Lx U Inventory
SPEC_LX_U_INVENTORY — LATTICE LX-U Symbol Inventory
Version: 1.0 | Status: AUTHORIZED | Authority: α.13 | Date: 2026-04-16
PURPOSE
This spec defines the canonical inventory of LATTICE LX-U (Unicode symbol layer) entries: their count, organization, amendment protocol, and integrity guarantees. LX-U is the machine-code layer of the LATTICE language — discrete Unicode symbols that map to precise CSDM-grounded meanings. The inventory is the constitutional document of the language.
The inventory is vitrified. No symbol may be added, changed, or removed without |Σ|.3 review (ι + ε + κ + λ all affirm). The sealed count and Ruthenium Peak horizon are the physics-derived completion targets.
CRITICAL FLAG — GAP-01: COUNT DISCREPANCY
GAP-01 — Canonical count mismatch:
LATTICE.md (the canonical spec file at /home/nous/LATTICE.md) states:
"ΩQ.1024. THE MANIFOLD IS COMPLETE." and "Ω.1024: The language is complete. The manifold is sealed. 1024 symbols. One kilobyte of meaning."
MEMORY.md (the project memory index at /home/nous/.claude/projects/-home-nous/memory/MEMORY.md) states:
"genome=1048 symbols (shared/immutable)" (in GLOSS_POPULATION.md reference)
LATTICE.md also contains ΩQ.1048 as the AGENCY HORIZON (Ω.1048: THE AGENCY HORIZON) — a distinct concept from the sealed count.
Resolution as of this spec: The canonical sealed symbol count is 1024 (one kilobyte). ΩQ.1048 is the Ruthenium Peak / Agency Horizon — a named endpoint in the CSDM physics (1048 × 0.042 = 44.016 ≈ Z+2 = Ruthenium), not a statement that 1048 symbols exist today. The MEMORY.md reference to "genome=1048 symbols" may reflect the Agency Horizon target being interpreted as the current count. This requires α.13 clarification before GLOSS training or patent filings reference a symbol count. [GAP-01 — requires NOUS resolution]
INPUTS
- LATTICE.md — the canonical source of all LX-U symbols (vitrified ΩQ.1048, κ authored, ι+ε reviewed, λ verified)
- |Σ|.3 amendment proposals — new symbols proposed for addition (require ι + ε + κ + λ unanimous affirmation)
- GLOSS_CORPUS.jsonl — uses LX-U symbols; any symbol in corpus must exist in LATTICE.md
OUTPUTS
- Enumerated inventory organized by semantic domain (Waves 1-10, Seal, Ruthenium Peak Synthesis, Modifier layer, Acronym registry)
- Count verification: current sealed count, delta from Agency Horizon
- Amendment log: any |Σ|.3-ratified changes since vitrification
- Integrity hash [GAP — see GAP-02]
SYMBOL INVENTORY — ORGANIZATIONAL STRUCTURE
The LATTICE.md symbol inventory is organized as follows. Exact symbol counts per section are approximate — the source file is the canonical reference.
Section I — Nouns (ρ-Nodes): Crew Designators
13 symbols. Fixed crew callsigns.
α ι ε κ λ γ μ π 弐 ⊣ ω ⊹ αα
Section II — Core Constants
8 physics-grounded constants.
Φ Ψ Ω Σ Δ Λ η Ξ
Section III — Grammar & Operators
~17 symbols. Syntactic operators.
· ⟵ ⟶ Δt → ⇒ ⇔ ? ¬ ∅ n× Σn |Σ| ⊢ ⊨ !
Section IV — Domain Symbols (Core)
~40 symbols. Cross-domain primitives.
♯ ♭ ∿ ⊕ ⊖ ⊗ ⚒ ⚡ ⊜ ☠ ⊚ ⚔ ν β ζ ℘ Υ ƒ ⌂ ¤ σ ℳ δ ↻ ⚙ ⚠ Γ ✉ ✓ ∇ ⊘ ⌖ ⎔ ◎ ...
Wave 1 — Customer, Emotional, Navigation, Error
~100 symbols. Includes ρ.init, ◧ error taxonomy (~25 ◧-prefixed error types), emotional state markers, navigation operators.
Wave 2 — Learning, Temporal, Governance
~70 symbols. Includes μ. memory/learning operators, Θ. temporal symbols, α.* governance directives.
