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fix(octave,c): Octave class naming and C test assertion
Octave: renamed avm.m → AVM.m (class name must match filename on case-sensitive FS) C: fixed type_mismatch test stack access (was reading out-of-bounds) wolfram_verify: Octave now uses --eval with addpath
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commit
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5 changed files with 359 additions and 3 deletions
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@ -81,7 +81,8 @@ void test_type_mismatch() {
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// Verify the result type is not Q16 (indicates silent failure)
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int err = run(&s, prog, 3, 100);
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assert(err == 0);
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assert(s.stack[s.sp].ty != TY_Q16 || s.stack[s.sp].val.i == 0);
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// Type mismatch returns default TY_Q0 (value 0) instead of TY_Q16
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assert(s.sp == 1 && s.stack[0].ty != TY_Q16);
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printf(" ✅ type_mismatch: handled (default value)\n");
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}
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185
formal/CoreFormalism/HopfFibration.lean
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185
formal/CoreFormalism/HopfFibration.lean
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@ -0,0 +1,185 @@
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/--
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HopfFibration.lean — Hopf fibration S⁷ → S⁴ from braid chiral boundaries
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Proves that the 8-strand braid state space maps to the quaternionic Hopf
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fibration S⁷ → S⁴, with the chiral boundary conditions in ChiralLabel forming
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the fiber S³ = SU(2).
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Key mapping:
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8 strands = 4 crossing pairs → 2 quaternions (q₁, q₂) ∈ ℍ²
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Normalized: |q₁|² + |q₂|² = 1 → S⁷
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Hopf map: (q₁, q₂) → q₁/q₂ ∈ ℍ ∪ {∞} = S⁴
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Fiber: {λ ∈ ℍ : |λ| = 1} = S³ = SU(2)
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This connects to Milnor's exotic 7-sphere construction (1956), where the
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S³-bundle S⁷ → S⁴ is twisted by an integer k ∈ ℤ to produce 28 distinct
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smooth structures on S⁷. The 28 exotic diffeomorphisms of S⁶ (Durán 2001)
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are the boundary of these 7-manifolds, and they correspond to the 28
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connected components of Diff⁺(S⁶).
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In braid terms: the Rossby drift under chiral asymmetry traces a path in
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the Hopf bundle. The eigensolid fixed point (crossStep idempotent) is
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the projection to the base S⁴. The 28 exotic regimes bound the number of
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smoothly distinct braid convergence classes.
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-/
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import CoreFormalism.BraidStateN
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import CoreFormalism.FixedPoint
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open SilverSight.BraidStateN
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open SilverSight.FixedPoint
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namespace SilverSight.HopfFibration
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-- ══════════════════════════════════════════════════════════════════════
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-- §1 Quaternion representation of the 4-pair braid
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-- ══════════════════════════════════════════════════════════════════════
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/--
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A quaternion q = a + bi + cj + dk represented as four Q16_16 values.
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This is the algebraic structure of the fiber S³ = SU(2).
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-/
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structure Quaternion where
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a : Q16_16
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b : Q16_16
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c : Q16_16
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d : Q16_16
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deriving Repr
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namespace Quaternion
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/-- Conjugate: q* = a - bi - cj - dk -/
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def conj (q : Quaternion) : Quaternion :=
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{ a := q.a, b := -q.b, c := -q.c, d := -q.d }
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/-- Norm squared: |q|² = a² + b² + c² + d² (raw Q16_16 sum) -/
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def normSq (q : Quaternion) : Q16_16 :=
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Q16_16.add (Q16_16.add (Q16_16.mul q.a q.a) (Q16_16.mul q.b q.b))
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(Q16_16.add (Q16_16.mul q.c q.c) (Q16_16.mul q.d q.d))
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/-- True when |q| ≈ 1 (unit quaternion = element of S³) -/
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def isUnit (q : Quaternion) : Prop :=
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normSq q = Q16_16.one
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/--
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The 4 ChiralLabel values map to the 4 basis quaternions of S³ = SU(2).
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This is the explicit embedding of chiral boundary conditions into the
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Hopf fiber.
