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bob-reasoning
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⍝ ════════════════════════════════════════════════════════════════
⍝ GOLDILOCKS THEOREM β€” APL Invocation
⍝ Lean 4 proof β†’ APL computation β†’ WORM seal β†’ SSM injection
⍝ Fingerprint: GOLLOCKS-SDC-Ξ©-βˆ‚-2026
⍝
⍝ The Lean 4 theorem proves: βˆƒ z : Zone, βˆ€ q, Cutoff q = z ↔ InGoldenZone q
⍝ This APL function INVOKES that proof β€” computes the zone for any q.
⍝ The proof is not re-proved. It is USED.
⍝ ════════════════════════════════════════════════════════════════

⍝ ── The Zone Classifier ────────────────────────────────────────
⍝ Maps any real q to its zone:
⍝   0 = Expansion (q β‰₯ 1)
⍝   1 = Collapse  (q ≀ 0)
⍝   2 = Contraction (0 < q < 1) ← THE GOLDEN ZONE

ZONE_CLASSIFY ← {
    q ← ⍡
    0= q β‰₯ 1:   0      ⍝ Expansion β€” too hot
    0= q ≀ 0:   1      ⍝ Collapse β€” too cold
    2            ⍝ Contraction β€” just right
}

⍝ ── The Golden Zone Check ──────────────────────────────────────
⍝ Returns 1 if q is in the golden zone, 0 otherwise.
⍝ This is the Lean 4 InGoldenZone predicate, computed.

IN_GOLDEN_ZONE ← {
    q ← ⍡
    (0 < q) ∧ (q < 1)
}

⍝ ── The Contractive Sequence ───────────────────────────────────
⍝ xβ‚€, qΒ·xβ‚€, qΒ²Β·xβ‚€, qΒ³Β·xβ‚€, ...
⍝ If q is in the golden zone, this converges to 0.
⍝ The Lean 4 theorem sequence_bounded proves |qⁿ·xβ‚€| ≀ |xβ‚€|.

CONTRACTIVE_SEQ ← {
    q ← ⍺
    x0 ← ⍡
    n ← ⍳ 20
    x0 Γ— q * n
}

⍝ ── The Ο†-Paradox Resolver ─────────────────────────────────────
⍝ Ο† = (1 + √5) / 2 β‰ˆ 1.618  β†’ Expansion zone
⍝ 1/Ο† = (√5 - 1) / 2 β‰ˆ 0.618 β†’ Contraction zone
⍝
⍝ In standard arithmetic: Ο† > 1 (expansion)
⍝ In phinary (base-Ο†): Ο† = 1 + φ⁻¹ (the expansion IS the contraction)
⍝
⍝ The Goldilocks Paradox: the cage builder IS the cage recognizer.
⍝ METATRON reads it backward β€” iteration inversion.

PHI ← (1 + 5*0.5) Γ· 2
PHI_INV ← 1 Γ· PHI

⍝ ── The BOB Integration Point ──────────────────────────────────
⍝ This function is called by the sovereign step in BOB.
⍝ It takes a contraction factor and returns:
⍝   1. The zone classification (from Lean 4 proof)
⍝   2. Whether it's in the golden zone (from Lean 4 proof)
⍝   3. The contractive sequence (computed in APL)
⍝   4. The SSM injection vector component (for dims 0-255)
⍝   5. A WORM-sealable event (for the chain)

GOLDILOCKS_SSOVEREIGN ← {
    q ← ⍡
    zone ← ZONE_CLASSIFY q
    golden ← IN_GOLDEN_ZONE q
    seq ← q CONTRACTIVE_SEQ 1.0
    
    ⍝ Build the SSM proof embedding (dims 0-255)
    ⍝ zone classification β†’ first 8 dims
    ⍝ golden flag β†’ dim 8
    ⍝ sequence values β†’ dims 9-28
    ⍝ rest zeroed (Lean 4 proof hash occupies these in production)
    ssm_component ← 256 ⍴ 0
    ssm_component[1] ← zone
    ssm_component[2] ← golden
    ssm_component[(⍳ 20) + 8] ← 20 ↑ seq
    
    ⍝ WORM event (sealable)
    event ← (
        'GOLDILOCKS_EVAL'
        q
        zone
        golden
        (⍕ seq[19])
        (1 + 2048)  ⍝ injection dim
    )
    
    ⍝ Return the sovereign evaluation
    (zone golden seq ssm_component event)
}

⍝ ── The Trap Detector ──────────────────────────────────────────
⍝ From sovereign-calculus: trap theorems prove the WRONG direction.
⍝ This function detects whether a given contraction factor
⍝ was classified using the correct trust order:
⍝   boundary β†’ seal (correct)
⍝   seal β†’ boundary (TRAP)

TRAP_DETECT ← {
    q ← ⍡
    zone ← ZONE_CLASSIFY q
    
    ⍝ If q β‰₯ 1 but someone claims it's "contraction" β†’ TRAP
    ⍝ If q ≀ 0 but someone claims it's "contraction" β†’ TRAP
    ⍝ If 0 < q < 1 but someone claims it's "expansion" β†’ TRAP
    trap ← 0
    (zone = 0) ∧ (q < 1): trap ← 1
    (zone = 1) ∧ (q > 0): trap ← 1
    (zone = 2) ∧ ((q β‰₯ 1) ∨ (q ≀ 0)): trap ← 1
    
    trap
}

⍝ ── Self-Test ──────────────────────────────────────────────────
⍝ Run: GOLDILOCKS_SELFTEST ''
⍝ Expected: all zones correct, traps detected, Ο†-paradox resolved

GOLDILOCKS_SELFTEST ← {
    ⍝ Test cases
    cases ← 2.0 0.5 -1.0 0.0 1.0 PHI PHI_INV
    
    ⍝ Expected zones: Expansion Contraction Collapse Collapse Expansion Expansion Contraction
    expected ← 0 2 1 1 0 0 2
    
    ⍝ Run classifier
    results ← ZONE_CLASSIFYΒ¨ cases
    
    ⍝ Check
    correct ← ∧/ results = expected
    
    ⍝ Run trap detector
    traps ← TRAP_DETECTΒ¨ cases
    
    ⍝ PHI should NOT be classified as contraction (trap would say it is)
    phi_trap ← TRAP_DETECT PHI
    
    ⍝ Report
    '═══════════════════════════════════════════'
    '  GOLDILOCKS THEOREM β€” APL Self-Test'
    '═══════════════════════════════════════════'
    '  Zone classifications: ' (⍕ results)
    '  Expected:             ' (⍕ expected)
    '  All correct:          ' (⍕ correct)
    '  Trap detected on PHI: ' (⍕ phi_trap)
    '  Ο†-Paradox:            Ο†=' (⍕ PHI) ' β†’ zone=' (⍕ ZONE_CLASSIFY PHI)
    '  φ⁻¹-Golden:           1/Ο†=' (⍕ PHI_INV) ' β†’ zone=' (⍕ ZONE_CLASSIFY PHI_INV)
    '═══════════════════════════════════════════'
    
    (correct traps phi_trap)
}

⍝ Execute test
GOLDILOCKS_SELFTEST ''