{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:2N46K45SNDTPB3KWYGXGWUV5BA","short_pith_number":"pith:2N46K45S","canonical_record":{"source":{"id":"1711.06174","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-11-16T16:25:41Z","cross_cats_sorted":[],"title_canon_sha256":"4b4c025446c1375bf0dff0c566feb2d24261164c8efbd673c20356edf4de00f4","abstract_canon_sha256":"88495860fb0a4f4f112438b9051bccf64d4ee451d5b7a7c667e6dfc4b3deb890"},"schema_version":"1.0"},"canonical_sha256":"d379e573b268e6f0ed56c1ae6b52bd0832912db33d743f7f6bf37adf2e6f1fb8","source":{"kind":"arxiv","id":"1711.06174","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.06174","created_at":"2026-05-18T00:30:23Z"},{"alias_kind":"arxiv_version","alias_value":"1711.06174v1","created_at":"2026-05-18T00:30:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.06174","created_at":"2026-05-18T00:30:23Z"},{"alias_kind":"pith_short_12","alias_value":"2N46K45SNDTP","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"2N46K45SNDTPB3KW","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"2N46K45S","created_at":"2026-05-18T12:30:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:2N46K45SNDTPB3KWYGXGWUV5BA","target":"record","payload":{"canonical_record":{"source":{"id":"1711.06174","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-11-16T16:25:41Z","cross_cats_sorted":[],"title_canon_sha256":"4b4c025446c1375bf0dff0c566feb2d24261164c8efbd673c20356edf4de00f4","abstract_canon_sha256":"88495860fb0a4f4f112438b9051bccf64d4ee451d5b7a7c667e6dfc4b3deb890"},"schema_version":"1.0"},"canonical_sha256":"d379e573b268e6f0ed56c1ae6b52bd0832912db33d743f7f6bf37adf2e6f1fb8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:30:23.171389Z","signature_b64":"h7nCfmhaYUl1GsWsKxtMDECcc+bmVPExQr/JrMOhXSew9ajzWWgFbBOyDVWHMXzYFKQREghHqZMReo7ldk06DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d379e573b268e6f0ed56c1ae6b52bd0832912db33d743f7f6bf37adf2e6f1fb8","last_reissued_at":"2026-05-18T00:30:23.170619Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:30:23.170619Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1711.06174","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":"2026-05-18T00:30:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7ILPLEF+UbNhWDYboM/gMr+YfGnVp6u2iZcC6LKWs7JStc+uSa2jbcce74luB8LiGFSy3kRjei4ri1jPF3jhDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T23:44:10.734225Z"},"content_sha256":"8255f33125209b20d8a7ef7f1b2721cd62b10459435aece567d196152837d537","schema_version":"1.0","event_id":"sha256:8255f33125209b20d8a7ef7f1b2721cd62b10459435aece567d196152837d537"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:2N46K45SNDTPB3KWYGXGWUV5BA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Linear differential equations with solutions in weighted Fock spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Guangming Hu, Juha-Matti Huusko","submitted_at":"2017-11-16T16:25:41Z","abstract_excerpt":"This research is concerned with the nonhomogeneous linear complex differential equation $$ f^{(k)}+A_{k-1}f^{(k-1)}+\\cdots+A_{1}f'+A_{0}f=A_{k} $$ in the complex plane. In the higher order case, the mutual relations between coefficients and solutions in weighted Fock spaces are discussed, respectively. In particular, sufficient conditions for the solutions of the second order case $$ f\"+Af=0 $$ to be in some weighted Fock space are given by Bergman reproducing kernel and coefficient $A$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.06174","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":"2026-05-18T00:30:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rAqKOSXgog238+8lvM1YRZueBFjqOR0Y51X9OwZaE0RbQQCXIrGy2H9IrQ3wwJFzLfoM+HixzyoG2j+M9veBAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T23:44:10.734605Z"},"content_sha256":"81f9a729f262e1de52eb212ed96d139278705fbe4b043dc7663d3cec9141be21","schema_version":"1.0","event_id":"sha256:81f9a729f262e1de52eb212ed96d139278705fbe4b043dc7663d3cec9141be21"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2N46K45SNDTPB3KWYGXGWUV5BA/bundle.json","state_url":"https://pith.science