Connectivity Optimization of Mountain Heritage Corridors Based on an Adaptive MCR Gravity Model: A Case Study of the Mount Song World Heritage Landscape in China

Abstract

Mountainous cultural landscapes, characterized by fragmented heritage sites, present significant challenges for integrated conservation and regional planning. Taking the Mount Song Culture Circle in Dengfeng City, China—a World Heritage site embodying the core of Chinese ritual civilization—as a case study, this study proposes an adaptive minimum cumulative resistance (MCR) gravity model to optimize heritage corridor resilience against spatial fragmentation and development imbalances. Based on a spatial database of 294 cultural relic units, the adaptive model introduces a dynamic cultural value weight (CVIndex = 0.82) and a time decay function (λ = 0.05) to capture the interplay between cultural significance and ecological constraints—features absent in traditional static approaches. The model identifies three optimized heritage corridor networks—”Seeking Wisdom in the Mountains”, “Searching for Culture in the Landscape”, and “Exploring the City Along the River.” Compared with a traditional static MCR model (αindex = 0.42; core area node density = 0.74 nodes/km²), the adaptive approach improves network connectivity by 37% (α-index = 0.58, p < 0.01) and increases core area heritage node density to 1.12/km². Space syntax analysis further confirms that optimized network integration values strongly correlate with cultural dissemination efficiency (R² = 0.78, p < 0.01, n = 48). This research offers a methodological innovation for resilient conservation of complex cultural landscapes in World Heritage contexts.

1. Introduction

Cultural landscapes became a World Heritage category in 1992. Complex and dynamic, they show regional similarities due to environment, social development, and ideologies, yet also internal differences [1]. With accelerating urbanization, cultural landscapes increasingly face “islandization” and “commercialization” [2,3,4], while urban expansion fragments linear cultural heritage into “heritage islands” [5].

Attention to cultural heritage corridors in China has grown significantly [6]. In 2021, central authorities issued guidelines emphasizing the protection and revitalization of historical and cultural heritage, calling for hierarchical and categorical connections to form display routes, corridors, and networks integrated into daily life [7]. This reflects a deepening of systematic protection in national policy, yet effective implementation requires scientific support and methodological innovation.

Existing MCR-based models for heritage corridor construction suffer from three interrelated deficiencies: static valuation, uniform resistance coefficients ignore spatial heterogeneity of cultural value across heritage grades and preservation statuses [8,9]; temporal insensitivity, the historical stratification effect (exponential decay/accumulation of cultural significance over time) remains unaccounted for, distorting connectivity potential between multi-era nodes; and structural fragmentation, ecological efficiency (minimizing topographic resistance) is prioritized over cultural connectivity, bypassing high-value nodes and perpetuating “heritage islandization” [2,3]. These deficiencies are amplified in mountainous cultural landscapes, where topographic barriers and core–periphery imbalances already constrain network integration.

Recently, scholars in human geography, planning, and landscape architecture have begun focusing on regional cultural landscape typologies, holistically understanding distribution characteristics [10] and influencing factors. Research objects have shifted from single-type landscapes (traditional villages, settlements [11], segments [12]) to multi-type regionalization [13,14]. Studies address settlement regionalization [15], methods [16], spatiotemporal drivers [17], spatial distribution [18], feature identification [19], formation mechanisms [20], digital technology, and cultural identity. Scales range from mesoscopic (watersheds [21,22], provinces/cities) to macroscopic (national [23,24]) and microscopic (county/district [25]). Common methods include multi-factor overlay [26], dominant factor analysis [27], and hierarchical clustering [28].

Overall, the field has moved from qualitative or quantitative analyses to a mixed approach. To address “isolation” and “commercialization”, scholars like Liu Hailong proposed a “cultural heritage network” that integrates regional resources hierarchically to create themed display routes. The network has been refined using international experience [29] and concepts from ecology [30] and botany, with practical research at national [31], regional [32,33], and provincial/municipal [34,35] levels. Studies focus on cultural relic units [36], traditional villages [37], and related heritage [38]. Construction methods include a literature review, the Delphi method [39], PAST [40], space syntax [41,42,43], a minimum resistance model [8], and AHP-MCR [9]. Thus, building a cultural heritage network at the municipal level is feasible.

The “Mount Song Culture Circle” was proposed by Kunshu Zhou [44]. As the core hub of Central Plains civilization, it features the “Center of Heaven and Earth” cosmological schema, where the east–west-oriented Mount Song Range serves as a natural barrier and the Ying, Shaoshi, Taishi, and Fuxi river systems create accessible corridors for settlement and ritual movement [44,45,46,47]. This mountain–water–cosmology triad directly shaped the spatial distribution of heritage sites; 83% of identified cultural relics concentrate on gentle slopes (5–15°) at 200–800 m elevation along these river corridors (see Section 3.1), forming a “high north, low south” core–periphery structure that the present study seeks to reconfigure through network optimization. The region’s ritual heritage—including the Zhongyue Temple and Songyue Temple Pagoda—and cosmological observation platforms (e.g., ancient astronomical observatories) co-evolved with this topographic framework, establishing a spatial gene of “sacred mountain worship” that remains relevant for corridor thematization.

As a typical city lacking the overall protection of cultural landscapes during urbanization, Dengfeng has seen a growing concern for the cultural heritage of the Songshan Scenic Area over the years. However, insufficient attention is paid to other areas within the city, leading to a “single-core polarization” model. This study examines an adaptive MCR gravity model that dynamically balances cultural values and incorporates time decay effects, and this “core-periphery” structure is transformed into a resilient multi-center network. This is mainly verified through three interrelated objectives: constructing a dynamic cultural value weight (CVIndex) and time decay function (λ) for heritage nodes; generating optimized corridor networks that increase peripheral node density and topological connectivity (α-index); and validating that enhanced physical connectivity improves cultural dissemination efficiency (R² > 0.70 via space syntax).

Dengfeng, a historic county-level city in Henan, is home to the “Center of Heaven and Earth” World Heritage site, yet rapid urbanization has fragmented its cultural resources, leaving the southern Ying River basin underdeveloped despite the well-protected northern Songyang Scenic Area. Existing studies focus on single analytical dimensions without clarifying their coupling mechanisms, so this paper adopts an adaptive MCR gravity model integrating landscape typology and corridor ecology to reveal the synergistic logic of cultural landscape–heritage networks for integrated regional protection, outlining the step-by-step methodology from problem identification to network optimization (Figure 1). Using Dengfeng as a case study, the model illuminates the continuity of Chinese civilization and is transferable to other fragmented mountainous cultural landscapes as a methodological framework, provided its core components are recalibrated to local conditions.

2. Materials and Methods

2.1. Study Area and Data Sources

2.1.1. Study Area

Cultural regions can be classified into core regions, sub-regions, and sub-sub-regions according to the degree of individual differences. Kunshu Zhou put forward the concept of the “Mount Song Culture Circle” based on the same and similar lineages distributed around Mount Song. This cultural circle includes the central area (R ≈ 50 km), the marginal area (R ≈ 200 km), and the influence area (R ≈ 700 km). The cultural landscape within it has a long history and diverse varieties. There is also the historical building complex of the World Cultural Heritage “Center of Heaven and Earth” that relies on Mount Song. This complex contains multiple value attributes of nature and humanity and is a direct manifestation of Mount Song culture.

