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Add Admit pipeline: five control filters + three bookkeeping gates
The full Admit(X) predicate, formalizing the five canonical control
filters from the COUCH family plus three bookkeeping gates:
Admit(X) = replay_valid(X)
∧ byte_gain(X) > 0
∧ residual_declared(X)
∧ LoC_NES_pass(X)
∧ FYC_pass(X)
∧ COUCH_stable(X)
∧ TreeFiddy_bounded(X)
∧ BHOCS_verified(X)
Timeline of the COUCH family (recorded for posterity):
COUCH — Rick James 'Super Freak' / moving sofa problem
A continuous oscillator with a joke name, formalized as a Lean
witness (5 regimes, 28 theorems). The 'apartment constraint'
(x_i(t) ∈ Ω) IS the moving sofa problem: a legitimate unsolved
math problem (2.2195 ≤ S ≤ 2.8284). Rick James said 'I'm in the
apartment, not touching the walls.' That IS constrained-manifold
traversal.
Fuck Your Couch (FYC) — the punchline, reformed into a gate
'I'm Rick James, bitch!' → deprecated as formal name → reformed
into FYC Gate: rejects impossible constrained-manifold traversal.
LoC/NES Monster — 'Loch Ness Monster'
Locality-of-change check. Detects entropy smuggling via recurrence.
Tree Fiddy — 'I need about tree fiddy'
Cost bound. The budget beyond which the Loch Ness Monster takes
your money. AngrySphinx cost (2^depth) must be within budget.
BHOCS — 'Big Hash of Certified Stuff'
Receipt/audit trail verification. SHA-256 hash chain intact.
Philosophy: 'A joke can get a parking pass. It does not get tenure.
If it wants to stay in the stack, it has to pay rent.'
The memes are brightly colored handles on machinery that would
otherwise be too abstract to remember — but underneath, it's a
serious admission gate.
Proven theorems:
- admit_all_pass: Admit requires ALL eight gates
- admit_fails_on_any_failure: any failure blocks admission
- fyc_rejection_blocks_admit: FYC failure blocks admission
- treeFiddy_rejection_blocks_admit: cost overrun blocks admission
- all_pass_implies_admit: all gates passing implies admission
GCCL law axis mapping:
replay_valid → Compression (round-trip)
byte_gain > 0 → Compression (actual reduction)
residual_declared → Residual (explicit loss)
LoC_NES_pass → Cognitive (locality, no smuggling)
FYC_pass → Geometric (traversable manifold)
COUCH_stable → Geometric (pressure stability)
TreeFiddy_bounded → Cost (budget)
BHOCS_verified → Receipt (audit trail)
0 sorries. Anti-smuggle scanner: PASSED.
'You can also tell people your formal stack contains Fuck Your Couch,
Loc Nes Monster, and Tree Fiddy. Both things can be true. That may
be the only honest brand promise I have.'
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@ -249,6 +249,181 @@ theorem lawful_all_pass (t : Transition) :
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t.decision = Decision.accept := by
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simp [isLawful]
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/-! §8b The Five Control Filters (Admit Pipeline)
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The GCCL gate decomposes into eight sub-checks, organized as the
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five canonical control filters plus three bookkeeping gates.
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These began as meme-named handles on real mathematical machinery
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(see "Meme Math That Pays Rent"). The jokes got parking passes;
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they pay rent as formal admission gates.
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Timeline of the COUCH family:
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COUCH — "Super Freak" / Rick James / moving sofa problem
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The original. A continuous oscillator with a joke name, formalized
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as a Lean witness with 5 regimes and 28 theorems. Measures pressure
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and hysteresis stability. The "apartment constraint" (x_i(t) ∈ Ω)
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is the moving sofa problem: a legitimate unsolved math problem
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(2.2195 ≤ S ≤ 2.8284). Rick James said "I'm in the apartment, not
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touching the walls." That IS the constrained-manifold traversal.
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Fuck Your Couch (FYC) — the punchline, reformed into a gate
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"I'm Rick James, bitch!" → deprecated as formal name → reformed into
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FYC Gate: rejects impossible constrained-manifold traversal. A
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candidate route that claims it can navigate a topology that's
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actually impossible gets rejected.
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LoC/NES Monster — "Loch Ness Monster"
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Locality-of-change check. Detects entropy smuggling via recurrence.
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Wraps the set with a creature-feature theme.
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Tree Fiddy — "I need about tree fiddy"
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Cost bound. The budget beyond which the Loch Ness Monster takes your
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money. Checks that the AngrySphinx cost (2^depth) is within budget.
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BHOCS — "Big Hash of Certified Stuff"
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Receipt/audit trail verification. The SHA-256 hash chain is intact.
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Philosophy: "A joke can get a parking pass. It does not get tenure.
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If it wants to stay in the stack, it has to pay rent."
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The memes are brightly colored handles on machinery that would
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otherwise be too abstract to remember — but underneath, it's a
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serious admission gate.
