{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:YGVKUW6ASG3WQY5XPCBYQTY65B","short_pith_number":"pith:YGVKUW6A","canonical_record":{"source":{"id":"1710.10491","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-10-28T16:42:08Z","cross_cats_sorted":[],"title_canon_sha256":"bbf5edc1f8ad351a449b6372c1b986169280d2f7b7783f3cbae64e74b7e9c396","abstract_canon_sha256":"a8f7970ccdb48c1f6242a1978a622f6c887c13b50964712632dd0384f70e3490"},"schema_version":"1.0"},"canonical_sha256":"c1aaaa5bc091b76863b77883884f1ee857d8f010ee61148df84820d9aabd079d","source":{"kind":"arxiv","id":"1710.10491","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.10491","created_at":"2026-05-18T00:31:49Z"},{"alias_kind":"arxiv_version","alias_value":"1710.10491v1","created_at":"2026-05-18T00:31:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.10491","created_at":"2026-05-18T00:31:49Z"},{"alias_kind":"pith_short_12","alias_value":"YGVKUW6ASG3W","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"YGVKUW6ASG3WQY5X","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"YGVKUW6A","created_at":"2026-05-18T12:31:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:YGVKUW6ASG3WQY5XPCBYQTY65B","target":"record","payload":{"canonical_record":{"source":{"id":"1710.10491","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-10-28T16:42:08Z","cross_cats_sorted":[],"title_canon_sha256":"bbf5edc1f8ad351a449b6372c1b986169280d2f7b7783f3cbae64e74b7e9c396","abstract_canon_sha256":"a8f7970ccdb48c1f6242a1978a622f6c887c13b50964712632dd0384f70e3490"},"schema_version":"1.0"},"canonical_sha256":"c1aaaa5bc091b76863b77883884f1ee857d8f010ee61148df84820d9aabd079d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:49.359926Z","signature_b64":"hkUskvWqiK7IT2ejb+9Rl9eTT53jgOVvjOq23DzWPBIjJmhL8JmuavKBBj5QWWiENkVoeoAC0VosmiBdI9UrAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c1aaaa5bc091b76863b77883884f1ee857d8f010ee61148df84820d9aabd079d","last_reissued_at":"2026-05-18T00:31:49.359330Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:49.359330Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.10491","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":"2026-05-18T00:31:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9SHA8M2QosPH2eKAqNcVBqcsn2PPI0xvLpNr/oSRadW2lsr3e063lcQvfTdNfbcNrJAacSbjUYbPEro7UL6RBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T10:00:12.071199Z"},"content_sha256":"95ba2a113f06cb79af660f2f6aa0728b053f82ceecb65dde3849e6d75fc6db5d","schema_version":"1.0","event_id":"sha256:95ba2a113f06cb79af660f2f6aa0728b053f82ceecb65dde3849e6d75fc6db5d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:YGVKUW6ASG3WQY5XPCBYQTY65B","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On $rth$ coefficient of divisors of $x^n-1$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Sai Teja Somu","submitted_at":"2017-10-28T16:42:08Z","abstract_excerpt":"Let $r,n$ be two natural numbers and let $H(r,n)$ denote the maximal absolute value of $r$th coefficient of divisors of $x^n-1$. In this paper, we show that $\\sum_{n\\leq x}H(r,n)$ is asymptotically equal to $c(r)x(\\log x)^{2^r-1}$ for some constant $c(r)>0$. Furthermore, we give an explicit expression of $c(r)$ in terms of $r$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.10491","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":"2026-05-18T00:31:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y2W7mxuMCA1CMJTaB6njV6f3fCwkHeFRuvCnaKKNg2EC43AZBNgo55rkex3WM9QXajXmQxcdaG/NW+4xIgwWCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T10:00:12.071564Z"},"content_sha256":"dfa2d4835737ef8fc396c6ec964fd6e9fc369d1c7606564784effcb382bf689c","schema_version":"1.0","event_id":"sha256:dfa2d4835737ef8fc396c6ec964fd6e9fc369d1c7606564784effcb382bf689c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YGVKUW6ASG3WQY5XPCBYQTY65B/bundle.json","state_url":"https://pith.science/