{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:SEKXDVMTVX7ZLJ5XHHO4NHFZ6F","short_pith_number":"pith:SEKXDVMT","canonical_record":{"source":{"id":"0903.3857","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2009-03-23T13:08:16Z","cross_cats_sorted":[],"title_canon_sha256":"e5005f70dba1de4e3286fcc57cb7ea1a8978d516b12d496b0d4c4f9e10101693","abstract_canon_sha256":"f4da555b4e68a132c4bb40c112190694d69c4487eaf7f852db665621eefa8924"},"schema_version":"1.0"},"canonical_sha256":"911571d593adff95a7b739ddc69cb9f16819f2d6e8d012680edbd18e25701430","source":{"kind":"arxiv","id":"0903.3857","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0903.3857","created_at":"2026-05-18T03:18:40Z"},{"alias_kind":"arxiv_version","alias_value":"0903.3857v1","created_at":"2026-05-18T03:18:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0903.3857","created_at":"2026-05-18T03:18:40Z"},{"alias_kind":"pith_short_12","alias_value":"SEKXDVMTVX7Z","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"SEKXDVMTVX7ZLJ5X","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"SEKXDVMT","created_at":"2026-05-18T12:26:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:SEKXDVMTVX7ZLJ5XHHO4NHFZ6F","target":"record","payload":{"canonical_record":{"source":{"id":"0903.3857","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2009-03-23T13:08:16Z","cross_cats_sorted":[],"title_canon_sha256":"e5005f70dba1de4e3286fcc57cb7ea1a8978d516b12d496b0d4c4f9e10101693","abstract_canon_sha256":"f4da555b4e68a132c4bb40c112190694d69c4487eaf7f852db665621eefa8924"},"schema_version":"1.0"},"canonical_sha256":"911571d593adff95a7b739ddc69cb9f16819f2d6e8d012680edbd18e25701430","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:18:40.671906Z","signature_b64":"z9GlBEu1rWSe+3+4WOPvQfRPyVS9CvIhmKn/DHzG1e0Utj8SQMLzEKDU/61mostPAitW1iGlBruJGF4dnHLHAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"911571d593adff95a7b739ddc69cb9f16819f2d6e8d012680edbd18e25701430","last_reissued_at":"2026-05-18T03:18:40.671168Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:18:40.671168Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0903.3857","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":"2026-05-18T03:18:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3OXcKtRmn314oEysjXWo33EIzvl5WQkqTCvVxyOfpSpD81q+Oc3W4gvGuIlAQgqMdzQJizWBdbFGh0hdxDyOAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T23:22:40.694202Z"},"content_sha256":"e598e8e88131340e66b96c24a46d54d9cc43e70bfb03d7fcbed8cdb40473eb84","schema_version":"1.0","event_id":"sha256:e598e8e88131340e66b96c24a46d54d9cc43e70bfb03d7fcbed8cdb40473eb84"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:SEKXDVMTVX7ZLJ5XHHO4NHFZ6F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Difference Picard theorem for meromorphic functions of several variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Risto Korhonen","submitted_at":"2009-03-23T13:08:16Z","abstract_excerpt":"It is shown that if three distinct values of a meromorphic function f:C^n -> P^1 of hyper-order strictly less than 2/3 have forward invariant pre-images with respect to a translation t:C^n -> C^n, t(z)=z+c, then f is a periodic function with period c. This result can be seen as a generalization of M. Green's Picard-type theorem in the special case where the hyper-order of f is less than 2/3, since the empty pre-images of the usual Picard exceptional values are by definition always forward invariant. In addition, difference analogues of the lemma on the logarithmic derivative and of the second "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.3857","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":"2026-05-18T03:18:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tTXYfuP8GR0I/amLYRLAyTIoRdlIR31M8Ku+OHbyNh0IavXebrm42Wjjup77VEBp6ygwOdrx2qUD1r3DoJcnBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T23:22:40.694593Z"},"content_sha256":"3ca95b54de88ed64f45eb83ff5a0e1d1c2f8cb0ebf304b9e10591b421c5ee0f7","schema_version":"1.0","event_id":"sha256:3ca95b54de88ed64f45eb83ff5a0e1d1c2f8cb0ebf304b9e10591b421c5ee0f7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SEKXDVMTVX7ZLJ5XHHO4NHFZ6F/bundle.json","state_url":"https://pith