{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:UPPJQY2UHDYCELNMNY36IVOAUL","short_pith_number":"pith:UPPJQY2U","canonical_record":{"source":{"id":"1806.07215","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2018-06-19T13:34:36Z","cross_cats_sorted":[],"title_canon_sha256":"8f0b31bf2e1c005e396c308206d2c09806a2eaa158689d64c6d976ebedb8e62f","abstract_canon_sha256":"88ff667d8d0e58085e4b9bf04bc954bccefc94a3c44a45ebd975d3510df17d53"},"schema_version":"1.0"},"canonical_sha256":"a3de98635438f0222dac6e37e455c0a2e996f90dd704eb713cae0501bc4f62d2","source":{"kind":"arxiv","id":"1806.07215","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.07215","created_at":"2026-05-18T00:12:31Z"},{"alias_kind":"arxiv_version","alias_value":"1806.07215v2","created_at":"2026-05-18T00:12:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.07215","created_at":"2026-05-18T00:12:31Z"},{"alias_kind":"pith_short_12","alias_value":"UPPJQY2UHDYC","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"UPPJQY2UHDYCELNM","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"UPPJQY2U","created_at":"2026-05-18T12:32:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:UPPJQY2UHDYCELNMNY36IVOAUL","target":"record","payload":{"canonical_record":{"source":{"id":"1806.07215","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2018-06-19T13:34:36Z","cross_cats_sorted":[],"title_canon_sha256":"8f0b31bf2e1c005e396c308206d2c09806a2eaa158689d64c6d976ebedb8e62f","abstract_canon_sha256":"88ff667d8d0e58085e4b9bf04bc954bccefc94a3c44a45ebd975d3510df17d53"},"schema_version":"1.0"},"canonical_sha256":"a3de98635438f0222dac6e37e455c0a2e996f90dd704eb713cae0501bc4f62d2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:31.396908Z","signature_b64":"fxgp4qOTHcXHjoySf0y0rZz5LPNXNU1Gfu91tgN5f6U3ov07QRRBxlUUJEYDPnXAdJkFgpEPdkyLN5i3TXzvAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a3de98635438f0222dac6e37e455c0a2e996f90dd704eb713cae0501bc4f62d2","last_reissued_at":"2026-05-18T00:12:31.396061Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:31.396061Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1806.07215","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":"2026-05-18T00:12:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MXrkebXCYlShxWsPbPdt9RrKLRHtNsojvEURBdhmbUyJOK9EMa3TWn+vmuIw7/uLotGS7Ua72P+KNJQDqCelAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T02:24:38.226190Z"},"content_sha256":"23ebc67bd76fc0210eaf51b1a80f0214b28bbd8e502ac73474a8b5cfa1c6cab6","schema_version":"1.0","event_id":"sha256:23ebc67bd76fc0210eaf51b1a80f0214b28bbd8e502ac73474a8b5cfa1c6cab6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:UPPJQY2UHDYCELNMNY36IVOAUL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Polynomial growth of subharmonic functions in a strongly symmetric Riemannian manifold","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Absos Ali Shaikh, Chandan Kumar Mondal","submitted_at":"2018-06-19T13:34:36Z","abstract_excerpt":"In this article we have studied some properties of subharmonic functions in a strongly symmetric Riemannian manifold with a pole. As a generalization of polynomial growth of a function we have introduced the notion of polynomial growth of some degree of a function with respect to a real function and proved that any non-negative twice differentiable subharmonic functions in an $n$-dimensional manifold always admit polynomial growth of degree $1$ with respect to a non-negative real valued subharmonic function on real line. We have also given a lower bound of the integration of a convex function "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.07215","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":""},"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":"2026-05-18T00:12:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1L5artt8EMhqGD5pmrUdqmETfOLxIntpfYmpP5EreMJyC/CfwvYt5FnQQjkHvhJRqhC0pvJTj/AiOSIyAub7DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T02:24:38.226809Z"},"content_sha256":"fead4dbdd708ec608459787eefaaf0a2e64e121b0d7f471ac9854daf3b9e5028","schema_version":"1.0","event_id":"sha256:fead4dbdd708ec608459787eefaaf0a2e64e121b0d7f471ac9854daf3b9e5028"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UPPJQY2UHDYCELNMNY36IVOAUL/bundle