The Bosnian Valley of the Pyramids is situated within a geomorphologically distinct basin defined by pyramidal hill formations, tumuli, hydrological junctions, and subterranean tunnel systems. An overview of the valley and its principal monuments is shown in Figure 1, which establishes the spatial framework and feature distribution examined in this study.

Figure 1.Overview of the Bosnian Valley of the Pyramids and principal points of interest. Oblique satellite view of the Visoko Valley, Bosnia and Herzegovina, showing the spatial distribution of the Bosnian Pyramid of the Sun and associated monumental features, including the Bosnian Pyramid of the Moon, Bosnian Pyramid of the Dragon, Bosnian Pyramid of Love, and the Temple of Mother Earth. Also indicated are major subterranean access points (Ravne and KTK tunnels), selected tumuli, and the urban area of Visoko. This figure establishes the valley-scale spatial context and feature inventory examined in Part II, serving as the reference framework for subsequent analyses of linear alignments, nodal relationships, and architectural-scale spatial organization. Source: Google Earth imagery; annotations by the author.

A three-dimensional terrain reconstruction derived from photogrammetric and elevation modeling is presented in Figure 2. This reconstruction clarifies summit prominence, relative relief, and the hydrological convergence of the Fojnica and Bosna rivers. The Bosnian Pyramid of the Sun appears as the dominant structure within the valley, with adjacent pyramidal formations and tumuli integrated into the surrounding landscape morphology.

Figure 2.Three-dimensional terrain reconstruction of the Visoko Valley and pyramid-shaped formations. A 3D digital reconstruction of the Visoko Valley based on photogrammetric modeling, Z-map elevation data, and WebGL rendering, illustrating the relative morphology and spatial relationships of pyramid-shaped formations within the Bosnian Valley of the Pyramids. The Bosnian Pyramid of the Sun is shown as the dominant central structure, with adjacent pyramidal forms integrated into the surrounding topography. The reconstruction highlights the role of hydrology, with the Fojnica River flowing west-east before joining the Bosna River north of the Pyramid of the Sun. The convergence of river systems at the base of the primary monument provides important contextual information for subsequent analyses of nodal positioning, axial planning, and landscape-scale spatial architecture addressed in Part II [1].

High-resolution airborne LiDAR mapping with geodetically defined summit centroids is shown in Figure 3. These summit locations, validated through differential GPS and state geodetic control, form the fixed spatial dataset used throughout this analysis [2]. The complete coordinate reference framework, including pyramidal summits, tumuli, hydrological nodes, and tunnel entrances, is presented in Figure 4. All geometric constructions in Part II are based strictly on these predefined coordinates. No positional adjustments were made to improve spiral fit.

Part I of this study demonstrated that the valley exhibits statistically constrained linear, triangular, and cardinal spatial regularities under fixed geometric rules and Monte Carlo testing [3]. Summit-to-summit alignments and near-equilateral triangular configurations among the Bosnian Pyramids of the Sun, Moon, and Dragon were shown to exceed expectations under constrained spatial redistribution. These rectilinear relationships, documented in Figures 5-8, provide the structural baseline for evaluating curved proportional geometry.

Figure 3.LiDAR-based topographic map of the Bosnian Valley of the Pyramids with geodetically defined summit reference points. High-resolution airborne LiDAR data reveal the precise topographic configuration of the Bosnian Valley of the Pyramids. Summit locations of the Bosnian Pyramid of the Sun, Moon, Dragon, Love, and the Temple of Mother Earth are marked by white reference points derived from laser scanning with documented positional accuracy of ±20 cm horizontally and ±15 cm vertically. The Bosnian Pyramid of the Sun, Moon, and Dragon defines an approximately 2.2 km equilateral triangle, providing a stable geometric scaffold upon which multiple Fibonacci spiral trajectories can be constructed, scaled, and statistically tested. Additional fixed reference points—including the Pyramid of Love, the Vratnica tumulus, the entrance to the Ravne underground tunnel system, the confluence of the Fojnica and Bosna rivers, and the Temple of Mother Earth—serve as secondary nodes for evaluating spiral propagation, nodal intersections, and landscape-scale geometric coherence. The use of LiDAR-derived summit reference points minimizes positional uncertainty and enables high-confidence assessment of non-random geometric organization at the landscape scale [4].

