{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:GKCYZ5JX2OFXUBSI447Z6GSEBB","short_pith_number":"pith:GKCYZ5JX","canonical_record":{"source":{"id":"0809.4049","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2008-09-23T23:17:19Z","cross_cats_sorted":[],"title_canon_sha256":"f26e260cb1dc8f47d49cfbc2db1db80aeb2de43ec7b7909068a6d9e61ac1176c","abstract_canon_sha256":"6cc1e5d84b2b2447876f0fda33eaf2ace969f832bfaa0a126d49ca0a9098815a"},"schema_version":"1.0"},"canonical_sha256":"32858cf537d38b7a0648e73f9f1a44085c531e052609cb1850cb12adf8c457b4","source":{"kind":"arxiv","id":"0809.4049","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0809.4049","created_at":"2026-05-18T04:20:50Z"},{"alias_kind":"arxiv_version","alias_value":"0809.4049v2","created_at":"2026-05-18T04:20:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0809.4049","created_at":"2026-05-18T04:20:50Z"},{"alias_kind":"pith_short_12","alias_value":"GKCYZ5JX2OFX","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"GKCYZ5JX2OFXUBSI","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"GKCYZ5JX","created_at":"2026-05-18T12:25:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:GKCYZ5JX2OFXUBSI447Z6GSEBB","target":"record","payload":{"canonical_record":{"source":{"id":"0809.4049","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2008-09-23T23:17:19Z","cross_cats_sorted":[],"title_canon_sha256":"f26e260cb1dc8f47d49cfbc2db1db80aeb2de43ec7b7909068a6d9e61ac1176c","abstract_canon_sha256":"6cc1e5d84b2b2447876f0fda33eaf2ace969f832bfaa0a126d49ca0a9098815a"},"schema_version":"1.0"},"canonical_sha256":"32858cf537d38b7a0648e73f9f1a44085c531e052609cb1850cb12adf8c457b4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:20:50.144207Z","signature_b64":"60gZTLv0d6AKUl36G5mQum8jBYNBHtttvWQ+cXiKMhKYCTLuj0WxqcLoeN4zgHJowWI/upqbS6q9r6Fk22llCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"32858cf537d38b7a0648e73f9f1a44085c531e052609cb1850cb12adf8c457b4","last_reissued_at":"2026-05-18T04:20:50.143434Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:20:50.143434Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0809.4049","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":"2026-05-18T04:20:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OoNFCe6qEWb5rFg9Xcq0POUWzEwL0e5zWgj/PrQHKxGyq2Bjq+z7YXd0wWl8vr/2kc6WHW8ZDfZzQvm5kqTMDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T17:06:28.285702Z"},"content_sha256":"04328a70b14dca1df7439f8ba34d8a8a9f4b4e77af3b306429c34493ab25e601","schema_version":"1.0","event_id":"sha256:04328a70b14dca1df7439f8ba34d8a8a9f4b4e77af3b306429c34493ab25e601"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:GKCYZ5JX2OFXUBSI447Z6GSEBB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sharp approximations to the Bernoulli periodic functions by trigonometric polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Emanuel Carneiro","submitted_at":"2008-09-23T23:17:19Z","abstract_excerpt":"We obtain optimal trigonometric polynomials of a given degree $N$ that majorize, minorize and approximate in $L^1(\\mathbb{R}/\\mathbb{Z})$ the Bernoulli periodic functions. These are the periodic analogues of two works of F. Littmann that generalize a paper of J. Vaaler. As applications we provide the corresponding Erd\\\"{o}s-Tur\\'{a}n-type inequalities, approximations to other periodic functions and bounds for certain Hermitian forms."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0809.4049","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":"2026-05-18T04:20:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zpB1clwQDPEZIBYJ7g13EgyoaTinVtwy9bj09N13V/KcF2vlwwflRzFzzAvAB+ClQZ6NPwZ/W119e/EvXM5DBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T17:06:28.286075Z"},"content_sha256":"da0453febeb9a1b5821e4d4f4b2ef10ebfb06170405acfeeb9f921ab745ed127","schema_version":"1.0","event_id":"sha256:da0453febeb9a1b5821e4d4f4b2ef10ebfb06170405acfeeb9f921ab745ed127"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GKCYZ5JX2OFXUBSI447Z6GSEBB/bundle.json","state_url":"https://