ordinal(buchholz): Slice 3 umbrella extension — _<ᵇ¹_ with joint-bplus + strict-head dispatch

[hyperpolymath]

Summary

• Extends RankMonoUmbrella._<ᵇ⁰_ (10/13 closed constructors) into a new _<ᵇ¹_ adding a <ᵇ¹-+1-+ constructor for the joint-bplus case where the target's left summand is itself a bplus (excluded by _<ᵇ⁰_'s atomic-target restriction).
• The umbrella rank-pow-mono-<ᵇ¹ dispatches inherited cases to rank-pow-mono-<ᵇ⁰ (via a thin <ᵇ¹-from-<ᵇ⁰ embedding) and the new case to Slice 3 headline rank-mono-<ᵇ-+1-via-head-Ω from RankPowSlice3Headline.
• Honest scope: bpsi-source-at-equality sub-case (ν = head-Ω y₁) is DOCUMENTED AS GATED pending a <ᵇ-+1-specific rank-lex primitive (the existing RankLex.rank-mono-<ᵇ-ψΩ≤-lex only discharges <ᵇ-ψΩ≤).

Files

• New: proofs/agda/Ordinal/Buchholz/RankMonoUmbrellaSlice3.agda (114 lines).
• Wired: proofs/agda/All.agda (1 line, adjacent to RankMonoUmbrella).
• Pinned: proofs/agda/Ordinal/Buchholz/Smoke.agda (own using block per CLAUDE.md "Working rules").

Headlines pinned: _<ᵇ¹_, <ᵇ¹-from-<ᵇ⁰, <ᵇ¹-+1-+, rank-pow-mono-<ᵇ¹.

Discipline

• --safe --without-K throughout; no postulates, no funext.
• New module compiles standalone; All.agda + top-level Smoke.agda + Ordinal/Buchholz/Smoke.agda all exit 0.
• bash scripts/kernel-guard.sh PASS.

Test plan

• agda -i proofs/agda proofs/agda/Ordinal/Buchholz/RankMonoUmbrellaSlice3.agda exits 0
• agda -i proofs/agda proofs/agda/Ordinal/Buchholz/Smoke.agda exits 0
• agda -i proofs/agda proofs/agda/Smoke.agda exits 0
• agda -i proofs/agda proofs/agda/All.agda exits 0
• bash scripts/kernel-guard.sh PASS

Forward path

When a <ᵇ-+1-specific rank-lex primitive lands (Route A from RankPowSlice3 design note), add a second constructor (e.g., <ᵇ¹-+1-+-eq) carrying the rank-lex witness for the equality sub-case and extend rank-pow-mono-<ᵇ¹ to dispatch on it. The current ship covers the strict-head subset cleanly without overclaim.

[github-actions]

🔍 Hypatia Security Scan

Findings: 74 issues detected

Severity	Count
🔴 Critical	17
🟠 High	36
🟡 Medium	21

⚠️ Action Required: Critical security issues found!

View findings

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  {
    "reason": "Issue in agda.yml",
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    "action": "flag",
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    "reason": "Issue in agda.yml",
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    "action": "flag",
    "rule_module": "workflow_audit",
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  },
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    "type": "unknown",
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    "action": "flag",
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  {
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    "type": "unknown",
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    "action": "flag",
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    "severity": "medium"
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  {
    "reason": "Issue in scorecard.yml",
    "type": "unknown",
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    "action": "flag",
    "rule_module": "workflow_audit",
    "severity": "medium"
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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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