Computability
Rules
The specification boundary for what canonical Survey truth must be able to represent, compute, validate, resolve, and return as an authoritative result.
This section translates accepted Foundational Survey Fabric requirements into the specification rules for computability. It now incorporates the candidate mathematical design selected through Formal Mathematical Decisions FMD-01 through FMD-09 wherever those decisions resolve finite exact representation, canonical precision, primitive geometry, deterministic validation, normalization, serialization, and implementation-independent canonical output.
The candidate core is now sufficiently deterministic for executable prototype and Conformance work across CRPC coordinates, Point / Segment / SCPE geometry, exact predicates, canonical normalization, FSF-CJSON-1.0 serialization, and ECEM precision semantics. The full computability specification remains intentionally incomplete where the broader FSF mathematics are still open, including general composition closure, exact non-rational measurement scalars, arbitrary rotation closure, final complexity limits, and the complete canonical error taxonomy.
Specification Principle Canonical truth must not only be exact. It must be reachable.
Executable Core Selected · Full Computational Closure Still Open
FMD-01 supplies exact finite CRPC coordinate representation. FMD-05 defines the current minimal primitive geometry. FMD-06 supplies exact deterministic predicates and validation. FMD-07 supplies canonical normalization. FMD-08 supplies deterministic canonical serialization. FMD-09 supplies exact precision and compatibility semantics.
FMD-02 through FMD-04 provide the inherited frame, origin, and Survey Domain validity envelope. Together, these decisions now define a computable candidate core that can be independently implemented and tested without floating-point tolerance or hidden state.
Every Authoritative Core Expression Is Finite
Every canonical Point, Segment, SCPE, CRPC scalar, and FSF-CJSON-1.0 expression in the current core shall possess a finite representation capable of exact interpretation under the governing Specification.
Canonical spatial truth shall not depend on infinitely long descriptions, unresolved mathematical limits, or irreducible numerical approximation.
Canonical Results Are Exact
Authoritative Survey results shall be produced through exact deterministic mathematics rather than implementation-specific floating-point tolerance, epsilon comparison, numerical convergence, or approximate snapping.
Approximate numerical methods may be used above the Foundational Survey Fabric for rendering, visualization, simulation, indexing, or convenience, but they shall not establish canonical Survey truth.
Precision Is Mathematical, Not Device-Defined
Canonical Point precision follows the Exact Coordinate Extension Model. A valid canonical Point is already exact and is not a coarse, approximate, parent, or uncertainty Point.
Storage precision, display precision, and rendering resolution remain implementation or presentation choices and shall not alter the exact canonical coordinate values.
Exact Addressability Without Pretending to Encode the Real Continuum
Every valid Point representable under the canonical coordinate mathematics shall be exactly addressable.
The Survey Fabric is not required to assign finite canonical references to every theoretical point of the unrestricted real-number continuum. A Point outside the governed representational domain of a Specification version is invalid for that version rather than approximated into validity.
Point · Segment · SCPE
The current candidate computable core uses the smallest selected primitive set: Point, Segment, and Simple Closed Polygonal Extent (SCPE).
Additional primitives shall be introduced only if a required Survey-layer truth cannot be expressed exactly, deterministically, and finitely using the existing core.
Finite, Parseable, Normalizable Expressions
Canonical expressions may contain as much exact detail as legitimately required, but they shall remain finite, parseable, unambiguous, and suitable for deterministic validation and normalization.
Exact redundant representation may normalize away where FMD-07 explicitly permits it. Invalid or unsupported complexity shall not be silently simplified into a different canonical object.
Final formal complexity limits, parser limits, maximum supported sizes, and resource bounds remain to be specified.
State May Accelerate Computation, Not Change Truth
Authoritative Survey results shall depend only on explicit canonical inputs and the governing Specification.
Cache history, database sequence, random state, user identity, ownership, session context, wall-clock time, process order, storage layout, or other hidden mutable conditions shall not alter canonical spatial meaning or operation results.
Core Canonical Operations Must Finish
For valid finite inputs in the current candidate core, parsing, CRPC normalization, Domain validation, Point / Segment / SCPE validation, exact predicates, normalization, and FSF-CJSON-1.0 serialization shall deterministically terminate.
Canonical interpretation shall not depend on indefinite convergence or implementation-specific approximation.
