Precision
Vectors

CRPC and ECEM Define the Candidate Precision Core

Canonical coordinate precision is represented by exact reduced rational Pang values:

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

Under ECEM, a valid Point denotes one exact Survey position. Additional representational capacity may make more exact Points expressible, but it does not refine an existing Point into a different place.

Canonical Precision Is Exact Rational Value

Reference Vectors shall include integer Pang values and exact rational sub-Pang values to prove that canonical precision is determined by exact value rather than decimal digit count.

Equivalent rational inputs shall normalize to the same CRPC value where such noncanonical input forms are permitted.

Exact Values Below One Pang Are Native

The corpus shall include exact values such as 1/2 Pang, 1/3 Pang, 7/16 Pang, and other reduced rational quantities.

These are canonical exact values, not approximate decimal renderings and not named subordinate units.

Greater Expressive Capacity Must Not Move Existing Points

Reference Vectors shall prove that later compatible support for additional exact CRPC values does not renumber, relocate, invalidate, or reinterpret previously valid canonical Points.

ECEM extends what can be expressed. It does not create hierarchical semantic refinement states for an already exact Point.

Implementation Representation Must Not Redefine Canonical Truth

Reference Vectors shall distinguish the exact canonical value from any implementation storage format or rendered display form.

A storage or rendering layer may choose a different internal or visible representation only where it preserves or explicitly marks any loss relative to the canonical value.

Equivalent Exact Representations Must Preserve Value

Where valid noncanonical rational forms are accepted, vectors shall prove lossless conversion to canonical CRPC.

For example, a permitted input representing 2/4 Pang shall normalize exactly to 1/2 Pang without changing mathematical meaning.

Information Loss Must Be Explicit and Detectable

The corpus shall include rounding, truncation, decimal approximation, display reduction, and other transformations that discard canonical information.

Such outputs shall be classified as derived or lossy representations and shall never be treated as exactly equivalent to the original canonical value merely because they appear visually close.

Exact Canonical Values Must Not Be Quietly Reduced

Reference Vectors shall include exact rational values close to common decimal or implementation boundaries to prove that conforming implementations do not silently round, truncate, snap, or quantize canonical input.

Any deliberate approximation must be explicit and distinguishable from canonical truth.

Different Exact Forms Must Compare by Mathematics, Not Appearance

Reference Vectors shall include mathematically equivalent exact inputs expressed through different permitted syntactic forms.

Equality shall follow normalized exact value rather than string length, decimal digit count, storage width, or display formatting.

Normalization Must Preserve All Canonical Information

CRPC normalization shall reduce representation without reducing mathematical precision.

A transformation that loses exact spatial information is not normalization. It is a lossy conversion and must be identified as such.

Canonical Interchange Must Preserve Exact CRPC Meaning

Reference Vectors shall include FSF-CJSON-1.0 objects containing exact CRPC values and exact expected canonical serialization.

Parsing and reserializing a canonical object shall restore the same exact canonical values and, where required, the same canonical bytes.

Lossless Parse / Serialize Cycles Must Preserve Exact Meaning

The corpus shall test exact round trips through supported canonical object and serialization layers.

Where the pathway is defined as lossless, the resulting canonical value shall be mathematically identical to the source value after every round trip.

Compatible Evolution May Add Values, Not Change Old Ones

Reference Vectors shall prove that a later compatible Specification may admit newly representable exact values while preserving the meaning of every previously valid canonical Point and measurement.

Version compatibility therefore concerns preservation of canonical meaning, not preservation of implementation limits.

Not Every Exact Result Is Necessarily Rational

Some derived operations may produce exact values outside CRPC, such as Euclidean distances involving square roots or arbitrary rotations producing non-rational coordinates.

Reference Vectors shall not force such results into rational or decimal form merely to fit the current coordinate scalar. Those cases remain open until the Specification selects the required exact derived-scalar representation.

Implementation Capacity Must Not Redefine Canonical Precision

A conforming implementation may have finite practical limits, but those limits shall not silently redefine which mathematically valid canonical values mean what.

Unsupported capability shall remain distinguishable from invalid canonical mathematics.

Every Implementation Must Preserve the Same Exact Precision Truth

Independent conforming implementations shall agree on exact CRPC value, normalized representation, semantic equality, lossless versus lossy classification, canonical serialization, and version-preserved meaning for identical supported inputs.

A mismatch indicates implementation defect, Specification ambiguity, version incompatibility, fixture defect, or a precision case tested beyond current mathematical closure.

Precision Has Moved From Mechanism-Agnostic Planning to an Exact Candidate Core

The original page correctly avoided choosing a precision mechanism while that decision remained open. The candidate Specification has now selected CRPC and ECEM for the canonical coordinate core.

Section 08 can therefore support exact candidate Precision Vectors now. The unresolved precision work no longer concerns basic sub-Pang coordinate representation; it concerns exact result classes for operations whose outputs may fall outside rational-coordinate closure.

Referenced Requirements

Precision Vectors will derive especially from Requirements Findings #9–#10, #20, #24, #41, #53–#54, #59, #64, #70–#75, and #78–#83.