{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:TV5OTIICYMIQ2MJJEQGZLBUFMP","short_pith_number":"pith:TV5OTIIC","canonical_record":{"source":{"id":"1407.3359","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-07-12T07:54:44Z","cross_cats_sorted":[],"title_canon_sha256":"d0bc2f1b6a65843d85631ef845bff98686a349b319bfc6457250c7db9681acb8","abstract_canon_sha256":"bba71cac0adeb31f28f8b40e0c683db2c3b73fa27011956cd4970d6d9aff48a9"},"schema_version":"1.0"},"canonical_sha256":"9d7ae9a102c3110d3129240d95868563c5c60e2290952558fbb6900b95bcdf8a","source":{"kind":"arxiv","id":"1407.3359","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.3359","created_at":"2026-05-18T01:11:57Z"},{"alias_kind":"arxiv_version","alias_value":"1407.3359v1","created_at":"2026-05-18T01:11:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.3359","created_at":"2026-05-18T01:11:57Z"},{"alias_kind":"pith_short_12","alias_value":"TV5OTIICYMIQ","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"TV5OTIICYMIQ2MJJ","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"TV5OTIIC","created_at":"2026-05-18T12:28:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:TV5OTIICYMIQ2MJJEQGZLBUFMP","target":"record","payload":{"canonical_record":{"source":{"id":"1407.3359","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-07-12T07:54:44Z","cross_cats_sorted":[],"title_canon_sha256":"d0bc2f1b6a65843d85631ef845bff98686a349b319bfc6457250c7db9681acb8","abstract_canon_sha256":"bba71cac0adeb31f28f8b40e0c683db2c3b73fa27011956cd4970d6d9aff48a9"},"schema_version":"1.0"},"canonical_sha256":"9d7ae9a102c3110d3129240d95868563c5c60e2290952558fbb6900b95bcdf8a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:57.962452Z","signature_b64":"NCaYbugZVlER3AGATCGN1KpBoDLvji4/hhzpwcpxVmxgdrP+JyNaTlwtngPkrg82X3z4RlZBDubJpUurOAeZAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9d7ae9a102c3110d3129240d95868563c5c60e2290952558fbb6900b95bcdf8a","last_reissued_at":"2026-05-18T01:11:57.961953Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:57.961953Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1407.3359","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":"2026-05-18T01:11:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Jdgozz7qs18dH39srCVCOhss8Mr/+38MacoQMkm+oFgTG29AlWSTnFRmR8+CYA6zkHX/40MdIMhkwMRLYAydBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T21:18:03.755394Z"},"content_sha256":"1cba26e17553301eabb72e3b67d3dd5de710383e4f6a4b5c1fad68d1cffea74d","schema_version":"1.0","event_id":"sha256:1cba26e17553301eabb72e3b67d3dd5de710383e4f6a4b5c1fad68d1cffea74d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:TV5OTIICYMIQ2MJJEQGZLBUFMP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On a generalization of Beiter Conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Bartlomiej Bzdega","submitted_at":"2014-07-12T07:54:44Z","abstract_excerpt":"We prove that for every $\\varepsilon>0$ and a nonnegative integer $\\omega$ there exist primes $p_1,p_2,\\ldots,p_\\omega$ such that for $n=p_1p_2\\ldots p_\\omega$ the height of the cyclotomic polynomial $\\Phi_n$ is at least $(1-\\varepsilon)c_\\omega M_n$, where $M_n=\\prod_{i=1}^{\\omega-2}p_i^{2^{\\omega-1-i}-1}$ and $c_\\omega$ is a constant depending only on $\\omega$; furthermore $\\lim_{\\omega\\to\\infty}c_\\omega^{2^{-\\omega}}\\approx0.71$. In our construction we can have $p_i>h(p_1p_2\\ldots p_{i-1})$ for all $i=1,2,\\ldots,\\omega$ and any function $h:\\mathbb{R}_+\\to\\mathbb{R}_+$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.3359","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":"2026-05-18T01:11:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Wb0AhYV3X6gGkeasa5bLj2uTTbvFbTMk6qzpUmDTO6HD6ZotuUMMtO8EqebpVKmC4qBYwUXaCBmJrglYnkpNDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T21:18:03.755752Z"},"content_sha256":"e040af2ad9feba3b6f12f6aea3235b15482037d1336bc8bd23b7ced38a945507","schema_version":"1.0","event_id":"sha256:e040af2ad9feba3b6f12f6aea3235b15482037d1336bc8bd23b7ced38a945507"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TV5OTIICYMIQ2MJJEQGZLBUFMP/bundle.json","state_url":"https://pith