{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:ZHVHSSZUNV23XZJFERVWF6FJOZ","short_pith_number":"pith:ZHVHSSZU","canonical_record":{"source":{"id":"1111.5401","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-11-23T05:07:25Z","cross_cats_sorted":[],"title_canon_sha256":"a7afe77f847438801846c0fddeedc178da9754ec4ce863acca1ad96ae2bcbd2b","abstract_canon_sha256":"2d938f2485f2accf12c2b17ab4049ed202a7d7c9105862b4f1367c950188221c"},"schema_version":"1.0"},"canonical_sha256":"c9ea794b346d75bbe525246b62f8a97678954bfb3e61ce47fe706c533da723fd","source":{"kind":"arxiv","id":"1111.5401","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.5401","created_at":"2026-05-18T04:07:52Z"},{"alias_kind":"arxiv_version","alias_value":"1111.5401v1","created_at":"2026-05-18T04:07:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.5401","created_at":"2026-05-18T04:07:52Z"},{"alias_kind":"pith_short_12","alias_value":"ZHVHSSZUNV23","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"ZHVHSSZUNV23XZJF","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"ZHVHSSZU","created_at":"2026-05-18T12:26:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:ZHVHSSZUNV23XZJFERVWF6FJOZ","target":"record","payload":{"canonical_record":{"source":{"id":"1111.5401","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-11-23T05:07:25Z","cross_cats_sorted":[],"title_canon_sha256":"a7afe77f847438801846c0fddeedc178da9754ec4ce863acca1ad96ae2bcbd2b","abstract_canon_sha256":"2d938f2485f2accf12c2b17ab4049ed202a7d7c9105862b4f1367c950188221c"},"schema_version":"1.0"},"canonical_sha256":"c9ea794b346d75bbe525246b62f8a97678954bfb3e61ce47fe706c533da723fd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:07:52.084382Z","signature_b64":"jSKM7tOrXhSREM9tHC85lfjjziSlEVFreXOsuQEa2H/XiBvfZgLS91tQs5/7BTg5v7z8PQXLDvu5FsVR3/9gDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c9ea794b346d75bbe525246b62f8a97678954bfb3e61ce47fe706c533da723fd","last_reissued_at":"2026-05-18T04:07:52.083732Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:07:52.083732Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1111.5401","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":"2026-05-18T04:07:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cz0IpRvOVfBMhZdiETeH4zy4FFTch1XcM6DJsxZ7hElE9Xumcn7sPukw5/IeBhsoBIpbgc515O+xGfcy+oXTBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T02:44:42.831111Z"},"content_sha256":"1870b8476b49e23d10e8c284269602050aff54a55fba70b6010ef5f92bf3f300","schema_version":"1.0","event_id":"sha256:1870b8476b49e23d10e8c284269602050aff54a55fba70b6010ef5f92bf3f300"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:ZHVHSSZUNV23XZJFERVWF6FJOZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Polynomials with divisors of every degree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Lola Thompson","submitted_at":"2011-11-23T05:07:25Z","abstract_excerpt":"We consider polynomials of the form t^n-1 and determine when members of this family have a divisor of every degree in Z[t]. With F(x) defined to be the number of such integers up to x, we prove the existence of two positive constants c_1 and c_2 such that $$c_1 x/(log x) \\leq F(x) \\leq c_2 x/(log x).$$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.5401","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":"2026-05-18T04:07:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cTSSDKL6ug+t2E0QUvdgKYO6KV4szDEC+zxRsrY4GLmOavivflnWEom4Rex7p4xTjkfp/MvfsK70KjKE5eZZBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T02:44:42.831472Z"},"content_sha256":"de4ba74b4ae7e0ef94243c6f5068105d3e15f7f0159ecf15be194cfe6cef3336","schema_version":"1.0","event_id":"sha256:de4ba74b4ae7e0ef94243c6f5068105d3e15f7f0159ecf15be194cfe6cef3336"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZHVHSSZUNV23XZJFERVWF6FJOZ/bundle.json","state_url":"https