# Spatial Ground Conformance **BitPangea · The Atlas · Spatial Ground** **Document Type:** Conformance Specification **Creator Period:** Day #122 · September 26, 2026 **Status:** DRAFT FOR GATE B / MATURITY REVIEW **Formal Model:** Canonical Membership Predicate Model (CMPM) **Canonical Representation:** SG-CJSON 1.0 **Limit Convention:** Closed World-Space **Normative Dependencies:** Adopted Spatial Ground Requirements; Spatial Ground Specification; FSF Dependency Declaration; Canon-Form Policy **Canonical Instance Effect:** None. Conformance does not create or alter World-space. --- ## 0. Purpose Spatial Ground Conformance defines how an implementation, validator, canonical Ground Definition, or derived artifact proves that it follows the adopted Spatial Ground Specification. The governing question is: > **How does an implementation prove that it produces the same exact Ground truth required by the Specification?** Conformance verifies. Conformance does not legislate. Conformance SHALL NOT: - invent new Ground semantics; - redefine the Spatial Ground Specification; - repair ambiguity through test precedent; - create canonical World-space; - override the canonical Ground Definition; - redefine Foundational Survey Fabric mathematics. The governing rule is: > **Specification defines truth. Conformance proves implementation fidelity to that truth.** --- # 1. Conformance Classes Spatial Ground defines four conformance classes. ## 1.1 SG-C1 — Definition Validator A conforming SG-C1 implementation validates whether a candidate Ground Definition artifact: - is structurally valid SG-CJSON 1.0; - uses only permitted constructs; - declares valid dependencies; - satisfies canonicalization rules; - contains no prohibited Ground semantics. SG-C1 does not need to evaluate membership. --- ## 1.2 SG-C2 — Membership Evaluator A conforming SG-C2 implementation SHALL: - satisfy SG-C1; - validate canonical Survey input through FSF; - evaluate `M_D(x)`; - return exactly `WORLD` or `NON_WORLD` for valid input; - distinguish invalid input from non-World membership; - terminate deterministically. --- ## 1.3 SG-C3 — Full Semantic Validator A conforming SG-C3 implementation SHALL: - satisfy SG-C1 and SG-C2; - test semantic equivalence where required; - test refinement closure where applicable; - test canonical-limit behavior; - verify declared FSF dependency compatibility; - test constitutional instance constraints where an actual candidate instance is supplied. --- ## 1.4 SG-C4 — Independent Reimplementation A conforming SG-C4 implementation SHALL: - be developed independently of the primary implementation; - satisfy SG-C1 through SG-C3; - reproduce the same canonical outputs from the same normative inputs; - avoid shared hidden runtime state, copied evaluator logic, or implementation-specific shortcuts. SG-C4 exists to test the Specification itself. --- # 2. Mandatory Conformance Core Every implementation claiming Spatial Ground conformance SHALL satisfy the following mandatory core. ## 2.1 Structural Validity The implementation SHALL correctly accept valid SG-CJSON 1.0 artifacts and reject invalid ones. ## 2.2 Deterministic Canonicalization The implementation SHALL canonicalize equivalent permitted SG-CJSON structures to the exact canonical byte form required by the Specification. ## 2.3 Exact Membership For every valid canonical Survey input: ```text M_D(x) ∈ {WORLD, NON_WORLD} ``` and no other canonical membership value. ## 2.4 Invalidity Separation Invalid Survey input SHALL NOT be returned as `NON_WORLD`. Invalid Ground Definitions SHALL NOT be evaluated as if valid. ## 2.5 Exact Limit Membership If FSF determines that a valid Survey location lies exactly on the canonical Ground limit: ```text M_D(x) = WORLD ``` ## 2.6 Hidden-State Independence Results SHALL NOT vary with: - cache state; - query history; - clock; - locale; - network availability; - thread scheduling; - user identity; - ownership state; - deployment environment. ## 2.7 Repeatability Repeated validation of unchanged normative input SHALL produce the same result. ## 2.8 Non-Mutation Validation and evaluation SHALL NOT alter the canonical Ground Definition being tested. --- # 3. Canonical Result Equivalence ## 3.1 Membership Equivalence Two conforming implementations evaluating the same canonical input under the same valid Ground Definition SHALL return identical membership. For implementations `A` and `B`: ```text M_D^A(x) = M_D^B(x) ``` for every Reference Vector input `x`. --- ## 3.2 Canonicalization Equivalence Two conforming implementations canonicalizing the same valid SG-CJSON artifact SHALL emit identical canonical UTF-8 bytes. --- ## 3.3 Artifact Identity vs Semantic Equivalence Conformance SHALL distinguish: - byte identity; - normalized structural identity; - semantic equivalence. Byte identity proves artifact identity. Semantic equivalence concerns induced membership truth. The two SHALL NOT be conflated. --- # 4. Definition Validation A conforming SG-C1 or higher validator SHALL reject a candidate Ground