EP4-C: EP4-C: Physical Consequences of the Morse Gradient Test (EP4A) — Locality of Gravity from Two Independent Geometric Perspectives

EP4-C documents the results of EP4A — a Lindblad Morse Gradient Test on the 3-qubit XXX Heisenberg spin chain using published ibmq_jakarta hardware parameters (T1=119 μs, T2=113 μs) — and identifies a structural consequence extending to the BCS superconductivity experiment (EP5-BCS).

Core findings:

(1) The Morse correlation dS = λ · D²_B is confirmed at 14.7× signal-to-noise on the Lindblad analytic trajectory. All thresholds were pre-declared before simulation. Decoherence parameters were taken from published hardware specs, not calibrated to match output. The Heisenberg revival F(|110⟩, U(π)|110⟩) = 1.000000 is verified.

(2) The observed drift in λ is explained analytically with 85% accuracy and zero free parameters as a geometric consequence of the trajectory approaching the pure-state boundary ∂D(H) of the density matrix manifold near the revival at t=π. The drift is carried entirely by D_B shrinking as rotating-frame steps become geometrically short near the turning point; dS remains flat (CV=0.175). This is not a post-hoc explanation — the prediction follows from local eigenvalue structure of ρ at each step with no fitting.

(3) Two independent aspects of the computation both indicate that the effective gravitational degree of freedom in EFT — f = |∇S|_B — is locally determined on D(H). First: λ(t) is predicted from local quantities only, with no non-local terms entering the drift explanation. Second: the Bures metric singularity near pure states is controlled entirely by the local eigenvalue spectrum of ρ at that point, directly analogous to how spacetime curvature in GR is determined by the local stress-energy tensor.

(4) The BCS experiment (EP5-BCS, pending CAN Superconductors disc samples) has the identical geometric structure: the BCS ground state at T=0 is a pure state on ∂D(H). The clean Morse window — where the Pearson correlation between dS and D²_B is predicted to be high (> 0.85) and λ to track the zero-parameter geometric prediction — is 0.2 < T/T_c < 0.8, derived from EFT geometry before any BCS measurement. Boundary drift zones near T=0 and T=T_c are predicted as positive confirmations of the same structure.

The document includes: full pre-declared threshold tables, per-step trajectory data, the zero-parameter λ prediction, all figures, reproducible Python code (NumPy/SciPy/Matplotlib only, no Qiskit required, runs in under 30 seconds), and the complete reasoning chain from initial results through geometric diagnosis to the locality finding.

Verification chain:
- EP4A (this document): Lindblad analytic trajectory — COMPLETE, 14.7× signal
- EP4B: IBM hardware tomography at steps 5, 10, 20, 30, 35 — PENDING (script ready)
- EP5-BCS: Superconducting disc, CAN Superconductors — PENDING, clean window 0.2 < T/T_c < 0.8

Related work:
- EFT standalone: DOI 10.5281/zenodo.18963986
- EQ(vT): DOI 10.5281/zenodo.18917317
- EP4A (Morse Gradient Test, Lindblad): DOI 10.5281/zenodo.18969071
- BCS pre-registration: DOI 10.5281/zenodo.18964362