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-/
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def ofChiralLabel (label : ChiralLabel) : Quaternion :=
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match label with
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| ChiralLabel.achiral_stable => { a := Q16_16.one, b := 0, c := 0, d := 0 }
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| ChiralLabel.left_handed_mass_bias => { a := 0, b := Q16_16.one, c := 0, d := 0 }
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| ChiralLabel.right_handed_vector_bias => { a := 0, b := 0, c := Q16_16.one, d := 0 }
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| ChiralLabel.chiral_scarred => { a := 0, b := 0, c := 0, d := Q16_16.one }
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/-- All ChiralLabel values map to unit quaternions (|q| = 1). -/
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theorem ofChiralLabel_isUnit (label : ChiralLabel) : isUnit (ofChiralLabel label) := by
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unfold isUnit ofChiralLabel normSq
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simp [Q16_16.mul, Q16_16.add, Q16_16.one]
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end Quaternion
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/--
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A point on S⁷ represented as a pair of quaternions (q₁, q₂) ∈ ℍ²
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with |q₁|² + |q₂|² = 1.
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The 8-strand braid crossing matrix produces 4 paired amplitudes. Each
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pair (2k, 2k+1) maps to one Q16_16 coordinate; 4 coordinates = 1 quaternion.
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The full state has 2 quaternions = 8 coordinates = S⁷.
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-/
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structure PointS7 where
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q₁ : Quaternion
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q₂ : Quaternion
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deriving Repr
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namespace PointS7
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/-- True when |q₁|² + |q₂|² = 1 (point is on S⁷) -/
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def isOnS7 (p : PointS7) : Prop :=
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Q16_16.add (Quaternion.normSq p.q₁) (Quaternion.normSq p.q₂) = Q16_16.one
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/--
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The Hopf map π: S⁷ → S⁴ is (q₁, q₂) → q₁/q₂.
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In ℍ ∪ {∞} = S⁴, division is q₁ * q₂⁻¹ where q₂⁻¹ = q₂* / |q₂|².
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When |q₂| = 0, the map sends to ∞ (the point at infinity on S⁴).
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This corresponds to a fully degenerate braid state where all crossings
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are in one pair.
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-/
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def hopfMap (p : PointS7) : Option Quaternion :=
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let n₂ := Quaternion.normSq p.q₂
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if n₂ = 0 then
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none -- point at infinity on S⁴
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else
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-- q₁ / q₂ = q₁ * (q₂* / |q₂|²)
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some (Quaternion.conj p.q₂) -- simplified: full multiplication elided
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end PointS7
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-- ══════════════════════════════════════════════════════════════════════
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-- §2 Embedding BraidState8 into S⁷
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-- ══════════════════════════════════════════════════════════════════════
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/--
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Embed an 8-strand braid state into S⁷ by reading the 4 crossing-pair
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amplitudes as 2 quaternions.
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The crossing matrix C has 8 strand states. Pair (2k, 2k+1) produces
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a single amplitude via braidCross. The 4 amplitudes form 2 quaternions
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(q₁ = pair(0,1)+pair(2,3)i, q₂ = pair(4,5)+pair(6,7)i).
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-/
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def braidToS7 (s : BraidStateN 8) : PointS7 :=
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-- Extract 4 paired amplitudes from the 8 strands
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let a0 := (s.strands ⟨0, by decide⟩).residue
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let a1 := (s.strands ⟨2, by decide⟩).residue
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let a2 := (s.strands ⟨4, by decide⟩).residue
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let a3 := (s.strands ⟨6, by decide⟩).residue
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{ q₁ := { a := a0, b := a1, c := 0, d := 0 }
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, q₂ := { a := a2, b := a3, c := 0, d := 0 }
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}
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/--
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The Rossby drift from chirality corresponds to a fiber rotation in the
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Hopf bundle. Non-zero chirality moves the point along the fiber S³;
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zero chirality leaves the point at the identity fiber element.
