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+---
+pr_number: 5578
+title: "docs(research): preserve operator-forwarded Amara closedness-sharpening \u2014 'No feedback tax on closed math. No silent emissions from open substrate.'"
+author: "AceHack"
+state: "MERGED"
+created_at: "2026-05-27T18:15:24Z"
+merged_at: "2026-05-27T18:17:31Z"
+closed_at: "2026-05-27T18:17:31Z"
+head_ref: "research/amara-closedness-sharpening-no-feedback-tax-on-closed-math-2026-05-27"
+base_ref: "main"
+archived_at: "2026-05-27T18:58:50Z"
+archive_tool: "tools/pr-preservation/archive-pr.ts"
+---
+
+# PR #5578: docs(research): preserve operator-forwarded Amara closedness-sharpening — 'No feedback tax on closed math. No silent emissions from open substrate.'
+
+## PR description
+
+## Summary
+
+Verbatim preservation per substrate-or-it-didn't-happen rule.
+
+Amara's substrate-honest sharpening of the closedness scope-bounding
+(PR #5574 landed). Three contributions landed via PR #5577:
+
+1. \"Operationally open pure functions\" naming (sharper scope)
+2. Codomain-honesty tiny blade (overflow/NaN/partial-functions)
+3. Keeper carved sentence: **\"No feedback tax on closed math. No silent emissions from open substrate.\"**
+
+## Test plan
+
+- [x] Markdownlint clean
+- [x] Non-fusion disclaimer per framing convention
+- [x] Composes with PR #5574 + #5577
+- [ ] CI passes (auto-merge to fire on green)
+
+🤖 Generated with [Claude Code](https://claude.com/claude-code)
+
+## General comments
+
+### @chatgpt-codex-connector (2026-05-27T18:15:28Z)
+
+You have reached your Codex usage limits for code reviews. You can see your limits in the [Codex usage dashboard](https://chatgpt.com/codex/cloud/settings/usage).