.science/pith/SEKXDVMTVX7ZLJ5XHHO4NHFZ6F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SEKXDVMTVX7ZLJ5XHHO4NHFZ6F/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":"2026-05-26T23:22:40Z","links":{"resolver":"https://pith.science/pith/SEKXDVMTVX7ZLJ5XHHO4NHFZ6F","bundle":"https://pith.science/pith/SEKXDVMTVX7ZLJ5XHHO4NHFZ6F/bundle.json","state":"https://pith.science/pith/SEKXDVMTVX7ZLJ5XHHO4NHFZ6F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SEKXDVMTVX7ZLJ5XHHO4NHFZ6F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:SEKXDVMTVX7ZLJ5XHHO4NHFZ6F","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":"f4da555b4e68a132c4bb40c112190694d69c4487eaf7f852db665621eefa8924","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2009-03-23T13:08:16Z","title_canon_sha256":"e5005f70dba1de4e3286fcc57cb7ea1a8978d516b12d496b0d4c4f9e10101693"},"schema_version":"1.0","source":{"id":"0903.3857","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0903.3857","created_at":"2026-05-18T03:18:40Z"},{"alias_kind":"arxiv_version","alias_value":"0903.3857v1","created_at":"2026-05-18T03:18:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0903.3857","created_at":"2026-05-18T03:18:40Z"},{"alias_kind":"pith_short_12","alias_value":"SEKXDVMTVX7Z","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"SEKXDVMTVX7ZLJ5X","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"SEKXDVMT","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:3ca95b54de88ed64f45eb83ff5a0e1d1c2f8cb0ebf304b9e10591b421c5ee0f7","target":"graph","created_at":"2026-05-18T03:18:40Z","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":"It is shown that if three distinct values of a meromorphic function f:C^n -> P^1 of hyper-order strictly less than 2/3 have forward invariant pre-images with respect to a translation t:C^n -> C^n, t(z)=z+c, then f is a periodic function with period c. This result can be seen as a generalization of M. Green's Picard-type theorem in the special case where the hyper-order of f is less than 2/3, since the empty pre-images of the usual Picard exceptional values are by definition always forward invariant. In addition, difference analogues of the lemma on the logarithmic derivative and of the second ","authors_text":"Risto Korhonen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2009-03-23T13:08:16Z","title":"Difference Picard theorem for meromorphic functions of several variables"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.3857","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:e598e8e88131340e66b96c24a46d54d9cc43e70bfb03d7fcbed8cdb40473eb84","target":"record","created_at":"2026-05-18T03:18:40Z","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":"f4da555b4e68a132c4bb40c112190694d69c4487eaf7f852db665621eefa8924","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2009-03-23T13:08:16Z","title_canon_sha256":"e5005f70dba1de4e3286fcc57cb7ea1a8978d516b12d496b0d4c4f9e10101693"},"schema_version":"1.0","source":{"id":"0903.3857","kind":"arxiv","version":1}},"canonical_sha256":"911571d593adff95a7b739ddc69cb9f16819f2d6e8d012680edbd18e25701430","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"911571d593adff95a7b739ddc69cb9f16819f2d6e8d012680edbd18e25701430","first_computed_at":"2026-05-18T03:18:40.671168Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:18:40.671168Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"z9GlBEu1rWSe+3+4WOPvQfRPyVS9CvIhmKn/DHzG1e0Utj8SQMLzEKDU/61mostPAitW1iGlBruJGF4dnHLHAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:18:40.671906Z","signed_message":"canonical_sha256_bytes"},"source_id":"0903.3857","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e598e8e88131340e66b96c24a46d54d9cc43e70bfb03d7fcbed8cdb40473eb84","sha256:3ca95b54de88ed64f45eb83ff5a0e1d1c2f8cb0ebf304b9e10591b421c5ee0f7"],"state_sha256":"dac2855ff2b08f914e91a752e671c4f6e6f2759f770e92a74990d1ee59536893"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5ndFPSmsoIHfhuPRc2P7kf8H/38pVdNByooWXfK0Vz5t8ZqfQgTWiDRxRAhGDyZyxKKA7zyBauCexgFdTXowAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T23:22:40.696907Z","bundle_sha256":"54731d7cf0aa25eded7b123663b7fc4e771b209c380cf5ff2ddfccb93de87464"}}