Definition if any of the following applies: - malformed JSON; - duplicate object member; - JSON numeric value present; - unknown semantic field; - unsupported operator; - malformed operator structure; - invalid top-level `type`; - invalid `format`; - unsupported `model`; - unsupported `limit_convention`; - missing FSF dependency declaration; - invalid or unresolved FSF leaf; - prohibited higher-layer semantics; - dependency on runtime or mutable state; - nondeterministic construct; - invalid canonicalization; - cyclic external dependency where external references are permitted; - failure to terminate under validation. --- # 5. SG-CJSON Canonicalization Tests Conformance SHALL test at minimum: 1. duplicate-key rejection; 2. JSON-number rejection; 3. NFC string normalization; 4. lexicographic object-key ordering; 5. whitespace elimination; 6. UTF-8 serialization without BOM; 7. commutative child sorting for `union`; 8. commutative child sorting for `intersection`; 9. duplicate child elimination for commutative operators; 10. nested same-operator flattening; 11. ordered preservation for `difference`; 12. stable canonical bytes across implementations. --- # 6. Operator Conformance ## 6.1 `fsf` A conforming implementation SHALL: - accept only canonical FSF spatial expressions; - delegate FSF spatial meaning to the governing FSF implementation or specification; - reject unresolved or invalid FSF leaves; - not reinterpret FSF geometry. --- ## 6.2 `union` For valid expressions `A1...An`: ```text Eval(union(A1...An),x) = Eval(A1,x) OR ... OR Eval(An,x) ``` Conformance SHALL test: - associativity of normalized structure where semantically applicable; - commutative canonical ordering; - duplicate elimination; - identical result across child ordering. --- ## 6.3 `intersection` For valid expressions `A1...An`: ```text Eval(intersection(A1...An),x) = Eval(A1,x) AND ... AND Eval(An,x) ``` Conformance SHALL test: - commutative canonical ordering; - duplicate elimination; - nested flattening; - identical result across child ordering. --- ## 6.4 `difference` For valid expressions `A` and `B`: ```text Eval(difference(A,B),x) = Eval(A,x) AND NOT Eval(B,x) ``` Conformance SHALL confirm that operand order is semantic. The validator SHALL NOT reorder `base` and `subtract`. --- # 7. Membership Test Families Every mature conformance suite SHALL contain the following test families. ## 7.1 Interior World Cases Valid Survey locations unambiguously inside World-space. Expected result: ```text WORLD ``` --- ## 7.2 Exterior Non-World Cases Valid Survey locations unambiguously outside World-space. Expected result: ```text NON_WORLD ``` --- ## 7.3 Exact Limit Cases Valid Survey locations exactly on the canonical Ground limit. Expected result: ```text WORLD ``` --- ## 7.4 Hole Interior Cases Where the candidate instance contains a hole: - locations strictly inside the hole → `NON_WORLD`; - locations exactly on the hole boundary → `WORLD`. --- ## 7.5 Equivalent Survey Reference Cases Different valid FSF expressions denoting the same canonical Survey location SHALL produce identical membership. --- ## 7.6 Non-Equivalent Survey Reference Cases Visually similar or numerically close but semantically different FSF locations SHALL remain distinct where FSF says they are distinct. --- ## 7.7 Invalid Survey Input Cases Malformed or invalid Survey expressions SHALL return: ```text INVALID_INPUT ``` and SHALL NOT be treated as `NON_WORLD`. --- # 8. Representation Trap Tests Conformance SHALL include cases where semantic meaning remains unchanged but representation differs. Examples include: - different whitespace; - different member ordering before canonicalization; - Unicode equivalent strings before normalization; - alternate commutative child order; - duplicate commutative child entries; - alternate derived storage layout; - alternate implementation language. Expected outcome: > identical canonical semantics. --- # 9. Transformation Trap Tests Conformance SHALL test transformed objects that are visually similar but spatially different. Examples may include: - translation; - rotation; - reflection; - scaling; - alternate origin-relative presentations. If FSF says the transformed location differs canonically, Ground membership SHALL follow that actual canonical location. Visual resemblance SHALL NOT imply identity. --- # 10. Hidden-State Trap Tests The conformance harness SHALL repeat selected membership evaluations under different: - cache states; - process restarts; - machine architectures; - locale settings; - time zones; - thread counts; - network conditions. Canonical membership results SHALL remain identical. --- # 11. Refinement Tests Conformance SHALL test that supported compatible FSF refinement: - permits finer evaluation; - does not create new Ground semantics; - does not move the canonical limit; - does not convert an established valid membership result merely because greater precision becomes available. Where exact coarse/fine semantics remain unresolved upstream, tests SHALL NOT invent