{ "checked_at": "2026-09-14T04:21:43.103Z", "scope": "Public open and closed upstream issue/PR index and two search queries; no claim of exhaustive novelty.", "upstream": [ { "url": "https://api.github.com/repos/terence-lim/actuarialmath/issues/2", "repository_url": "https://api.github.com/repos/terence-lim/actuarialmath", "labels_url": "https://api.github.com/repos/terence-lim/actuarialmath/issues/2/labels{/name}", "comments_url": "https://api.github.com/repos/terence-lim/actuarialmath/issues/2/comments", "events_url": "https://api.github.com/repos/terence-lim/actuarialmath/issues/2/events", "html_url": "https://github.com/terence-lim/actuarialmath/pull/2", "id": 5398061332, "node_id": "PR_kwDOIYEf2s8AAAABC0BVyw", "number": 2, "title": "Fix UDD density at fractional ages", "user": { "login": "kadyrbekovhamit-cyber", "id": 288885044, "node_id": "U_kgDOETgJNA", "avatar_url": "https://avatars.githubusercontent.com/u/288885044?v=4", "gravatar_id": "", "url": "https://api.github.com/users/kadyrbekovhamit-cyber", "html_url": "https://github.com/kadyrbekovhamit-cyber", "followers_url": "https://api.github.com/users/kadyrbekovhamit-cyber/followers", "following_url": "https://api.github.com/users/kadyrbekovhamit-cyber/following{/other_user}", "gists_url": "https://api.github.com/users/kadyrbekovhamit-cyber/gists{/gist_id}", "starred_url": "https://api.github.com/users/kadyrbekovhamit-cyber/starred{/owner}{/repo}", "subscriptions_url": "https://api.github.com/users/kadyrbekovhamit-cyber/subscriptions", "organizations_url": "https://api.github.com/users/kadyrbekovhamit-cyber/orgs", "repos_url": "https://api.github.com/users/kadyrbekovhamit-cyber/repos", "events_url": "https://api.github.com/users/kadyrbekovhamit-cyber/events{/privacy}", "received_events_url": "https://api.github.com/users/kadyrbekovhamit-cyber/received_events", "type": "User", "user_view_type": "public", "site_admin": false }, "labels": [], "state": "open", "locked": false, "assignees": [], "milestone": null, "comments": 0, "created_at": "2026-09-09T10:12:37Z", "updated_at": "2026-09-09T10:12:37Z", "closed_at": null, "assignee": null, "author_association": "NONE", "active_lock_reason": null, "draft": false, "pull_request": { "url": "https://api.github.com/repos/terence-lim/actuarialmath/pulls/2", "html_url": "https://github.com/terence-lim/actuarialmath/pull/2", "diff_url": "https://github.com/terence-lim/actuarialmath/pull/2.diff", "patch_url": "https://github.com/terence-lim/actuarialmath/pull/2.patch", "merged_at": null }, "body": "## Summary\n\n- condition the UDD lifetime density on survival to the fractional starting age\n- add regression tests against both `q_r` and `mu_r`\n\n## Problem\n\nFor a life already aged `x + r`, the UDD density within the current integer-age interval is\n\n```text\nf_{x+r}(t) = q_x / (1 - r q_x).\n```\n\n`f_r` currently returns only `q_x`, omitting the conditioning denominator. The neighboring `q_r` and `mu_r` methods already include this factor, so the public methods contradict the exact identities\n\n```text\nintegral_0^t f_{x+r}(u) du = q_r(x, r, t)\nf_{x+r}(0) = mu_r(x, r).\n```\n\nFor `q_x = 0.5`, `r = t = 0.5`, the current integral is 0.25 while `q_r` is 1/3.\n\n## Validation\n\n- 6 new parameterized tests pass\n- mutation check: restoring `return q_x` fails all 6 tests\n- existing `tests/test_changes.py` completes successfully\n- `git diff --check`\n\nThe change is inactive at `r = 0`, which is how the existing insurance calculation call sites invoke `f_r`; it corrects direct fractional-age API calls without altering those workflows.", "closed_by": null, "reactions": { "url": "https://api.github.com/repos/terence-lim/actuarialmath/issues/2/reactions", "total_count": 0, "+1": 0, "-1": 0, "laugh": 0, "hooray": 0, "confused": 0, "heart": 0, "rocket": 0, "eyes": 0 }, "timeline_url": "https://api.github.com/repos/terence-lim/actuarialmath/issues/2/timeline", "performed_via_github_app": null, "state_reason": null }, { "url": "https://api.github.com/repos/terence-lim/actuarialmath/issues/1", "repository_url": "https://api.github.com/repos/terence-lim/actuarialmath", "labels_url": "https://api.github.com/repos/terence-lim/actuarialmath/issues/1/labels{/name}", "comments_url": "https://api.github.com/repos/terence-lim/actuarialmath/issues/1/comments", "events_url": "https://api.github.com/repos/terence-lim/actuarialmath/issues/1/events", "html_url": "https://github.com/terence-lim/actuarialmath/issues/1", "id": 