SilverSight/docs/reviews/COLD_REVIEWER_FORMULA.md

Cold Reviewer Formula

Protocol for independent verification of the Unified Covariant Field Theory

A reviewer needs only a calculator and this checklist. No knowledge of Lean, braid theory, or Temperley–Lieb algebras is required to pass the arithmetic and structural gates.

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Arithmetic Gate

Verify the following four invariants independently.

I₁. Golden-ratio identity

[ \phi = \frac{1 + \sqrt{5}}{2}, \qquad \phi^2 - \phi - 1 = 0. ]

Check: Compute \phi^2, subtract \phi + 1, obtain 0.

I₂. Fixed-point gap

[ \sigma = \frac{9984}{65536} = \frac{39}{256}, \qquad \tau = \frac{1}{7}, ]

[ \sigma - \tau = \frac{39}{256} - \frac{1}{7} = \frac{273 - 256}{1792} = \frac{17}{1792} > 0. ]

Check: Common denominator 1792. Numerator 273 - 256 = 17 > 0.

I₃. Fibonacci values

[ F_7 = 13, \qquad F_8 = 21. ]

Check: Run the recurrence F_0=0,\;F_1=1,\;F_{n+2}=F_{n+1}+F_n to term 8.

I₄. Binary / Sidon uniqueness

For a,b,c,d \in \{0,\dots,7\},

[ 2^a + 2^b = 2^c + 2^d ;\Longrightarrow; {a,b} = {c,d}. ]

Reason: Binary expansion of integers is unique. A sum of two powers of two has either one bit set (a=b, yielding 2^{a+1}) or exactly two bits set (a \neq b). Equality therefore forces the same exponent multiset.

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Structural Gate

Ensure the manuscript does not make any of the following claims.

Red Flag 1 — Wrong endomorphism relation

✗ Prohibited	✓ Correct
J^2 = -I	J^2 = J + I

where J = \phi \cdot \mathrm{id}_V. This operator satisfies the golden-ratio polynomial x^2 - x - 1 = 0, with eigenvalues \phi and -1/\phi. It is not an almost-complex structure.

Red Flag 2 — Kähler on the simplex

✗ Prohibited	✓ Correct
\Delta_7 is Kähler	\dim \Delta_7 = 7 (odd, impossible)

The open probability simplex

[ \Delta_7 = { p \in \mathbb{R}_{>0}^8 \mid \sum p_i = 1 } ]

has dimension 8 - 1 = 7. Every Kähler manifold is even-dimensional, so \Delta_7 cannot carry a Kähler structure. If a Kähler example is desired, work on \mathbb{CP}^7 (real dimension 14) with the standard Fubini–Study metric.

Red Flag 3 — Temperley–Lieb dimension

✗ Prohibited	✓ Correct
\dim(\mathrm{TL}_7) = 13	\dim(\mathrm{TL}_7) = C_7 = 429

The (n)-th Catalan number is

[ C_n = \frac{1}{n+1}\binom{2n}{n}, \qquad C_7 = \frac{1}{8}\binom{14}{7} = \frac{3432}{8} = 429. ]

The value 13 arises only in specialized settings: the Fibonacci category or Fibonacci anyon model at q = e^{i\pi/5} (quantum dimension \phi), where the fusion rule is \phi \times \phi = 1 + \phi and simple-object dimensions follow the Fibonacci sequence. It is not the dimension of the ordinary Temperley–Lieb algebra.

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Reviewer Decision Procedure

1. Verify I₁–I₄. Reject immediately if any arithmetic invariant fails.
2. Check that none of the three red-flag claims appear. Reject if any is present.
3. Only after both gates pass should higher-level geometric, categorical, or dynamical constructions be evaluated.

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Source

The reference implementation is:

• File: formal/SilverSight/PIST/UnifiedCovariant.lean
• Proof status: I₁–I₄ verified at compile time by norm_num/dec_trivial (0 sorries, 0 axioms). Red flags explicitly documented and avoided. Layer 3 conjectures tagged sorry pending Mathlib's differential geometry API.
• Build: lake build SilverSight — 3307 jobs, 0 errors.