{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:CZM7EYPJCQBB6ZD2VFKLSSKNCT","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":"ddfde58ee65f4a605d484df0d85c5a2725722fdb5f7eaa862435540536ab0641","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.DS","submitted_at":"2017-07-14T14:00:36Z","title_canon_sha256":"8f2a694f37491be0cae611c4710df373aca38283ce7481c6d18132472d16c893"},"schema_version":"1.0","source":{"id":"1707.04513","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.04513","created_at":"2026-05-18T00:40:17Z"},{"alias_kind":"arxiv_version","alias_value":"1707.04513v1","created_at":"2026-05-18T00:40:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.04513","created_at":"2026-05-18T00:40:17Z"},{"alias_kind":"pith_short_12","alias_value":"CZM7EYPJCQBB","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"CZM7EYPJCQBB6ZD2","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"CZM7EYPJ","created_at":"2026-05-18T12:31:10Z"}],"graph_snapshots":[{"event_id":"sha256:5d2a6eb892175d3d5f6e4330042355483b2605859ef9b8e2f2469015d12c7e1f","target":"graph","created_at":"2026-05-18T00:40:17Z","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":"As a consequence of the main result of this paper efficient conditions guaranteeing the existence of a $T-$periodic solution to the second order differential equation \\begin{equation*} u\"=\\frac{h(t)}{u^{\\lambda}} \\end{equation*} are established. Here, $h\\in L(\\mathbb{R}/T\\mathbb{Z})$ is a piecewise-constant sign-changing function where the non-linear term presents a weak singularity at 0 (i.e. $\\lambda\\in (0,1)$).","authors_text":"Jos\\'e Godoy, Manuel Zamora","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.DS","submitted_at":"2017-07-14T14:00:36Z","title":"Periodic solutions for indefinite singular equations with applications to the weak case"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.04513","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:d100e61c89bfdf82c5d5bb0f7fa7c249d27ed2059e3756177e2af59da8364e50","target":"record","created_at":"2026-05-18T00:40:17Z","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":"ddfde58ee65f4a605d484df0d85c5a2725722fdb5f7eaa862435540536ab0641","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.DS","submitted_at":"2017-07-14T14:00:36Z","title_canon_sha256":"8f2a694f37491be0cae611c4710df373aca38283ce7481c6d18132472d16c893"},"schema_version":"1.0","source":{"id":"1707.04513","kind":"arxiv","version":1}},"canonical_sha256":"1659f261e914021f647aa954b9494d14e8a89c7cc8c6245c0f7e604c244bc7f8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1659f261e914021f647aa954b9494d14e8a89c7cc8c6245c0f7e604c244bc7f8","first_computed_at":"2026-05-18T00:40:17.939867Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:17.939867Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dBBz0smuqyQY3a1PNW/QCeFLttdtHhcefSaKCKP8OasKRgZVBl2lS21cSwwatH4Yl3Lky8aHUmKJDBzGJEW9AA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:17.940591Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.04513","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d100e61c89bfdf82c5d5bb0f7fa7c249d27ed2059e3756177e2af59da8364e50","sha256:5d2a6eb892175d3d5f6e4330042355483b2605859ef9b8e2f2469015d12c7e1f"],"state_sha256":"41c380f388c83af325f87ae9ee06323f85d3613db1612ee0b6619aa000617058"}