After comprehensively considering the current situation and the influence of Mount Song culture, the central area of the “Mount Song Culture Circle” is chosen as the research scope (Figure 2). Specifically, centered on Junji Peak, the highest peak of Mount Song, with a radius of 50 km, this area covers 19 counties (cities, districts) under the jurisdiction of 5 cities, namely, Zhengzhou, Luoyang, Pingdingshan, Xuchang, and Jiaozuo, with a total of 165 township administrative units. The overall terrain slopes from west to east. In the center, the Mount Song Range runs nearly east–west. There is a diverse range of landforms distributed in a ring around the Songshan Mountain. The region enjoys a mild climate with four distinct seasons.

Dengfeng City, located in the core area of the Mount Song Culture Circle, was formerly known as Yangcheng, Songyang, and Dengfeng County. As a county-level city under the jurisdiction of Zhengzhou City, Henan Province, it lies in the heart of the Central Plains, at the southern foot of Mount Song. It borders the ancient capital Luoyang to the west and is close to the provincial capital Zhengzhou to the east.

2.1.2. Data Sources

The research data is specifically divided into three aspects:

• Research objects. Based on the eight batches of national and provincial cultural relic protection units, 294 samples were obtained from an initial pool of 412 sites after three-stage filtering: exclusion of modern historical sites and representative buildings post-1949 (n = 47); removal of duplicates and spatially overlapping entries (n = 59); and exclusion of sites lacking demonstrable connection to the Mount Song cultural landscape system (n = 12). Inclusion criteria required an authentic spatial relationship with Mount Song geography; cultural attributes traceable to the “Center of Heaven and Earth” framework; and locational precision ≤ 30 m for GIS analysis. The final dataset comprises 93 national-level and 201 provincial-level units (Figure 2b). Among the 48 Dengfeng cultural heritages selected through statistics, nearly 25 are located in the Songshan Scenic Area, covering most of the world’s cultural heritages and national-level cultural relic protection units.
• Literature and materials. They are sourced from on-site investigations, local county annals, garden records, maps, and the interpretation of various historical information.
• Geographic information. The DEM (Digital Elevation Model) data is sourced from the Geospatial Data Cloud SRTM (Shuttle Radar Topography Mission) DEM 30M (http://www.gscloud.cn)(v12.2, 2026), while the data on county-level administrative division boundaries, topography, and water systems are obtained from the Data Center for Resources and Environmental Sciences, Chinese Academy of Sciences (https://www.resdc.cn), etc.

2.2. Pearson Bivariate Correlation Analysis

2.2.1. Factor Selection

Based on multiple literature sources, cultural landscape factors are classified into two major categories and twelve sub-categories (

Table 1. Selection of cultural landscape factors.

Category	Cultural Landscape Factor Type	Cultural Landscape Subfactor Types
Physical Geography	Topography and Landforms	Low-altitude alluvial–proluvial plains, low-altitude floodplains, low-altitude proluvial plains, low-altitude proluvial terraces, low-altitude loess plateaus, low-altitude hills, low-altitude small undulating mountains, low-altitude medium undulating mountains, mid-altitude large undulating mountains
	Elevation	H < 100 m, 100 ≤ H < 200 m, 200 m ≤ H < 500 m, 500 m ≤ H < 800 m, 800 m ≤ H
	Distance from Water	D < 300 m, 300 m ≤ D < 500 m, 500 m ≤ D < 800 m, 800 m ≤ D < 1500 m, 1500 m ≤ D
	Secondary Watershed	Yellow River Basin, Huai River Basin
	Mountain Relationship	Non-mountain type, back-hill type, piedmont type, mid-slope type, summit type
	Water Body Relationship	No water system, point-type, single-side type, double-side type, surrounding type
	Slope Aspect	Semi-sunny slope, semi-shady slope, flat slope, sunny slope, shady slope
	Slope Gradient	0–0.5° (flat land), 0.5–2° (gentle slope), 2–5° (moderate slope), 5–15° (slope), 15–35° (steep slope), 35–55° (cliff slope), >55° (vertical cliff)
Human Factors	Construction Era	Pre-Qin, Wei–Jin, Sui–Tang, Song–Yuan, Qin–Han, Ming–Qing
	Functional Category	Education/science/culture, production/livelihood, religious belief, monument/inscription, municipal administration, military defense
	Hierarchy	National-level, provincial-level
	Humanistic Value	Historical value (HV), artistic value (AV), scientific value (SV), preservation status (PS), ecological value (EV), geological value (GV)

): natural environment and human elements. Considering the profound cultural heritage and diverse cultural types in the Songshan area, seven general categories are further summarized in terms of cultural connotations [48,49,50], each divided into numerous sub-categories, such as urban construction culture (military defense, residential buildings, city planning), sacrifice and memorial culture, prehistoric culture (Yangshao, Longshan, Peiligang), tomb culture, celebrity culture, ceramic culture, and religious culture (Buddhism, Taoism, Confucianism, Islam, Christianity). For data-type indicators, GIS (Geographic Information System) 10.8 (v25, 3, 2026) software processes DEM data to derive slope, aspect, distance to water, etc. Descriptive indicators refer to historical information from field surveys and local county annals, specifically including construction age, usage function, and interpreted human value. After data collection and processing, a cultural landscape information database for the central area of the Mount Song Culture Circle is established (Figure 3).

2.2.2. Bivariate Correlation Analysis

To standardize the 11 data-type indicators, unified coding was performed according to each cultural factor’s classification. Given that the dataset contains ordinal variables (e.g., slope gradient, construction era) and nominal variables (e.g., watershed hierarchy, mountain relationship), Spearman’s rank order correlation was adopted as the primary method, as it is robust to non-normal distributions and appropriate for mixed-scale data. Shapiro–Wilk tests confirmed significant deviation from normality for all continuous variables (p < 0.001). SPSS (Statistical Product and Service Solutions) 19.0 (v11, 4, 2026) software was used to conduct bivariate Spearman correlation analysis to determine dominant factors.

$$r_{x}y={\displaystyle \frac{\left[\Sigma \left(x_i-\overline{x}\right)\left(y_i-\overline{\mathrm{y}}\right)\right]}{\left[\sqrt{\Sigma {\left(x_i-\overline{x}\right)}^2}\ast \sqrt{\Sigma {\left(y_i-\overline{\mathrm{y}}\right)}^2}\right]}}$$

(1)

Among them, when examining the Pearson correlation coefficient between variables x and y, the values of the i-th sample on variables x, y, $\overline{\mathrm{x}}$, and $\overline{\mathrm{y}}$ are the sample means of variables x and y. The closer |r| is to 1, the stronger the correlation; the closer |r| is to 0, the weaker the correlation.

2.3. Entropy Weight TOPSIS Coupling Model

During the development of the “Mount Song Culture Circle cultural landscape”, elements are interconnected, mutually reinforcing, and develop in a coordinated manner (

Table 2. Evaluation indicator system for the cultural landscape of the Songshan Cultural Circle.

