{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:63PBW2MFRVFHHMXB3ZAZFJXNYT","short_pith_number":"pith:63PBW2MF","canonical_record":{"source":{"id":"1709.03705","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-09-12T06:56:07Z","cross_cats_sorted":[],"title_canon_sha256":"c301ef2ebdffdbc4ae49a3f8f338c647f850182b4ec666c792c631a9dbb4595c","abstract_canon_sha256":"66f776d35b511084f407d04016a0f9adf79a372aef14ddf2cc8563291204f9e2"},"schema_version":"1.0"},"canonical_sha256":"f6de1b69858d4a73b2e1de4192a6edc4ede5a57390f6e5f030c8a6525331724c","source":{"kind":"arxiv","id":"1709.03705","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.03705","created_at":"2026-05-18T00:35:29Z"},{"alias_kind":"arxiv_version","alias_value":"1709.03705v1","created_at":"2026-05-18T00:35:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.03705","created_at":"2026-05-18T00:35:29Z"},{"alias_kind":"pith_short_12","alias_value":"63PBW2MFRVFH","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"63PBW2MFRVFHHMXB","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"63PBW2MF","created_at":"2026-05-18T12:31:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:63PBW2MFRVFHHMXB3ZAZFJXNYT","target":"record","payload":{"canonical_record":{"source":{"id":"1709.03705","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-09-12T06:56:07Z","cross_cats_sorted":[],"title_canon_sha256":"c301ef2ebdffdbc4ae49a3f8f338c647f850182b4ec666c792c631a9dbb4595c","abstract_canon_sha256":"66f776d35b511084f407d04016a0f9adf79a372aef14ddf2cc8563291204f9e2"},"schema_version":"1.0"},"canonical_sha256":"f6de1b69858d4a73b2e1de4192a6edc4ede5a57390f6e5f030c8a6525331724c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:35:29.745469Z","signature_b64":"F/7BDIzuOGDVyy8l9eratgfYFf+ZDfvqZcgLJVXlKXyLyxlYbPI5UwXXClZ/fr6dNb1h6hiYzXJGtoCSDFcUAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f6de1b69858d4a73b2e1de4192a6edc4ede5a57390f6e5f030c8a6525331724c","last_reissued_at":"2026-05-18T00:35:29.744798Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:35:29.744798Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1709.03705","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":"2026-05-18T00:35:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hz6kYrqDUhgN7dczlDnOi5rjtgvTnTP1rOO9UDHFPbthYO5hUhb3wMoOGfodBpVLuwHYT3FLE7xf1r7YOpgRAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T08:48:21.927245Z"},"content_sha256":"37445ed3224d21dad4e1321d035d2aa9958c6115fc4704c7cb9b8aaf3553cf1e","schema_version":"1.0","event_id":"sha256:37445ed3224d21dad4e1321d035d2aa9958c6115fc4704c7cb9b8aaf3553cf1e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:63PBW2MFRVFHHMXB3ZAZFJXNYT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Random power series near the endpoint of the convergence interval","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Bal\\'azs Maga, P\\'eter Maga","submitted_at":"2017-09-12T06:56:07Z","abstract_excerpt":"In this paper, we are going to consider power series $$ \\sum_{n=1}^{\\infty} a_nx^n, $$ where the coefficients $a_n$ are chosen independently at random from a finite set with uniform distribution. We prove that if the expected value of the coefficients is positive (resp. negative), then $$ \\lim_{x\\to 1-}\\sum_{n=1}^{\\infty} a_nx^n=\\infty\\qquad (\\text{resp. }\\lim_{x\\to 1-}\\sum_{n=1}^{\\infty} a_nx^n=-\\infty) $$ with probability $1$. Also, if the expected value of the coefficients is $0$, then $$ \\limsup_{x\\to 1-}\\sum_{n=1}^{\\infty} a_nx^n=\\infty,\\qquad \\liminf_{x\\to 1-}\\sum_{n=1}^{\\infty} a_nx^n=-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.03705","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":"2026-05-18T00:35:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"reA0FYfqvEB3L6/8qmSQY4UnqyLazf093nMfwc4nkHHbKtCtK7fJ1SaUMGCUMocHt+qh5LScFqYVBYWrWY+9Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T08:48:21.927645Z"},"content_sha256":"42875d80b05cd1f5efe1b5d7ab8561161e1dbec01ae529e9ca1bf01a8886a47b","schema_version":"1.0","event_id":"sha256:42875d80b05cd1f5efe1b5d7ab8561161e1dbec01ae529e9ca1bf01a8886a47b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/63PBW2MFRVFHHMXB3ZAZFJXNYT/bundle.json","state_url":"https://pith.science/pith/63PBW2MFRVFHHMXB3ZAZFJXNYT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/63PBW2MFRVFHHMXB3ZAZFJXNYT/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":"2026-05-31T08:48:21Z","links":{"resolver":"https://pith.science/pith/63PBW2MFRVFHHMXB3ZAZFJXNYT","bundle":"https://pith.science/pith/63PBW2MFRVFHHMXB3ZAZFJXNYT/bundle.json","state":"https://pith.science/pith/63PBW2MFRVFHHMXB3ZAZFJXNYT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/63PBW2MFRVFHHMXB3ZAZFJXNYT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:63PBW2MFRVFHHMXB3ZAZFJXNYT","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":"66f776d35b511084f407d04016a0f9adf79a372aef14ddf2cc8563291204f9e2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-09-12T06:56:07Z","title_canon_sha256":"c301ef2ebdffdbc4ae49a3f8f338c647f850182b4ec666c792c631a9dbb4595c"},"schema_version":"1.0","source":{"id":"1709.03705","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.03705","created_at":"2026-05-18T00:35:29Z"},{"alias_kind":"arxiv_version","alias_value":"1709.03705v1","created_at":"2026-05-18T00:35:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.03705","created_at":"2026-05-18T00:35:29Z"},{"alias_kind":"pith_short_12","alias_value":"63PBW2MFRVFH","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"63PBW2MFRVFHHMXB","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"63PBW2MF","created_at":"2026-05-18T12:31:03Z"}],"graph_snapshots":[{"event_id":"sha256:42875d80b05cd1f5efe1b5d7ab8561161e1dbec01ae529e9ca1bf01a8886a47b","target":"graph","created_at":"2026-05-18T00:35:29Z","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 paper, we are going to consider power series $$ \\sum_{n=1}^{\\infty} a_nx^n, $$ where the coefficients $a_n$ are chosen independently at random from a finite set with uniform distribution. We prove that if the expected value of the coefficients is positive (resp. negative), then $$ \\lim_{x\\to 1-}\\sum_{n=1}^{\\infty} a_nx^n=\\infty\\qquad (\\text{resp. }\\lim_{x\\to 1-}\\sum_{n=1}^{\\infty} a_nx^n=-\\infty) $$ with probability $1$. Also, if the expected value of the coefficients is $0$, then $$ \\limsup_{x\\to 1-}\\sum_{n=1}^{\\infty} a_nx^n=\\infty,\\qquad \\liminf_{x\\to 1-}\\sum_{n=1}^{\\infty} a_nx^n=-","authors_text":"Bal\\'azs Maga, P\\'eter Maga","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-09-12T06:56:07Z","title":"Random power series near the endpoint of the convergence interval"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.03705","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":"sha256:37445ed3224d21dad4e1321d035d2aa9958c6115fc4704c7cb9b8aaf3553cf1e","target":"record","created_at":"2026-05-18T00:35:29Z","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":"66f776d35b511084f407d04016a0f9adf79a372aef14ddf2cc8563291204f9e2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-09-12T06:56:07Z","title_canon_sha256":"c301ef2ebdffdbc4ae49a3f8f338c647f850182b4ec666c792c631a9dbb4595c"},"schema_version":"1.0","source":{"id":"1709.03705","kind":"arxiv","version":1}},"canonical_sha256":"f6de1b69858d4a73b2e1de4192a6edc4ede5a57390f6e5f030c8a6525331724c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f6de1b69858d4a73b2e1de4192a6edc4ede5a57390f6e5f030c8a6525331724c","first_computed_at":"2026-05-18T00:35:29.744798Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:35:29.744798Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"F/7BDIzuOGDVyy8l9eratgfYFf+ZDfvqZcgLJVXlKXyLyxlYbPI5UwXXClZ/fr6dNb1h6hiYzXJGtoCSDFcUAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:35:29.745469Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.03705","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:37445ed3224d21dad4e1321d035d2aa9958c6115fc4704c7cb9b8aaf3553cf1e","sha256:42875d80b05cd1f5efe1b5d7ab8561161e1dbec01ae529e9ca1bf01a8886a47b"],"state_sha256":"156aa1b27454ebb141ddf240df42d75cc867e9844dca1881b06a9a20eef516bf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tDFdyVK5mYjlQG+EeoJCdaeiH0e70b/bD4h3k2bOoZoDgCypVGUcEIfPujWyjayYlfY9eQ1NnFBWAozUbSnTCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T08:48:21.930167Z","bundle_sha256":"0c114ee7a1901727f0da74d0df9b550022656bb56037f278fe78f90b3df60893"}}