Survey Domain
& Ground Model

Selected Mathematics, Not Yet Adopted Canon

This section now integrates the Domain-relevant results of the candidate FSF mathematical design. In particular, FMD-01 supplies exact reduced rational Pang coordinates; FMD-03 supplies the permanent origin rule; and FMD-04 supplies the candidate Domain geometry and closed-boundary convention while leaving numerical capacity open under FMD-04B.

FMD-02, FMD-05 through FMD-08, and FMD-09 remain compatible with this section but primarily govern the frame, primitive geometry, predicates, normalization, serialization, and precision semantics specified elsewhere. Their relevant consequences are reflected here only where needed to define Domain validity and preserve the boundary between foundational reference capacity and higher-layer meaning.

Finite Reference Domain

The Foundational Survey Fabric shall define one finite canonical Survey Domain. The Domain establishes the exact scope within which canonical BitPangea spatial reference is valid.

Under the current candidate mathematical design, the Survey Domain is one closed, axis-aligned square centered on the permanent Survey origin and expressed through exact CRPC Pang coordinates.

The Survey Domain is a reference architecture, not a cartographic declaration of World membership. A location may be validly referenceable within the Survey Domain without thereby becoming BitPangea World-space.

Two-Dimensional Planar Ground

The canonical Survey Domain shall be modeled as a two-dimensional planar spatial ground. Vertical, volumetric, immersive, nested, terrain, elevation, and other higher-dimensional or surface expressions belong above the Foundational Survey Fabric.

The Survey Fabric therefore anchors permanent ground position without becoming the visible, geographic, architectural, rendered, or experiential surface of BitPangea.

One Connected Closed Reference Space

The canonical Survey Domain shall be one connected and internally coherent reference domain rather than a collection of disconnected sectors or a domain containing arbitrary internal holes where canonical reference is unavailable.

Under the current candidate mathematics, the Domain is a single closed square and is therefore connected, path-connected, bounded, and hole-free as a foundational reference extent.

Higher spatial layers may designate portions of that reference capacity differently without requiring corresponding gaps in the foundational reference system.

Closed Square · Parameterized Exact Pang Bounds

Under the candidate mathematical design, the canonical Survey Domain is expressed parametrically as:

D_H = [-H,+H] × [-H,+H], with exact H > 0.

The Domain therefore has exact width 2H Pang, exact height 2H Pang, and exact area 4H² square Pang. Its four boundary edges and four corner points are included in valid Survey space.

The square geometry and closed boundary are candidate-resolved. The numerical value of H remains OPEN under FMD-04B and shall not be inferred from the superseded ±1,000,000 Pang working candidate.

These limits determine where valid canonical Survey reference ends once H is selected. They shall not themselves be treated as BitPangea’s World boundary, Extent expression, Verge, coastline, Exterior, or other cartographic feature.

Valid Survey Position or Invalid Reference

Let a candidate canonical Point be p = (x,y), with both coordinates expressed as valid normalized CRPC Pang values.

The Point belongs to the Survey Domain exactly when: -H ≤ x ≤ +H and -H ≤ y ≤ +H, for the governing exact positive half-span H.

The comparison is exact. No tolerance, epsilon, snapping, rounding, or nearest-valid-position rule is permitted. A Point outside either bound is invalid as a canonical Survey Point rather than merely classified as non-World.

Until the governing Specification selects the numerical value of H, concrete numerical edge cases remain parameterized rather than canonically fixed.

Reference Capacity and World Membership

World membership shall be established by higher spatial Architecture domains using valid canonical Survey Fabric references. The Foundational Survey Fabric determines where canonical reference is possible; higher spatial domains determine what portions of that reference capacity constitute The World.

The Survey Domain is therefore not required to geometrically match BitPangea’s irregular supercontinental World Form. The selected production Spatial Ground design may occupy a strict subset of the Survey Domain, but that production choice shall not redefine the foundational meaning of the Domain itself.

No Required Alignment to Survey Subdivision

Higher-layer spatial entities shall not be required to align their authoritative geometry with Survey Fabric subdivisions, grid lines, tiles, cells, or indexing structures merely because such derived structures may exist.

The current candidate precision model uses exact coordinate extension rather than a mandatory hierarchical grid or parent/child Point system. The Survey Fabric provides reference. Higher layers remain responsible for shape.

Mathematical Origin Without Semantic Privilege

The permanent canonical origin is (0,0), the midpoint of the symmetric parameterized Domain bounds [-H,+H] on both axes. It is mathematically privileged as the zero-reference of the Survey frame and nothing more.

The Survey Domain shall not establish a privileged civic, cultural, geographic, political, economic, or institutional center. Internal sectors, quadrants, regions, zones, grids, or partitions used for indexing, computation, precision, or serialization shall likewise remain semantically neutral at the foundational level.

Primary Derived Findings

This specification section is derived especially from Requirements Findings #18–#19, #23, #28–#29, #48–#49, #51–#52, and #76–#77.

Specification 01 Is Mathematically Ready for Core Prototype Use

No contradiction was found between this integrated Domain model and FMD-01 through FMD-09 after the FMD-04A / FMD-04B split. The Domain-relevant candidate mathematics are sufficiently exact to support parameterized validation of canonical Points and capacity-independent prototype work. Concrete numerical Domain-edge validation and final Spatial Ground placement remain dependent on closure of the numerical-capacity question or another formally governed capacity mechanism.

This readiness does not constitute formal adoption. Canonical adoption remains contingent on Specification-wide integration, Conformance, Reference Vectors, independent implementation, adversarial testing, traceability, and the applicable adoption act.