Addressing
Vectors

The Candidate Address Semantics Are Now Concrete

A canonical Survey Point is represented by an ordered pair (x, y) in the canonical frame, where each coordinate is an exact reduced rational Pang value.

q = n/d Pang, with n ∈ Z, d ∈ N+, gcd(|n|, d) = 1, and zero normalized as 0/1.

The canonical frame is +x = Panoris (East), -x = Panvel (West), +y = Pankor (North), and -y = Panvath (South).

Under ECEM, every valid canonical Point denotes one exact Survey position. It is not a cell, uncertainty region, parent reference, rounded location, or set of finer descendants.

Exact References in the Canonical Frame

The vector set shall include exact canonical Points sufficient to prove that independent implementations interpret identical CRPC coordinate pairs as the same exact Survey position.

Capacity-independent fixtures should favor positions whose in-Domain validity does not depend upon the unresolved numerical half-span, including the canonical origin (0,0) and other coordinates that may be explicitly framed as conditional upon H where necessary.

Equivalent Rational Inputs Must Reduce Identically

The corpus shall include mathematically equivalent rational coordinate components expressed in nonreduced form where the input pathway permits them, together with the exact normalized CRPC result.

Examples shall prove sign normalization, denominator positivity, greatest-common-divisor reduction, and canonical zero representation without rounding or decimal approximation.

Greater Expressive Precision Must Not Move Place

Addressing Vectors shall demonstrate the ECEM rule that exact Points do not possess coarse and fine semantic states. A previously valid Point continues to denote the same exact place when future compatible Specification versions support additional exact coordinate values.

The corpus shall therefore test meaning preservation, not hierarchical refinement of an existing Point into descendants.

Equal Coordinates Mean One Exact Place

Point equality shall be demonstrated through exact normalized CRPC component equality. Two supported Point representations denote the same canonical Point exactly when their normalized x-components are equal and their normalized y-components are equal.

No epsilon, tolerance, floating comparison, display precision, or rendering proximity may participate in canonical Point equality.

Deterministic Ordering Supports Canonical Geometry

The corpus shall include Point ordering cases sufficient to prove deterministic lexicographic ordering under exact CRPC comparison.

These vectors support later canonical Segment endpoint ordering, SCPE start-vertex selection, and other normalization rules that depend upon one implementation-independent Point order.

Canonical Points Stand Without Higher-Layer Objects

Reference Vectors shall demonstrate that canonical Survey Points resolve independently of Parcels, Regions, landmarks, ownership, membership, or other higher-layer semantics.

The expected result shall be derivable solely from the canonical Point representation and governing Survey mathematics.

Coordinate Sign and Native Direction Must Agree

The corpus shall include exact cases demonstrating the canonical directional interpretation of coordinate sign.

+x Panoris · -x Panvel · +y Pankor · -y Panvath.

These vectors shall prove consistent interpretation of quadrants, axes, and the origin without assigning higher-layer geographic meaning.

Canonical Meaning Must Survive Machine Interchange

Addressing Vectors shall include canonical FSF-CJSON-1.0 Point fixtures demonstrating structured CRPC components, canonical integer-string form, deterministic object-key order, UTF-8 canonical bytes, and exact parse/serialize round-trip behavior.

Where one canonical byte sequence is required, every conforming implementation shall produce the same bytes for the same normalized Point.

Equivalent Input May Normalize; Invalid Input May Not Be Repaired

Where the implementation interface permits valid noncanonical rational or object representation, vectors shall demonstrate deterministic normalization to canonical CRPC and canonical Point form.

Invalid input shall remain invalid. Reference Vectors shall not use normalization as a mechanism for guessing, snapping, coercing, or silently repairing malformed or semantically invalid coordinates.

Compatible Evolution Must Preserve Established Point Meaning

The corpus shall include compatibility cases proving that a Point valid under an earlier compatible Specification remains the same exact Survey position under a later compatible Specification.

Expansion of representational capacity may add newly expressible exact Points. It may not migrate, renumber, reinterpret, or reuse established Points.

Concrete Edge Cases Must Wait for the Numerical Domain Capacity

The candidate Survey Domain geometry is a closed axis-aligned square centered at the canonical origin and may be expressed parametrically as:

D_H = {(x,y) : -H ≤ x ≤ H and -H ≤ y ≤ H}, with exact positive CRPC parameter H.

Because the numerical value of H remains unresolved, Reference Vectors shall not yet publish concrete canonical fixtures whose pass/fail status depends upon one specific numerical Domain edge.

Symbolic or parameterized Domain-boundary cases may document the intended rule, but final numerical edge fixtures require the governing Specification to select H.

Positive Addressing Cases and Negative Input Cases Remain Distinct

This section shall primarily establish exact valid Point meaning, normalization, equality, ordering, frame interpretation, serialization, and compatible meaning preservation.

Malformed CRPC, malformed Point structures, prohibited JSON forms, ambiguous input, and concrete out-of-Domain cases belong primarily in the dedicated Invalid-Input Vectors corpus, with cross-reference here where needed.

Addressing Has Moved From Category Planning to Exact Candidate Fixtures

The original page correctly refused to invent an address grammar before the mathematics existed. That condition has now changed for the capacity-independent core: CRPC, canonical Point semantics, ECEM, normalization, the canonical frame, and FSF-CJSON-1.0 provide enough exact behavior for real Reference Vectors.

The unresolved numerical Survey Domain capacity remains a real boundary. Reference Vectors may prove the rules around exact reference and Domain membership, but they may not choose the missing numerical half-span on the Specification's behalf.

Referenced Requirements

Addressing Vectors will derive especially from Requirements Findings #7–#10, #17, #20–#22, #30, #41–#42, #54, #57, #59, #64, #70–#75, and #78–#83.