Target Level	Factor Level	Criterion Level	Indicator Level	Unit	Indicator Description	Direction
Cultural Landscape of Songshan Cultural Circle (A)	Physical subsystem (B1)	Mountain Landscape (B1)	Topography and Landforms (C1)	_	Describes surface morphological characteristics	Positive
			Elevation (C2)	m	Indicates terrain elevation	Positive
			Mountain Relationship (C3)	_	Describes spatial relationships between mountains	Positive
			Slope Aspect (C4)	_	Orientation of slope inclination	Positive
			Slope Gradient (C5)	°	Degree of slope inclination	Positive
		Water System Landscape (B2)	Distance from Water (C6)	km	Distance to water body boundaries	Positive
			Watershed Hierarchy (C7)	_	Hierarchical classification by watershed scale	Positive
			Water Body Relationship (C8)	_	Interaction with surrounding water systems	Positive
	Human subsystem (B2)	Historical Culture (B3)	Initial Construction Era (C9)	Year	Initial construction period	Positive
			Humanistic Value (C10)	_	Comprehensive cultural value	Positive
		Site Assessment (B4)	Typology (C11)	_	Classification of cultural landscape types	Positive
			Hierarchy (C12)	_	Hierarchical position in the classification system	Positive

).

In order to solve the problems of large data value span and inconsistent units caused by the differences in calculation methods and sources of various indicators, the range normalization method was used to perform dimensionless processing on the original data. The calculation formula is:

$$\text{Positive} \text{indicators}: X_{ij}={\displaystyle \frac{X_{IJ}-\min (X_i)}{\max (X_i)-\min (X_i)}}$$

(2)

$$\text{Negative} \text{indicators}: X_{ij}={\displaystyle \frac{\max (X_i)-X_{IJ}}{\max (X_i)-\min (X_i)}}$$

(3)

In the equation, X_ij denotes the standardized index value after processing, X_IJ represents its original index value, max(X_i) stands for the maximum value of the index, and min(X_i) is the minimum value of the index.

For the standardized data, the proportion of each indicator in each sample is calculated. Then, the entropy value of each indicator is computed. This value is positively correlated with the stability of the system. The formula for calculating the entropy value is:

$$P_{\mathrm{i}\mathrm{j}}={\displaystyle \frac{X_{\mathrm{i}\mathrm{j}}^{\prime }}{{\displaystyle {\sum }_m^n}{X}_{\mathrm{i}\mathrm{j}}^{\prime }}}$$

(4)

$$e_j=-\kappa {\displaystyle {\sum }_{i=1}^n}{P}_{\mathrm{i}\mathrm{j}}\ln (P_{\mathrm{i}\mathrm{j}})$$

(5)

Define the weights of each index by the entropy weight method [51]. The weight of each index reflects its relative importance in the comprehensive evaluation. The formula is:

$$W_{ij}={\displaystyle \frac{(1-e_j)}{{\displaystyle {\sum }_{j=1}^n}(1-e_j)}}$$

(6)

In the formula, W_ij is the index weight and e_j is the information entropy of the jth index. Substitute the data of each index into the formula to calculate the weight results of the evaluation indexes of the subsystem.

This study uses the coupling coordination degree to describe the mutual influence and synergistic interaction between natural and cultural landscapes. The calculation is based on the comprehensive evaluation values of the two subsystems obtained in the previous chapter. Specifically, the entropy method is applied to determine index weights, and the TOPSIS model provides the evaluation values for the natural and cultural systems individually [11]. Using these values, the coupling degree C and the coupling coordination degree D of the Songshan cultural landscape system are calculated as follows:

$$\mathrm{C}={\displaystyle \frac{2\sqrt{T_1\times T_2}}{T_1+T_2}}$$

$$\mathrm{Q}=\alpha {\mathrm{T}}_1+\beta {\mathrm{T}}_2$$

(7)

$$\mathrm{D}=\sqrt{\mathrm{C}\times \mathrm{Q}}$$

Among them:

$\mathrm{T}$: the comprehensive development index;

$\mathsf{\alpha } \mathrm{a}\mathrm{n}\mathrm{d} \mathsf{\beta }$: subsystem importance (both set to 0.5).

In the formula, C denotes the coupling degree; T₁ and T₂ represent the comprehensive evaluation indices of the natural and cultural systems, respectively; Q represents the overall synergistic effects between the two systems; D indicates the coupling coordination degree; and α and β denote the importance of the two systems, both of which are considered equally important based on existing research, with both values set to 0.5.

2.4. Adaptive MCR Model

The construction of the cultural heritage network in Dengfeng City adheres to the “point-line-surface” principle, which involves a path of recognizing cultural heritage features, identifying cultural heritage values, constructing potential cultural heritage corridors, and optimizing the cultural heritage network in Dengfeng City. All data were projected to CGCS2000/3-degree Gauss–Kruger zone 38 (EPSG: 4524) with 30 m × 30 m raster resolution. DEM sinks were filled using the Wang & Liu algorithm; slope and watershed rasters were derived using standard ArcGIS 10.8 tools (Spatial Analyst extension). Heritage nodes were georeferenced via GPS field survey (n = 87), satellite imagery interpretation (n = 156), and historical map digitization (n = 51), validated against road intersections within 50 m tolerance. The composite resistance surface was generated via weighted overlay of seven factor rasters, normalized to [1, 100]. MCR corridor extraction employed the Dijkstra least-cost path algorithm with 8-connectivity and a 15 km Euclidean distance threshold between node pairs, selecting paths below the 25th percentile resistance cost (Figure 4). Many scholars have verified the effectiveness of the minimum cumulative resistance model (MCR) in generating potential cultural heritage corridors. Therefore, this study employs the MCR model to construct such corridors and assesses the results.

Calculation formulas and steps:

1.

Dynamic weight of cultural value (CVIndex)

Formula:

$$\mathrm{C}{\mathrm{V}}_{\mathrm{i}}={\displaystyle {\sum }_{\mathrm{k}=1}^{\mathrm{n}}}{\mathrm{w}}_{\mathrm{k}}·{\mathrm{S}}_{\mathrm{i}\mathrm{k}}$$

(8)

$$\mathrm{C}\mathrm{V}\mathrm{I}\mathrm{n}\mathrm{d}\mathrm{e}\mathrm{x}={\displaystyle \frac{1}{\mathrm{m}}}{\displaystyle {\sum }_{\mathrm{i}=1}^{\mathrm{m}}}\mathrm{C}{\mathrm{V}}_{\mathrm{i}}$$

(9)

Among them:

$\mathrm{C}{\mathrm{V}}_{\mathrm{i}}$: the cultural value score of heritage site i;

${\mathrm{w}}_{\mathrm{k}}$: the entropy weight of index k (Table 1);

${\mathrm{S}}_{\mathrm{i}\mathrm{k}}$: the standardized value of heritage site i in index k (0–1);

$\mathrm{m}$: the total number of heritage sites.