.json","state_url":"https://pith.science/pith/UPPJQY2UHDYCELNMNY36IVOAUL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UPPJQY2UHDYCELNMNY36IVOAUL/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":"2026-05-26T02:24:38Z","links":{"resolver":"https://pith.science/pith/UPPJQY2UHDYCELNMNY36IVOAUL","bundle":"https://pith.science/pith/UPPJQY2UHDYCELNMNY36IVOAUL/bundle.json","state":"https://pith.science/pith/UPPJQY2UHDYCELNMNY36IVOAUL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UPPJQY2UHDYCELNMNY36IVOAUL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:UPPJQY2UHDYCELNMNY36IVOAUL","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":"88ff667d8d0e58085e4b9bf04bc954bccefc94a3c44a45ebd975d3510df17d53","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2018-06-19T13:34:36Z","title_canon_sha256":"8f0b31bf2e1c005e396c308206d2c09806a2eaa158689d64c6d976ebedb8e62f"},"schema_version":"1.0","source":{"id":"1806.07215","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.07215","created_at":"2026-05-18T00:12:31Z"},{"alias_kind":"arxiv_version","alias_value":"1806.07215v2","created_at":"2026-05-18T00:12:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.07215","created_at":"2026-05-18T00:12:31Z"},{"alias_kind":"pith_short_12","alias_value":"UPPJQY2UHDYC","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"UPPJQY2UHDYCELNM","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"UPPJQY2U","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:fead4dbdd708ec608459787eefaaf0a2e64e121b0d7f471ac9854daf3b9e5028","target":"graph","created_at":"2026-05-18T00:12:31Z","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":"In this article we have studied some properties of subharmonic functions in a strongly symmetric Riemannian manifold with a pole. As a generalization of polynomial growth of a function we have introduced the notion of polynomial growth of some degree of a function with respect to a real function and proved that any non-negative twice differentiable subharmonic functions in an $n$-dimensional manifold always admit polynomial growth of degree $1$ with respect to a non-negative real valued subharmonic function on real line. We have also given a lower bound of the integration of a convex function ","authors_text":"Absos Ali Shaikh, Chandan Kumar Mondal","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2018-06-19T13:34:36Z","title":"Polynomial growth of subharmonic functions in a strongly symmetric Riemannian manifold"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.07215","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":"sha256:23ebc67bd76fc0210eaf51b1a80f0214b28bbd8e502ac73474a8b5cfa1c6cab6","target":"record","created_at":"2026-05-18T00:12:31Z","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":"88ff667d8d0e58085e4b9bf04bc954bccefc94a3c44a45ebd975d3510df17d53","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2018-06-19T13:34:36Z","title_canon_sha256":"8f0b31bf2e1c005e396c308206d2c09806a2eaa158689d64c6d976ebedb8e62f"},"schema_version":"1.0","source":{"id":"1806.07215","kind":"arxiv","version":2}},"canonical_sha256":"a3de98635438f0222dac6e37e455c0a2e996f90dd704eb713cae0501bc4f62d2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a3de98635438f0222dac6e37e455c0a2e996f90dd704eb713cae0501bc4f62d2","first_computed_at":"2026-05-18T00:12:31.396061Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:12:31.396061Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fxgp4qOTHcXHjoySf0y0rZz5LPNXNU1Gfu91tgN5f6U3ov07QRRBxlUUJEYDPnXAdJkFgpEPdkyLN5i3TXzvAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:12:31.396908Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.07215","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:23ebc67bd76fc0210eaf51b1a80f0214b28bbd8e502ac73474a8b5cfa1c6cab6","sha256:fead4dbdd708ec608459787eefaaf0a2e64e121b0d7f471ac9854daf3b9e5028"],"state_sha256":"00e51078255f5d8dd97c0f1bcb9d3e7eeac77105177f148dbcb3f2ae5f018da8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wZNrKw3dOyhfCCJPT8979F4dEwt2kfCaULDvd/sMQztXDquJO32V7A8wTSCeGjyh8/bIzPorStMeFvEgOi2jCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T02:24:38.230152Z","bundle_sha256":"c20c8162f59b07dc4ed25f5743d56145febad42be41f01a0ae249c6214a82549"}}