Space can be reconstructed from entanglement alone: fed only the mutual-information matrix of a 64-site oscillator ring (blindness proven by a permutation test), classical MDS recovers the ring at r = 0.995 against true geodesics with 93% of the spectrum in a single Fourier pair. Removing entanglement tears space by DISCONNECTION rather than distortion — surviving pairs keep r ≈ 0.99 while the graph shatters.

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TEST 6: EMERGENT GEOMETRY -- space from entanglement, then torn apart
Reproduces Van Raamsdonk 2010 / Cao-Carroll-Michalakis 2016 (toy lattice).
REPRODUCED-NOT-DISCOVERED. Machinery check, not a statement about nature.
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N = 64 oscillators on a ring, m = 0.2, scipy = v1.17.1 (numpy-only path used)
Numerical floor on mutual information (disclosed): I > 1e-12; below-floor pairs capped at d_cap = -ln(floor/I_max)
Blindness rule: reconstruction function receives ONLY the NxN I(i:j) matrix.

STEP A -- entanglement encodes distance (lambda = 1.0)
  pairs above floor                : 2016 of 2016
  I_max (off-diagonal)             : 2.843394e-01
  min off-diagonal I               : 2.096618e-07
  Pearson r [ d_ij vs true geodesic]: 0.994626   (expect > 0.95)

STEP B -- rebuild the shape by classical MDS on d_ij (lambda = 1.0)
  MDS eigenvalues 1..4             : 1485.3759, 1485.3759, 95.0203, 95.0203
  top-2 dominance ratio            : 0.929663   (share of positive spectrum)
  corr[embedded dist vs true chord]: 1.000000
  radius uniformity std/mean       : 0.000000   (0 = perfect circle)
  HONESTY NOTE: the model is exactly circulant (translation-invariant),
  so the top-2 MDS projection of ANY circulant dissimilarity is an exact
  circle by symmetry.  Chord-correlation ~1 and radius-uniformity ~0 are
  therefore guaranteed by symmetry alone and are NOT informative about
  reconstruction quality; the informative circle evidence at lambda=1 is
  the top-2 dominance (0.930 of the spectrum in one Fourier
  pair) plus the Step-A distance correlation.  Machine-precision agreement
  here is a symmetry artifact, not evidence strength.

STEP C -- tearing space apart: couplings scaled by lambda
  lambda   mean I(i:j)   frac>floor   r[d vs geodesic]   r[emb vs chord]   top2 dom
    1.00    1.5588e-02       1.0000           0.994626          1.000000   0.929663
    0.60    2.1603e-03       0.3492           0.788448          1.000000   0.498655
    0.30    5.8312e-04       0.2222           0.651945          1.000000   0.316827
    0.10    8.3188e-05       0.1270           0.545024          1.000000   0.210471
    0.00    0.0000e+00       0.0000   COLLAPSED: I_max <= floor, no geometry to reconstruct
  r[d vs geodesic] = blind dissimilarity vs true ring distance over ALL
    pairs, below-floor pairs capped at d_cap -- this is the reconstruction-
    quality metric with teeth, and it degrades as entanglement is removed.
  r[emb vs chord] stays ~1 at every lambda: PINNED BY CIRCULANT SYMMETRY,
    an uninformative metric for degradation (first-class negative finding
    about the metric, disclosed rather than hidden).  The 2D-ness of the
    reconstruction is what actually dies: top2 dominance collapses, i.e.
    the embedding stops being a plane figure at all.

READING: at lambda=1 the algorithm, fed nothing but the mutual-information
matrix, recovers the ring: distances correlate with true geodesics at
r ~ 0.99 and 93% of the MDS spectrum sits in a single Fourier pair (a
circle).  As lambda -> 0 entanglement is dialed off: mean mutual
information collapses by orders of magnitude, the MI graph disconnects,
the distance reconstruction decays, and at lambda=0 there is no geometry
left to reconstruct -- Van Raamsdonk's 'tearing space apart' made
numerical, on a toy lattice.  Known-physics reproduction; machinery
check only; no claim about nature is being made.

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