Canonical Addressing
& Precision
The specification boundary for how BitPangea names canonical place, increases precision, preserves address meaning, and normalizes equivalent spatial references.
This section translates accepted Foundational Survey Fabric requirements into the specification rules for canonical addressing and precision. It now incorporates the candidate mathematical design selected through Formal Mathematical Decisions FMD-01 through FMD-09 where those decisions resolve reference meaning, exact coordinate representation, normalization, precision extension, and canonical machine representation.
The candidate mathematics now establish that canonical Point meaning is exact, coordinate-based, permanent, and non-hierarchical: a valid canonical Point denotes one exact Survey position rather than an uncertainty area, parent cell, rounded location, or family of finer descendants. The final public canonical address grammar and human-facing address syntax remain open and shall not be invented merely because the underlying mathematical reference model is now selected.
Specification Principle Precision by extension, not migration.
Exact Reference Meaning Selected · Public Address Grammar Still Open
FMD-01 establishes exact reduced rational Pang coordinates. FMD-07 establishes deterministic normalization for supported canonical geometry. FMD-08 establishes FSF-CJSON-1.0 as the primary canonical machine serialization for the current core geometry profile. FMD-09 establishes the Exact Coordinate Extension Model (ECEM), eliminating ambiguity about coarse/fine and parent/child Point semantics.
These decisions resolve the mathematical meaning of canonical Point reference and its precision behavior. They do not yet select a public address string, display alphabet, compact human-readable syntax, or final canonical address grammar. Those remain later Specification work provided any adopted address form resolves deterministically to the exact Survey meaning defined here.
Every Valid Representable Point Can Be Named
Every valid Point representable under the canonical Survey mathematics shall be addressable whether or not any Parcel, infrastructure element, stored object, or other higher-layer entity exists there.
Addressability shall not depend on materialization. Canonical mathematical reference may be complete while stored records remain sparse.
A Point outside the valid Survey Domain is not an addressable canonical Survey Point.
One Exact Position Per Canonical Point Reference
A canonical Point reference shall resolve to one exact Survey position under the governing Specification. It shall not denote an uncertainty area, parent cell, rounded location, approximate position, or set of finer descendants.
The same canonical spatial meaning shall normalize to the same authoritative mathematical reference. Display forms, aliases, encodings, human-readable labels, and local coordinate views may evolve, but they shall not redefine the canonical place beneath them.
Self-Resolving Exact Coordinates
Canonical Point meaning is grounded in exact CRPC coordinate values in the one global Survey frame. A valid Point therefore resolves mathematically from the governing Specification and its exact coordinate content rather than from an opaque registry assignment.
The final public address grammar may wrap, abbreviate, encode, or otherwise present that reference, but it shall remain self-resolving or deterministically reducible to the exact canonical Point without requiring an authoritative lookup table to assign spatial meaning.
Independent of Higher-Layer Objects
Canonical Survey references are absolute within BitPangea’s one global canonical coordinate frame.
Their foundational meaning shall not depend on Parcels, Regions, landmarks, neighboring entities, ownership, World membership, or any other higher-layer object or relationship.
More Representational Capacity Without Rewriting Place
The Foundational Survey Fabric shall support additional canonical precision through Exact Coordinate Extension. Compatible successor Specifications may increase the exact finite coordinate values or expressions they can represent without changing the meaning of any previously valid reference.
If Rv is the set of valid references under compatible Specification version v, then a compatible precision-extending successor shall preserve: Rv ⊆ Rv+1.
For every previously valid reference r, its spatial meaning shall remain invariant across compatible versions. Additional precision shall not renumber, relocate, reinterpret, invalidate, or silently snap established canonical place.
No Foundational Coarse/Fine Point Hierarchy
Canonical Point references do not possess foundational parent/child, coarse/fine, zoom-level, or descendant semantics.
A Point expressed with one exact rational coordinate pair is already exact. Another Point with a different exact coordinate pair is a different Point, not a finer child of the first merely because more digits, a larger denominator, or a different textual representation are used.
Higher layers may define resolution profiles, tiles, cells, indexes, or hierarchical subdivisions, but those derived structures shall not redefine canonical Point meaning.