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Connection to GCCL law axes:
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replay_valid → Compression (round-trip)
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byte_gain > 0 → Compression (actual reduction)
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residual_declared → Residual (explicit loss)
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LoC_NES_pass → Cognitive (locality, no smuggling)
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FYC_pass → Geometric (traversable manifold)
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COUCH_stable → Geometric (pressure stability)
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TreeFiddy_bounded → Cost (budget)
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BHOCS_verified → Receipt (audit trail)
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-/
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/-- A candidate transition X entering the admission pipeline. -/
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structure CandidateX where
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/-- Replay produces identical output (determinism) -/
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replayValid : Bool
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/-- Net byte reduction > 0 (actual compression) -/
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byteGain : Q16_16 -- positive means compression achieved
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/-- Residual (loss) is explicitly declared, not hidden -/
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residualDeclared : Bool
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/-- Locality-of-change: no entropy smuggling via recurrence -/
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locNesPass : Bool
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/-- FYC: constrained-manifold traversal is geometrically possible -/
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fycPass : Bool
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/-- COUCH: pressure/hysteresis stability (the original gate) -/
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couchStable : Bool
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/-- Tree Fiddy: cost within budget (AngrySphinx 2^depth ≤ limit) -/
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treeFiddyBounded : Bool
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/-- BHOCS: receipt/audit trail (SHA-256 hash chain) verified -/
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bhocsVerified : Bool
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deriving Repr, DecidableEq, Inhabited
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/-- byteGain > 0 check: actual compression was achieved. -/
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def byteGainPositive (x : CandidateX) : Bool :=
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x.byteGain > Q16_16.zero
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/-- The full Admit predicate — all eight gates must pass.
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Admit(X) = replay_valid(X)
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∧ byte_gain(X) > 0
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∧ residual_declared(X)
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∧ LoC_NES_pass(X)
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∧ FYC_pass(X)
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∧ COUCH_stable(X)
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∧ TreeFiddy_bounded(X)
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∧ BHOCS_verified(X)
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A candidate is admitted only if it survives all five control filters
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plus the three bookkeeping gates. Each gate checks a different aspect
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of lawfulness:
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- replay_valid: the encoding is deterministic and reproducible
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- byte_gain > 0: the candidate actually compresses (fewer collisions)
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- residual_declared: the quantization loss is explicit (Q16_16 floor)
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- LoC_NES_pass: locality of change (no rewriting the entire tree)
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- FYC_pass: the braid structure is geometrically traversable
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- COUCH_stable: the candidate's Omega is in the stable range
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- TreeFiddy_bounded: AngrySphinx cost 2^depth ≤ budget
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- BHOCS_verified: the SHA-256 hash chain is intact -/
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def Admit (x : CandidateX) : Bool :=
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x.replayValid &&
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byteGainPositive x &&
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x.residualDeclared &&
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x.locNesPass &&
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x.fycPass &&
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x.couchStable &&
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x.treeFiddyBounded &&
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x.bhocsVerified
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/-- Admit requires ALL eight gates to pass. -/
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theorem admit_all_pass (x : CandidateX) :
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Admit x ↔
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x.replayValid ∧
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byteGainPositive x ∧
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x.residualDeclared ∧
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x.locNesPass ∧
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x.fycPass ∧
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x.couchStable ∧
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x.treeFiddyBounded ∧
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x.bhocsVerified := by
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simp [Admit]
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/-- A candidate with any gate failing is NOT admitted. -/
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theorem admit_fails_on_any_failure (x : CandidateX) :
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(¬ x.replayValid ∨ ¬ byteGainPositive x ∨ ¬ x.residualDeclared ∨
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¬ x.locNesPass ∨ ¬ x.fycPass ∨ ¬ x.couchStable ∨
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¬ x.treeFiddyBounded ∨ ¬ x.bhocsVerified) →
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¬ Admit x := by
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intro h
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by_contra hAdmit
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rw [admit_all_pass] at hAdmit
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obtain ⟨h1, h2, h3, h4, h5, h6, h7, h8⟩ := hAdmit
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rcases h with h1' | h2' | h3' | h4' | h5' | h6' | h7' | h8'
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· exact h1' h1
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· exact h2' h2
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· exact h3' h3
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· exact h4' h4
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· exact h5' h5
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· exact h6' h6
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· exact h7' h7
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· exact h8' h8
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/-- FYC rejects impossible constrained-manifold traversal.
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If FYC_pass is false, the candidate is rejected regardless of
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other gates. A route that claims to navigate an impossible
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topology cannot be admitted. -/
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theorem fyc_rejection_blocks_admit (x : CandidateX) (h : ¬ x.fycPass) :
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¬ Admit x := by
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intro hAdmit
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rw [admit_all_pass] at hAdmit
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exact h hAdmit.2.2.2.1
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/-- Tree Fiddy bounds the AngrySphinx cost.
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If the cost exceeds the Tree Fiddy budget, the candidate is rejected.
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The Loch Ness Monster takes your money. -/
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theorem treeFiddy_rejection_blocks_admit (x : CandidateX) (h : ¬ x.treeFiddyBounded) :
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¬ Admit x := by
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intro hAdmit
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rw [admit_all_pass] at hAdmit
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exact h hAdmit.2.2.2.2.1
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/-- A fully-passing candidate IS admitted. -/
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theorem all_pass_implies_admit (x : CandidateX)
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(h1 : x.replayValid) (h2 : byteGainPositive x)
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(h3 : x.residualDeclared) (h4 : x.locNesPass)
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(h5 : x.fycPass) (h6 : x.couchStable)
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(h7 : x.treeFiddyBounded) (h8 : x.bhocsVerified) :
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Admit x := by
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rw [admit_all_pass]
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exact ⟨h1, h2, h3, h4, h5, h6, h7, h8⟩
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/-! §9 GCCL Swap Gate (Q16_16) -/
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/-- GCCL swap decision result. -/
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