pith.science/pith/GKCYZ5JX2OFXUBSI447Z6GSEBB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GKCYZ5JX2OFXUBSI447Z6GSEBB/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":"2026-05-29T17:06:28Z","links":{"resolver":"https://pith.science/pith/GKCYZ5JX2OFXUBSI447Z6GSEBB","bundle":"https://pith.science/pith/GKCYZ5JX2OFXUBSI447Z6GSEBB/bundle.json","state":"https://pith.science/pith/GKCYZ5JX2OFXUBSI447Z6GSEBB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GKCYZ5JX2OFXUBSI447Z6GSEBB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:GKCYZ5JX2OFXUBSI447Z6GSEBB","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":"6cc1e5d84b2b2447876f0fda33eaf2ace969f832bfaa0a126d49ca0a9098815a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2008-09-23T23:17:19Z","title_canon_sha256":"f26e260cb1dc8f47d49cfbc2db1db80aeb2de43ec7b7909068a6d9e61ac1176c"},"schema_version":"1.0","source":{"id":"0809.4049","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0809.4049","created_at":"2026-05-18T04:20:50Z"},{"alias_kind":"arxiv_version","alias_value":"0809.4049v2","created_at":"2026-05-18T04:20:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0809.4049","created_at":"2026-05-18T04:20:50Z"},{"alias_kind":"pith_short_12","alias_value":"GKCYZ5JX2OFX","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"GKCYZ5JX2OFXUBSI","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"GKCYZ5JX","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:da0453febeb9a1b5821e4d4f4b2ef10ebfb06170405acfeeb9f921ab745ed127","target":"graph","created_at":"2026-05-18T04:20:50Z","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 obtain optimal trigonometric polynomials of a given degree $N$ that majorize, minorize and approximate in $L^1(\\mathbb{R}/\\mathbb{Z})$ the Bernoulli periodic functions. These are the periodic analogues of two works of F. Littmann that generalize a paper of J. Vaaler. As applications we provide the corresponding Erd\\\"{o}s-Tur\\'{a}n-type inequalities, approximations to other periodic functions and bounds for certain Hermitian forms.","authors_text":"Emanuel Carneiro","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2008-09-23T23:17:19Z","title":"Sharp approximations to the Bernoulli periodic functions by trigonometric polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0809.4049","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":"sha256:04328a70b14dca1df7439f8ba34d8a8a9f4b4e77af3b306429c34493ab25e601","target":"record","created_at":"2026-05-18T04:20:50Z","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":"6cc1e5d84b2b2447876f0fda33eaf2ace969f832bfaa0a126d49ca0a9098815a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2008-09-23T23:17:19Z","title_canon_sha256":"f26e260cb1dc8f47d49cfbc2db1db80aeb2de43ec7b7909068a6d9e61ac1176c"},"schema_version":"1.0","source":{"id":"0809.4049","kind":"arxiv","version":2}},"canonical_sha256":"32858cf537d38b7a0648e73f9f1a44085c531e052609cb1850cb12adf8c457b4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"32858cf537d38b7a0648e73f9f1a44085c531e052609cb1850cb12adf8c457b4","first_computed_at":"2026-05-18T04:20:50.143434Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:20:50.143434Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"60gZTLv0d6AKUl36G5mQum8jBYNBHtttvWQ+cXiKMhKYCTLuj0WxqcLoeN4zgHJowWI/upqbS6q9r6Fk22llCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:20:50.144207Z","signed_message":"canonical_sha256_bytes"},"source_id":"0809.4049","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:04328a70b14dca1df7439f8ba34d8a8a9f4b4e77af3b306429c34493ab25e601","sha256:da0453febeb9a1b5821e4d4f4b2ef10ebfb06170405acfeeb9f921ab745ed127"],"state_sha256":"58ea5e87ea854e9c8088d26b6c7eaa923882adc2d5a3f097d9cf23dd9a966f63"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ubR6gyyv9tD/Sckf3U3o6rYlMpNh7FvXQ0n5RPh0ZKh22p9vJNU7fjGXD4LYP3Mze8FSe+y9RgJRXxPZpAo+DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T17:06:28.289107Z","bundle_sha256":"27ad98fe7322c536aab6393d84d49ed7168a5278856d377a69c5604713587c6c"}}