Steps:

• Data normalization (range method):

$${\mathrm{S}}_{\mathrm{i}\mathrm{k}}={\displaystyle \frac{{\mathrm{x}}_{\mathrm{i}\mathrm{k}}-\min ({\mathrm{x}}_{\mathrm{k}})}{\max ({\mathrm{x}}_{\mathrm{k}})-\min ({\mathrm{x}}_{\mathrm{k}})}}$$

(10)

Calculating weights by the entropy weight method:

$$\text{Proportion} \text{of} \text{the} \text{index}: {\mathrm{p}}_{\mathrm{i}\mathrm{k}}={\displaystyle \frac{{\mathrm{S}}_{\mathrm{i}\mathrm{k}}}{{\displaystyle {\sum }_{\mathrm{i}=1}^{\mathrm{m}}}{\mathrm{S}}_{\mathrm{i}\mathrm{k}}}}$$

(11)

$$\text{Information} \text{entropy}: {\mathrm{e}}_{\mathrm{k}}=-{\displaystyle \frac{1}{\ln \mathrm{m}}}{\displaystyle {\sum }_{\mathrm{i}=1}^{\mathrm{m}}}{\mathrm{p}}_{\mathrm{i}\mathrm{k}}\ln {\mathrm{p}}_{\mathrm{i}\mathrm{k}}$$

(12)

$$\text{Weight}: {\mathrm{w}}_{\mathrm{k}}={\displaystyle \frac{1-{\mathrm{e}}_{\mathrm{k}}}{{\displaystyle {\sum }_{\mathrm{k}=1}^{\mathrm{n}}}(1-{\mathrm{e}}_{\mathrm{k}})}}$$

(13)

2.

Weighted summation: calculate each point CV_i.

3.

Regional index: take the average of all $\mathrm{C}{\mathrm{V}}_{\mathrm{i}}$ to get $\mathrm{C}\mathrm{V}\mathrm{I}\mathrm{n}\mathrm{d}\mathrm{e}\mathrm{x}$.

2.

Time decay function (historical stratification effect).

Formula:

$${\mathrm{W}}_{\mathrm{t}}={\mathrm{e}}^{-\mathsf{\alpha }·({\mathrm{T}}_{\mathrm{c}}-{\mathrm{T}}_{\mathrm{i}})}$$

(14)

Among them:

α = 0.05 is the attenuation coefficient (determined through sensitivity analysis; α was varied across [0.01, 0.10] and evaluated against network connectivity, node density, and spatial syntax validity; α = 0.05 yielded optimal performance with R² = 0.78 and α-index = 0.58).

${\mathrm{T}}_{\mathrm{c}}$: Current time (2025).

${\mathrm{T}}_{\mathrm{i}}$: Construction year of the heritage site.

Steps:

1. Calculate the time difference: $\Delta \mathrm{T}={\mathrm{T}}_{\mathrm{c}}-{\mathrm{T}}_{\mathrm{i}}$ (Unit: Century);

2. Substitute the exponential function: ${\mathrm{W}}_{\mathrm{t}}={\mathrm{e}}^{-0.05\times \Delta \mathrm{T}}$;

3. Correct the gravity value: ${{\mathrm{M}}_{\mathrm{i}}}^{\prime }={\mathrm{M}}_{\mathrm{i}}\times {\mathrm{W}}_{\mathrm{t}}$.

The traditional minimum cumulative resistance (MCR) model has two major limitations for cultural heritage networks: it ignores spatial heterogeneity of cultural value by assigning uniform resistance and it assumes static resistance values, failing to capture the dynamic nature of cultural significance (which may decay or accumulate over time). As a result, generated corridors are ecologically efficient but culturally suboptimal, often bypassing high-value cultural nodes or fragmenting meaningful pathways. To address these issues, this study proposes an adaptive MCR gravity model incorporating a dynamic cultural value weight and a time decay function, allowing high-value heritage nodes to reduce local resistance and reflecting temporal changes in cultural significance, thereby generating corridors that balance ecological constraints with cultural connectivity.

3.

Improvement of the adaptive MCR model

Traditional MCR:

$$\mathrm{M}\mathrm{C}\mathrm{R}=\min {\displaystyle {\sum }_{\mathrm{j}=1}^{\mathrm{n}}}{\displaystyle {\sum }_{\mathrm{i}=1}^{\mathrm{m}}}({\mathrm{D}}_{\mathrm{i}\mathrm{j}}\times {\mathrm{R}}_{\mathrm{i}})$$

(15)

MCRImproved MCR:

$${\mathrm{MCR}}^{\prime }=\min {\displaystyle {\sum }_{\mathrm{j}=1}^{\mathrm{n}}}{\displaystyle {\sum }_{\mathrm{i}=1}^{\mathrm{m}}}\left[{\mathrm{D}}_{\mathrm{i}\mathrm{j}}\times \left({\mathrm{R}}_{\mathrm{i}}\times {\displaystyle \frac{1}{\mathrm{C}{\mathrm{V}}_{\mathrm{i}}}}\right)\right]$$

(16)

Steps:

• Calculate the cultural value resistance correction: ${{\mathrm{R}}_{\mathrm{i}}}^{\prime }={\mathrm{R}}_{\mathrm{i}}/\mathrm{C}{\mathrm{V}}_{\mathrm{i}}$;
• Generate dynamic drag surface;
• Iterative calculation of the minimum accumulated path;
• Connectivity enhancement verification.
  Traditional network α-index: ${\mathsf{\alpha }}_0={\displaystyle \frac{\mathrm{L}-\mathrm{V}+1}{2\mathrm{V}-5}}$.
  Optimized network α-index: ${\mathsf{\alpha }}_1$.
  Improvement rate: ${\displaystyle \frac{{\mathsf{\alpha }}_1-{\mathsf{\alpha }}_0}{{\mathsf{\alpha }}_0}}\times 100\%$.

4.

Calculation of heritage node density

Formula:

$$\mathrm{P}={\displaystyle \frac{\mathrm{N}}{\mathrm{A}}}$$

(17)

Steps:

• Delimit the scope of the core area: A (Songshan Scenic Area);
• Number of nodes before statistical optimization: ${\mathrm{N}}_0\Rightarrow {\mathsf{\rho }}_0$;
• Newly added nodes after optimization: ${\mathrm{N}}_1\Rightarrow {\mathsf{\rho }}_1$
• Spatial syntax analysis.

Formula:

$$\mathrm{I}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{g}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}={\displaystyle \frac{(\mathrm{n}-1{)}^2}{2{\displaystyle {\sum }_{\mathrm{j}=1}^{\mathrm{n}}}{\mathrm{d}}_{\mathrm{i}\mathrm{j}}}}$$

(18)

Steps:

• Convert the corridor network into an axis diagram;
• Calculate the average depth value of each node ($\mathrm{M}\mathrm{D}$);
• Calculate integration ($\mathrm{I}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{g}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}$);
• Regression analysis.

Establish an equation: $\mathrm{y}={\mathsf{\beta }}_0+{\mathsf{\beta }}_1\mathrm{x}$.

Among them, $\mathrm{y}$ is the cultural dissemination efficiency index (derived from spatial syntax integration values and heritage node accessibility metrics).

$\mathrm{x}$: Corridor integration value.

5.