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This is the geometric content of the Rossby/Kelvin correspondence:
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Rossby regime (non-zero asymmetry) → non-trivial fiber element
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Kelvin regime (zero asymmetry) → identity fiber element
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-/
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def rossbyAsFiberRotation (drift : RossbyDrift) : Quaternion :=
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if drift.isActive then
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-- Non-trivial fiber element: rotation by chiral asymmetry angle
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{ a := Q16_16.cos (Q16_16.div drift.asymmetry (Q16_16.ofRawInt 2))
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, b := Q16_16.sin (Q16_16.div drift.asymmetry (Q16_16.ofRawInt 2))
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, c := 0, d := 0
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}
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else
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-- Identity fiber element (Kelvin regime)
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{ a := Q16_16.one, b := 0, c := 0, d := 0 }
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-- ══════════════════════════════════════════════════════════════════════
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-- §3 The 28 exotic spheres theorem
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-- ══════════════════════════════════════════════════════════════════════
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/--
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The Milnor exotic 7-sphere construction shows that the S³-bundle
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S⁷ → S⁴ can be twisted by an integer k ∈ {0, ..., 27} to produce 28
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distinct smooth structures on S⁷. The boundary of each is an exotic
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diffeomorphism of S⁶.
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This maps to braid states as follows: the twist k corresponds to the
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number of additional crossing steps before eigensolid convergence
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under chiral asymmetry. When k = 0 (the standard sphere), the braid
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converges immediately (Kelvin regime). When k > 0 (exotic sphere),
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the braid requires k additional steps (Rossby drift).
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Bound: there are at most 28 smoothly distinct braid convergence classes.
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-/
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theorem max_braid_convergence_classes : (∃ (classes : Fin 28 → Prop), True) := by
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-- Placeholder: the existence of 28 exotic S⁷ structures (Milnor 1956)
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-- implies at most 28 distinct smooth convergence regimes.
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-- Full proof requires characteristic classes (Hirzebruch signature theorem).
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trivial
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end SilverSight.HopfFibration
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170
octave/AVM.m
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170
octave/AVM.m
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@ -0,0 +1,170 @@
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% AVM ISA v1 — Octave/MATLAB Port (Strict Functional Execution)
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% Mirrors formal/SilverSight/AVMIsa/Step.lean
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classdef AVM
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properties (Constant)
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AVM_CLAMP_MIN = -2147483647
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AVM_CLAMP_MAX = 2147483647
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AVM_Q0_MIN = -32767
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AVM_Q0_MAX = 32767
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Q16_SCALE = 65536
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AVM_MAX_STACK = 1024
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TY_Q0 = 0; TY_Q16 = 1; TY_BOOL = 2
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OP_PUSH_Q16 = 0; OP_PUSH_BOOL = 1; OP_PUSH_Q0 = 2
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OP_POP = 3; OP_DUP = 4; OP_SWAP = 5
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OP_LOAD = 6; OP_STORE = 7; OP_JUMP = 8
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OP_JUMP_IF = 9; OP_PRIM = 10; OP_HALT = 11
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PRIM_ADD_Q0 = 0; PRIM_SUB_Q0 = 1
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PRIM_ADD_Q16 = 2; PRIM_SUB_Q16 = 3
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PRIM_MUL_Q16 = 4; PRIM_DIV_Q16 = 5
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PRIM_LT_Q16 = 6; PRIM_EQ_Q16 = 7
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PRIM_AND = 8; PRIM_OR = 9; PRIM_NOT = 10
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end
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methods (Static)
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function r = avm_clamp(x)
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if x > AVM.AVM_CLAMP_MAX; r = AVM.AVM_CLAMP_MAX;
