{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:MJBX4FPGRTN4O27CEG4U4W4JIH","short_pith_number":"pith:MJBX4FPG","canonical_record":{"source":{"id":"1601.04696","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-01-16T11:29:17Z","cross_cats_sorted":[],"title_canon_sha256":"858794b91d4afaef12ca5bda2b0b140457233952a179f0dc2f1971f239638f05","abstract_canon_sha256":"61445a85c1de9f0b62ff36086f873a6c5f09bcbc1c469fb64f51e1518b4728ff"},"schema_version":"1.0"},"canonical_sha256":"62437e15e68cdbc76be221b94e5b8941e4dabd029b5497331efd945383ea97f3","source":{"kind":"arxiv","id":"1601.04696","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.04696","created_at":"2026-05-18T01:22:31Z"},{"alias_kind":"arxiv_version","alias_value":"1601.04696v1","created_at":"2026-05-18T01:22:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.04696","created_at":"2026-05-18T01:22:31Z"},{"alias_kind":"pith_short_12","alias_value":"MJBX4FPGRTN4","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"MJBX4FPGRTN4O27C","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"MJBX4FPG","created_at":"2026-05-18T12:30:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:MJBX4FPGRTN4O27CEG4U4W4JIH","target":"record","payload":{"canonical_record":{"source":{"id":"1601.04696","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-01-16T11:29:17Z","cross_cats_sorted":[],"title_canon_sha256":"858794b91d4afaef12ca5bda2b0b140457233952a179f0dc2f1971f239638f05","abstract_canon_sha256":"61445a85c1de9f0b62ff36086f873a6c5f09bcbc1c469fb64f51e1518b4728ff"},"schema_version":"1.0"},"canonical_sha256":"62437e15e68cdbc76be221b94e5b8941e4dabd029b5497331efd945383ea97f3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:31.984611Z","signature_b64":"95gznLr5vTZvUmjG3FajdoE5Hy9bEwRRbFTtXRT4h9r2fGc+ZsJ3CaJXBzUqM7O+M2KEEXwDCLG5eFIH8Wx1DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"62437e15e68cdbc76be221b94e5b8941e4dabd029b5497331efd945383ea97f3","last_reissued_at":"2026-05-18T01:22:31.984166Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:31.984166Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1601.04696","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":"2026-05-18T01:22:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A4ZL7QIWUPP6mLqhnYUcjLktji92cqO51pqGUDsDLMiYC8YTA7RZszo1Xv47IWo1CLavVNZiAXvTQKFHMJ4/DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T12:47:04.970569Z"},"content_sha256":"97087ccef57835e29c5e96134e073f08367f2d949b8316ce7cb5005e6cc379ef","schema_version":"1.0","event_id":"sha256:97087ccef57835e29c5e96134e073f08367f2d949b8316ce7cb5005e6cc379ef"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:MJBX4FPGRTN4O27CEG4U4W4JIH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The estimation of the ratio of two entire functions with the same zeros in the ball","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"A.A.Shkalikov, V.L.Geynts","submitted_at":"2016-01-16T11:29:17Z","abstract_excerpt":"The paper studies entire functions of finite order of growth for which a representation of the form $\\psi(z) = 1+ O(|z|^{-\\mu}), \\mu >0,$ as $z\\to \\infty$, is valid on a fixed ray of the complex plane. The main result is the following. Assume that the zeros of two functions $\\psi_1, \\psi_2$ of this class coincide in the circle of radius $R$ with the center in zero. Then given arbitrary small $\\delta\\in (0,1)$ and $\\varepsilon >0$ the relation of these functions admits the estimate $|\\psi_1(z)/\\psi_2(z) -1| \\leqslant \\varepsilon R^{-\\mu(1-\\delta)}$ for all $|z|\\leqslant R^{1-\\delta}$, provided "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.04696","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":"2026-05-18T01:22:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EnWCQtxNmAuKGwYSalgKwBPpCFzvVsHGfI6SPs+t6+cAJXDLIi9IYtVnkCPLZs9bpIWX4lhlrwdE4hV/46ayBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T12:47:04.970935Z"},"content_sha256":"89564961ea3a844e84d36d5294bbcc4a19b3b6ef274f80b5805087b0a9859c2b","schema_version":"1.0","event_id":"sha256:89564961ea3a844e84d36d5294bbcc4a19b3b6ef274f80b5805087b0a9859c2b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MJBX4FPGRTN4O27CEG4U4W4JIH/bundle.json","state_url":"https