pith/YGVKUW6ASG3WQY5XPCBYQTY65B/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YGVKUW6ASG3WQY5XPCBYQTY65B/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":"2026-06-28T10:00:12Z","links":{"resolver":"https://pith.science/pith/YGVKUW6ASG3WQY5XPCBYQTY65B","bundle":"https://pith.science/pith/YGVKUW6ASG3WQY5XPCBYQTY65B/bundle.json","state":"https://pith.science/pith/YGVKUW6ASG3WQY5XPCBYQTY65B/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YGVKUW6ASG3WQY5XPCBYQTY65B/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:YGVKUW6ASG3WQY5XPCBYQTY65B","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":"a8f7970ccdb48c1f6242a1978a622f6c887c13b50964712632dd0384f70e3490","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-10-28T16:42:08Z","title_canon_sha256":"bbf5edc1f8ad351a449b6372c1b986169280d2f7b7783f3cbae64e74b7e9c396"},"schema_version":"1.0","source":{"id":"1710.10491","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.10491","created_at":"2026-05-18T00:31:49Z"},{"alias_kind":"arxiv_version","alias_value":"1710.10491v1","created_at":"2026-05-18T00:31:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.10491","created_at":"2026-05-18T00:31:49Z"},{"alias_kind":"pith_short_12","alias_value":"YGVKUW6ASG3W","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"YGVKUW6ASG3WQY5X","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"YGVKUW6A","created_at":"2026-05-18T12:31:56Z"}],"graph_snapshots":[{"event_id":"sha256:dfa2d4835737ef8fc396c6ec964fd6e9fc369d1c7606564784effcb382bf689c","target":"graph","created_at":"2026-05-18T00:31:49Z","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":"Let $r,n$ be two natural numbers and let $H(r,n)$ denote the maximal absolute value of $r$th coefficient of divisors of $x^n-1$. In this paper, we show that $\\sum_{n\\leq x}H(r,n)$ is asymptotically equal to $c(r)x(\\log x)^{2^r-1}$ for some constant $c(r)>0$. Furthermore, we give an explicit expression of $c(r)$ in terms of $r$.","authors_text":"Sai Teja Somu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-10-28T16:42:08Z","title":"On $rth$ coefficient of divisors of $x^n-1$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.10491","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":"sha256:95ba2a113f06cb79af660f2f6aa0728b053f82ceecb65dde3849e6d75fc6db5d","target":"record","created_at":"2026-05-18T00:31:49Z","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":"a8f7970ccdb48c1f6242a1978a622f6c887c13b50964712632dd0384f70e3490","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-10-28T16:42:08Z","title_canon_sha256":"bbf5edc1f8ad351a449b6372c1b986169280d2f7b7783f3cbae64e74b7e9c396"},"schema_version":"1.0","source":{"id":"1710.10491","kind":"arxiv","version":1}},"canonical_sha256":"c1aaaa5bc091b76863b77883884f1ee857d8f010ee61148df84820d9aabd079d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c1aaaa5bc091b76863b77883884f1ee857d8f010ee61148df84820d9aabd079d","first_computed_at":"2026-05-18T00:31:49.359330Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:31:49.359330Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hkUskvWqiK7IT2ejb+9Rl9eTT53jgOVvjOq23DzWPBIjJmhL8JmuavKBBj5QWWiENkVoeoAC0VosmiBdI9UrAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:31:49.359926Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.10491","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:95ba2a113f06cb79af660f2f6aa0728b053f82ceecb65dde3849e6d75fc6db5d","sha256:dfa2d4835737ef8fc396c6ec964fd6e9fc369d1c7606564784effcb382bf689c"],"state_sha256":"494b95cf8dc3837855a2b1510590f3044cc69110a9f1eaa6833aa2e30a5c541a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r6IEBhzBjjvSPUttTQrSn3vbu0XwD2IJ+E8KiEH/UlLc/WGdDnTbu4Obo7lyPtvC0xVCt0H6aaU5PM458+Q2BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T10:00:12.073494Z","bundle_sha256":"5cc888d87c3fd3f57b46548298db6b90ce7981bd5a0d80b8d8d8bdc55343b74a"}}