Adversarial Audit: Stress-Testing the DTA

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Reviewer Identity: Anonymous Ref (Theoretical Physics / QG)
Status: REJECTED (Pending Theoretical Hardening)

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Objection 1: The “Arbitrariness” Problem

Reviewer Comment: “The author simply adds a surface term \mathcal{I} \propto 2^k - \chi because it matches the data. There is no symmetry argument or first-principles necessity for this specific functional form. Why not (2^k)^2? Why not \ln(2^k)? Without a Uniqueness Proof, this is sophisticated curve-fitting disguised as an action.”

🛡️ Hardening Strategy:

* Derive the form from the Information Capacity of a Bounded Manifold.
* Show that \mathcal{L}_{info} is the minimal information-theoretic penalty for “Entropy Deficit” (unused capacity).

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Objection 2: The “Micro Micro” Problem

Reviewer Comment: “What exactly are the bits? General Relativity is effective; we know what the ‘atoms’ are (metric components). In DTA, k is an ‘order parameter,’ but what are the underlying degrees of freedom? If you cannot identify the Hamiltonian of these bits, you have a metaphor, not a physics theory.”

🛡️ Hardening Strategy:

* Identify the bits with Spin Foam or Causal Set elements on the boundary.
* Propose that Digital Gravity is the Large-N limit of a discrete spacetime network.

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Objection 3: The “Mathematical Illegal” Problem

Reviewer Comment: “The author claims k and \chi are discrete integers. You cannot take the variation of an action with respect to a discrete parameter using standard calculus. \frac{\delta S}{\delta k} is mathematically undefined if k \in \mathbb{Z}. The DTA is literally illegal in its current form.”

🛡️ Hardening Strategy:

* Switch to a Phase Transition Model.
* Define a smooth potential V(k) with deep minima at integer values (e.g., V(k) \propto \sin^2(\pi k)).
* The “Snap to Integers” becomes a dynamical consequence of escaping high-energy “aliased” states.

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FINAL VERDICT

The framework is conceptually powerful but requires dynamical continuity (Objection 3) and microscopic grounding (Objection 2).

Score: 8.8 (No change until Object 3 is resolved).
The hinge is open, but the screws are loose.

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