{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:SAMWNEUTDJ3OL2SRIPLGSTHFQ7","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":"b24deb7efd06285465b8ff14bf69623db74d70033977804189289c5187b826b0","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-05-14T05:59:17Z","title_canon_sha256":"2b8e56c94b4ddc2f59158eb3e77dcb150361a6477b54c2ebb5124bfa3e54695f"},"schema_version":"1.0","source":{"id":"1905.05403","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.05403","created_at":"2026-05-17T23:46:02Z"},{"alias_kind":"arxiv_version","alias_value":"1905.05403v1","created_at":"2026-05-17T23:46:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.05403","created_at":"2026-05-17T23:46:02Z"},{"alias_kind":"pith_short_12","alias_value":"SAMWNEUTDJ3O","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"SAMWNEUTDJ3OL2SR","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"SAMWNEUT","created_at":"2026-05-18T12:33:27Z"}],"graph_snapshots":[{"event_id":"sha256:a444ea497c6f61acaf2c07eac57dcc41c9c1a0c2ecb3cbe35d85fa102da0a139","target":"graph","created_at":"2026-05-17T23:46:02Z","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":"Considering Wirtinger's inequality for piece-wise equipartite functions we find a discrete version of this classical inequality. The main tool we use is the theorem of classification of isometries. Our approach provides a new elementary proof of Wirtinger's inequality that also allows to study the case of equality. Moreover it leads in a natural way to the Fourier series development of $2\\pi$-periodic functions.","authors_text":"Agust\\'i Revent\\'os, Carlos J. Rodr\\'iguez, Juli\\`a Cuf\\'i","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-05-14T05:59:17Z","title":"A discrete approach to Wirtinger's inequality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.05403","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":"sha256:766a7fbe4a926f24926940057f67606a7cc94f98b59d8e7c8dfb7d0ae1e2618e","target":"record","created_at":"2026-05-17T23:46:02Z","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":"b24deb7efd06285465b8ff14bf69623db74d70033977804189289c5187b826b0","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-05-14T05:59:17Z","title_canon_sha256":"2b8e56c94b4ddc2f59158eb3e77dcb150361a6477b54c2ebb5124bfa3e54695f"},"schema_version":"1.0","source":{"id":"1905.05403","kind":"arxiv","version":1}},"canonical_sha256":"90196692931a76e5ea5143d6694ce587f652a2693f1bea11c22cd6573e01ae85","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"90196692931a76e5ea5143d6694ce587f652a2693f1bea11c22cd6573e01ae85","first_computed_at":"2026-05-17T23:46:02.908743Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:46:02.908743Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YN5llmQf6PWBFX2MfeP8bUfpFcDaJy5uDV+qCTXm7/xS+NkxgPjjybQU1VjVXWn2z0JWDb8jCAQv9704dCjCDA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:46:02.909370Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.05403","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:766a7fbe4a926f24926940057f67606a7cc94f98b59d8e7c8dfb7d0ae1e2618e","sha256:a444ea497c6f61acaf2c07eac57dcc41c9c1a0c2ecb3cbe35d85fa102da0a139"],"state_sha256":"ecbb99295b660a87dd94d23e4d90a09044f899944b23bf0dc2dab876be39d51e"}