{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:WYDEP4UIA7MB4KZJES4DB4GU36","short_pith_number":"pith:WYDEP4UI","canonical_record":{"source":{"id":"1805.03497","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-05-09T13:17:25Z","cross_cats_sorted":[],"title_canon_sha256":"06e5786212b0bd39a30267412baa455c62c48c60d4b8a4ccf3802f837283ec2a","abstract_canon_sha256":"c12ccbe1acc320b7694110652c7c8a9346ce9d61ee12cad9247b452a060f4e8f"},"schema_version":"1.0"},"canonical_sha256":"b60647f28807d81e2b2924b830f0d4df8398375ab4f7f9d255507bfdf2ddb94f","source":{"kind":"arxiv","id":"1805.03497","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.03497","created_at":"2026-05-18T00:16:20Z"},{"alias_kind":"arxiv_version","alias_value":"1805.03497v1","created_at":"2026-05-18T00:16:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.03497","created_at":"2026-05-18T00:16:20Z"},{"alias_kind":"pith_short_12","alias_value":"WYDEP4UIA7MB","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"WYDEP4UIA7MB4KZJ","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"WYDEP4UI","created_at":"2026-05-18T12:33:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:WYDEP4UIA7MB4KZJES4DB4GU36","target":"record","payload":{"canonical_record":{"source":{"id":"1805.03497","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-05-09T13:17:25Z","cross_cats_sorted":[],"title_canon_sha256":"06e5786212b0bd39a30267412baa455c62c48c60d4b8a4ccf3802f837283ec2a","abstract_canon_sha256":"c12ccbe1acc320b7694110652c7c8a9346ce9d61ee12cad9247b452a060f4e8f"},"schema_version":"1.0"},"canonical_sha256":"b60647f28807d81e2b2924b830f0d4df8398375ab4f7f9d255507bfdf2ddb94f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:16:20.050794Z","signature_b64":"BgiEmbPx0gqzAWk/dU+OKydi2dnXLiojc/WpjMu4FulGk+NXfjvBBID74uGHDC2TdAJ3D4pe5mRsMBfuKgJ+Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b60647f28807d81e2b2924b830f0d4df8398375ab4f7f9d255507bfdf2ddb94f","last_reissued_at":"2026-05-18T00:16:20.050283Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:16:20.050283Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.03497","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":"2026-05-18T00:16:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N1oSA9LZfaZzD5CbL/Sw1RYjT5JavUktnqleg1aDrMijpXQI3JlrzRgTk+eKXsSxvXpVwl/SFV9Eg8N2WOdFDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T20:56:23.556531Z"},"content_sha256":"60971cd2c23e1c30ef3124c33d8db95437e6774d15131dc056b4ef7793a238f5","schema_version":"1.0","event_id":"sha256:60971cd2c23e1c30ef3124c33d8db95437e6774d15131dc056b4ef7793a238f5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:WYDEP4UIA7MB4KZJES4DB4GU36","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Pseudo-differential calculus in anisotropic Gelfand-Shilov setting","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Ahmed Abdeljawad, Joachim Toft, Marco Cappiello","submitted_at":"2018-05-09T13:17:25Z","abstract_excerpt":"We study some classes of pseudo-differential operators with symbols $a$ admitting anisotropic exponential growth at infinity and we prove mapping properties for these operators on Gelfand-Shilov spaces of type S. Moreover, we deduce algebraic and certain invariance properties of these classes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.03497","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":"2026-05-18T00:16:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hKqETVMCaGUWbsQTS2tEx9Nq1fm8f6MZMKMt78a4E9Bu8IjOwBxvR5+M0kr3cAZ//XtZLU5quhY766Uz1y0SBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T20:56:23.557041Z"},"content_sha256":"075bc5c24b8aeeeebb6dc0ab6127215847c92620dc970d8b02db220b74c34b8c","schema_version":"1.0","event_id":"sha256:075bc5c24b8aeeeebb6dc0ab6127215847c92620dc970d8b02db220b74c34b8c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WYDEP4UIA7MB4KZJES4DB4GU36/bundle.json","state_url":"https://pith.science