZTMOTBI6ZH47MLMMZQYDBUOQ5I/bundle.json","state_url":"https://pith.science/pith/ZTMOTBI6ZH47MLMMZQYDBUOQ5I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZTMOTBI6ZH47MLMMZQYDBUOQ5I/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":"2026-08-13T08:04:01Z","links":{"resolver":"https://pith.science/pith/ZTMOTBI6ZH47MLMMZQYDBUOQ5I","bundle":"https://pith.science/pith/ZTMOTBI6ZH47MLMMZQYDBUOQ5I/bundle.json","state":"https://pith.science/pith/ZTMOTBI6ZH47MLMMZQYDBUOQ5I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZTMOTBI6ZH47MLMMZQYDBUOQ5I/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:ZTMOTBI6ZH47MLMMZQYDBUOQ5I","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":"d0929b3ff08e3ae63d949525097e8201aaa88cc5a131b65cbd7e04226b26881e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2021-05-20T16:25:47Z","title_canon_sha256":"6fe86a61e262c015c8becb0f51869cad67f94eb6c2b74876e2ae1ea6f5f196db"},"schema_version":"1.0","source":{"id":"2105.09879","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2105.09879","created_at":"2026-07-05T10:50:39Z"},{"alias_kind":"arxiv_version","alias_value":"2105.09879v2","created_at":"2026-07-05T10:50:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2105.09879","created_at":"2026-07-05T10:50:39Z"},{"alias_kind":"pith_short_12","alias_value":"ZTMOTBI6ZH47","created_at":"2026-07-05T10:50:39Z"},{"alias_kind":"pith_short_16","alias_value":"ZTMOTBI6ZH47MLMM","created_at":"2026-07-05T10:50:39Z"},{"alias_kind":"pith_short_8","alias_value":"ZTMOTBI6","created_at":"2026-07-05T10:50:39Z"}],"graph_snapshots":[{"event_id":"sha256:ee0b5b123ec272cf1ac1faab4b461384f943b739f091501526cc9bcf7eea9a91","target":"graph","created_at":"2026-07-05T10:50:39Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2105.09879/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this note, we derive a blow-up result for a semilinear generalized Tricomi equation with damping and mass terms having time-dependent coefficients. We consider these coefficients with critical decay rates. Due to this threshold nature of the time-dependent coefficients (both for the damping and for the mass), the multiplicative constants appearing in these lower-order terms strongly influence the value of the critical exponent, determining a competition between a Fujita-type exponent and a Strauss-type exponent.","authors_text":"Alessandro Palmieri","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2021-05-20T16:25:47Z","title":"On the the critical exponent for the semilinear Euler-Poisson-Darboux-Tricomi equation with power nonlinearity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2105.09879","kind":"arxiv","version":2},"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":"sha256:802c70aced264db52a9c4a7f847f28b6e5ad65f08699583ed5b0ed9ec7c494da","target":"record","created_at":"2026-07-05T10:50:39Z","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":"d0929b3ff08e3ae63d949525097e8201aaa88cc5a131b65cbd7e04226b26881e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2021-05-20T16:25:47Z","title_canon_sha256":"6fe86a61e262c015c8becb0f51869cad67f94eb6c2b74876e2ae1ea6f5f196db"},"schema_version":"1.0","source":{"id":"2105.09879","kind":"arxiv","version":2}},"canonical_sha256":"ccd8e9851ec9f9f62d8ccc3030d1d0ea1fb092de4a88cdb7ef26ea78227c89ca","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ccd8e9851ec9f9f62d8ccc3030d1d0ea1fb092de4a88cdb7ef26ea78227c89ca","first_computed_at":"2026-07-05T10:50:39.297482Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:50:39.297482Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"l6Qglj1OJXPpGaXPht1P7kp/kA3JYyonbxeLsQxLtwIsHp27BQv0KmgDeG08rRZL4LFRYBfGf8RbwZhz6K1bBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T10:50:39.297968Z","signed_message":"canonical_sha256_bytes"},"source_id":"2105.09879","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:802c70aced264db52a9c4a7f847f28b6e5ad65f08699583ed5b0ed9ec7c494da","sha256:ee0b5b123ec272cf1ac1faab4b461384f943b739f091501526cc9bcf7eea9a91"],"state_sha256":"2efbcaa5369807026889754b5154a2703bd6c9bbed1ad22bfa7e94c428644c46"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ygjsPc82AHXybHuqz/A0bo9Q+JlG32+m6tRWphpXxX2j9TyYAc5m+bLggGnTu8MA4N0mHXKNFdPSNRzLFZqsCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T08:04:01.098275Z","bundle_sha256":"359bc1043417a1159d8c05c801ece58f078f652621433b34619f7dc1b134aacc"}}