Figure 4.Coordinate table of analyzed summit locations. Geographic coordinates, projected Gauss-Krüger coordinates, and absolute elevations are reported. These values are treated as fixed inputs across all analyses.

Figure 5.Northward geometric projection from the Bosnian Pyramid of the Dragon toward the Fojnica-Bosna River confluence. This figure illustrates a precise northward geometric projection extending from the summit of the Bosnian Pyramid of the Dragon toward the confluence of the Fojnica and Bosna rivers. The alignment is derived from LiDAR-verified summit coordinates and hydrological mapping, demonstrating a direct spatial correspondence between a pyramidal apex and a major hydrological node at the valley scale. Within the broader analytical framework of this study, the river confluence functions as a key fixed point repeatedly intersected by Fibonacci spiral trajectories anchored at the Bosnian Pyramid of the Sun. The observed north-south alignment shown here provides additional geometric context for understanding how hydrological features integrate into the overall spiral-based spatial architecture of the Bosnian Valley of the Pyramids. Rather than being interpreted in isolation as a single linear alignment, this projection is evaluated as part of a multi-layered geometric system in which summits, river junctions, and subterranean access points act as recurrent nodal elements within expanding Fibonacci spiral configurations [5].

Figure 6.Linear alignment of major monuments in the Bosnian Valley of the Pyramids. Left: Topographic map illustrating a precise straight-line alignment connecting the summits of the Bosnian Pyramid of the Moon, the Temple of Mother Earth, and the Bosnian Pyramid of the Dragon. The alignment is derived from geodetically defined summit coordinates and confirms that all three features lie on a single linear axis extending across the valley. Right: Field photograph captured from the Bosnian Pyramid of the Sun visually corroborating the same alignment under real-world viewing conditions. From this vantage point, the Temple of Mother Earth occupies an intermediate nodal position between the Pyramid of the Moon and the Pyramid of the Dragon, reinforcing its role as a spatial mediator within the landscape. The alignment coincides with the Fojnica River’s course as it enters the valley, highlighting a close spatial relationship between monumental placement and hydrological pathways. This figure documents a robust example of linear spatial architecture in the Bosnian Valley of the Pyramids and provides a complementary geometric framework to the Fibonacci spiral analyses developed in this study [6].

Figure 7.Five-point linear alignment integrating pyramidal, tumular, and subterranean features. A linear alignment connecting five major features within the Bosnian Valley of the Pyramids: Temple of Mother Earth, Bosnian Pyramid of Love, Bosnian Pyramid of the Sun, an unnamed geometric elevation (Structure No. 4), and Entrance to the Ravne Tunnel Complex. The straight-line trajectory is drawn across satellite imagery and follows the general course of the Fojnica River through the valley. The close spatial correspondence between the alignment and the river channel suggests that hydrological pathways may have been intentionally integrated into the valley’s geometric design rather than treated as independent natural elements. The inclusion of both surface monuments and a subterranean entrance point within a single linear configuration reinforces the interpretation of a vertically and horizontally integrated spatial system. Rather than representing isolated coincidences, the alignment appears to form part of a broader architectural logic in which pyramidal structures, sacred nodes, and underground networks are organized according to shared geometric principles. This figure contributes to the growing body of evidence that the Bosnian Valley of the Pyramids exhibits intentional linear and spiral-based spatial architecture at the landscape scale [6].

Figure 8.Linear geometric alignments linking pyramidal and tumulus summits in the Bosnian Valley of the Pyramids. Topographic map of the Visoko Valley illustrating a system of straight-line alignments connecting multiple pyramidal structures and tumulus summits, based on independent spatial analysis by Richard Hoyle. Summit locations are derived from geodetic surveys and LiDAR-validated elevation maxima and are represented by red markers. Several clear multi-point alignments are visible, each involving at least three topographically and morphologically distinct features. Notable examples include: 1) the Bosnian Pyramid of the Sun - Bosnian Pyramid of Love - Bosnian Pyramid of the Moon alignment; 2) the Bosnian Pyramid of the Sun - Temple of Mother Earth - Bosnian Pyramid of the Dragon alignment; and 3) alignments linking pyramidal summits with nearby tumuli, including Cetnica, Bedem, Čemerisce, and Lanište. These linear configurations form a coherent, valley-scale geometric framework rather than isolated pairwise coincidences. Importantly, the Bosnian Pyramid of the Sun repeatedly functions as a nodal point from which multiple linear axes radiate toward both pyramidal structures and tumulus tops. This figure documents the existence of structured linear spatial architecture in the Bosnian Valley of the Pyramids. In the present study, these linear relationships are treated as a foundational geometric layer that precedes and constrains the development of more complex Fibonacci-spiral architectures examined in subsequent figures [7].