Canonical Valid · Valid Noncanonical · Invalid
The current core shall distinguish: canonical valid, valid noncanonical, and invalid.
A valid noncanonical representation may normalize to canonical form only when exact mathematical meaning is preserved. Invalid input shall not be silently repaired, guessed, snapped, rounded, or reinterpreted into canonical truth.
Precision Loss Must Be Detectable
A transformation or conversion is lossless only when the exact mathematical object is unchanged.
Any reduction, truncation, decimal approximation, rasterization, simplification, or other operation that discards canonical information shall be identifiable as lossy and shall not be represented as fully equivalent canonical truth.
What Counts as Canonical Output
An authoritative Survey result shall be valid under the governing Specification, derived solely from explicit canonical inputs, exactly and finitely resolvable, deterministically reproducible, and expressible in a canonical output form defined for that operation.
A mathematically meaningful result does not automatically become a canonical FSF result when the Specification lacks a governed result type, normalization rule, serialization, or Conformance behavior for that output.
Many Implementations, One Canonical Result
Independent conforming implementations shall be capable of deriving identical canonical results from identical canonical inputs for every operation they claim to support.
Internal algorithms, programming languages, cache strategies, data structures, optimization methods, or storage systems may differ so long as those choices do not alter authoritative output.
Same Normalized Meaning, Same Bytes
For supported Point / Segment / SCPE geometry, canonical computational output may be serialized through FSF-CJSON-1.0 after successful validation and normalization.
Under the same governing format version, the same normalized supported geometry shall produce identical canonical UTF-8 bytes across conforming implementations.
Implementation Limits Must Not Redefine Mathematics
Implementations may impose practical limits on memory, runtime, input size, denominator size, vertex count, or other resources.
Such implementation limits shall not silently redefine canonical mathematics. The final Specification shall distinguish normative complexity limits, if adopted, from implementation-specific operational limits.
Final canonical complexity limits remain open.
Open Mathematics Must Fail Explicitly
Where the complete FSF Specification has not yet defined canonical output closure—such as arbitrary Boolean composition, arbitrary exact rotation, or exact general non-rational measurement scalars—an implementation shall not invent a private canonical answer.
Such cases shall remain unsupported or invalid under the claimed profile until the governing Specification defines their exact semantics and result forms.
The Solved Core May Now Be Implemented and Attacked
The current candidate core is sufficiently deterministic to support executable validators, Reference Vectors, independent reimplementation, cross-implementation comparison, and adversarial testing for CRPC, Point / Segment / SCPE geometry, exact predicates, normalization, and FSF-CJSON-1.0.
This readiness applies only to the solved profile. It does not imply that unresolved full-FSF operations have become canonical by omission.
Executable Does Not Mean Adopted
Candidate mathematics may enter prototype and Conformance work once their deterministic rules are sufficiently complete, but canonical adoption remains a later institutional gate.
Adoption shall require Specification-wide traceability, Conformance analysis, Reference Vectors, independent implementation, adversarial testing, resolution or explicit scoping of material open gates, and the applicable adoption act.
Integrated Candidate Computability
Finite CRPC representation; exact Point / Segment / SCPE core; deterministic validation and predicates; canonical normalization; exact-or-invalid behavior; ECEM precision semantics; lossless/lossy distinction; hidden-state independence; deterministic termination for the solved core; FSF-CJSON-1.0 canonical output; independent implementation readiness.
Still Open in the Specification
Final formal complexity limits; complete parser/resource limits; full canonical error taxonomy; exact scalar representation for general distance and path length; arbitrary rotation closure; general union/intersection/difference output closure; complete composition result types; and computability rules for future geometry beyond the current core.
Computable Core Ready for Executable Proof
No contradiction was found between Specification 07 and FMD-01 through FMD-09 for the solved Point / Segment / SCPE profile. The prerequisites previously identified by this section are now sufficiently selected to begin serious prototype and Conformance testing for that profile.
The complete FSF computability specification is not yet closed. Full adoption remains blocked by the unresolved mathematical and governance gates explicitly preserved above.
Primary Derived Findings
This specification section is derived particularly from Requirements Findings #71–#83.
Specification Standing The solved FSF core is now sufficiently deterministic for prototype, Conformance, Reference Vector, independent implementation, and adversarial work. The complete Specification remains open where the mathematics remain open, and canonical adoption remains a later gate requiring successful proof and institutional adoption.