/pith/WYDEP4UIA7MB4KZJES4DB4GU36/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WYDEP4UIA7MB4KZJES4DB4GU36/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":"2026-06-06T20:56:23Z","links":{"resolver":"https://pith.science/pith/WYDEP4UIA7MB4KZJES4DB4GU36","bundle":"https://pith.science/pith/WYDEP4UIA7MB4KZJES4DB4GU36/bundle.json","state":"https://pith.science/pith/WYDEP4UIA7MB4KZJES4DB4GU36/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WYDEP4UIA7MB4KZJES4DB4GU36/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:WYDEP4UIA7MB4KZJES4DB4GU36","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":"c12ccbe1acc320b7694110652c7c8a9346ce9d61ee12cad9247b452a060f4e8f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-05-09T13:17:25Z","title_canon_sha256":"06e5786212b0bd39a30267412baa455c62c48c60d4b8a4ccf3802f837283ec2a"},"schema_version":"1.0","source":{"id":"1805.03497","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.03497","created_at":"2026-05-18T00:16:20Z"},{"alias_kind":"arxiv_version","alias_value":"1805.03497v1","created_at":"2026-05-18T00:16:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.03497","created_at":"2026-05-18T00:16:20Z"},{"alias_kind":"pith_short_12","alias_value":"WYDEP4UIA7MB","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"WYDEP4UIA7MB4KZJ","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"WYDEP4UI","created_at":"2026-05-18T12:33:01Z"}],"graph_snapshots":[{"event_id":"sha256:075bc5c24b8aeeeebb6dc0ab6127215847c92620dc970d8b02db220b74c34b8c","target":"graph","created_at":"2026-05-18T00:16:20Z","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 study some classes of pseudo-differential operators with symbols $a$ admitting anisotropic exponential growth at infinity and we prove mapping properties for these operators on Gelfand-Shilov spaces of type S. Moreover, we deduce algebraic and certain invariance properties of these classes.","authors_text":"Ahmed Abdeljawad, Joachim Toft, Marco Cappiello","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-05-09T13:17:25Z","title":"Pseudo-differential calculus in anisotropic Gelfand-Shilov setting"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.03497","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":"sha256:60971cd2c23e1c30ef3124c33d8db95437e6774d15131dc056b4ef7793a238f5","target":"record","created_at":"2026-05-18T00:16:20Z","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":"c12ccbe1acc320b7694110652c7c8a9346ce9d61ee12cad9247b452a060f4e8f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-05-09T13:17:25Z","title_canon_sha256":"06e5786212b0bd39a30267412baa455c62c48c60d4b8a4ccf3802f837283ec2a"},"schema_version":"1.0","source":{"id":"1805.03497","kind":"arxiv","version":1}},"canonical_sha256":"b60647f28807d81e2b2924b830f0d4df8398375ab4f7f9d255507bfdf2ddb94f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b60647f28807d81e2b2924b830f0d4df8398375ab4f7f9d255507bfdf2ddb94f","first_computed_at":"2026-05-18T00:16:20.050283Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:16:20.050283Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BgiEmbPx0gqzAWk/dU+OKydi2dnXLiojc/WpjMu4FulGk+NXfjvBBID74uGHDC2TdAJ3D4pe5mRsMBfuKgJ+Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T00:16:20.050794Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.03497","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:60971cd2c23e1c30ef3124c33d8db95437e6774d15131dc056b4ef7793a238f5","sha256:075bc5c24b8aeeeebb6dc0ab6127215847c92620dc970d8b02db220b74c34b8c"],"state_sha256":"fa6eda084667fdd616ee9a6d5fc1f3971c8736c92473688ec436371d387d6934"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l9nrXuTsaYAunViyoPMfUe73sZPBMKTnKDSR9R6Dyn7pFnsG/qxXlTQ/gq9ze0oZHMT7svFRX9mgv8z26SGVDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T20:56:23.560778Z","bundle_sha256":"36196ed1cc35a6bf9aecb8bd8e68a7feeca57630498c021b19a1a67efbd37310"}}