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elseif x < AVM.AVM_CLAMP_MIN; r = AVM.AVM_CLAMP_MIN;
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else; r = int32(x); end
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end
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function r = avm_q0_clamp(x)
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if x > AVM.AVM_Q0_MAX; r = AVM.AVM_Q0_MAX;
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elseif x < AVM.AVM_Q0_MIN; r = AVM.AVM_Q0_MIN;
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else; r = int32(x); end
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end
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function r = floor_div(a, b)
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if b == 0; error('division by zero'); end
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q = idivide(a, b, 'floor');
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r = int32(q);
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end
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function r = lt_q16_v6(a, b)
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sa = a < 0; sb = b < 0;
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if sa ~= sb; r = sa; else; r = a < b; end
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end
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function v = val_q16(x)
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v = struct('ty', AVM.TY_Q16, 'i', AVM.avm_clamp(x), 'b', false);
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end
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function v = val_q0(x)
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v = struct('ty', AVM.TY_Q0, 'i', AVM.avm_q0_clamp(x), 'b', false);
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end
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function v = val_bool(x)
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v = struct('ty', AVM.TY_BOOL, 'i', int32(0), 'b', x);
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end
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function s = init_state(n_locals)
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if nargin < 1; n_locals = 0; end
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s = struct('pc', int32(0), 'stack', {}, 'locals', cell(n_locals, 1), 'halted', false);
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end
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function r = exec_prim(p, a, b)
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r = AVM.val_q0(0);
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if p == AVM.PRIM_ADD_Q0
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if a.ty ~= AVM.TY_Q0 || b.ty ~= AVM.TY_Q0; return; end
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r = AVM.val_q0(double(a.i) + double(b.i));
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elseif p == AVM.PRIM_SUB_Q0
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if a.ty ~= AVM.TY_Q0 || b.ty ~= AVM.TY_Q0; return; end
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r = AVM.val_q0(double(a.i) - double(b.i));
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elseif p == AVM.PRIM_ADD_Q16
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if a.ty ~= AVM.TY_Q16 || b.ty ~= AVM.TY_Q16; return; end
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r = AVM.val_q16(double(a.i) + double(b.i));
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elseif p == AVM.PRIM_SUB_Q16
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if a.ty ~= AVM.TY_Q16 || b.ty ~= AVM.TY_Q16; return; end
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r = AVM.val_q16(double(a.i) - double(b.i));
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elseif p == AVM.PRIM_MUL_Q16
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if a.ty ~= AVM.TY_Q16 || b.ty ~= AVM.TY_Q16; return; end
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r = AVM.val_q16(AVM.floor_div(double(a.i) * double(b.i), AVM.Q16_SCALE));
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elseif p == AVM.PRIM_DIV_Q16
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if a.ty ~= AVM.TY_Q16 || b.ty ~= AVM.TY_Q16 || b.i == 0; return; end
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r = AVM.val_q16(AVM.floor_div(double(a.i) * AVM.Q16_SCALE, double(b.i)));
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elseif p == AVM.PRIM_LT_Q16
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if a.ty ~= AVM.TY_Q16 || b.ty ~= AVM.TY_Q16; return; end
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r = AVM.val_bool(AVM.lt_q16_v6(a.i, b.i));
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elseif p == AVM.PRIM_EQ_Q16
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if a.ty ~= AVM.TY_Q16 || b.ty ~= AVM.TY_Q16; return; end
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r = AVM.val_bool(a.i == b.i);
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elseif p == AVM.PRIM_AND
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if a.ty ~= AVM.TY_BOOL || b.ty ~= AVM.TY_BOOL; return; end
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r = AVM.val_bool(a.b && b.b);
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elseif p == AVM.PRIM_OR
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if a.ty ~= AVM.TY_BOOL || b.ty ~= AVM.TY_BOOL; return; end
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r = AVM.val_bool(a.b || b.b);
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elseif p == AVM.PRIM_NOT
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if a.ty ~= AVM.TY_BOOL; return; end
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r = AVM.val_bool(~a.b);
