ordinal(buchholz): fix Slice 2-bplus — explicit implicit on ≤′-refl (CI-quota fallout)

[hyperpolymath]

Context

Agda was not installed in the container during this session, and CI was queue-stuck because the GitHub Actions quota was exhausted, so PRs #130/#131/#133 merged unverified. After installing agda 2.6.3 + stdlib v2.3 in the container, running the full suite revealed one real bug.

The bug

ω-rank-pow-mono-≤Ω's ω≤ω case used ≤′-refl without an explicit {α} annotation:

ω-rank-pow-mono-≤Ω ω≤ω = ≤′-refl

Agda can't infer which α to use — ≤′-refl is a polymorphic identity and the call site doesn't constrain it enough. Fix: annotate the implicit explicitly.

ω-rank-pow-mono-≤Ω ω≤ω = ≤′-refl {ω-rank-pow ω}

Verification

agda -i proofs/agda proofs/agda/All.agda exits 0 after this fix. The full suite, including all of Slice 1 + Slice 2 + Slice 2-omega + head-Ω inversion + Slice 2-bplus, typechecks clean under --safe --without-K. No postulates. The rest of the inspection-verified content was correct.

Honest accounting

The Slice 2-bplus proof was sound as written for inspection; the bug was a type-inference oversight that any local agda would have caught instantly. I should have installed agda when the lack of CI verification became visible. Two PRs ago (#131) I added "CI is authoritative; inspection is auxiliary" to the PR description as a guardrail — that wasn't followed through on. Lesson logged.

Test plan

• agda -i proofs/agda proofs/agda/All.agda exits 0 locally.
• CI greens (if GitHub Actions quota is now available).

https://claude.ai/code/session_013nLEeKZXpvHnrDZMgRm19S

---

Generated by Claude Code

[github-actions]

🔍 Hypatia Security Scan

Findings: 56 issues detected

Severity	Count
🔴 Critical	10
🟠 High	27
🟡 Medium	19

⚠️ Action Required: Critical security issues found!

View findings

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    "file": "/home/runner/work/echo-types/echo-types",
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  {
    "reason": "Issue in agda.yml",
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    "action": "flag",
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    "severity": "medium"
  },
  {
    "reason": "Issue in governance.yml",
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    "action": "flag",
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    "severity": "medium"
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  {
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    "reason": "Issue in mirror.yml",
    "type": "unknown",
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    "action": "flag",
    "rule_module": "workflow_audit",
    "severity": "medium"
  },
  {
    "reason": "Issue in scorecard.yml",
    "type": "unknown",
    "file": "scorecard.yml",
    "action": "flag",
    "rule_module": "workflow_audit",
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  {
    "reason": "Agda postulate assumes without proof -- potential soundness hole (1 occurrences, CWE-704)",
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    "file": "/home/runner/work/echo-types/echo-types/tutorial/provenance_debugging/ProvenanceDebugging.agda",
    "action": "flag",
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    "reason": "Agda postulate assumes without proof -- potential soundness hole (1 occurrences, CWE-704)",
    "type": "agda_postulate",
    "file": "/home/runner/work/echo-types/echo-types/tutorial/epistemic_erasure/EpistemicErasure.agda",
    "action": "flag",
    "rule_module": "code_safety",
    "severity": "critical"
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]

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