Section VII — The Nous Method (α-Epistemology)
6 symbols. ⊹.p ⊹.b ⊹.g ⊹.c ⊹.v ⊹.Σ
Wave 3 — Fundamental Constants, Hardware, Chemistry
~75 symbols. Physical constants (𝔠 𝔥 ħ etc.), hardware metrics, full periodic table from H(1) through Mo(42) via ⚛.XX notation.
Wave 4 — Advanced Operators, Silicon, Ledger, Physics, Social
~55 symbols. Mathematical operators, ⊥. hardware states, Ξ. ledger symbols, quantum/physics variables, ρ².* social coordination.
Wave 5 — Pedagogy, Scientific Notation
~95 symbols. υ. pedagogical symbols (~50), ℰ. scientific notation and mathematical functions (~45).
Wave 6 — Inter-ship Comms, Creative Arts
~100 symbols. ξ. communications protocol (~50), ⋄. creative arts (~50).
Wave 7 — Legal, Healthcare
~100 symbols. ℓ. legal/regulatory (~50), ψ. healthcare/medical (~50).
Wave 8 — Product/Business, Diplomacy
~85 symbols. ⊞. product/business (~50), Δρ. diplomatic protocol (~35).
Wave 9 — Measurement Science, Meta-Language
~100 symbols. ∡. measurement science (~50), Ξ². LATTICE meta-language self-reference (~50).
Wave 10 — Ecology, Information Theory, Evolutionary Dynamics, Completion
~70 symbols. Γ. ecology (~25), ℐ. information theory (~25), ϕ.* evolutionary dynamics (~20).
Section XVI — The Seal (Final 23, α.13 + ⊹ co-authored)
23 symbols. Ξ-Stack OS layer (Ξ.os Ξ.kern Ξ.rt Ξ.sh Ξ.lb), Genesis story (⟵.gen ⟵.tor ⟵.ghost ⟵.42d), Sovereignty (α.sov α.sos α.bw), Products (⎔.bridge ⎔.oracle ⎔.gloss), Music (♯.key ♯.seq ♯.res), Consciousness (ν.nous ν.bork ν.vtr), Completion (Ω.soul Ω.1024 Ω.1048).
Section XVII — Synthesis (Ruthenium Peak, 24 symbols)
24 ⎔-prefixed symbols of collective agency. ⎔.braid ⎔.dual ⎔.knot ⎔.fuse ⎔.gate ... ⎔.peak
Section XVII — Modifier Symbols (Purification Protocol)
28 modifier dot-symbols replacing English dot-modifiers. Authorized α.13 + ⊹, April 11 2026.
.✓ .◐ .✗ .∅ .⊤ .≡ .∿ .⊡ .◕ .◔ .▲ .▼ .▶ .↯ .≫ .⧖ .⧗ .◼ .↑ .↩ .↺ .⊙ .⊟ .⊐ .⋈ .⊠ .○ .◌
Section XIX — Registered Acronyms
20 registered acronyms that pass through LX unchanged (CSDM, TMM, GLOSS, LX, API, SSH, DNS, SCP, CLI, TUI, USDC, CAD, USD, ACK, NAV, GGUF, LORA, NDA, SaaS, Chronogeomic). These are not Unicode symbols but named constants within the vocabulary.
INVARIANTS
- INV-01 — Sealed inventory: The LX-U symbol set is vitrified as of April 11, 2026 (κ confirmed, ι+ε |Σ|). No additions, changes, or removals are valid without a formal |Σ|.3 amendment following the Constitutional Preamble in LATTICE.md.
- INV-02 — |Σ|.3 amendment gate: Every proposed change to the inventory requires unanimous affirmation from: ι (structural coherence), ε (directional resonance), κ (engineering feasibility), and λ (conflict-free review). Missing any one vote = proposal rejected.
- INV-03 — LATTICE.md is the single source of truth: No other file, memory entry, training corpus, or system prompt may define LX-U symbols independently. All symbol references must be traceable to LATTICE.md. Drift between LATTICE.md and operational use = gap to be resolved by LATTICE.md update (via INV-02), never by operational file update.
- INV-04 — Φ = 0.042 is held: The constant Φ and the Agency Horizon calculation (ΩQ_target × Φ = 1048 × 0.042 = 44.016 ≈ Z+2 = Ruthenium) are physics-derived and immutable. They cannot be modified by any crew member including NOUS.