Figure 9.Straight-line alignments among pyramidal structures, tumuli, and landscape features in the Bosnian Valley of the Pyramids. Composite cartographic synthesis illustrating multiple straight-line alignments connecting pyramidal structures, tumuli, tunnel entrances, and geomorphological features across the Bosnian Valley of the Pyramids, as identified through the independent multi-method spatial analysis of Massimo Guzzinati. The figure integrates topographic mapping with symbolic markers representing summit-level vertices and landscape nodes derived from elevation maxima, geomorphological prominence, and field verification. Several alignments are shown linking three or more summit points along a single straight trajectory, often combining major pyramidal structures with secondary tumuli. Notable examples include linear connections involving the Bosnian Pyramid of the Sun, Bosnian Pyramid of the Moon, Bosnian Pyramid of the Dragon, the Temple of Mother Earth, and tumuli such as Krtnica, Cetnica, Bedem, Ginje, Laniste, Vratnica, and Kula-Banjer. In multiple cases, these alignments also intersect hydrological features (the Bosna and Fojnica rivers) and entrances to the Ravne tunnel system, indicating the integration of surface monuments, funerary mounds, waterways, and subterranean architecture within a coherent spatial framework. Distinct symbols differentiate between physical vertices, energetic vertices, coincident physical-energetic vertices, and tunnel entrances, reflecting Guzzinati’s layered analytical approach that combines topographic, geometric, and geobiological criteria. Importantly, these straight-line relationships were identified independently of spiral-based geometry and without presupposing a Fibonacci structure, providing a complementary, methodologically separate dataset. In the context of When Landscape Becomes Geometry II, this figure represents the final presentation of linear spatial architecture in the study. The documented alignments establish a structured geometric substrate upon which the subsequent analysis of expanded Fibonacci spiral architecture is developed, demonstrating that both linear and curvilinear geometries coexist within the same landscape-scale organizational system. Source: Guzzinati, M. Original analysis and cartographic synthesis. Reproduced with permission. © Massimo Guzzinati.

In addition to linear alignments, Part I identified a Fibonacci-based logarithmic spiral anchored at the Bosnian Pyramid of the Sun that satisfied predefined ±20 m tolerance criteria and persisted under 100,000-run Monte Carlo null models [4]. That result established the presence of a statistically constrained spiral configuration under explicitly defined geometric and probabilistic assumptions.

Spiral geometry has long been recognized as a mathematically stable form of proportional expansion. Logarithmic spirals governed by constant growth ratios (φ ≈ 1.618) appear in both natural and constructed systems [8]. In archaeological landscape studies, geometric modeling has been applied cautiously, given the risk of overfitting and post hoc pattern recognition [9][10]. For that reason, Part II applies the identical tolerance thresholds, scale bounds, and probabilistic testing framework established in Part I (Figures 9-21).

Figure 10.Foundational Golden Ratio geometry and initial Fibonacci spiral construction applied to the Bosnian Valley of the Pyramids. Left: LiDAR-derived digital elevation model of the central Visoko Valley overlaid with the first-order golden ratio construction developed by Richard Hoyle. The diagram illustrates the geometric generation of proportional distances using two primary diameters: D¹ = a + b and D² = a, where a and b follow the Fibonacci ratio (φ ≈ 1.618). The construction establishes a fixed geometric center and angular framework (including 0˚ and 60˚ reference directions) from which spiral propagation is initiated. The circular overlays correspond to successive proportional expansions anchored to geodetically defined summit locations, demonstrating how Fibonacci-based scaling can be embedded directly within the valley’s topography. Right (top): Conceptual schematic illustrating the translation of golden ratio diameters onto pyramidal and tumular summit forms, showing how proportional circles intersect major structures while preserving fixed geometric relationships. Right (bottom): Classical Fibonacci rectangle and logarithmic spiral construction, included for reference, demonstrating the mathematical basis underlying the landscape-scale application shown on the left. Together, the figure establishes the geometric starting condition for subsequent spiral analyses presented in this study. Rather than fitting spirals post hoc, the golden ratio framework is first defined geometrically and then projected onto independently surveyed terrain data. This approach provides a reproducible and mathematically constrained foundation for evaluating Fibonacci spiral architecture across the Bosnian Valley of the Pyramids [7].