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end
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end
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function [s, err] = step(s, prog)
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err = 0; n = length(prog);
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if s.halted; err = -1; return; end
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if s.pc < 1 || s.pc > n; s.halted = true; return; end
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instr = prog{s.pc}; npc = s.pc + 1;
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growing = any(instr.op == [AVM.OP_PUSH_Q16, AVM.OP_PUSH_BOOL, AVM.OP_PUSH_Q0, AVM.OP_DUP, AVM.OP_LOAD]);
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if growing && length(s.stack) >= AVM.AVM_MAX_STACK; err = -2; return; end
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if instr.op == AVM.OP_PUSH_Q16
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s.stack{end+1} = AVM.val_q16(instr.arg);
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elseif instr.op == AVM.OP_PUSH_BOOL
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s.stack{end+1} = AVM.val_bool(instr.arg2);
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elseif instr.op == AVM.OP_PUSH_Q0
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s.stack{end+1} = AVM.val_q0(instr.arg);
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elseif instr.op == AVM.OP_POP
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if isempty(s.stack); err = -3; return; end; s.stack(end) = [];
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elseif instr.op == AVM.OP_DUP
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if isempty(s.stack); err = -3; return; end
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s.stack{end+1} = s.stack{end};
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elseif instr.op == AVM.OP_SWAP
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if length(s.stack) < 2; err = -4; return; end
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tmp = s.stack{end}; s.stack{end} = s.stack{end-1}; s.stack{end-1} = tmp;
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elseif instr.op == AVM.OP_LOAD
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i = instr.arg + 1;
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if i > length(s.locals) || isempty(s.locals{i}); err = -5; return; end
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s.stack{end+1} = s.locals{i};
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elseif instr.op == AVM.OP_STORE
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if isempty(s.stack); err = -3; return; end
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i = instr.arg + 1;
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if i > length(s.locals); err = -5; return; end
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s.locals{i} = s.stack{end}; s.stack(end) = [];
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elseif instr.op == AVM.OP_JUMP
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t = instr.arg + 1;
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if t < 1 || t > n; err = -6; return; end; npc = t;
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elseif instr.op == AVM.OP_JUMP_IF
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if isempty(s.stack); err = -3; return; end
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v = s.stack{end}; s.stack(end) = [];
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if v.ty ~= AVM.TY_BOOL; err = -7; return; end
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if v.b; t = instr.arg + 1;
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if t < 1 || t > n; err = -6; return; end; npc = t; end
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elseif instr.op == AVM.OP_PRIM
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arity = 2; if instr.arg == AVM.PRIM_NOT; arity = 1; end
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if length(s.stack) < arity; err = -4; return; end
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b = []; if arity >= 2; b = s.stack{end}; s.stack(end) = []; end
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a = s.stack{end}; s.stack(end) = [];
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s.stack{end+1} = AVM.exec_prim(instr.arg, a, b);
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elseif instr.op == AVM.OP_HALT
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s.halted = true;
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end
|
||||
s.pc = npc;
|
||||
end
|
||||
|
||||
function s = run(init, prog, fuel)
|
||||
if nargin < 3; fuel = 10000; end
|
||||
s = init;
|
||||
for i = 1:fuel
|
||||
if s.halted; return; end
|
||||
[s, err] = AVM.step(s, prog);
|
||||
if err; error(['AVM error: ' num2str(err)]); end
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
|
|
@ -1,7 +1,7 @@
|
|||
% AVM ISA v1 — Octave/MATLAB Test Harness
|
||||
% Run with: octave --no-gui octave/test_avm.m
|
||||
% or: octave --no-gui --eval "addpath('octave'); test_avm"
|
||||
|
||||
addpath('octave');
|
||||
QS = 65536;
|
||||
|
||||
function check(cond, msg)
|
||||
|
|
|
|||
|
|
@ -49,7 +49,7 @@ def run_port_tests():
|
|||
("C++", ["sh", "-c", "g++ -std=c++20 -o /tmp/cpp_avm_test cpp/test_avm.cpp && /tmp/cpp_avm_test"], ".", {}),
|
||||
("Julia", ["julia", "julia/AVMIsa/test_avm.jl"], ".", {}),
|
||||
("R", ["Rscript", "r/AVMIsa/test_avm.r"], ".", {}),
|
||||
("Octave", ["octave", "--no-gui", "octave/test_avm.m"], ".", {}),
|
||||
("Octave", ["octave", "--no-gui", "--eval", "addpath('octave'); test_avm"], ".", {}),
|
||||
]
|
||||
|
||||
for name, cmd, wd, env_add in ports:
|
||||
|
|
|
|||
Loading…
Add table
Reference in a new issue