.science/pith/TV5OTIICYMIQ2MJJEQGZLBUFMP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TV5OTIICYMIQ2MJJEQGZLBUFMP/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":"2026-05-30T21:18:03Z","links":{"resolver":"https://pith.science/pith/TV5OTIICYMIQ2MJJEQGZLBUFMP","bundle":"https://pith.science/pith/TV5OTIICYMIQ2MJJEQGZLBUFMP/bundle.json","state":"https://pith.science/pith/TV5OTIICYMIQ2MJJEQGZLBUFMP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TV5OTIICYMIQ2MJJEQGZLBUFMP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:TV5OTIICYMIQ2MJJEQGZLBUFMP","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":"bba71cac0adeb31f28f8b40e0c683db2c3b73fa27011956cd4970d6d9aff48a9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-07-12T07:54:44Z","title_canon_sha256":"d0bc2f1b6a65843d85631ef845bff98686a349b319bfc6457250c7db9681acb8"},"schema_version":"1.0","source":{"id":"1407.3359","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.3359","created_at":"2026-05-18T01:11:57Z"},{"alias_kind":"arxiv_version","alias_value":"1407.3359v1","created_at":"2026-05-18T01:11:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.3359","created_at":"2026-05-18T01:11:57Z"},{"alias_kind":"pith_short_12","alias_value":"TV5OTIICYMIQ","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"TV5OTIICYMIQ2MJJ","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"TV5OTIIC","created_at":"2026-05-18T12:28:52Z"}],"graph_snapshots":[{"event_id":"sha256:e040af2ad9feba3b6f12f6aea3235b15482037d1336bc8bd23b7ced38a945507","target":"graph","created_at":"2026-05-18T01:11:57Z","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 prove that for every $\\varepsilon>0$ and a nonnegative integer $\\omega$ there exist primes $p_1,p_2,\\ldots,p_\\omega$ such that for $n=p_1p_2\\ldots p_\\omega$ the height of the cyclotomic polynomial $\\Phi_n$ is at least $(1-\\varepsilon)c_\\omega M_n$, where $M_n=\\prod_{i=1}^{\\omega-2}p_i^{2^{\\omega-1-i}-1}$ and $c_\\omega$ is a constant depending only on $\\omega$; furthermore $\\lim_{\\omega\\to\\infty}c_\\omega^{2^{-\\omega}}\\approx0.71$. In our construction we can have $p_i>h(p_1p_2\\ldots p_{i-1})$ for all $i=1,2,\\ldots,\\omega$ and any function $h:\\mathbb{R}_+\\to\\mathbb{R}_+$.","authors_text":"Bartlomiej Bzdega","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-07-12T07:54:44Z","title":"On a generalization of Beiter Conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.3359","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":"sha256:1cba26e17553301eabb72e3b67d3dd5de710383e4f6a4b5c1fad68d1cffea74d","target":"record","created_at":"2026-05-18T01:11:57Z","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":"bba71cac0adeb31f28f8b40e0c683db2c3b73fa27011956cd4970d6d9aff48a9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-07-12T07:54:44Z","title_canon_sha256":"d0bc2f1b6a65843d85631ef845bff98686a349b319bfc6457250c7db9681acb8"},"schema_version":"1.0","source":{"id":"1407.3359","kind":"arxiv","version":1}},"canonical_sha256":"9d7ae9a102c3110d3129240d95868563c5c60e2290952558fbb6900b95bcdf8a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9d7ae9a102c3110d3129240d95868563c5c60e2290952558fbb6900b95bcdf8a","first_computed_at":"2026-05-18T01:11:57.961953Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:57.961953Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NCaYbugZVlER3AGATCGN1KpBoDLvji4/hhzpwcpxVmxgdrP+JyNaTlwtngPkrg82X3z4RlZBDubJpUurOAeZAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:57.962452Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.3359","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1cba26e17553301eabb72e3b67d3dd5de710383e4f6a4b5c1fad68d1cffea74d","sha256:e040af2ad9feba3b6f12f6aea3235b15482037d1336bc8bd23b7ced38a945507"],"state_sha256":"111f24881013ed7beb14d1ebcd0cbda0cec1c8c4be1394edcfb35adabc23cead"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YykPkb5r5HrkQiKq7ZIJMHvMAq0jHEa/XNir8Adr75LMTwA6uztdoC+QmEr5halt7ydXPkDtxTMaJiHmFf8tAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T21:18:03.758825Z","bundle_sha256":"7b299dc79caa4532d51b51283d333d9212353f0f7069008ca0ddda32023d5408"}}