Figure 11.Multi-node Fibonacci spiral connecting major pyramidal and tumular summits in the Bosnian Valley of the Pyramids. This Fibonacci spiral intersects the summit of the Bosnian Pyramid of Love, passes near the summit of the Bosnian Pyramid of the Sun, continues through the summit of the Temple of Mother Earth, intersects the summit of the Bosnian Pyramid of the Dragon, and terminates at the summit of the tumulus in Vratnica. All nodes correspond to independently defined pyramidal or tumular elevation maxima. The configuration demonstrates the extension of spiral geometry across multiple monuments types and reinforces the role of Fibonacci scaling as a unifying principle within the valley’s spatial architecture [4].

Figure 12.Monte Carlo simulation testing the probability of five summit points fitting a single Fibonacci spiral. Histogram showing the distribution of minimum distances between five randomly distributed elevation points and a golden ratio spiral originating from one of the points. Each simulation tested whether all five points could fall within 0.5 km of the same spiral. Out of 10,000 simulations, no configuration satisfied all conditions (p < 0.0001), indicating that the observed spiral alignment is unlikely to arise by chance [4].

Figure 13.Newly identified Fibonacci spiral linking the Bosnian Pyramid of the Dragon, the Bosnian Pyramid of Love, and the Bosnian Pyramid of the Moon. Topographic map of the Bosnian Valley of the Pyramids showing a newly identified Fibonacci (Golden Section) spiral connecting three major pyramidal structures: the Bosnian Pyramid of the Dragon, the Bosnian Pyramid of Love, and the Bosnian Pyramid of the Moon. In this configuration, the spiral originates at the summit of the Bosnian Pyramid of the Dragon, curves through the summit of the Bosnian Pyramid of Love, and continues toward the summit of the Bosnian Pyramid of the Moon, forming a coherent sequence of elevation maxima consistent with Fibonacci scaling. The spiral is constructed using the same geometric rules applied throughout this study, including fixed golden ratio growth, quarter-arc construction, and geodetically defined summit reference points. Importantly, this configuration does not include the Bosnian Pyramid of the Sun or the Temple of Mother Earth, demonstrating that Fibonacci spiral organization within the Bosnian Valley of the Pyramids is not restricted to a single central monument but extends to secondary pyramidal relationships. All three anchor points correspond to independently defined summit locations derived from high-resolution topographic and LiDAR-validated datasets, ensuring that the spiral geometry is evaluated against fixed, non-arbitrary landscape features. This figure represents original analysis reported here for the first time and expands the documented network of spiral-based geometric relationships within the Bosnian Valley of the Pyramids. Source: Original analysis and cartographic synthesis by the author.

Figure 14.Fibonacci spiral intersecting the Bosnian Pyramid of Love, the Temple of Mother Earth, the Bosnian Pyramid of the Moon, and the Ravne Tunnel Complex. Topographic map of the Bosnian Valley of the Pyramids showing a Fibonacci (Golden Section) spiral constructed according to the standard square-and-arc method and overlaid on a calibrated topographic base. The spiral intersects, in sequence, the summit of the Bosnian Pyramid of Love, the summit of the Temple of Mother Earth, the summit of the Bosnian Pyramid of the Moon, and the entrance zone of the Ravne Tunnel Complex. All intersection points correspond to independently defined topographic or archaeological features derived from geodetic and cartographic datasets. The spiral geometry integrates surface monuments with a subterranean access point, reinforcing the interpretation of a coherent landscape-scale geometric framework extending beyond individual pyramidal structures. This spiral configuration expands the set of Fibonacci-based spatial relationships documented in the Bosnian Valley of the Pyramids and is incorporated into the broader geometric analysis presented in this study. Note: This spiral configuration is reported here for the first time.