/pith/2N46K45SNDTPB3KWYGXGWUV5BA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2N46K45SNDTPB3KWYGXGWUV5BA/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":"2026-06-25T23:44:10Z","links":{"resolver":"https://pith.science/pith/2N46K45SNDTPB3KWYGXGWUV5BA","bundle":"https://pith.science/pith/2N46K45SNDTPB3KWYGXGWUV5BA/bundle.json","state":"https://pith.science/pith/2N46K45SNDTPB3KWYGXGWUV5BA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2N46K45SNDTPB3KWYGXGWUV5BA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:2N46K45SNDTPB3KWYGXGWUV5BA","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":"88495860fb0a4f4f112438b9051bccf64d4ee451d5b7a7c667e6dfc4b3deb890","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-11-16T16:25:41Z","title_canon_sha256":"4b4c025446c1375bf0dff0c566feb2d24261164c8efbd673c20356edf4de00f4"},"schema_version":"1.0","source":{"id":"1711.06174","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.06174","created_at":"2026-05-18T00:30:23Z"},{"alias_kind":"arxiv_version","alias_value":"1711.06174v1","created_at":"2026-05-18T00:30:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.06174","created_at":"2026-05-18T00:30:23Z"},{"alias_kind":"pith_short_12","alias_value":"2N46K45SNDTP","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"2N46K45SNDTPB3KW","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"2N46K45S","created_at":"2026-05-18T12:30:55Z"}],"graph_snapshots":[{"event_id":"sha256:81f9a729f262e1de52eb212ed96d139278705fbe4b043dc7663d3cec9141be21","target":"graph","created_at":"2026-05-18T00:30:23Z","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":"This research is concerned with the nonhomogeneous linear complex differential equation $$ f^{(k)}+A_{k-1}f^{(k-1)}+\\cdots+A_{1}f'+A_{0}f=A_{k} $$ in the complex plane. In the higher order case, the mutual relations between coefficients and solutions in weighted Fock spaces are discussed, respectively. In particular, sufficient conditions for the solutions of the second order case $$ f\"+Af=0 $$ to be in some weighted Fock space are given by Bergman reproducing kernel and coefficient $A$.","authors_text":"Guangming Hu, Juha-Matti Huusko","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-11-16T16:25:41Z","title":"Linear differential equations with solutions in weighted Fock spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.06174","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":"sha256:8255f33125209b20d8a7ef7f1b2721cd62b10459435aece567d196152837d537","target":"record","created_at":"2026-05-18T00:30:23Z","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":"88495860fb0a4f4f112438b9051bccf64d4ee451d5b7a7c667e6dfc4b3deb890","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-11-16T16:25:41Z","title_canon_sha256":"4b4c025446c1375bf0dff0c566feb2d24261164c8efbd673c20356edf4de00f4"},"schema_version":"1.0","source":{"id":"1711.06174","kind":"arxiv","version":1}},"canonical_sha256":"d379e573b268e6f0ed56c1ae6b52bd0832912db33d743f7f6bf37adf2e6f1fb8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d379e573b268e6f0ed56c1ae6b52bd0832912db33d743f7f6bf37adf2e6f1fb8","first_computed_at":"2026-05-18T00:30:23.170619Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:30:23.170619Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"h7nCfmhaYUl1GsWsKxtMDECcc+bmVPExQr/JrMOhXSew9ajzWWgFbBOyDVWHMXzYFKQREghHqZMReo7ldk06DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:30:23.171389Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.06174","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8255f33125209b20d8a7ef7f1b2721cd62b10459435aece567d196152837d537","sha256:81f9a729f262e1de52eb212ed96d139278705fbe4b043dc7663d3cec9141be21"],"state_sha256":"9356cf6ec56768785e77eca5ce4c2d94f167b96fbe0a87d86f7e9e4131700f95"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gtyllTBMjne/7tSduk+C7k0foA0UfBM9pNYpme6eKc/wQBR0HQ2GOToXYfDRfIk+5Pe57fLGhQWHN/oJsmpUCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T23:44:10.736491Z","bundle_sha256":"4d82c8a3fd6339e53fb0b1622682de5f3211f9bea8cf2da16bf6a14eeadc3efa"}}