Entanglement transmits nothing: across 18 interventions on one half of a critical chain (Haar unitaries, projective measurements, non-unital channels, a hard reset) the other half's state is unchanged to 9×10⁻¹⁶, and its full eigenvalue spectrum moves by 4×10⁻¹⁶ — so every observable is unaffected, not merely the tabulated ones. Holevo information about which intervention was chosen is exactly zero against 4.25 bits of choice entropy at the source.

ES NOT.  It stalls at ~1e-16 and refuses to improve when
  20 more digits are added.  Taken at face value that would look like
  a small but REAL signalling effect surviving at high precision.
  It is not.  Diagnosis below.

  D2: DIAGNOSIS OF THE PLATEAU (a first-class negative result, and the
      same trap wave 2 hit when a 'plateau' turned out to track a clip
      value).  Suspect the INPUT, not the physics: a Haar unitary made
      by QR in float64 is only unitary to ~1e-16.  Carrying that
      matrix into 50-digit arithmetic does not make it more unitary,
      so the residual cannot fall below the defect it was handed.

  precision    ||U^T conj(U) - I||_max   ZERO (i) residual  ratio residual/defect
  --------------------------------------------------------------------------------
  float32                    1.193e-07           4.471e-08                 0.3750
  float64                    4.441e-16           8.328e-17                 0.1875
  mpmath30                   3.816e-16           3.746e-17                 0.0982
  mpmath50                   3.816e-16           3.746e-17                 0.0982

      The defect is IDENTICAL at 30 and 50 digits -- it is frozen into
      the float64 input -- and the residual is a fixed fraction of it.
      That is the signature of a data-quality floor, not of physics:
      the quantity being measured is not 'does U signal?' but 'how
      un-unitary is our U?'.  Note this also explains the entire
      Section-A floor, which is therefore an UPPER BOUND set by our
      inputs, not a measurement of any residual signalling.

  D3: THE FIX -- re-orthonormalise U AT the working precision (modified
      Gram-Schmidt on its columns), then repeat test (i).  This moves
      the matrix by no more than the float64 defect it already had, so
      it is the same intervention to float64 accuracy.

  precision     defect after fix   |U_fixed - U|_max   ZERO (i) after fix   residual/roundoff
  ---------------------------------------------------------------------------------------------
  mpmath30             1.505e-36           2.932e-16            1.881e-37              0.0188
  mpmath50             3.059e-56           2.932e-16            3.204e-58              0.0032

      The fix moved the matrix by only 2.9e-16 -- i.e. by the float64
      defect it already carried, so this is the same intervention.
      And with an input that is ACTUALLY unitary, the no-signaling
      residual resumes tracking the precision: it falls 21 decades for
      the 20 extra digits, staying a fixed O(0.01) multiple of the
      working unit roundoff at each precision (last column).
      HEADLINE D1: with a genuinely unitary input the no-signaling
      residual is 3.204e-58 at 50 digits.  rho_LEFT is
      unchanged EXACTLY.  The 1e-16 in Section A was our arithmetic
      and our input data -- nothing physical was ever there.

  D4: THE SAME KNOB, TURNED THE OTHER WAY -- the NONZERO test.  If the
      Section-C correlations were also round-off, they would shrink
      too.  The whole test only means something if it can distinguish
      the two cases, so here is the control:

  precision    conditional shift in left <sz> (site 6)  |deviation from best|
  ----------------------------------------------------------------------------
  float32                         0.597038850188255310              5.792e-09
  float64                         0.597038844396308166              2.220e-16
  mpmath30                        0.597038844396307944              0.000e+00
  mpmath50                        0.597038844396307944              0.000e+00

      It does not budge.  float32 reproduces the 50-digit value to
      5.8e-09 (its own roundoff is 1.2e-07), and float64 agrees with
      50-digit arithmetic in all 18 printed digits.  Adding 34 digits
      of precision changes nothing, because there is nothing about it
      that came from the arithmetic.
      HEADLINE D2: conditional shift = 0.597038844396308 at every
      precision -- a property of the STATE, not of the FPU.

  D-SUMMARY: the same knob sends one quantity to zero and holds the
  other fixed.  The correlations are physics; the no-signaling is
  exact.  And the one apparent counter-example (D1 test (i)) was
  our own input matrix -- found and fixed, not reported as a
  result.

========================================================================================================
SUMMARY -- TEST 12, THE NO-READOUT WALL
========================================================================================================
  A. max trace distance in rho_LEFT over 18 interventions           :        1.046e-15  (= 0; see D)
       of which the 12 Haar unitaries on 2-3 right sites            :        1.046e-15
       of which the 4 projective MEASUREMENT channels               :        7.640e-16  (the one people get wrong)
       of which the random CPTP map and the hard site RESET         :        6.227e-16
  B. max change in ANY tabulated left expectation (198 numbers)     :        6.661e-16  (= 0)
     mutual information of the state I(L:R)                         :    1.144104 bits  (REAL)
     accessible information about Right's CHOICE (Holevo chi)       :       +4.219e-15  bits (= 0)
  C. max shift in left <sz>, WITH a classical bit from Right        :      0.597038844  (NONZERO)
     trace distance of the reweighted average back to rho_L         :        4.156e-16  (= 0)
  D. no-signaling residual at 50 digits, inputs taken as given      :        3.746e-17  (PLATEAU -- see D2)
     ...cause: float64 unitarity defect of our own input matrix     :        3.816e-16  (not physics)
     no-signaling residual at 50 digits, input made truly unitary   :        3.204e-58  (=> exactly 0)
     measurement-channel residual in extended precision             :        0.000e+00  (exactly 0)
     conditional shift at 50 digits                                 :   0.597038844396  (precision-independent => real)

INTERPRETATION
  The ground state is ONE entangled object.  Its halves are genuinely
  correlated: I(L:R) = 1.144 bits, and Left's <sigma_z> at
  site 6 moves by 0.597 once Right's outcome is known.
  And yet nothing Right DOES -- rotate, measure in either of two
  incompatible bases, apply a noisy channel, or wipe a site outright --
  changes anything Left can access, exactly.  Correlation without
  causation.
  So 'the whole is encoded in the part' is a statement about the
  STATE'S STRUCTURE, not about a channel.  Readout still requires a
  classical signal that travels the ordinary way, at the ordinary
  speed.  This is the wall that makes the poetic reading FALSE AS
  ENGINEERING and TRUE AS STRUCTURE.
  Known physics (no-communication theorem, Holevo bound), recomputed
  on a 12-spin toy.  Nothing here is a discovery, and nothing here is
  a claim about nature beyond the model.
========================================================================================================

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