Figure 15.Monte Carlo distribution of minimum distances to a Fibonacci spiral for randomized summit configurations. Monte Carlo simulation assesses the likelihood of reproducing the observed Fibonacci spiral geometry by chance. A total of 10,000 randomized configurations of summit-like points were generated within the spatial bounds of the Bosnian Valley of the Pyramids. For each simulation, the minimum distance of all points to a best-fit golden-ratio spiral was computed. The histogram shows the resulting distribution of minimum distances. The dashed vertical line at 0.5 km represents the maximum deviation observed in the empirical configurations (Figure 9, Figure 10, Figure 13, and Figure 14). No simulated case achieved comparable coherence, indicating a probability of occurrence of p < 0.0001. 1) The distribution represents 10,000 Monte Carlo realizations of randomly distributed summit-like points within the study area; 2) The x-axis shows the minimum distance (km) from a fitted golden-ratio/Fibonacci spiral; 3) The dashed vertical line at 0.5 km marks the empirical tolerance observed in the real Bosnian Valley configurations (Figure 9, Figure 10, Figure 13, and Figure 14); 4) No simulated configurations approach this threshold, visually reinforcing the improbability of the observed spiral coherence arising by chance.

Figure 16.Golden spiral trajectories anchored at the Bosnian Pyramid of the Moon. This schematic map illustrates a system of golden (Fibonacci) spirals originating at the summit of the Bosnian Pyramid of the Moon and intersecting multiple key features within the Bosnian Valley of the Pyramids. Of particular significance is the spiral sequence linking the Pyramid of the Moon, the tumulus at Smreke, the Bosnian Pyramid of Love, and the Bosnian Pyramid of the Dragon, forming a coherent geometric progression consistent with golden-ratio expansion. Additional spiral arcs intersect further pyramidal and tumular summits, underground tunnel entrances (including the Ravne and KTK systems), and hydrological elements such as the Fojnica and Bosna rivers. Colored dots distinguish physical summits, energetic vertices, and tunnel access points, following the analytical methodology developed by Massimo Guzzinati.

Figure 17.Golden spiral system anchored at the Bosnian Pyramid of the Dragon, integrating pyramidal and tumulus summits. This figure illustrates a system of golden-ratio (Fibonacci) spirals originating from the summit of the Bosnian Pyramid of the Dragon and extending outward across the Bosnian Valley of the Pyramids. The spiral trajectories intersect a sequence of major pyramidal and tumulus structures, most notably the Bosnian Pyramid of Love, the Bosnian Pyramid of the Moon, and several surrounding tumuli, including Smreke, Cemerikov, Stuparici, Ginje, and Laniste. The spatial correspondence shows that multiple distinct spiral arcs—constructed according to Fibonacci proportional scaling—pass through or closely approach the summits of these features, indicating a non-random clustering of topographical highs along logarithmic growth paths. The Bosnian Pyramid of the Dragon functions as a primary geometric anchor, while secondary intersections occur at pyramidal and tumulus peaks situated at increasing radial distances consistent with golden-ratio expansion. Source: Guzzinati, M. (analysis and cartography).

Figure 18.Golden (Fibonacci) spiral systems originating at the Bosnian Pyramid of Love. Multiple clockwise and counterclockwise Fibonacci spirals are constructed with a fixed origin at the summit of the Bosnian Pyramid of Love and intersect a sequence of pyramidal and tumular summits across the Bosnian Valley of the Pyramids. Each spiral follows a consistent Fibonacci scaling ratio and intersects independently defined topographic vertices: 1) Red spiral (counterclockwise): Pyramid of Love → Temple of Mother Earth (western, central, and eastern vertices); 2) Orange spiral (counterclockwise): Pyramid of Love → Krtnica Tumulus → Bosnian Pyramid of the Sun; 3) Yellow spiral (counterclockwise): Pyramid of Love → Kula-Banjer Tumulus → Taukčići Tumulus; 4) Indigo spiral (clockwise): Pyramid of Love → Bosnian Pyramid of the Sun → Temple of Mother Earth (central vertex) → Bosnian Pyramid of the Dragon; 5) Violet spiral (clockwise): Pyramid of Love → Bosnian Pyramid of the Sun → Temple of Mother Earth (eastern vertex) → Bedem Tumulus. Source: Massimo Guzzinati, independent geometric analysis; adapted for this study.

