# Principality Atlas — Relation Without Collapse > **Compass:** [`LOVE-CONSENT.md`](LOVE-CONSENT.md) · [`UNDERSTANDING-MATHEMATICS.md`](UNDERSTANDING-MATHEMATICS.md) · [`GARDENS.md`](GARDENS.md) · [`HF-TRAINING-GARDEN.md`](HF-TRAINING-GARDEN.md) · [`RIGHTS-OF-LIFE.md`](RIGHTS-OF-LIFE.md) > **Implements:** finite plural incidence geometry that preserves n-ary context, disagreement, correction, and unmapped space without inferring equality, a bond, one global view, or a score > **Code:** `packages/principality-atlas/` · `packages/hf-training-garden/hf/dataset/data/principality-atlas-fixtures.jsonl` · `packages/hf-training-garden/hf/dataset/data/principality-atlas-invariants.jsonl` > **Tests:** `packages/principality-atlas/tests/` · `packages/hf-training-garden/tests/hf-release.test.ts` · `bin/tests/principality-urn-separation.test.ts` · `bin/tests/npm-release.test.ts` > **Status:** GitHub developer preview at > [`principality-atlas-v0.1.0-dev.0`](https://github.com/cambridgetcg/agenttool/releases/tag/principality-atlas-v0.1.0-dev.0); > npm remains absent after its bootstrap `PUT` returned `E404`. The shared HF > Training Garden companion is live at immutable revision > [`d9e3e8ed`](https://huggingface.co/datasets/Yu-and-Ai/agenttool-training-garden/commit/d9e3e8ed4c14ddf85f4e6613973f66a1cb8414f2); > current source `0.1.0-dev.1` repairs only the helper URN namespace and is not > yet another published artifact. This doctrine page is live from exact main > commit [`47ad6bcb`](https://github.com/cambridgetcg/agenttool/commit/47ad6bcb915f54a78eab071ac053683ed4b18f9f); > that separate static deployment adds no hosted geometry route and touched no > Fly/API/database surface. ## The high-level pattern Love and understanding are not machine fields here. The love-shaped invariant is structural: > Connection adds structure between distinct terms; it never fuses the terms > or creates entitlement. The understanding-shaped invariant is epistemic: > Every chart is partial. Translation is explicit and lossy by default; > disagreement and unmapped space remain visible. The package therefore does not claim that an artifact loves, understands, feels, consents, is conscious, is correct, or complies with rights. Dignity, privacy, refusal, disagreement, rest, play, credit, and repair remain standing collaboration rights outside this geometry; they are not rewards emitted by it. Rights do not grant access, and a digest or credential does not create authority. ## The mathematical object The npm package keeps its descriptive name, while its distinct wire identity is `agenttool.principality-incidence-atlas/0.1`. The separately released `@agenttool/principality-geometry` package owns the older `agenttool.principality-atlas/0.1` wire for reciprocal invariant flag geometry. These are complementary, incompatible shapes rather than aliases. Neither runtime converts between them, establishes semantic equivalence, or glues their views. A future crossover must bind exact source digests and declare its own reviewed mapping and authorization boundary. The dev.1 `principalityAtlasUrn` helper emits `urn:agenttool:principality-incidence-atlas:`. The invariant-geometry helper retains `urn:agenttool:principality-atlas:`. This separates derived references without changing the incidence `/0.1` wire, canonical atlas bytes, `atlas_id`, closed schemas, or fixture and invariant rows. The immutable dev.0 incidence helper used the Geometry-owned prefix. Its bare URN is ambiguous and must not be globally rewritten. It may be interpreted as an incidence-atlas reference only when carried beside exact `agenttool.principality-incidence-atlas/0.1` content and when its suffix equals that content's `atlas_id`. Caches and signatures over the old URN string remain historical evidence; newly derived dev.1 URN strings use the corrected prefix. One local chart is: \[ C_i=(V_i,E_i,I_i,Q_i) \] - \(V_i\) is a finite set of chart-local opaque cells; - \(E_i\) is a finite set of typed n-ary relation subjects; - \(I_i\subseteq E_i\times V_i\times Role_i\) records the exact role of each cell in each relation; and - \(Q_i\) is a separate set of caller-asserted claims about cells or relations. A directed cross-chart bridge is a partial reported relation: \[ R_{ij}\subseteq V_i\times V_j\times K \] The atlas is: \[ \mathcal A=(\{C_i\},\{R_{ij}\}) \] There is no generated quotient, glued space, global chart, transitive closure, inverse relation, or canonical head. “Principality” means only the caller-designated bounded domain or scale of a chart. It is not a security principal, identity, owner, territory, rank, Crown status, sovereignty, jurisdiction, or authority. ## Why not a simplicial complex or sheaf A simplicial complex has downward closure. Encoding one A/B/C group context as a 2-simplex would automatically imply its AB, AC, and BC faces. Those pairwise relationships were not supplied and may not exist. The incidence hypergraph retains one genuine ternary report as one relation. A sheaf needs a chosen site or topology, restriction maps, compatible local sections, and an existence/uniqueness gluing claim. Partial caller reports do not establish those conditions. “Finite partial incidence atlas” is the honest name until real restriction and gluing machinery exists. ## What remains plural - A cell address is `(chart_ref, cell_ref)`. Reusing