them. Such tests SHALL be marked: ```text BLOCKED_BY_FSF ``` rather than silently defining FSF behavior. --- # 12. Limit Convention Tests The Closed World-Space Convention SHALL be tested explicitly. For any valid FSF location `x` such that: ```text x ∈ ∂W_D ``` expected membership is: ```text WORLD ``` This applies to: - outer World limit; - internal hole boundaries; - exact contact points; - exact edge segments; - exact boundary intersections. No geometry-library default may override this requirement. --- # 13. Constitutional Instance Tests Where a candidate canonical instance is being evaluated, SG-C3 conformance SHALL test: ## 13.1 Singularity Exactly one candidate primary Ground Definition is identified for adoption. ## 13.2 Non-Emptiness ```text W_D ≠ ∅ ``` ## 13.3 Connectedness The candidate `W_D` is connected under governing FSF topology. ## 13.4 Refinement-Stable Connectedness Supported compatible refinement does not alter the connectedness result. ## 13.5 Extent Conformity The candidate is accompanied by the required institutional determination that it conforms to constitutional Extent. Conformance may verify the prescribed evidence. Conformance SHALL NOT independently redefine constitutional Extent. --- # 14. Error Classes A conforming implementation SHALL distinguish at minimum: ```text VALID INVALID_DEFINITION INVALID_INPUT DEPENDENCY_ERROR UNSUPPORTED_FSF_SEMANTIC NONCONFORMING_RESULT IMPLEMENTATION_ERROR BLOCKED_BY_FSF ``` Where a membership result is successfully produced, the membership value remains only: ```text WORLD NON_WORLD ``` --- # 15. Failure Conditions A claimed conforming implementation fails conformance if it: - produces a third membership state; - returns different answers for the same canonical input; - treats invalid Survey input as non-World-space; - gives NON_WORLD to an exact canonical-limit location; - depends on hidden mutable state; - silently tolerates malformed Ground Definitions; - accepts prohibited higher-layer semantics; - redefines FSF truth; - uses tolerance where exactness is required; - produces canonical bytes differing from the required canonicalization; - cannot reproduce required Reference Vector outputs; - disagrees with an independent conforming implementation without a Specification defect being demonstrated. --- # 16. Conformance Report Every formal conformance run SHALL produce a report containing at minimum: - implementation name; - implementation version; - conformance class claimed; - Spatial Ground Specification version; - SG-CJSON version; - governing FSF specification / lineage; - test-suite version; - Reference Vector corpus version; - test date; - total tests; - passed; - failed; - blocked; - skipped; - failure details; - canonical environment notes; - implementation declaration; - final status. --- # 17. Conformance Status Values The final conformance status SHALL be one of: ```text CONFORMING NONCONFORMING CONDITIONALLY_CONFORMING BLOCKED ``` ### CONFORMING All mandatory tests required for the claimed class pass. ### NONCONFORMING One or more mandatory requirements fail. ### CONDITIONALLY_CONFORMING All executable mandatory tests pass, but one or more formally reserved upstream FSF dependencies prevent full maturity determination. ### BLOCKED The implementation cannot be meaningfully tested because a required normative dependency is absent or unresolved. --- # 18. Independent Implementation Requirement Before Spatial Ground is considered mature enough for final canonical instance adoption, at least one SG-C4 independent implementation SHALL reproduce the primary implementation's required results. Independent implementation is a Specification test. If two independently built implementations disagree, the disagreement SHALL trigger review of: 1. implementation correctness; 2. Reference Vector correctness; 3. Specification clarity; 4. FSF dependency clarity. Disagreement SHALL NOT be accepted as canonical plurality. --- # 19. Independence Criteria An implementation qualifies as independent only if it is not merely: - a wrapper around the primary evaluator; - a translation of the same source code; - a shared binary library invocation; - a copy of the same parser/evaluator logic; - a client of the primary implementation's API; - dependent on the same hidden state. Shared public normative documents are expected. Shared implementation logic is not. --- # 20. Conformance and Reference Vectors Reference Vectors provide exact fixtures. Conformance defines the procedures and conditions for passing them. The relationship is: ```text Specification → Conformance → Reference Vectors ``` Reference Vectors SHALL NOT create semantics absent from the Specification. If a vector exposes ambiguity, the Specification SHALL be repaired before the vector is treated as canonical. --- # 21. Minimal Conformance Vector Families The future canonical Reference Vector corpus SHALL include at minimum: 1. SG-CJSON valid structure; 2. SG-CJSON invalid structure; 3. canonicalization equality; 4. canonicalization inequality; 5. FSF