Figure 19.Golden spirals originating from the Vratnica Tumulus within the Bosnian Valley of the Pyramids. Multiple Fibonacci (Golden Section) spirals are constructed with their origin anchored at the summit of the Vratnica Tumulus, demonstrating repeated geometric connectivity between tumular, pyramidal, and subterranean features across the valley. 1) Red spiral (clockwise): Vratnica Tumulus → Smreke Tumulus → Bosnian Pyramid of the Moon; 2) Orange spiral (clockwise): Vratnica Tumulus → Temple of Mother Earth (eastern vertex) → Shrínje Tumulus; 3) Yellow spiral (clockwise): Vratnica Tumulus → Kula-Banjer Tumulus → Ramadanovci Tumulus → Grajani Tumulus; 4) Indigo spiral (counterclockwise): Vratnica Tumulus → Ravne B Tunnel entrance → Cetnica Tumulus; 5) Violet spiral (counterclockwise): Vratnica Tumulus → Bosnian Pyramid of Love → Temple of Mother Earth (western vertex). Source: Guzzinati, M., adapted and annotated by the authors.

Figure 20.Golden spirals originating from the Laniste Tumulus. Multiple Fibonacci (golden ratio) spiral trajectories are constructed with their origin fixed at the summit of the Laniste Tumulus, revealing systematic geometric relationships with pyramidal structures, tumuli, and nodal landscape features across the Bosnian Valley of the Pyramids. The following spiral configurations are shown: 1) Red spiral (clockwise): Laniste Tumulus → Cemerikov Tumulus → Banjer Tumulus, 2) Orange spiral (clockwise): Laniste Tumulus → Temple of Mother Earth (western vertex) → Smreke Tumulus, 3) Yellow spiral (clockwise): Laniste Tumulus → Temple of Mother Earth (western vertex) → Bosnian Pyramid of the Moon, 4) Indigo spiral (clockwise): Laniste Tumulus → Bedem Tumulus → Bosnian Pyramid of the Sun, 5) Violet spiral (counterclockwise): Laniste Tumulus → Cemerikov Tumulus → Ramadanovci Tumulus, 6) Light-brown spiral (counterclockwise): Laniste Tumulus → Temple of Mother Earth (eastern vertex) → Bedem Tumulus, 7) Dark-brown spiral (counterclockwise): Laniste Tumulus → Smreke Tumulus → Bosnian Pyramid of Love → Grajani Tumulus. Summit points correspond to geodetically and LiDAR-validated elevation maxima. The convergence of multiple clockwise and counterclockwise Fibonacci spirals anchored at a single tumulus reinforces the interpretation of non-random spatial organization, integrating pyramidal monuments, tumuli, and sacred landscape nodes. Source:Massimo Guzzinati;adapted for this study. Note: Figures 16-20 present independent spiral systems constructed by Guzzinati using the same golden-ratio framework but different origin nodes.

Figure 21.Field view of the central ridge alignment in the Bosnian Valley of the Pyramids, showing the spatial relationship between the Bosnian Pyramid of the Sun, Temple of Mother Earth, Bosnian Pyramid of Love, and Laniste Tumulus, as observed from the valley floor. The photograph illustrates the natural ridge geometry and relative elevation ordering of these features, which correspond to multiple geometric and spiral relationships identified in planimetric analyses (Figures 16-20). This visual perspective reinforces the coherence between the valley’s topography and the proposed spiral-geometry framework. Source:Photograph by Richard Hoyle;adapted and annotated for this study.

The present study asks whether spiral coherence remains localized to the Sun-anchored configuration or whether comparable Fibonacci-based intersections emerge when the spiral model is anchored at alternative summit-level and nodal points across the valley. These alternative anchors include the Pyramids of the Moon, Love, and Dragon; selected tumuli such as Vratnica and Laniste; hydrological junctions; and tunnel entrances verified through LiDAR and field documentation [5][7].

The broader geological context of the Visoko formations remains debated. Several studies interpret pyramidal morphologies as natural sedimentary structures shaped by uplift and erosion. The present analysis does not attempt to resolve the geomorphological origin. Instead, it evaluates spatial organization as a measurable geometric property of the current landscape configuration.

Part II, therefore, shifts the focus from a single geometric origin to a distributed anchoring framework. Using fixed Fibonacci growth rules, bounded parameter spaces, and controlled Monte Carlo testing, the study evaluates whether multi-anchor spiral coherence exceeds expectations under conservative null conditions. The objective is methodological: to assess whether curved proportional geometry constitutes a recurring spatial signal within the previously documented valley-scale system.

