Exactness
Requirements

Exactness Is Now Executable for the Solved Core

Specification Sections 01–07 now provide deterministic candidate mathematics sufficient to test exact canonical behavior across the current Mandatory Core.

Conformance may therefore require exact agreement in coordinate value, validity, predicates, normalization, precision semantics, and canonical byte output wherever the Specification defines a unique result.

No Tolerance-Based Equality

Canonical equality and equivalence shall be determined by the exact rules of the governing Specification.

Floating tolerances, epsilon bands, “close enough” comparison, display precision, implementation-specific rounding, or device-dependent approximation shall not determine whether two canonical values or spatial expressions are equal.

Coordinate Truth Is Rational and Exact

Mandatory Core coordinate arithmetic shall preserve CRPC values exactly through the rational mathematics defined by the Specification.

Reduction, equality, ordering, sign, and comparison shall use exact integer/rational logic rather than floating approximation.

Conversion to approximate machine numerics may occur only outside authoritative canonical evaluation unless exact equivalence is independently proven and preserved.

Predicates Must Resolve Deterministically

Survey-layer predicates in the solved core shall resolve exactly under canonical mathematics.

These include Point equality and ordering, orientation, Point-on-Segment, Segment intersection, Point-on-boundary, Point-in-SCPE, polygon validity, connectedness, containment, and geometric equivalence where defined by the Specification.

Approximate geometric tests shall not substitute for canonical predicate truth.

Canonicalization Must Not Move Place

Canonical coordinates and geometry shall not be silently moved to nearby grid lines, preferred increments, vertices, subdivision boundaries, render pixels, or other derived structures.

Snapping may exist as an explicit higher-layer or implementation convenience, but it shall never be disguised as canonical interpretation, normalization, or validation.

Mutable Context Must Not Change the Answer

Authoritative results shall depend only on explicit canonical inputs and the governing Specification profile.

Cache history, database order, random state, user identity, ownership, session state, process history, storage order, machine locale, wall-clock time, or other hidden mutable conditions shall not alter canonical output.

Normalization Preserves Identical Meaning

Canonicalization shall normalize only mathematically equivalent representations.

For the current core this includes exact CRPC reduction, lexicographic Segment endpoint ordering, and deterministic SCPE normalization through exact redundant-collinear removal, counterclockwise traversal, lexicographically least start vertex, and omission of repeated terminal closure.

Required invariants include: N(N(G)) = N(G) and geom(N(G)) = geom(G).

Selected Measurement Mathematics Must Be Reproducible

Polygonal area for supported SCPE geometry shall be computed exactly under the governing rational coordinate mathematics.

Exact shoelace-style area evaluation is therefore eligible for direct Conformance proof.

The exact general scalar representation for all possible distance, path-length, and boundary-length results remains outside the solved Mandatory Core until the Specification closes those questions.

Do Not Claim Exactness Where the Scalar Model Is Still Open

Conformance shall not treat unresolved measurement mathematics as canonically solved merely because an implementation can produce a numerical approximation or symbolic answer.

General straight-line distance and general path / boundary-length scalar closure remain open in the Specification and therefore outside current mandatory exactness proof except where a specific exact result form is already defined.

Canonical Precision Must Not Be Lost Invisibly

A conforming implementation shall distinguish complete canonical mathematical precision from reduced storage, transmission, display, or rendering precision.

Any lossy conversion shall be detectable and shall not be represented as exact equivalence to the original authoritative object.

A Canonical Point Is Already Exact

Under ECEM, every valid canonical Point denotes one exact Survey position.

Conformance shall reject foundational interpretations that treat a canonical Point as approximate, coarse, parent, child, uncertainty-based, or implicitly dependent on a refinement hierarchy.

Compatible representational extension may expand what can be expressed without changing the meaning of previously valid Points.

Authoritative Truth Must Be Exactly Representable

Canonical CRPC values, Points, Segments, SCPEs, and FSF-CJSON-1.0 expressions in the solved profile shall remain finitely representable and exactly resolvable.

A conformance claim shall not depend on irreducible approximation or indefinite numerical convergence to determine canonical meaning.

Exactness Must Be Reachable

Required solved-core operations shall terminate deterministically for valid finite inputs.

Parsing, validation, exact predicates, normalization, and canonical serialization shall not depend on unresolved iterative convergence.

Canonical Bytes Must Be Deterministic

For supported normalized geometry, FSF-CJSON-1.0 shall produce one deterministic canonical UTF-8 byte sequence under the governing format rules.

Conformance shall therefore test exact structured CRPC encoding, required key order, string normalization, duplicate-key rejection, governed unknown-field behavior, semantic array order, and byte identity where applicable.

Semantically equivalent but byte-different output is nonconforming where the format requires one unique canonical serialization.

Approximate Methods Belong Outside Canonical Truth

Rendering, visualization, interaction, simulation, indexing, search acceleration, engineering convenience, or local presentation may use approximate methods where appropriate.

Such approximation shall remain explicitly outside the authoritative canonical result and shall not redefine Survey-layer truth.

Optimization Must Prove Exact Result Preservation

An implementation may use optimized or approximate internal techniques only if the final authoritative result is provably identical to the exact result required by the Specification.

If exact result preservation cannot be demonstrated, the method shall not be used to establish canonical output.

The detailed proof obligations for optimized internal algorithms remain part of later executable Conformance design.

Exactness Must Survive Independent Implementation

Independent conforming implementations shall reproduce the same authoritative canonical meaning from identical canonical inputs without relying on shared hidden state or common proprietary software.

Where the governing Specification requires one unique normalized form or canonical serialization, that representation shall also agree exactly.

Exactness shall be a property of the published Specification, not of one favored implementation.

Exactness Must Be Demonstrated With Exact Fixtures

Exactness requirements shall be tested through Reference Vectors or equivalent executable fixtures whose expected results are themselves exact.

The current solved profile is sufficiently mature for vectors covering CRPC normalization, exact predicate outcomes, SCPE normalization, exact polygon area, ECEM semantics, invalid approximation cases, and canonical FSF-CJSON-1.0 bytes.

Approximate expected values shall not be used as substitutes for exact canonical expected results where the Specification defines exact truth.

Approximate Canonical Results Are Nonconforming

Tolerance-based equality, incorrect rational reduction, silent snapping, hidden mutable state, undetected lossy conversion, approximate predicate truth, non-idempotent normalization, semantic drift, or incorrect canonical bytes shall constitute Conformance failure when used to establish authoritative Survey truth.

Approximate or lossy behavior may still exist as explicitly noncanonical functionality above the Foundational Survey Fabric, but it shall not be presented as canonical FSF output.

Exactness Has Moved From Principle to Executable Candidate Proof

The original section correctly established that canonical truth must never depend on tolerance, snapping, approximation, or mutable hidden state.

The integrated Specification now provides enough exact mathematics to test those principles directly across the solved Mandatory Core while preserving unresolved measurement and transformation mathematics outside current canonical proof.

Primary Referenced Findings

This Conformance section is derived especially from Requirements Findings #24, #30, #53–#57, #66, #72–#75, and #78–#83.