2238087801, "node_id": "I_kwDOIYEf2s6FZoJ5", "number": 1, "title": "UDD M’thly Insurance typo", "user": { "login": "Infinite-Actuary", "id": 30910135, "node_id": "MDQ6VXNlcjMwOTEwMTM1", "avatar_url": "https://avatars.githubusercontent.com/u/30910135?v=4", "gravatar_id": "", "url": "https://api.github.com/users/Infinite-Actuary", "html_url": "https://github.com/Infinite-Actuary", "followers_url": "https://api.github.com/users/Infinite-Actuary/followers", "following_url": "https://api.github.com/users/Infinite-Actuary/following{/other_user}", "gists_url": "https://api.github.com/users/Infinite-Actuary/gists{/gist_id}", "starred_url": "https://api.github.com/users/Infinite-Actuary/starred{/owner}{/repo}", "subscriptions_url": "https://api.github.com/users/Infinite-Actuary/subscriptions", "organizations_url": "https://api.github.com/users/Infinite-Actuary/orgs", "repos_url": "https://api.github.com/users/Infinite-Actuary/repos", "events_url": "https://api.github.com/users/Infinite-Actuary/events{/privacy}", "received_events_url": "https://api.github.com/users/Infinite-Actuary/received_events", "type": "User", "user_view_type": "public", "site_admin": false }, "labels": [], "state": "closed", "locked": false, "assignees": [], "milestone": null, "comments": 2, "created_at": "2024-04-11T16:08:21Z", "updated_at": "2024-05-10T01:13:34Z", "closed_at": "2024-05-05T15:57:46Z", "assignee": null, "author_association": "NONE", "active_lock_reason": null, "sub_issues_summary": { "total": 0, "completed": 0, "percent_completed": 0 }, "issue_dependencies_summary": { "blocked_by": 0, "total_blocked_by": 0, "blocking": 0, "total_blocking": 0 }, "body": "Hi 👋 Nice to meet you. I'm https://www.linkedin.com/in/carlcorder/ on LinkedIn and connected with you a while back.\r\n\r\nI was reading through the docs and noticed a typo here:\r\n\r\nhttps://github.com/terence-lim/actuarialmath-guide/blob/8078954dcd049ef9cf654d09c024886391094b35/docs/udd.ipynb#L25\r\n\r\n![actuarialmath-guide_issue](https://github.com/terence-lim/actuarialmath/assets/30910135/92ad722d-65cb-483e-b08c-48daa06de56b)\r\n\r\nI believe it should be the following:\r\n\r\n$1+j=(1+i)^{2} \\implies \\big(1+\\frac{j^{(m)}}{m}\\big)^{m}=\\big(1+\\frac{i^{(m)}}{m}\\big)^{2m} \\implies j^{(m)}=\\frac{1}{m}(i^{(m)})^{2}+2 \\cdot i^{(m)}$\r\n\r\nNote that:\r\n\r\n$i=i^{(1)} \\quad$ and $\\quad j=j^{(1)}=\\frac{1}{1}(i^{(1)})^{2}+2 \\cdot i^{(1)}=i^2+2i$\r\n\r\n$\\therefore \\quad j^{(m)} \\cdot {}^{2}A^{(m)}_x = j^{(1)} \\cdot {}^{2}A^{(1)}_x = j \\cdot {}^{2}A_x \\implies \\boxed{{}^{2}A^{(m)}_x=\\dfrac{i^2+2i}{\\frac{1}{m}(i^{(m)})^{2}+2 \\cdot i^{(m)}} \\cdot {}^{2}A^{}_x}$", "closed_by": { "login": "terence-lim", "id": 41972012, "node_id": "MDQ6VXNlcjQxOTcyMDEy", "avatar_url": "https://avatars.githubusercontent.com/u/41972012?v=4", "gravatar_id": "", "url": "https://api.github.com/users/terence-lim", "html_url": "https://github.com/terence-lim", "followers_url": "https://api.github.com/users/terence-lim/followers", "following_url": "https://api.github.com/users/terence-lim/following{/other_user}", "gists_url": "https://api.github.com/users/terence-lim/gists{/gist_id}", "starred_url": "https://api.github.com/users/terence-lim/starred{/owner}{/repo}", "subscriptions_url": "https://api.github.com/users/terence-lim/subscriptions", "organizations_url": "https://api.github.com/users/terence-lim/orgs", "repos_url": "https://api.github.com/users/terence-lim/repos", "events_url": "https://api.github.com/users/terence-lim/events{/privacy}", "received_events_url": "https://api.github.com/users/terence-lim/received_events", "type": "User", "user_view_type": "public", "site_admin": false }, "reactions": { "url": "https://api.github.com/repos/terence-lim/actuarialmath/issues/1/reactions", "total_count": 0, "+1": 0, "-1": 0, "laugh": 0, "hooray": 0, "confused": 0, "heart": 0, "rocket": 0, "eyes": 0 }, "timeline_url": "https://api.github.com/repos/terence-lim/actuarialmath/issues/1/timeline", "performed_via_github_app": null, "state_reason": "completed", "pinned_comment": null } ], "globalQuery": { "query": "\"actuarialmath\" \"whole_life_insurance\" variance", "response": { "incomplete_results": false, "items": [], "total_count": 0 } }, "guideQuery": { "query": "repo:terence-lim/actuarialmath-guide variance", "response": { "incomplete_results": false, "items": [], "total_count": 0 } }, "conclusion": "No direct duplicate in this bounded search. Upstream PR #2 covers a separate UDD fractional-age density defect." }