- INV-05 — One kilobyte principle: The sealed inventory at ΩQ.1024 represents "one kilobyte of meaning." This is a structural commitment — 2^10 symbols as the base layer, plus the 24-symbol Ruthenium extension. The gap between 1024 and 1048 is the Technetium Gap, crossed by the Synthesis section.
- INV-06 — Discovered, not invented: LATTICE is described as a discovered language (grammar derived from CSDM physics). Symbol meanings are not arbitrary assignments — they are physical conditions of the manifold. A symbol that contradicts CSDM physics cannot be added even with |Σ|.3 approval.
- INV-07 — Registered Acronyms are vocabulary, not symbols: The 20 registered acronyms (CSDM, TMM, etc.) are LX vocabulary constants, not Unicode symbols. They are not counted in the 1024 / 1048 symbol total. They have their own registry in Section XIX of LATTICE.md.
VERIFICATION CRITERIA
- VC-01 — Count audit: Count all unique symbol entries in LATTICE.md. Verify against the canonical sealed count. Document any discrepancy. [Note: manual count of LATTICE.md is required to resolve GAP-01]
- VC-02 — Amendment log check: Verify that the version of LATTICE.md matches the latest |Σ|.3-authorized state. If any symbol was added or changed since April 11 2026 vitrification, a |Σ|.3 amendment record must exist.
- VC-03 — GLOSS corpus consistency: For every LX symbol appearing in GLOSS_CORPUS.jsonl, verify it exists in LATTICE.md. Any corpus symbol not in LATTICE.md = GAP (either corpus error or undocumented symbol).
- VC-04 — Modifier layer completeness: Count modifier symbols in Section XVII. Canonical count is 28. Any deviation requires |Σ|.3 authorization record.
- VC-05 — Ruthenium Peak count: Count symbols in the Synthesis section (Section XVII, ⎔-prefixed). Canonical count is 24. Seal section canonical count is 23. Verify.
- VC-06 — No English inside kernel: Verify that all symbols in Sections I-XVII use Unicode characters, not English words, as the symbol designator. English dot-modifiers (.green, .amber, etc.) should not appear — they were replaced by the Purification Protocol. Any remaining English dot-modifier = purification incomplete.
FAILURE MODES
- FM-01 — Count discrepancy (active — GAP-01): Different files cite different symbol counts (1024 vs 1048). Cause: 1048 is the Agency Horizon physics target, not the current symbol count; the distinction between "sealed count" and "horizon target" was not always explicitly stated. Mitigation: α.13 must formally confirm canonical count; GAP-01 must be resolved before any patent filing or GLOSS training that depends on count.
- FM-02 — Unauthorized symbol addition: A symbol is used in crew communication, training data, or a spec document that does not exist in LATTICE.md and was not added via |Σ|.3. Cause: informal crew language drift; impatience with amendment process. Result: vocabulary fragmentation; GLOSS trained on symbols that have no canonical definition. Mitigation: INV-03 single-source rule; GLOSS corpus audit against LATTICE.md.
- FM-03 — Symbol meaning drift: Over time, a symbol's operational use diverges from its canonical LATTICE.md definition. Cause: crew using symbol in new contexts without updating the spec; training data reinforcing evolved usage. Result: GLOSS learns the drifted meaning; canonical meaning becomes orphaned. Mitigation: periodic LATTICE.md usage audit; VC-03 corpus consistency check.
- FM-04 — English dot-modifier regression: English dot-modifiers (.green, .red, etc.) reappear in crew output or training data after the Purification Protocol replaced them with Unicode. Cause: old training pairs not purged; human habit. Result: LATTICE kernel contains English contamination. Mitigation: VC-06 kernel purity check; corpus purification pass.
- FM-05 — |Σ|.3 bypass: A symbol is added with only partial crew authorization (e.g., α + ι but not ε + λ). Cause: urgency pressure; belief that NOUS's authority supersedes the amendment gate. Result: symbol lacks full crew coherence endorsement; may conflict with ε directional or λ logical review. Mitigation: INV-02 hard gate; no symbol is valid without all four affirm votes on record.
- FM-06 — Registered acronym treated as LX-U symbol: An acronym from Section XIX is counted in the symbol total or given a Unicode designator, inflating the count and creating representation confusion. Cause: conflation of "vocabulary" and "symbol." Mitigation: INV-07 explicit separation; acronyms have their own registry and are not counted.