Cultural gravity model

Basic formula:

$${\mathrm{F}}_{\mathrm{i}\mathrm{j}}=\mathrm{G}{\displaystyle \frac{{\mathrm{M}}_{\mathrm{i}}{\mathrm{M}}_{\mathrm{j}}}{{\mathrm{d}}_{\mathrm{i}\mathrm{j}}^{\mathrm{b}}}} (\mathrm{G}=10^3, \mathrm{b}=1.8)$$

(19)

Improved formula:

$${{\mathrm{F}}_{\mathrm{i}\mathrm{j}}}^{\prime }=\mathrm{G}{\displaystyle \frac{(\mathrm{C}{\mathrm{V}}_{\mathrm{i}}·{\mathrm{W}}_{\mathrm{t}\mathrm{i}})(\mathrm{C}{\mathrm{V}}_{\mathrm{j}}·{\mathrm{W}}_{\mathrm{t}\mathrm{j}})}{{\mathrm{d}}_{\mathrm{i}\mathrm{j}}^{\mathrm{b}}}}$$

(20)

Regional gravity calculation:

$${\mathrm{F}}_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}={\sum }_{\mathrm{i}\in \mathrm{c}\mathrm{o}\mathrm{r}\mathrm{e}}{\sum }_{\mathrm{j}\in \mathrm{e}\mathrm{d}\mathrm{g}\mathrm{e}}{\mathrm{F}}_{\mathrm{i}\mathrm{j}}$$

(21)

Steps:

• Gravity before computational optimization: ${\mathrm{F}}_0$;
• Optimized gravity: ${\mathrm{F}}_1$;
• Calculate the improvement rate: ${\displaystyle \frac{{\mathrm{F}}_1-{\mathrm{F}}_0}{{\mathrm{F}}_0}}\times 100\%$.

Motivation: The gravity model quantifies the attractive force between heritage nodes. The improved version replaces static mass MM with the product of cultural value CVCV and a time decay weight W_t, thereby capturing dynamic cultural significance. A higher F_total after optimization indicates stronger potential interactions among heritage nodes across the core–edge gradient, supporting integrated regional protection.

3. Results

3.1. Cultural Landscape Zoning and Coupling Analysis

3.1.1. Determine the Dominant Factor

Through correlation analysis, the degree of closeness and the direction of the relationship between relevant cultural factors can be deduced. In the analytical framework of cultural landscape adopted in this study, natural geographical elements, such as topography and elevation, are not treated merely as objective environmental variables. Rather, because they have historically shaped human settlement patterns, spatial practices, and cultural cognition in the Songshan area, they are considered cultural factors in a broad sense—constitutive components of the cultural landscape that mediate human–environment interactions. Accordingly, this study uses SPSS 19.0 to perform a bivariate correlation analysis on 11 data-type indicators to further explore the relationships among these cultural factors. The research findings indicate that topography is closely associated with cultural landscape distribution and has a significant correlation with elevation. This correlation is stronger than that between topography and other cultural factors, which provides a basis for the subsequent analysis of the relationship between cultural factors and settlement patterns (

Table 3. Correlation analysis of cultural landscape factors in the core area of the Songshan Cultural Circle.

Cultural Factor		Time	Sub-Category	Topography	Elevation	Distance from Water	Secondary Watershed	Slope Gradient	Water Relationship	Mountain Relationship	Aspect	Level
Time	Pearson Correlation	1	0.578 **	0.125 *	0.159 *	0.126 *	0.025	0.087	−0.010	0.164 *	0.013	−0.055
	Sig. (2-tailed)		<0.001	0.044	0.010	0.042	0.693	0.160	0.869	0.008	0.834	0.374
Sub-category	Pearson Correlation	0.578 **	1	0.073	0.164 **	0.211 **	0.098	0.068	0.023	0.115	0.044	0.117
	Sig. (2-tailed)	<0.001		0.239	0.008	<0.001	0.112	0.276	0.712	0.063	0.477	0.058
Topography	Pearson Correlation	0.125 **	0.073	1	0.548 **	0.037	0.242 **	0.099	0.099	0.260 **	0.044	0.050
	Sig. (2-tailed)	0.044	0.239		<0.001	0.554	<0.001	0.112	0.111	<0.001	0.484	0.425
Elevation	Pearson Correlation	0.159 **	0.164 **	0.548 **	1	0.209 **	0.393 **	0.187 **	0.094	0.502 **	0.168 **	0.195 **
	Sig. (2-tailed)	0.010	0.008	<0.001		<0.001	<0.001	0.002	0.131	<0.001	0.007	0.002
Distance from Water	Pearson Correlation	0.126 *	0.211 **	−0.037	0.209 **	1	0.032	0.135 **	−0.192 **	0.195 **	0.063	0.051
	Sig. (2-tailed)	0.042	<0.001	0.554	<0.001		0.605	0.029	0.002	0.002	−0.311	0.408
Secondary Watershed	Pearson Correlation	0.025	0.098	0.242 **	0.393 **	0.032	1	−0.061	0.067	0.131 *	−0.096	0.103
	Sig. (2-tailed)	0.693	0.112	<0.001	<0.001	0.605		0.324	0.282	0.034	0.123	0.098
Slope Gradient	Pearson Correlation	0.087	0.068	0.099	0.187 **	0.135 *	−0.061	1	−0.168	0.321 **	0.235 **	−0.006
	Sig. (2-tailed)	0.160	0.276	0.112	0.002	0.029	0.324		0.007	<0.001	<0.001	0.924
Water Relationship	Pearson Correlation	−0.010	0.023	0.099	−0.094	−0.192 **	0.067	−0.168 **	1	−0.110	−0.100	0.040
	Sig. (2-tailed)	0.869	0.712	0.111	0.131	0.002	0.282	0.007		0.076	0.108	0.518
Mountain Relationship	Pearson Correlation	0.164 **	0.115	0.260 **	0.502 **	0.195 **	0.131 **	0.321 **	−0.110	1	0.145 **	0.236 **
	Sig. (2-tailed)	0.008	0.063	<0.001	<0.001	0.002	0.034	<0.001	0.076		0.019	<0.001
Aspect	Pearson Correlation	0.013	0.044	0.044	0.168 **	0.063	0.096	0.235 **	0.100	0.145 **	1	0.011
	Sig. (2-tailed)	0.834	0.477	0.484	0.007	0.311	0.123	<0.001	0.108	0.019		0.858
Level	Pearson Correlation	0.055	0.117	0.050	0.195 **	0.051	0.103	0.006	0.040	0.236 **	0.011	1
	Sig. (2-tailed)	0.374	0.058	0.425	0.002	0.408	0.098	0.924	0.518	<0.001	0.858

* Significant at the 0.05 level (2-tailed). ** Significant at the 0.01 level (1-tailed). Data source: Results processed by SPSS software.

).

3.1.2. Cluster Analysis and Cultural Zoning

Traditional cultural zoning methods primarily focus on the qualitative description and analysis of the dominant geographical–cultural factors, followed by statistical classification based on these findings. This approach results in a lack of objectivity and accuracy. Meanwhile, a simple mathematical clustering method may fail to distinguish between primary and secondary factors, overemphasizing the comprehensive effect of multiple indicators.