leaf validity; 6. WORLD interior; 7. NON_WORLD exterior; 8. exact outer limit; 9. exact hole limit; 10. invalid Survey input; 11. equivalent Survey reference; 12. non-equivalent Survey reference; 13. union; 14. intersection; 15. difference; 16. commutative reordering; 17. duplicate-child normalization; 18. difference ordering; 19. hidden-state repeatability; 20. reconstruction; 21. independent implementation agreement; 22. connectedness; 23. refinement behavior; 24. pathological edge conditions. --- # 22. Reconstruction Test A mature conformance suite SHALL include at least one reconstruction test in which an implementation is given only: ```text Spatial Ground Specification + canonical Ground Definition + declared governing FSF semantics + canonical Reference Vectors ``` The implementation SHALL reproduce the expected canonical Ground behavior without access to: - the original runtime; - the original database; - original caches; - original deployment environment; - historical event replay. --- # 23. Adversarial Test Families Conformance SHALL include adversarial cases designed to expose: - ambiguous parsing; - duplicate key exploitation; - Unicode normalization disagreement; - ordering disagreement; - malicious unsupported fields; - expression blow-up; - deeply nested expressions; - redundant expressions; - exact boundary contact; - hole-boundary behavior; - FSF dependency mismatch; - invalid lineage claims; - hidden-state leakage; - nontermination attempts; - tolerance substitution; - representation-dependent result drift. --- # 24. Performance Is Not Canonical Truth Performance MAY be measured. Performance SHALL NOT alter canonical membership semantics. A slow conforming implementation may still be conforming. A fast implementation returning a wrong canonical result is nonconforming. Resource limits may be declared operationally, but they SHALL NOT silently redefine valid canonical meaning. --- # 25. Security and Integrity Conformance MAY include: - artifact hash checks; - signature checks; - manifest validation; - supply-chain integrity checks. These support evidence and preservation. They do not replace semantic validation. A cryptographically intact wrong artifact remains wrong. --- # 26. Conformance Declaration A conforming implementation SHOULD publish a declaration stating: ```text Implementation: Version: Claimed class: Spatial Ground Specification: SG-CJSON: FSF dependency: Reference Vector corpus: Conformance report: Status: ``` The declaration SHALL point to preserved evidence. A declaration without test evidence SHALL NOT constitute proof of conformance. --- # 27. No Self-Certification Privilege An implementation MAY run its own conformance suite. Self-testing does not grant special canonical authority. Independent reproduction remains required for mature architecture. --- # 28. Gate-B and Maturity Consequences This Conformance framework completes the architectural design of how Spatial Ground implementations will be tested. Before Gate B adoption of the final Specification, BitPangea SHOULD ensure that: - every normative rule in the Specification maps to at least one Conformance obligation; - no Conformance rule invents a new Specification rule; - unresolved FSF dependencies are marked rather than silently resolved; - canonical serialization and limit rules are fully testable. Before final canonical instance adoption, BitPangea SHALL additionally require: - canonical Reference Vectors; - at least one primary implementation; - at least one independent SG-C4 implementation; - adversarial testing; - reconstruction testing. --- # 29. Conformance Matrix | Area | Required Class | Mandatory | |---|---:|---:| | SG-CJSON structure | SG-C1 | Yes | | Canonicalization | SG-C1 | Yes | | FSF dependency validation | SG-C1 | Yes | | Membership evaluation | SG-C2 | Yes | | Invalid-input separation | SG-C2 | Yes | | Exact limit membership | SG-C2 | Yes | | Hidden-state independence | SG-C2 | Yes | | Semantic equivalence | SG-C3 | Yes | | Refinement closure | SG-C3 | Yes where FSF permits | | Connectedness | SG-C3 | Candidate instance | | Non-emptiness | SG-C3 | Candidate instance | | Extent evidence | SG-C3 | Candidate instance | | Cross-platform reproduction | SG-C4 | Yes | | Independent implementation | SG-C4 | Yes for maturity | --- # 30. Standing **SPATIAL GROUND CONFORMANCE — BUILT** **CONFORMANCE CLASSES — ESTABLISHED** **MANDATORY CORE — ESTABLISHED** **FAILURE CONDITIONS — ESTABLISHED** **INDEPENDENT IMPLEMENTATION CLASS — ESTABLISHED** **RECONSTRUCTION REQUIREMENT — ESTABLISHED** **REFERENCE VECTOR TEST FAMILIES — DEFINED** **CANONICAL REFERENCE VECTOR CORPUS — NEXT** **GATE B — NOT YET OPEN** --- # 31. Governing Closing Statements > **Specification defines the truth. Conformance proves that an implementation follows it.** > **A validator may detect Ground truth. It may not create Ground truth.** > **Many implementations. One membership truth.** > **If independent implementations disagree, the architecture has discovered a problem—not a second canon.**