{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:NOS4ZWVQPTCVEHMCTCGTGZQS35","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":"616bd15d63eaaaa1873da8b05f6afce58d09763f69ccc200b25036ec9602520b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-06-28T20:30:54Z","title_canon_sha256":"2dd88cfb8d49aec5123076019dbbec18bbf5bf0f7d3ead0d0b32735e28d544c1"},"schema_version":"1.0","source":{"id":"1706.09475","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.09475","created_at":"2026-05-18T00:41:14Z"},{"alias_kind":"arxiv_version","alias_value":"1706.09475v1","created_at":"2026-05-18T00:41:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.09475","created_at":"2026-05-18T00:41:14Z"},{"alias_kind":"pith_short_12","alias_value":"NOS4ZWVQPTCV","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"NOS4ZWVQPTCVEHMC","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"NOS4ZWVQ","created_at":"2026-05-18T12:31:34Z"}],"graph_snapshots":[{"event_id":"sha256:ee1ef1e2b880c1b6df6ae6de466d6555df57fd9c8dfcdd35d1a3266cd1ca9bab","target":"graph","created_at":"2026-05-18T00:41:14Z","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":"Recently, new classes of positive and measurable functions, $\\mathcal{M}(\\rho)$ and $\\mathcal{M}(\\pm \\infty)$, have been defined in terms of their asymptotic behaviour at infinity, when normalized by a logarithm (Cadena et al., 2015, 2016, 2017). Looking for other suitable normalizing functions than logarithm seems quite natural. It is what is developed in this paper, studying new classes of functions of the type $\\displaystyle \\lim_{x\\rightarrow \\infty}\\log U(x)/H(x)=\\rho <\\infty$ for a large class of normalizing functions $H$. It provides subclasses of $\\mathcal{M}(0)$ and $\\mathcal{M}(\\pm\\i","authors_text":"Edward Omey, Marie Kratz, Meitner Cadena","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-06-28T20:30:54Z","title":"New results on the order of functions at infinity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.09475","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":"sha256:7c7fe2136a352844062ae78fd29a649a3e15b56e1c70dd08d262d8e46d3daa80","target":"record","created_at":"2026-05-18T00:41:14Z","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":"616bd15d63eaaaa1873da8b05f6afce58d09763f69ccc200b25036ec9602520b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-06-28T20:30:54Z","title_canon_sha256":"2dd88cfb8d49aec5123076019dbbec18bbf5bf0f7d3ead0d0b32735e28d544c1"},"schema_version":"1.0","source":{"id":"1706.09475","kind":"arxiv","version":1}},"canonical_sha256":"6ba5ccdab07cc5521d82988d336612df4fdec945b686f6ffc93476c31a6f522a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6ba5ccdab07cc5521d82988d336612df4fdec945b686f6ffc93476c31a6f522a","first_computed_at":"2026-05-18T00:41:14.983012Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:14.983012Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"x1EI0pOAtvfrO0isSIx7SObMKMIEU55JDzUmiInEQhg5uty3hb4gfo+KMzMmeabeWMLjdg3lq+pl27rGkozOBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:14.983594Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.09475","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7c7fe2136a352844062ae78fd29a649a3e15b56e1c70dd08d262d8e46d3daa80","sha256:ee1ef1e2b880c1b6df6ae6de466d6555df57fd9c8dfcdd35d1a3266cd1ca9bab"],"state_sha256":"22e14c7a48a0804ca218c2df8b4f15a240316dcd6c2e8120c9c2192bda87ca02"}