Newton's Constant and Rest-Frame Schroedinger Evolution from K_7 Graph-State Information Theory

Papers 13-16 derived the Standard Model parameters, the fine-structure constant alpha, the 24-particle hadron mass spectrum, and the gravitational coupling G from the topology of torus-knot vortex defects in a relativistic condensate. Paper 16 proposed the Planck-hierarchy expression m_e/m_Pl = (8/7)(1+alpha/7) alpha^(21/2) as a numerical identity to 0.014%. This paper gives a quantum-information-theoretic derivation of the factors in that expression. Within the NWT framework, m_e/m_Pl is interpreted as the encoded fidelity of an electron worldtube traversing the K_7 stabiliser state under alpha-strength interaction-event noise, and Newton's constant G is interpreted as the transduction ratio between momentum-changing interaction events and topological-information creation. The closed form, valid at NNLO under the framework's normalisation choices and with alpha as input from Paper 8a's Aharonov-Bohm calculation, agrees with CODATA m_e/m_Pl to 0.0001% (a 140x improvement over Paper 14) and predicts G within 11 ppm of CODATA G, inside the 22 ppm experimental uncertainty on G itself. The information-theoretic spine is a structural identity: for the K_7 stabiliser graph state |K_7> on 7 qubits and the two-body Pauli-YY Hamiltonian H_YY, _{|K_N>} = dim(Adj_so(N))^n exactly for all n, verified across the so(2n+1) family at N in {7, 9, 11}. The bracket coefficients in m_e/m_Pl are the first two normalised moments of H_YY. A 3-body operator probe shows _{|K_7>} = 0 for all 35 basis triples, supporting truncation of the bracket at alpha^2 through a representation-theoretic mechanism rather than accidental cancellation. The classical prefactor 8/7 = dim(S)/dim(V) is the trace ratio of the Cartan-graded subspace of |K_7>. Beyond the gravitational-coupling derivation, the same K_7 graph-state framework yields a derived effective evolution equation i hbar d_t |K_7> = m_e c^2 |K_7> within the model, from Bremermann's bound, the Paper 16 b2.13 bijection, and the PSL(2,7) edge-transitive symmetry of K_7. The framework is supported by IBM Heron R2 hardware measurements in eight datasets across three backends (ibm_kingston, ibm_marrakesh, ibm_fez). Direct measurement of on hardware-prepared |K_7> gives values 16.00 +/- 0.21, 16.4715 +/- 0.0448, and 15.2815 +/- 0.0493 across three runs, all consistent with the predicted noiseless value 21 within hardware-noise expectations, with Z-scores above the random-state null of +75, +368, and +310 sigma. Zero-noise extrapolation on the same backend sharpens the cross-group K_9/K_7 ratio to 1.767 +/- 0.024 vs the structural prediction 36/21 = 1.714, agreeing to 3.07% (+2.16 sigma deviation) and bracketing M(K_9) in [36, 39] at 3 sigma with the framework's M = 36 at the centre. The 3-body null test (12,000 shots/triple) confirms = 0 with chi^2_red = 2.26 and rules out a Fano-line anisotropy hypothesis at +0.7 sigma. The syndrome-attractor experiment finds P(0000000 | |K_7> input) = 0.482 vs the random-input expectation 1/128, with measurement entropy difference Delta H_2 = 2.66 bits, supporting |K_7> as the natural fixed point of the preparation-plus-uncompute dynamics within the protocol. Within NWT, the remaining input data reduce to a topological sector, a single absolute mass scale, and the post-2019 SI conventions. The model achieves a strong form of internal parsimony once the framework's normalisation choices are fixed. Reproducibility: all analysis code (K_N graph-state moment numerics, bracket-truncation probes, Heron submission and analysis scripts, PSL(2,7) edge-transitivity re-analysis, forward-prediction and zero-noise extrapolation analyses, and raw Heron job outputs) is available at https://github.com/JimGalasyn/null-worldtube.