brouwer(arithmetic): checked refutations of strict-left-mono of _⊕_ and additive-principal closure on generic sums

[hyperpolymath]

Summary

Promotes the two routes flagged as "structurally blocked" by RankLexSlice3's design note (and Phase13's ⊕-mono-≤-left block comment) into CHECKED REFUTATIONS — named ¬-theorems with explicit counterexamples and irreflexivity-derived ⊥.

Both routes are now checked dead-ends rather than prose claims; the consumer cannot accidentally "rediscover" them and the next session's exploration knows exactly which routes are foreclosed.

What lands

StrictLeftMonoRefuted

• StrictLeftMonoSum (hypothesised property)
• <′-irrefl derived from wf-<′ (standalone helper)
• osuc-oz-⊕-ω≤oz-⊕-ω — both olims denote ω
• strict-left-mono-refuted headline at α = oz, β = osuc oz, γ = ω

AdditivePrincipalGenericRefuted

• AdditivePrincipalGenericSum (hypothesised generalisation of additive-principal-ω-rank-pow)
• ω<′ω⊕ω premise witness (branch 1 of the olim suffices)
• additive-principal-generic-sum-refuted at X = Y = α = β = ω; both premises ω<′ω⊕ω; conclusion ω ⊕ ω <′ ω ⊕ ω refuted

What this does NOT refute

The genuinely open structural route is the parallel-rank refactor (rank-lex-jb : BT → RankLex with a richer bplus-case second-component) mentioned at the bottom of RankLexSlice3's design note — that one is NOT refuted, just non-local to attempt.

Why one PR for two routes

(a) imports <′-irrefl from (b), so the modules ship as a logical pair.

Test plan

• Both modules compile standalone under --safe --without-K, zero postulates, no funext.
• scripts/kernel-guard.sh PASS.
• Pinned in proofs/agda/Smoke.agda, wired into proofs/agda/All.agda.
• Top-level All / Smoke via CI.

[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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    "severity": "medium"
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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/epistemic_erasure/EpistemicErasure.agda",
    "action": "flag",
    "rule_module": "code_safety",
    "severity": "critical"
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]

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