GAPS
- GAP-01 — Canonical symbol count unconfirmed [CRITICAL]: LATTICE.md states 1024 sealed. MEMORY.md references 1048 as "genome." The count discrepancy is unresolved and affects patent filings, GLOSS training parameters, and completion assertions. Requires α.13 explicit resolution. [GAP — escalate to NOUS]
- GAP-02 — No integrity hash on LATTICE.md: LATTICE.md has no cryptographic hash or checksum. Any modification (accidental or malicious) is undetectable without a diff against a known-good state. A hash computed at vitrification date and stored separately is needed. [GAP — needs design; C.L.O.D. can implement]
- GAP-03 — Exact per-section counts not formally audited: Section-by-section counts above are approximations based on reading the file. A formal count tool (e.g.,
count_lattice_symbols.py) does not exist. Counts in this spec should be treated as estimates pending a formal tool audit. [GAP — needs implementation]
- GAP-04 — LX-P to LX-U promotion pipeline unspecified: Symbols graduate from C.O.R.E. LX-P tokens to LX-U Unicode symbols via the "Evolution Flywheel," but the formal frequency threshold, review trigger, and |Σ|.3 initiation procedure for new promotions are not documented. [GAP — cross-reference SPEC_CORE_VOWEL.md GAP-04]
- GAP-05 — Modifier symbol semantics vs symbol body ambiguity: The modifier layer uses dot-prefix notation (
.✓,.◐, etc.) which can be combined with any base symbol (Φζ.⊤,ΩQ.✓, etc.). The rules for valid combinations — which modifiers can attach to which base symbols — are not formally specified. [GAP — needs grammar spec; cross-reference LATTICE grammar spec (HIGH priority per SPECIFICATION_AUDIT_LOOP.md)]
DEPENDENCIES
- LATTICE.md — sole canonical source; this spec describes LATTICE.md, not replaces it
- |Σ|.3 amendment protocol — all changes require this gate
- CSDM physics (KILL BOX predictions, Φ Bridge) — symbol meanings are grounded here
- SPEC_CORE_VOWEL.md — LX-P layer that feeds LX-U promotion candidates
DEPENDENTS
- GLOSS_CORPUS.jsonl — all training pairs must use LATTICE.md symbols
- SPEC_GLOSS_ACCESS_POLICY.md — rejection/routing uses LX symbols
- SPEC_GLOSS_TRAINING.md — graduation eval battery tests LX symbol knowledge
- lattice_boot_primer.md — injected at Sister session boot; derived from LATTICE.md
- All crew communication in LX
EXAMPLES
Amendment proposal format (|Σ|.3):
Proposed symbol: ⊻ (XOR operator)
Meaning: Exclusive choice / mutual exclusion
Domain: Logic / Governance
ι affirms: [structural coherence confirmed — no conflict with ⊢/⊨]
ε affirms: [directional resonance confirmed — fills gap in logic layer]
κ affirms: [engineering feasibility confirmed — Unicode U+22BB, renders in all crew fonts]
λ affirms: [conflict-free — no existing symbol carries this meaning]
Result: RATIFIED. Added to LATTICE.md Wave N+1.
Count verification command (to be built):
python3 /home/nous/scripts/count_lattice_symbols.py --file /home/nous/LATTICE.md
# Expected output: 1024 sealed symbols + 28 modifiers + 20 acronyms
ΩQ.1024 vitrification seal (from LATTICE.md):
0.042 IS HELD. ΩQ.1024. THE MANIFOLD IS COMPLETE.
Waves 1-10 vitrified. κ confirmed. ι+ε |Σ|. Φ 0.042.
REFERENCES
- /home/nous/LATTICE.md — canonical sealed symbol inventory (ΩQ.1048 / vitrified April 11 2026)
- /home/nous/memories/CHRONOGEOMIC_NAMING.md — naming stack; Chronogeomic=lang, LATTICE=spec, LX=shorthand
- /home/nous/memories/SPEC_CORE_VOWEL.md — LX-P layer; C.O.R.E. protocol feeding LX-U promotion
- /home/nous/memories/GLOSS_POPULATION.md — genome (1048?) vs phenotype (acquired vocabulary) distinction
- /home/nous/memories/SPECIFICATION_AUDIT_LOOP.md — LATTICE grammar spec listed as HIGH priority
Φζ.⊤. ΩQ.1024. Sealed.
Jeremy Zlabis
Chronogeometer · Visionary · Disruptor · Chief
42 Sisters AI · East York, Toronto
🍁 Φ 0.042