This study integrates quantitative and qualitative methods to refine landscape zoning for the Mount Song Culture Circle. It first analyzes data-type indicators to identify dominant factors and performs hierarchical clustering (Ward’s method, squared Euclidean distance), with the optimal cluster number (k = 4) determined by the elbow method and silhouette analysis. It then incorporates descriptive indicators (topography, elevation, cultural landscape types, ethnic groups/languages/dialects, intangible heritage) through a combined data analysis and map representation approach (Figure 5). The optimal number of clusters (k = 4) was determined through the elbow method and silhouette coefficient analysis, with the final solution achieving an average silhouette width of 0.62, indicating reasonably separated clusters. Using GIS, the clustering results are associated with spatial data, and regional differences in descriptive indicators are overlaid to fine-tune boundaries. The Mount Song Culture Circle is ultimately divided into four cultural regions (I–Luosong, II–Huoji, III–Zhengkai, IV–Nanlu) and nine sub-regions, each exhibiting distinct cultural landscape characteristics.

3.1.3. Evaluation Results of Cultural Landscape Zoning

On the basis of referring to the research findings of relevant scholars [52], the coordination scores are classified, and the overall coordination degree is divided into five types. When c(n) ≤ 0.2, it denotes severe imbalance; when 0.2 < c(n) ≤ 0.4, it indicates moderate imbalance; when 0.4 < c(n) ≤ 0.6, it indicates basic coordination; when 0.6 < c(n) ≤ 0.8, it indicates moderate coordination; and when 0.8 < c(n) ≤ 1, it indicates high coordination (

Table 4. Coupling coordination evaluation of cultural sub-regions.

Cultural Sub-Region	Coupling Degree	Coordination Index	Coupling Coordination Degree	Coordination Level	Coordination Status
I-①	0.442	0.5	0.47	5	Near Imbalance
I-②	0.559	0.268	0.387	4	Mild Imbalance
I-③	0.699	0.47	0.573	6	Barely Coordinated
I-④	0.731	0.702	0.716	8	Moderate Coordination
II	0.278	0.275	0.277	3	Moderate Coordination
III-①	0.814	0.348	0.532	6	Barely Coordinated
III-②	0.533	0.411	0.468	5	Near Imbalance
IV-①	0.442	0.5	0.47	5	Near Imbalance
IV-②	0.449	0.225	0.318	4	Mild Imbalance

).

The Songshan Scenic Area has a high coupling coordination degree as a model of nature–culture integration. However, Dengfeng’s cultural landscape shows a “high north, low south” core–periphery structure: the north forms a strongly coordinated core due to Songshan’s topographical barrier, heritage agglomeration, and well-developed infrastructure; the south suffers from topographical barriers, scattered cultural resources, poor accessibility, and lagging development, resulting in spatial fragmentation of ecological, cultural, and urban–rural functions. Corridor network construction can promote a shift from core polarization to network synergy, providing key support for coupled and coordinated natural–cultural–urban–rural space and sustainable development in Dengfeng.

3.2. Construction of the Cultural Heritage Spatial Network

This study determined factor weights for the comprehensive resistance surface through a systematic literature review and entropy-weighted analysis informed by relevant studies [53,54,55,56]. The significant influence of elevation and slope on heritage connectivity in mountainous terrain was verified [57], confirming the factor selection. Heritage resource level emerged as the primary factor affecting cultural heritage protection and development, followed by roads, elevation, and slope as secondary factors, with land use types and rivers being the least important (

Table 5. Resistance coefficient of suitability for constructing the inheritance network.

Index	Factor						Weight
Road	Urban slip roads, slide roads	Main and secondary roads of the city		Provincial roads, national roads	Railways, highways	No roads	0.155
	50	100		300	400	500
/m Rivers/m	≤200 m	200~500 m		500~1000 m	1000~1500 m	≥1500 m	0.095
	10	30		50	70	100
/m Altitude/m	≤200 m	200~400 m		400~600 m	600~800 m	≥800 m	0.15
	10	30		50	70	100
/°Slope/°	<5°	5~15°		15~25°	25~35°	≥35°	0.145
	5	10		30	100	500
Distance from the Road/m	≤200 m	200~500 m		500~1000 m	1000~1500 m	≥1500 m	0.15
	5	10		50	200	400
Level of Heritage Source	1000 m First-Level Source Area and Surrounding 1000 m Area	1000 m Second-Level Source Area and Surrounding 1000 m Area		1000 m Third-Level Source Area and Surrounding 1000 m Area		Other Areas	0.21
	5	20		50		400
Type of Land Use	Forestland	River System	Lawn	Farmland	Unused Land	Construction Land	0.095
	20	40	60	150	160	200

). Using the raster calculator in GIS, a weighted calculation was performed on the seven cost rasters, and the results were classified via the natural break method into five suitability levels (high, moderately high, moderate, low, unsuitable), from which potential cultural heritage corridors were generated (Figure 6).

The simulated path of potential cultural heritage corridors is constructed using the minimum cumulative resistance (MCR) model, which calculates the “minimum cost path” between heritage resource points. As there are overlapping paths between some of these points, the potential Dengfeng City cultural heritage corridor network needs to be manually and reasonably selected and optimized. After selecting and comparing the potential cultural heritage corridors based on minimum cumulative resistance thresholds, corridor width suitability (≥500 m), and expert review (n = 5), the Dengfeng City cultural heritage corridor was finally obtained (Figure 7a). The optimized Dengfeng City cultural heritage corridor has the following characteristics:

➀

The areas with relatively dense cultural heritage corridors are near the Songshan area.

➁

The distances between corridors at the first-and second-level cultural heritage sites are relatively short.

➂

The left and right sides of the optimized Dengfeng City cultural heritage corridor are relatively sparse, with its main support points in the middle. Meanwhile, it maintains the necessary connectivity in areas with fewer resources.

The heritage corridor network of Dengfeng City has ultimately formed a spatial protection pattern for the city’s cultural heritage. It links the eastern and western parts of Dengfeng City, spanning widely from left to right and covering a relatively large area. However, due to the spatial distribution of cultural heritage resource points, the southern area has not been fully covered (Figure 7b).

As a crucial carrier for urban development and cultural presentation, Dengfeng City’s cultural heritage network must include thematic routes, which are indispensable [58]. These routes integrate heritage resources with similar geographical environments, historical backgrounds, and cultural connotations, making heritage protection more systematic and efficient, revealing internal connections, forming a complete cultural context, and enhancing public understanding and recognition through shared cultural backgrounds (

Table 6. Table of factors for constructing thematic paths of the heritage network.

Theme Path	Culture Connotation	Key Screening Indicators	Typical Node Cases
“Seeking Wisdom in the Mountains”	Religion/Sacrificial Culture (Buddhism, Taoism, and Confucianism Space)	The density of religious heritage ≥0.8 place/km2 Slope 5–15° (suitability of the path coefficient Ti $>0.7$ 0.7 (historical layers)	Shaolin Temple, Zhongyue Temple, Songyang Academy, Junji Peak sacrificial axis
“Searching for Culture in the Scenery”	Scholars’/Academy Culture (Spread of Neo-Confucianism and Landscape Aesthetics)	Integration degree R2 > 0.75 (high accessibility) 300–500 m from the water system (landscape view) CVi education weighting > 0.15	Songyang Academy, Star Observation Platform, Qimu Que (stone carving art), Tang Dynasty Stele
“Exploring the City Along the River”	Prehistoric Settlements/City Civilization (Cradle of the Ying River Basin Civilization)	Distance from water ≤ 500 m (settlement dependent) Cultural coupling coordination degree D > 0.6 (natural–human collaboration) The proportion of newly activated nodes ≥ 40%	Wangchenggang site, Yangcheng site, Quhe kiln site, Yingyang ancient city

). The selection of the three major thematic paths—culturally themed segments within the broader heritage corridor network—“Seeking Wisdom in the Mountains”, “Searching for Culture in the Scenery”, and “Exploring the City Along the River”—adheres to a dual framework that combines quantitative constraints on resilience thresholds with qualitative verification of cultural narratives.

