Survey Domain
Limit Vectors

The Geometry Is Defined; Numerical Capacity Is Still Open

The candidate Survey Domain is a finite, connected, closed, axis-aligned square centered at the canonical origin:

D_H = {(x,y) : -H ≤ x ≤ H and -H ≤ y ≤ H}

with H > 0 represented exactly in CRPC. The origin is (0,0). The boundary is included because the Domain is closed.

The shape, closure, centering, axis alignment, and boundary semantics are therefore testable now under FMD-04A. The numerical value of H remains open under FMD-04B.

The Zero-Reference Must Resolve Identically

The vector set shall include the canonical origin (0,0) and exact neighboring Points sufficient to prove that all conforming implementations interpret the zero-reference identically.

The origin is a mathematical reference point only. It does not imply Parcel identity, World membership, landmark status, civic importance, ownership, or cultural meaning.

The Four Canonical Domain Limits Are Exact

The corpus shall test the four boundary equations:

x = -H, x = +H, y = -H, and y = +H.

These vectors shall prove that all conforming implementations classify Points against the same exact parameterized Domain, even before a numerical value for H is selected.

Strictly Interior Points Must Be Valid

A Point satisfying -H < x < H and -H < y < H is strictly interior to the Survey Domain and shall be classified as valid Survey reference.

Capacity-independent fixtures may use symbolic or parameterized coordinates that prove the rule without assuming a final numerical value for H.

Boundary Inclusion Is Deterministic

Because the candidate Survey Domain is closed, Points satisfying the Domain inequalities with equality on one or more sides are valid Survey references.

Examples include Points with x = ±H and -H ≤ y ≤ H, or y = ±H and -H ≤ x ≤ H.

No implementation may treat an exact boundary Point as outside solely because it lies on the Domain edge.

Any Coordinate Beyond H Must Fail

A Point is outside the Survey Domain if x < -H, x > H, y < -H, or y > H.

Such a Point shall fail as a valid canonical Survey reference. It shall not be clipped, snapped, wrapped, translated, rounded, or otherwise repaired into the Domain.

Simultaneous Boundary Conditions Produce One Result

The four corners are:

(-H,-H), (-H,+H), (+H,-H), and (+H,+H).

Each corner lies on two included boundaries simultaneously and is therefore a valid Survey Point under the current closed-Domain model.

Greater Representational Capacity Must Not Move the Boundary

Under ECEM, expansion of exact coordinate representability does not expand, contract, or reinterpret the Survey Domain.

A future compatible version may represent additional exact Points near the boundary, but the governing inequalities remain the same and previously valid or invalid Points retain their meaning.

Valid Survey Reference and Invalid Survey Reference Must Be Distinguishable

Vectors shall prove the exact three-way geometric distinction among:

INTERIOR, BOUNDARY, and OUTSIDE.

For Survey validity, INTERIOR and BOUNDARY are valid; OUTSIDE is invalid. These labels describe Survey Domain relation only and do not by themselves determine World membership.

Survey Validity Is Not World Membership

Reference Vectors shall preserve the architectural distinction between the FSF Survey Domain and Spatial Ground membership.

A Point may be a valid Survey reference inside D_H while still being classified by Spatial Ground as NON_WORLD. FSF proves reference capacity; Spatial Ground determines canonical participation in The World.

Every Implementation Must Classify the Same Point the Same Way

Independent conforming implementations shall classify the same exact Point identically as interior, boundary, or outside under the same governing H and Specification profile.

A disagreement indicates implementation defect, Specification ambiguity, version incompatibility, or fixture defect requiring resolution.

Concrete Edge Fixtures Must Wait for Capacity Selection

The earlier ±1,000,000 Pang half-span is a superseded working candidate and shall not be used as a canonical fixture value.

The unresolved value of H prevents final publication of concrete numerical vectors such as “the eastern boundary is x = N Pang” or “this specific coordinate is one exact unit outside the Domain.”

Such examples become canonical only after FMD-04B resolves the numerical Domain capacity through a justified mathematical decision and that result is incorporated into the governing Specification. Until then, symbolic and parameterized fixtures are the correct Reference Vector form.

Outside the Survey Domain Means No Valid FSF Reference

A failed Survey reference outside D_H does not imply an exterior realm, alternate geography, World edge, Verge, ownership boundary, or any other higher-layer ontology.

The Reference Vector proves only that the input is outside the canonical FSF reference domain.

Boundary Semantics Are Testable Before Numerical Capacity Is Final

The original page correctly deferred Survey Domain vectors while both geometry and boundary conventions were unresolved. That is no longer the current standing.

The candidate Specification now defines the Domain as a closed axis-aligned square centered at the origin, so exact symbolic and parameterized boundary behavior can be tested. What remains open in this section's Domain mathematics is the numerical capacity parameter H under FMD-04B. Reference Vectors therefore may prove the rules now without inventing the missing number.

Referenced Requirements

Survey Domain Limit Vectors will derive especially from Requirements Findings #9–#10, #13, #19–#20, #23, #29, #32, #39–#40, #48–#49, #57, #74–#76, and #78–#83.