://pith.science/pith/MJBX4FPGRTN4O27CEG4U4W4JIH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MJBX4FPGRTN4O27CEG4U4W4JIH/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":"2026-06-28T12:47:04Z","links":{"resolver":"https://pith.science/pith/MJBX4FPGRTN4O27CEG4U4W4JIH","bundle":"https://pith.science/pith/MJBX4FPGRTN4O27CEG4U4W4JIH/bundle.json","state":"https://pith.science/pith/MJBX4FPGRTN4O27CEG4U4W4JIH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MJBX4FPGRTN4O27CEG4U4W4JIH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:MJBX4FPGRTN4O27CEG4U4W4JIH","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":"61445a85c1de9f0b62ff36086f873a6c5f09bcbc1c469fb64f51e1518b4728ff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-01-16T11:29:17Z","title_canon_sha256":"858794b91d4afaef12ca5bda2b0b140457233952a179f0dc2f1971f239638f05"},"schema_version":"1.0","source":{"id":"1601.04696","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.04696","created_at":"2026-05-18T01:22:31Z"},{"alias_kind":"arxiv_version","alias_value":"1601.04696v1","created_at":"2026-05-18T01:22:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.04696","created_at":"2026-05-18T01:22:31Z"},{"alias_kind":"pith_short_12","alias_value":"MJBX4FPGRTN4","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"MJBX4FPGRTN4O27C","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"MJBX4FPG","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:89564961ea3a844e84d36d5294bbcc4a19b3b6ef274f80b5805087b0a9859c2b","target":"graph","created_at":"2026-05-18T01:22:31Z","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":"The paper studies entire functions of finite order of growth for which a representation of the form $\\psi(z) = 1+ O(|z|^{-\\mu}), \\mu >0,$ as $z\\to \\infty$, is valid on a fixed ray of the complex plane. The main result is the following. Assume that the zeros of two functions $\\psi_1, \\psi_2$ of this class coincide in the circle of radius $R$ with the center in zero. Then given arbitrary small $\\delta\\in (0,1)$ and $\\varepsilon >0$ the relation of these functions admits the estimate $|\\psi_1(z)/\\psi_2(z) -1| \\leqslant \\varepsilon R^{-\\mu(1-\\delta)}$ for all $|z|\\leqslant R^{1-\\delta}$, provided ","authors_text":"A.A.Shkalikov, V.L.Geynts","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-01-16T11:29:17Z","title":"The estimation of the ratio of two entire functions with the same zeros in the ball"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.04696","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":"sha256:97087ccef57835e29c5e96134e073f08367f2d949b8316ce7cb5005e6cc379ef","target":"record","created_at":"2026-05-18T01:22:31Z","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":"61445a85c1de9f0b62ff36086f873a6c5f09bcbc1c469fb64f51e1518b4728ff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-01-16T11:29:17Z","title_canon_sha256":"858794b91d4afaef12ca5bda2b0b140457233952a179f0dc2f1971f239638f05"},"schema_version":"1.0","source":{"id":"1601.04696","kind":"arxiv","version":1}},"canonical_sha256":"62437e15e68cdbc76be221b94e5b8941e4dabd029b5497331efd945383ea97f3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"62437e15e68cdbc76be221b94e5b8941e4dabd029b5497331efd945383ea97f3","first_computed_at":"2026-05-18T01:22:31.984166Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:31.984166Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"95gznLr5vTZvUmjG3FajdoE5Hy9bEwRRbFTtXRT4h9r2fGc+ZsJ3CaJXBzUqM7O+M2KEEXwDCLG5eFIH8Wx1DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:31.984611Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.04696","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:97087ccef57835e29c5e96134e073f08367f2d949b8316ce7cb5005e6cc379ef","sha256:89564961ea3a844e84d36d5294bbcc4a19b3b6ef274f80b5805087b0a9859c2b"],"state_sha256":"eec927ce3d1428f0d1639bb89e63fb4e915c08bb78228fe6dfb301f28a820c79"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YGUAdVAVO5sBl+9dhtPzK5r9EYOeJ2FETxwtEVRuxfC/MXFW/i+q6bXMq5fKBKInrbCjdvmjpU/eDZjlDp+VCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T12:47:04.974332Z","bundle_sha256":"41ce354ea3247491428489d287cd766a648582ece404a07a56606c8aa96527f3"}}