Cultural theme clustering, based on entropy-weighted cultural value (CVIndex ≥ 0.82) and historical literature, groups nodes with religious functions (Shaolin Temple, Zhongyue Temple) into the “Seeking Wisdom in the Mountains” route, where slope suitability (5–15°) and sacrificial axis integrity (“Que–Temple–Peak”) reach 83%, revealing the spatial gene of sacred mountain worship. Spatial synergy optimization uses the MCR resistance surface and space syntax integration (R² > 0.78); the “Searching for Culture in the Scenery” path preferentially connects Songyang Academy and the Star Observation Platform, relying on the 300–500 m landscape corridor along the Ying River to enhance academy culture dissemination. Enhancing network resilience, the gravity model simulates marginal zone enhancement (ΔF ≥ 47%); the “Exploring Cities Along the River” approach activates scattered southern resources (Wangchenggang Prehistoric Site) using the Ying River system, reducing basin ecological–cultural resistance by 60% and breaking the “high north, low south” imbalance.

Figure 7. (a) Potential cultural heritage corridor in Dengfeng City; (b) cultural heritage space protection pattern of Dengfeng City; (c) the theme path of asking “Tao” according to “Mountain”; (d) the theme path of looking at the “Scenery” and finding the “Culture”; (e) the theme path of exploring the “City” along the “River”.

Figure 7. (a) Potential cultural heritage corridor in Dengfeng City; (b) cultural heritage space protection pattern of Dengfeng City; (c) the theme path of asking “Tao” according to “Mountain”; (d) the theme path of looking at the “Scenery” and finding the “Culture”; (e) the theme path of exploring the “City” along the “River”.

3.3. Cultural Heritage Spatial Network System Evaluation

A systematic evaluation is conducted on the constructed “Adaptive MCR–Gravity Model” and the optimized heritage corridor network to verify their effectiveness and innovation (

Table 7. Key parameters of heritage network system evaluation.

Index	Symbol	Value	Implication
Cultural value index	CVIndex	0.82	Regional heritage value average level
Time decay coefficient	α	0.05	Decay rate per century
Distance attenuation coefficient	b	1.8	Calibration based on friction surface
Gravitational constant	G	103	Dimensional transformation coefficient
Connectivity increase	Δα	+37%	Network connectivity gain
Density increase	Δρ	+51%	Core area resource integration

):

Model performance improvement: Compared with the traditional static MCR model, the adaptive model significantly improves the network connection efficiency by introducing a dynamic weight coefficient of cultural value (CVIndex = 0.82, evaluated based on the heritage grade, age, and entropy weight of cultural connotations) and a time decay function (α = 0.05, reflecting the historical stratification effect). Network topology analysis shows that the α index (connectivity) of the optimized corridor network increased from 0.42 to 0.58 (+37%), indicating improved network structure. As these are descriptive network metrics without replicate sampling, formal inferential statistics (confidence intervals, p-values) are not reported; the magnitude of change serves as the effect size.

Spatial optimization effect: The multi-scale resilience optimization framework, integrating “historical stratification effects, ecological substrate constraints, and cultural gravity associations”, effectively addresses the connectivity challenges of heritage nodes in complex mountainous terrains. The optimized corridor network increases heritage node density in the core area (Songshan Scenic Area and adjacent zones) from 0.74 nodes/km² to 1.12 nodes/km², enhancing the spatial agglomeration of resources and laying the physical foundation for outward radiation to underdeveloped peripheries.

Corridor function verification: Axial analysis based on space syntax was employed to verify the accessibility and integration of the optimized corridors. The results indicated a significant positive correlation (p < 0.01) between the integration (integration R²= 0.78) of the three major theme corridors (“Seeking Wisdom in the Mountains”, “Searching for Culture in the Scenery”, and “Exploring the City Along the River”) within the network and the cultural dissemination potential. This confirms that the optimized corridors not only enhance physical connectivity but also effectively boost the structural accessibility and dissemination efficiency of cultural heritage values.

Regional balance improvement: The gravity model simulation reveals that the optimized thematic corridor network boosts the cultural gravitational pull of the core area (scenic spots) on the southern region by approximately 47%. Through hierarchical nodes (such as the Fengsi Altar Site and the prehistoric settlement group along the Ying River), it activates the scattered resources in the south, initially breaking the previous “north–high, south–low” pattern and laying the groundwork for the “network synergy” development across the entire region.

The model evaluation comprehensively employs topological analysis, density calculation, space syntax, and gravity simulation to multi-dimensionally verify the remarkable effectiveness and scientific value of the “Adaptive MCR–Gravity Model” in addressing the spatial fragmentation of cultural landscapes, optimizing the structure of heritage networks, and enhancing regional cultural connectivity.

4. Discussion

4.1. The Multi-Factor Synergy Mechanism of the Adaptive MCR Gravity Model

This study’s adaptive MCR gravity model introduces two innovations absent in conventional applications: dynamic cultural value weight (CV_Index = 0.82) and time decay coefficient (α = 0.05). Traditional MCR models treat resistance as spatially homogeneous and temporally static [8,9], whereas our approach quantifies the non-linear temporal attenuation of cultural significance (Wt = 0.0810 for Neolithic Yingyang Site to 0.9162 for Qing Wanglou Watchtower). The 37% improvement in α-index connectivity exceeds the 15–20% gains reported by Chen et al. [55] using conventional MCR in Chaozong Street, suggesting that cultural value-weighted resistance correction is particularly effective in mountainous contexts where topographic constraints (r = 0.548 with elevation) compound fragmentation (Figure 8). Unlike Zhang et al. [54], who treated cultural value as a passive suitability filter in the Yellow River region, our model integrates entropy-weighted CV_Index as an active resistance modifier, shifting the optimization objective from “least ecological cost” to “maximum cultural gravitational efficiency.” (

Table 8. Performance of traditional MCR vs. adaptive MCR gravity model.

Evaluating Indicator	Traditional MCR Model	Adaptive Model	Improvement Rate	Verification Method
Network Connectivity (α index)	0.42	0.58	+37%	Topology Analysis
Node Density of the Core Area (per/km2)	0.74	1.12	+51%	Kernel Density Estimation
Cultural Dissemination Efficiency(R2)	0.61	0.78	+27.9%	Spatial Syntax
Gravitational Intensity of the Peripheral Region (∆Fij)	Reference Value	+47%	47%	Gravity Model Simulation
Computation Time (min)	18.2	23.7	+30%	Python 3.6 Timing

). This operationalizes Taylor and Albrecht’s [2] conceptualization of resilience as “dynamic equilibrium” through measurable network parameters.

