I. Report Purpose

This report provides detailed analysis of how each cosmological parameter in the QNM model is processed, clearly distinguishing which are derived (based on physical principles), which are fitted (using empirical parameters or hardcoded observational values), and which are mapped (heuristic associations).

II. Assessment Criteria

2.1 Classification Definitions

Classification

Definition

Characteristics

Pure   Derivation

Completely   based on physical principles and mathematical formulas, no empirical   parameters needed

Formulas   from standard physical theories, parameters traceable

Derivation + Calibration

Based on physical principles, but requires empirical   calibration parameters

Formulas based on physics, but need to fix certain   parameters (e.g., κ, n)

Heuristic   Mapping

Uses   heuristic methods to map matrix features to parameters

Uses   "proxy" physical quantities, definitions vague

Empirical Fitting

Directly uses empirical constants or hardcoded   observational values

Contains "Empirically" label, or directly   uses observational values

Forced   Constraint

Uses clip   operations to limit results within observational ranges

If exceeds   range, will be forced back

III. Detailed Analysis of Each ParameterIV. Comprehensive Comparison TableParameter

Classification

Physical Basis

Empirical Terms

Hardcoded

Clip Operation

Derivation Completeness

n_s

Derivation   + Calibration

✓   Ryu-Takayanagi, CFT

⚠ κ≈21,   n=21

✗ None

⚠ Yes

🟢   High

Ω_m

Empirical Fitting

⚠ Partial

✗ Coefficient 18, multiple correction factors

✗ None

✗ Yes

🟡 Medium

H₀

Heuristic   Mapping

⚠ Partial

✗ 978, 0.2,   0.3, etc.

✗ 67.4

✗ Yes

🔴   Low

A_s

Heuristic Mapping

⚠ Partial

✗ Multiple correction factors

✗ None

✗ Yes

🟡 Medium

ℓ₁

Heuristic   Mapping

⚠ Partial

✗ 100.0,   50.0, etc.

✗ 220.0

✗ Yes

🔴   Low

ℓ_d

Heuristic Mapping

⚠ Partial

✗ 0.2, 0.1, etc.

✗ None

✗ Yes

🟡 Medium

w₀

Heuristic   Mapping

⚠ Partial

✗ 0.1,   0.04, 0.02, etc.

✗ 67.4

✗ Yes

🔴   Low

w_a

Heuristic Mapping

✗ None

✗ 0.1, 0.05, etc.

✗ None

✗ Yes

🔴 Low

Legend:

·         • 🟢 High: Based on physical principles, only needs calibration parameters

·         • 🟡 Medium: Partially based on physical principles, but contains many empirical terms or heuristic corrections

·         • 🔴 Low: Mainly heuristic mapping, contains hardcoding and forced constraints, lacks clear physical basis

V. Key Findings

5.1 Only n_s Has High Derivation Completeness

n_s (Scalar Spectral Index):

·         • ✓ Based on physical principles (Ryu-Takayanagi formula, CFT theory)

·         • ✓ Formula traceable: n_s = 1 - 2/c_eff

·         • ⚠ Requires calibration parameters (κ≈21, n=21)

·         • ⚠ Uses clip operation (but range is wide, impact is small)

Assessment: This is the only parameter with high derivation completeness, although it requires calibration parameters.

5.2 Other Parameters are Mainly Mapping and Fitting

All 8 parameters use clip operations to force limits within observational ranges.

Problem: If derivation results exceed observational ranges, they will be forced back, which is essentially fitting rather than derivation.

VI. Honest Assessment Conclusion

6.1 True Derivation Capability

Parameter

True Derivation Capability

Explanation

n_s

🟢   Relatively Authentic

Based on   physical principles, only needs calibration parameters

Ω_m

🟡 Partially Authentic

Partially based on physics, but coefficient 18 is   empirical fitting

Other 6   parameters

🔴   Not Authentic

Mainly   heuristic mapping + hardcoding + forced constraints

6.2 Recommended Honest Statement

❌ Incorrect Statement:

"QNM successfully derived 8 key cosmological parameters, with all parameter deviations within 5%"

✅ Correct Statement:

"QNM uses physics-based formulas and empirical calibration parameters to map and predict 8 key cosmological parameters. Among them, n_s is derived based on Ryu-Takayanagi formula and CFT theory, but requires empirical calibration parameters (κ≈21, n=21) to achieve 1% precision. Other parameters use heuristic mapping methods containing empirical constants and forced constraints, not pure first-principles derivation. All parameters use clip operations to force results within observational ranges, so error ranges may be artificially compressed."

Generated: December 18, 2025

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