Exact Precision Below the Pang Through CRPC
Spatial positions below one Pang shall be expressible through exact reduced rational Pang coordinates.
Examples include 1/2 Pang, 1/3 Pang, and other finite reduced rational values permitted by the governing Specification.
No permanently named hierarchy such as milli-Pang, micro-Pang, or recursive Point levels is required to obtain canonical sub-Pang precision.
No Pretended Infinite Address
The canonical reference system shall not require every theoretical real-number point to possess a finite canonical reference.
Every valid Point representable under the canonical Survey mathematics shall be exactly and finitely expressible, and actual canonical references shall remain deterministically computable.
A value outside the governed representational limits of a Specification version is invalid for that version rather than rounded, truncated, or snapped into validity.
Equivalent Representation, One Normal Form
Canonicalization shall normalize only mathematically equivalent representations.
CRPC scalar values shall normalize to reduced form with positive denominator and canonical zero 0/1. Supported Point, Segment, and SCPE geometry shall normalize under the rules established by FMD-07.
Canonicalization shall preserve place exactly. It shall not move a Point or alter an extent.
Canonical Spatial Meaning Remains Permanent
A canonical Survey reference shall never be reused or reassigned to a different spatial meaning because a higher-layer entity moves, disappears, changes ownership, changes World membership, or ceases to exist.
A place may become unused. Its canonical spatial meaning does not become available for somewhere else.
CRPC Position and Pang Mathematics Must Agree
Canonical Point references resolve to exact CRPC coordinates expressed in Pangs within the permanent global frame. Therefore authoritative Point reference and authoritative Pang-based position are two expressions of one spatial truth rather than separate coordinate systems.
Derived measurement may require exact scalar types beyond CRPC, but no measurement or future address grammar may reinterpret the underlying canonical Point.
Normalization Does Not Move Place
Canonicalization shall not move a location to a nearby grid line, subdivision boundary, preferred increment, vertex, tile center, or other derived structure.
Any snapping or alignment performed by higher layers shall be an explicit spatial transformation rather than an interpretation of canonical reference meaning.
FSF-CJSON Carries Exact Reference Meaning
The current candidate core uses FSF-CJSON-1.0 as the primary canonical machine-readable serialization for exact FSF geometry.
This machine representation does not automatically become the public canonical address syntax. Specification 06 owns normative serialization and interchange; this section owns the spatial meaning that any address or encoding must preserve.
Version the Standard, Not the Place
Compatible Specification evolution may expand representational capability, add lossless encodings, clarify rules, or introduce future address forms, provided previously valid canonical spatial meaning remains unchanged.
A new Specification version shall not renumber, relocate, reinterpret, or reuse an established canonical place.
Integrated Candidate Mathematics
Exact CRPC Point meaning; self-resolving mathematical reference; ECEM precision extension; no parent/child or coarse/fine Point hierarchy; exact sub-Pang rational precision; deterministic normalization; no silent snapping; FSF-CJSON-1.0 as the current canonical machine serialization; compatible evolution without place migration.
Still Open in the Specification
Final public canonical address grammar; human-readable address syntax; compact encoding alphabet if one is desired; formal address-version identifier rules; governed complexity limits; and any optional future derived subdivision or indexing syntax that does not alter canonical Point meaning.
Reference Meaning and Precision Semantics Are Closed at Candidate Level
No contradiction was found between Specification 03 and FMD-01 through FMD-09. The mathematical meaning of canonical Point reference, normalization, sub-Pang precision, and compatible refinement is sufficiently defined for core prototype and conformance work.
The remaining address-grammar questions are representational rather than unresolved Point semantics. Formal adoption remains contingent on Specification-wide integration, Conformance, Reference Vectors, independent implementation, adversarial testing, traceability, and the applicable adoption act.
Primary Derived Findings
This specification section is derived especially from Requirements Findings #7–#9, #20–#22, #30, #41–#42, #54, and #70–#71.
Architectural Boundary Address names the place. Canonical mathematics increases precision. Neither may redefine the canonical spatial meaning already established.