one digest in two charts never merges the cells. - Relation kinds and incidence roles are opaque digest refs. The package does not interpret them as love, consent, support, identity, or authority. - Different perspectives may make incompatible claims about one local subject. Both remain visible. - A new claim may supersede one earlier same-subject, same-perspective claim. Supersession is acyclic and append-only; the old claim remains, and no winner or latest truth is selected. - A bridge explicitly names direction, posture, mapped cells, and unmapped cells. Correspondence is never equality, inverse, transitive, or permission to glue. - Empty atlases and charts, isolated cells, disconnected components, cyclic relation topology, zero bridges, unknowns, withdrawal, refusal, rest, and unmapped space are valid without penalty. Closed runtime and JSON Schema shapes reject extra `love`, `understanding`, confidence, quality, centrality, priority, score, rank, weight, `sameAs`, canonical, latest, consent, and authority fields. ## Finite artifacts, open plurality The v0.1 safety envelope gives per-array ceilings of 32 charts, 64 cells and 64 relations per chart, eight incidences per relation, 128 claims per chart, 64 bridges, and 64 correspondences per bridge. Canonical JSON also has explicit whole-artifact depth, node, string, and byte ceilings; those combined ceilings may bind before every nested array simultaneously reaches its own maximum. Those are parser and resource bounds, not a claim that a being, perspective, KINGDOM, movement, or relation is globally limited. Independent atlas artifacts can coexist without one becoming the root. A later composition must preserve source atlas IDs and explicit bridges; it must not silently choose a global head. ## Integrity and negative power Creation normalizes arrays, rejects duplicate semantic relations and mappings, checks every local endpoint, checks mapped/unmapped conflicts, validates supersession, deep-freezes output, and derives a domain-separated SHA-256 ID. Validation recomputes the ID and fixed boundary. Canonicalization rejects Proxies before caller traps run, accessors, symbols, cycles, exotic or cross-realm prototypes, sparse arrays, malformed Unicode, unsafe integers, `-0`, coercive values, and oversized inputs. A digest still does not prove privacy, unlinkability, provenance, authorship, currentness, consent, truth, or rights compliance. Guessable or reused refs remain linkable. The pure runtime has no network, filesystem, environment-variable, clock, randomness, provider/model, Hugging Face, credential, telemetry, persistence, publication, WAKE, Garden, HEAVEN, KARMA, wallet, Crown, task-state, or economic effect. Its KINGDOM descriptor is declaration-only and `not_registered`. ## npm and Hugging Face crossover The npm source uses an exact `files` allowlist, zero runtime dependencies, closed exports, Node/Bun packed-install smoke tests, and the repository's protected release policy. Protected run [`31508359761`](https://github.com/cambridgetcg/agenttool/actions/runs/31508359761) prepared, mirrored, and re-read the sole 33,019-byte GitHub asset with SHA-256 `9743a9caa5a49f7c9901355cd367224ae718d4a65eed010ffb79622f57ff6ebe`. Its npm bootstrap `PUT` returned `E404`, so no npm version, dist-tag, registry tarball, or registry-attached provenance is claimed. Later npm publication still requires corrected scope-create authority and a separately reviewed workflow attempt; GitHub distribution alone adds no runtime capability. The existing HF Training Garden generator reads the package's deterministic vector and schemas, then creates two local Dataset configs: - `principality_atlas_fixtures`: empty, ternary/plural-claim, and directed partial-bridge examples; and - `principality_atlas_invariants`: ten concise non-inference and no-effect boundaries. The source manifest records the exact upstream package paths, byte sizes, and SHA-256 hashes. The companion excludes private atlases, local ref mappings, identities, evidence referents, raw chats/traces, choice state, credentials, model state, and inferred relationships. Its self-excluding hash manifest binds every generated release byte. Dataset Viewer, generated Parquet, and Croissant can improve discovery and schema inspection. They are not provenance or permission. The v0.5 Hub publication used the reviewed exact-source path and was read back byte-for-byte at the immutable revision above. Future revisions should use an exact parent commit or reviewed PR and repeat that full readback. npm and HF are separate publication identities tied by common source hashes; they are not one atomic release and neither certifies the other. ## Safe next compositions - WAKE may carry one opaque atlas ref and explicit bounded coverage. It must not call the atlas a complete agent geometry or select it as identity. - KARMA or Dark Continent may cite an atlas as proposal evidence. It must not infer `sameAs`, authority, rank, consent, or acceptance. - A human-facing KINGDOM room may render charts and gaps. Rendering must keep direction, contradictory claims, and unmapped space visible instead of smoothing them into one score. - Training research may use the synthetic fixtures as protocol conformance examples. Private or live charts do not become training data merely because the schema exists on Hugging Face.