://pith.science/pith/ZHVHSSZUNV23XZJFERVWF6FJOZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZHVHSSZUNV23XZJFERVWF6FJOZ/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":"2026-06-30T02:44:42Z","links":{"resolver":"https://pith.science/pith/ZHVHSSZUNV23XZJFERVWF6FJOZ","bundle":"https://pith.science/pith/ZHVHSSZUNV23XZJFERVWF6FJOZ/bundle.json","state":"https://pith.science/pith/ZHVHSSZUNV23XZJFERVWF6FJOZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZHVHSSZUNV23XZJFERVWF6FJOZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:ZHVHSSZUNV23XZJFERVWF6FJOZ","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":"2d938f2485f2accf12c2b17ab4049ed202a7d7c9105862b4f1367c950188221c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-11-23T05:07:25Z","title_canon_sha256":"a7afe77f847438801846c0fddeedc178da9754ec4ce863acca1ad96ae2bcbd2b"},"schema_version":"1.0","source":{"id":"1111.5401","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.5401","created_at":"2026-05-18T04:07:52Z"},{"alias_kind":"arxiv_version","alias_value":"1111.5401v1","created_at":"2026-05-18T04:07:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.5401","created_at":"2026-05-18T04:07:52Z"},{"alias_kind":"pith_short_12","alias_value":"ZHVHSSZUNV23","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"ZHVHSSZUNV23XZJF","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"ZHVHSSZU","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:de4ba74b4ae7e0ef94243c6f5068105d3e15f7f0159ecf15be194cfe6cef3336","target":"graph","created_at":"2026-05-18T04:07:52Z","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":"We consider polynomials of the form t^n-1 and determine when members of this family have a divisor of every degree in Z[t]. With F(x) defined to be the number of such integers up to x, we prove the existence of two positive constants c_1 and c_2 such that $$c_1 x/(log x) \\leq F(x) \\leq c_2 x/(log x).$$","authors_text":"Lola Thompson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-11-23T05:07:25Z","title":"Polynomials with divisors of every degree"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.5401","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":"sha256:1870b8476b49e23d10e8c284269602050aff54a55fba70b6010ef5f92bf3f300","target":"record","created_at":"2026-05-18T04:07:52Z","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":"2d938f2485f2accf12c2b17ab4049ed202a7d7c9105862b4f1367c950188221c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-11-23T05:07:25Z","title_canon_sha256":"a7afe77f847438801846c0fddeedc178da9754ec4ce863acca1ad96ae2bcbd2b"},"schema_version":"1.0","source":{"id":"1111.5401","kind":"arxiv","version":1}},"canonical_sha256":"c9ea794b346d75bbe525246b62f8a97678954bfb3e61ce47fe706c533da723fd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c9ea794b346d75bbe525246b62f8a97678954bfb3e61ce47fe706c533da723fd","first_computed_at":"2026-05-18T04:07:52.083732Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:07:52.083732Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jSKM7tOrXhSREM9tHC85lfjjziSlEVFreXOsuQEa2H/XiBvfZgLS91tQs5/7BTg5v7z8PQXLDvu5FsVR3/9gDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:07:52.084382Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.5401","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1870b8476b49e23d10e8c284269602050aff54a55fba70b6010ef5f92bf3f300","sha256:de4ba74b4ae7e0ef94243c6f5068105d3e15f7f0159ecf15be194cfe6cef3336"],"state_sha256":"98469e380a01818b4359f942e7e0ceff6fc385054b7c37b6e2a95a436ab43a8f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8Wm0ieAT8Bw25BfJhjD+j65N8rWgVSmDbVvCZithvscN/ckRiJu+2SErzZrxSZM+rm3VXayGZ7IaZjp7k0XXCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T02:44:42.833553Z","bundle_sha256":"47804032244870c906c3d69710e3743be798d45b7a03c47ec73957a208760017"}}