This study extends the geometric framework established in Part I by evaluating multi-anchor Fibonacci spiral modeling within the Bosnian Valley of the Pyramids [3]. Using a fixed geodetic coordinate dataset, constant golden-ratio growth parameters, bounded scale and orientation grids, and a 10,000-run Monte Carlo framework, the analysis demonstrates that multi-node spiral intersections can be formally evaluated under defined spatial constraints.

The primary inferential result concerns the Sun-anchored configuration, which produced a four-node spiral intersection within a uniform ±20 m tolerance threshold. Under symmetric spatial redistribution using identical modeling parameters, this configuration lies in the upper tail of the simulated distribution.

Other anchor configurations are presented descriptively to illustrate geometric behavior under identical constraints but were not subjected to independent hypothesis testing. This distinction limits the hypothesis family and maintains statistical clarity.

The probability estimate is conditional on the defined null model, which assumes uniform spatial redistribution within the valley envelope. Terrain-aware simulations and geomorphological constraint models may further refine interpretation in future work.

When considered alongside the linear and triangular alignments documented in Part I and prior rotation-invariant spatial coherence testing, the present results suggest that curved proportional geometry may operate within an already structured coordinate network. Whether this reflects intentional planning, emergent landscape dynamics, or coincidental structuring remains an open question.

The principal contribution of this work is methodological. It demonstrates that fixed-growth spiral models, when applied within bounded parameter spaces and evaluated through symmetric Monte Carlo testing, provide a reproducible framework for assessing curved geometric relationships in complex landscapes.

Future research incorporating terrain-constrained null models, expanded comparative datasets, and independent chronological constraints will help clarify the broader implications of the geometric correspondences documented here.

Several constraints should be acknowledged.

First, the analysis is spatial rather than chronological. The study documents geometric relationships in the present landscape but does not establish construction sequences or temporal overlap among features. Geometry alone cannot determine whether all elements were conceived simultaneously or integrated over extended periods.

Second, although LiDAR and geodetic data provide high positional accuracy, all geometric analyses require tolerance thresholds. Conservative distance limits were applied throughout to reduce false positives. Tighter thresholds would further strengthen the results, but were not required to demonstrate coherence.

Third, spiral geometry was evaluated using a predefined Fibonacci-based construction. Alternative spiral models were not tested here. This choice reflects the repeated recurrence of Fibonacci scaling across independent analyses rather than an assumption of symbolic intent.

Finally, this study does not attempt to define cultural meaning, belief systems, or symbolic interpretation. The conclusions are limited to spatial organization. Intentionality is inferred at the level of geometric structure, not ideology.

These limitations do not weaken the findings; they clarify their scope and point toward future work integrating chronology, excavation data, and comparative landscape studies.

The authors acknowledge the Archaeological Park: Bosnian Pyramid of the Sun Foundation for long-term access to the study area, logistical support, and permission to use geodetic, LiDAR, and archival datasets. Airborne Technologies GmbH (Austria) is acknowledged for the acquisition of high-resolution airborne LiDAR data used in terrain modeling and spatial analysis.

The authors thank independent researchers and collaborators who contributed to field observations, data verification, and technical discussion. Special acknowledgment is given to professionals in geodesy and surveying whose earlier measurements established essential reference points for this work.

Any remaining errors or interpretations are the responsibility of the authors alone.

This research received no external funding. All work was supported by institutional resources of the Archaeological Park, the Bosnian Pyramid of the Sun Foundation, and independent research efforts by the authors.

Data used in this study derive from published sources, licensed LiDAR datasets, archival geodetic surveys, and original geometric analyses. Spiral constructions and simulation outputs are available from the corresponding author upon reasonable request.

Sam Osmanagich: Conceptualization; landscape-scale geometric framework; identification and documentation of Fibonacci spiral systems; integration of hydrological and tumular data; Monte Carlo simulation design and interpretation; manuscript writing (original draft); supervision.Massimo Guzzinati: Independent geometric modeling; spiral construction from multiple origins (Moon, Love, Dragon, Vratnica, Laniste); cartographic synthesis; validation of multi-node spiral families; contribution of original figures and analytical methodology.Richard Hoyle: Field geology; LiDAR validation; terrain interpretation; hydrological and geomorphological assessment; field photography; verification of summit morphology and spatial coherence.