{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:YCRT5VJXKDQIMAXBNNPJSVD2YC","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":"5110db7165aa03151badc91c0802e34edb76fb4eb42ff861661f51f7ac198861","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-05-26T13:07:42Z","title_canon_sha256":"5be6e220b71722d1d11b75ddcf56a44939bdd2ee3a7ad01417eb671c1fee202b"},"schema_version":"1.0","source":{"id":"1805.10480","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.10480","created_at":"2026-05-18T00:14:43Z"},{"alias_kind":"arxiv_version","alias_value":"1805.10480v2","created_at":"2026-05-18T00:14:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.10480","created_at":"2026-05-18T00:14:43Z"},{"alias_kind":"pith_short_12","alias_value":"YCRT5VJXKDQI","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_16","alias_value":"YCRT5VJXKDQIMAXB","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_8","alias_value":"YCRT5VJX","created_at":"2026-05-18T12:33:04Z"}],"graph_snapshots":[{"event_id":"sha256:478fba78d589dab526897649ed13219d953246684a77dbe01776b25fb73af8d8","target":"graph","created_at":"2026-05-18T00:14:43Z","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":"This paper presents an analytical closed-form solution to improper integral $\\mu(r)=\\int_0^{\\infty} x^r dx$, where $r \\geq 0$. The solution technique is based on splitting the improper integral into an infinite sum of definite integrals with successive integer limits. The exact solution of every definite integral is obtained by making use of the binomial polynomial expansion, which then allows expression of the entire summation equivalently in terms of a weighted sum of Riemann zeta functions. It turns out that the solution fundamentally depends on whether or not $r$ is an integer. If $r$ is a","authors_text":"Farhad Aghili, Siamak Tafazoli","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-05-26T13:07:42Z","title":"Analytical Solution to Improper Integral of Divergent Power Functions Using The Riemann Zeta Function"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.10480","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":"sha256:28ca484cb2c04bc276b083ccff056926a5e789ebf4ed05f133baaef813081caa","target":"record","created_at":"2026-05-18T00:14:43Z","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":"5110db7165aa03151badc91c0802e34edb76fb4eb42ff861661f51f7ac198861","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-05-26T13:07:42Z","title_canon_sha256":"5be6e220b71722d1d11b75ddcf56a44939bdd2ee3a7ad01417eb671c1fee202b"},"schema_version":"1.0","source":{"id":"1805.10480","kind":"arxiv","version":2}},"canonical_sha256":"c0a33ed53750e08602e16b5e99547ac0ae3ad01242d87b9f47ad658327956082","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c0a33ed53750e08602e16b5e99547ac0ae3ad01242d87b9f47ad658327956082","first_computed_at":"2026-05-18T00:14:43.730757Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:14:43.730757Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/3nqrsRsuDeG2VxK0EGnGMIGYVyYV43G7AkW/1L83qaMO6Gy3bZhwGmBR8p1u+Ipq8IL8lbJlxPLuVl70JyNCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:14:43.731201Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.10480","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:28ca484cb2c04bc276b083ccff056926a5e789ebf4ed05f133baaef813081caa","sha256:478fba78d589dab526897649ed13219d953246684a77dbe01776b25fb73af8d8"],"state_sha256":"a16fd68d5b7260d3a48650ffcbba51f1ca418aca608a889e781c5473f737fec0"}