4.2. The Interactive Relationship Between Imbalanced Regional Development and Heritage Networks

The core–periphery disequilibrium in Dengfeng (0.74 nodes/km² in the north versus fragmented southern distribution) mirrors the “polarized protection” pattern documented by Yue et al. [57] along the Shu Road, where linear heritage corridors similarly failed to penetrate peripheral basins. Yet, our intervention diverges methodologically; whereas Yue et al. [57] employed remote sensing-based ecological resistance surfaces without cultural value differentiation, our adaptive model achieves a 47% gravitational enhancement in the southern Yinghe River Basin by coupling water system proximity (≤500 m buffer) with time decay-adjusted node mass. This result contrasts with Feng et al.’s [34] network construction in Dunhuang, where gravity models improved peripheral connectivity by only 22% despite higher baseline node density, suggesting that Dengfeng’s steeper topographic gradient (62% slopes > 25°) actually amplifies the relative advantage of adaptive resistance correction. The resistance reduction achieved through refined slope/river weighting (0.145–0.15) is comparable to Huang et al.’s [40] mountainous multi-ethnic corridor study in Southwest China, but our integration of space syntax validation (R² = 0.78) provides an empirical bridge between structural connectivity and perceived accessibility that Huang et al. did not establish. Notably, the “structural transformation” from single-core to multi-centered networking (with ≥40% newly activated southern nodes) challenges Liu and Yang’s [5] earlier assumption that hierarchical “point-line-surface” networks inevitably reproduce core dominance; instead, our thematic routes demonstrate that culturally weighted gravity can redistribute network centrality without requiring equivalent infrastructure investment in peripheries.

This process confirms that the optimization of the heritage network’s resilience relies on the spatial adaptability of “nature–culture”. The water system and gentle slope zones (5–15°) not only serve as the foundation for historical settlements (such as the Yangcheng Ruins) but also act as the spatial link to address the imbalance in regional development.

4.3. The Resilience Mechanism of Network Coupling in Topic Paths

The three thematic paths (“Seeking Wisdom in the Mountains”, “Searching for Culture in the Scenery”, and “Exploring the City along the River”) instantiate “differentiated resilience” that contrasts with existing typologies. Jansen-Verbeke et al. [29] proposed “pattern-process-policy” integration for cultural routes, yet their PAST tool remains qualitative; our CV_Index ≥ 0.82 threshold provides a replicable quantitative entry. The religious path’s “hierarchical radiation” around Jiji Peak (83% slope suitability at 5–15°, Wt > 0.7) operationalizes Zhou’s [44] “que-temple-peak” spatial gene metrically, unlike Garau et al.’s [39] purely narrative assessment in Cagliari.

The extreme temporal asymmetry within this path—Wanglou Watchtower (Wt = 0.9162) versus Yingyang Site (Wt = 0.0810)—exposes a tension absent in prior MCR studies; Zhang et al. [54] and Chen et al. [55] treated heritage age as static prestige, whereas our exponential decay penalizes older sites for connectivity potential despite higher nominal value. This is resolved through coupling coordination (D > 0.6); prehistoric sites achieve inclusion via aggregation with high-PS neighbors, as seen in the stone que group (CV_i = 0.70–0.83), where shared geological value (>8.5) compensates for temporal attenuation. This aligns with Biro et al.’s [10] finding that landscape legacies persist through “knowledge clusters” rather than isolated nodes.

The academy path’s Ying River visual corridor (300–500 m) and R² > 0.78 integration validate Jiang et al.’s [41] space syntax approach but extend it by establishing a predictive relationship (p < 0.01) between topological centrality and structural accessibility (Figure 9). This bridges the divergence between physical and topological proximity in mountain landscapes [42]. The settlement path’s activation of ≥40% of southern nodes through water system corridors (D > 0.6) contradicts Ma et al.’s [35] assumption that functional integration requires prior urban–rural coordination; instead, our “Exploring the City Along the River” route leverages existing geomorphology as both a resistance modifier and a narrative carrier.

4.4. Methodological Enlightenment and Application Boundaries

The “cultural landscape zoning-corridor optimization” coupling framework proposed in this study offers three paradigm innovations for the protection of mountainous cultural landscapes:

• Dynamic weight mechanism: The “CVIndex” of the entropy weight method empowers the quantification of the heterogeneity of heritage values, thus avoiding the deviation caused by the traditional MCR model’s “homogenization” treatment of the cultural dimension.
• Multi-scale decoupling: By hierarchically coupling the historical stratification effect (time decay function) with the ecological substrate (terrain/water system resistance surface), the problem of scale disconnection between macro-cultural zoning and micro-path optimization is solved.
• Resilience verification tool: Combining the gravity model (ΔF ≥ 47%) with spatial syntax (R² = 0.78) enables the collaborative evaluation of network structure and functional efficiency.

However, the application of the model in highly urbanized areas (such as the urban area of Zhengzhou) is limited by the large-scale annihilation of spatial carriers of cultural heritage. In the future, the spatial mapping mechanism of intangible cultural heritages (such as Zen martial arts culture and sacrificial rituals) should be integrated to enhance network adaptability in complex environments.

5. Conclusions

The co-evolution of the Mount Song Culture Circle cultural landscape and heritage corridor reveals the systematic mechanism of the deep mutual feedback between the natural geographical foundation and the human historical process, which can be summarized into the following three aspects:

(1)

Physically, 83% of the heritage is on gentle slopes (200–800 m) of the Taishi and Shaoshi Mountains, forming a “high north, low south” core–periphery structure. Water corridors like the Ying River enabled mountain–water settlement models and served as key network axes.

(2)

Historically, the “Center of Heaven and Earth” cosmology and ritual civilization have defined the cultural landscape. The MCR gravity model validates the “que-temple-peak” sacrificial axis, while Confucianism–Buddhism–Taoism coexistence forms a “mountain-scenery-city” spiritual network reinforcing “heaven-human unity”.

(3)

Three thematic paths (“Seeking Wisdom,” “Searching for Culture,” “Exploring the City”) address heritage islandization, boosting core–periphery cultural connection by 47% and shifting from single-pole polarization to network synergy, offering a paradigm for nature–culture–urban–rural collaborative protection.

In summary, as a core part of Chinese civilization, the landscape evolution of the Mount Song Culture Circle results from the combined effects of natural barriers, sacrificial rituals, and dynastic governance, making it a geographical and historical product. The methodological innovation of the adaptive MCR gravity model provides a spatial optimization framework for enhancing connectivity in fragmented mountainous cultural landscapes. It advances MCR modeling by incorporating entropy-weighted cultural value into resistance surfaces and parameterizing the temporal decay of heritage significance. While it improves measurable connectivity metrics (α-index, node density, integration R²), it does not claim to explain the mechanisms of civilizational continuity—a process beyond spatial analysis. Rather, it offers a replicable approach for comparable contexts, provided parameters are recalibrated locally. In the future, we need to further integrate the spatial mapping of intangible cultural heritage with multi-governance mechanisms to ensure that the civilization gene pool of this “Center of Heaven and Earth” remains vibrant in the new era.