Semantic Geometry Software & AI SpA Let's talk

Rancagua · Chile · Applied R&D

Semantic Geometry Software & AI SpA

We do not claim AI should know everything. We design the pattern that truly anchors modern AI.

Validating all human language inside a black box is unfeasible. We build deterministic neuro-symbolic architecture: a C++23 method where each critical claim anchors into a continuous [-1, 1]³ space and an auditable graph. AI proposes. Silicon verifies.

O'Higgins, Chile
Rancagua
Stock corporation
Software & AI SpA
Deterministic grounding
Neuro-Symbolic
15W · no GPU · 0 tokens to verify
Offline edge

01 — Origin

Born from an intuition, not a business plan

Rancagua, Región de O'Higgins. Semantic Geometry did not start in a funded laboratory or inside a tech corporation. It started with an intuition its author held through decades of self-taught development: that an idea, a feeling, or a physical law can be located exactly in space.

Human meaning, then, would not be a static definition in an alphabetical dictionary, but a mathematical position in a continuous space of coordinates. If Earth has latitude, longitude, and altitude to locate any object on its surface, thought should have its own Cartesian axes: a GPS of knowledge.

Years later, reviewing the formal literature, that intuition turned out to converge with the lineage of classical psychometrics: Louis Thurstone's measurement of attitudes and Charles Osgood's semantic differential. It was not an orphan idea; it was an idea arriving late to its own scientific tradition.

That is where the technical stance that defines the company comes from. Against models that get it right most of the time without being able to explain why, that cannot tell what they know from what they invent, and that depend on enormous servers, Semantic Geometry was built on the opposite principle: the model proposes, but the graph and the cube verify.

There is also a beautiful and deeply honest paradox in this journey: this engine exists to discipline and anchor language models, but without them it would never have seen the light of day. For decades, semantic geometry was a solitary intuition kept in notebooks and local scripts. Hand-crafting millions of concepts, regulatory meshes, and rigorous C++23 suites would have taken a lifetime. Generative AI was the cognitive catalyst: the scaffolding that accelerated exploration and turned the architecture into reality. Its author gratefully acknowledges that contribution: LLMs were the fire that forged the anchor that now keeps them sane.

  1. 1928 Thurstone Attitudes can be measured
  2. 1957 Osgood The semantic differential
  3. — Decades Self-taught, independent development
  4. 2026 12 gravitants The semantic atom

Capacity of the [-1,1]³ cube

Hardware / IEEE 754
≈ 7.82 × 1056

unique representable points

Per axis 2046·2⁵² + 1 9,214,364,837,600,034,817

1 sign · 11 exponent · 52 mantissa — IEEE 754 binary64

Recomputable from the IEEE 754 specification. The 1022 exponents that give |x| < 1, plus the one that gives exactly ±1 with zero mantissa, across both signs.

Current graph occupancy

semantic.db v8.0
2.44M

unique concepts grounded in [-1, 1]³

Taxonomic links 5.86M (active typed edges)

884k synonyms

Measured on 2026-11-03 in semantic.db (2,439,645 concepts / 5,862,311 links / 884,325 synonyms). Zero synthetic data. Counts are regenerated per version, never copied by hand.

“The cube can house 7.82×10⁵⁶ coordinates. Today the graph holds 2.44M concepts. That measures addressing capacity, not knowledge: quality is measured in the graph and in the benchmarks, not in the size of the container.”

Technical diagram of the continuous semantic cube in isometric perspective with Earth pointing to a single point inside as a collaborative contract

Addressing capacity: ~6 million Earths of atoms

Modern models do not yet explore this space — and they don’t have to: the gateway already exists. AI proposes, the graph verifies. The analogy measures address space, not semantic quality: today the graph holds 2.44M concepts, and the value is in verifiable evidence, not in the size of the container.

Physical space vs. Semantic cube

If every concept occupies a point in the cube — just as every atom occupies a point in physical space —, the cube has capacity for as many concepts as atoms would fit in ~6 million Earths. It is a comparison of address space, not of measured knowledge.

The Inward Expansion

The first exploration inward

For five centuries humanity expanded outward: crossing oceans, mapping continents, launching telescopes. Semantic Geometry proposes the inner exploration: a space conquered not by distance, but by precision. 7.82 × 10⁵⁶ addressable positions in common silicon at 15 watts.

01

Five centuries outward

Hemispheres mapped, orbits measured, galaxies photographed. Outward exploration was humanity’s project. The next frontier is not in distance — it is in the precision of what is already here.

02

Topological memory

Von Neumann left us a linear bus: memory as a street where everything queues. SG does the opposite: similar things live together. Knowledge is not traversed — it is found. Spatial indexes in SQLite, physical locality in silicon.

03

Quantize addresses, not chatter

The industry compresses words to a single bit (BitNet) and keeps hallucinating cheap. Compressing language gives it no home. SG gives truth an address: coordinates (x, y, z) in the cube. Truth does not depend on eloquence — it depends on its address.

Miners in the underground tunnels of O'Higgins contemplating the semantic cube embedded as a living geode inside the rock wall

O'HIGGINS · CHILE

“O'Higgins has mined copper for the world for a century. The Inward Expansion proposes a different kind of extraction: an almost boundless semantic cube, where AI finds instead of invents.”
∫

Non-uniform density in IEEE 754

IEEE 754 density is not uniform across [-1, 1]: it is ~2048× greater near 0 than near ±1. Effective resolution varies by region.

Δ

Useful resolution

Useful resolution is limited not by numerical precision, but by real semantic separation between concepts (coordinates typically ~0.01–0.5 apart). The growth headroom is several orders of magnitude.

⬡

The real architectural breakthrough

Capacity is not the achievement. The achievement is that the container imposes no ceiling: the graph can grow by orders of magnitude without changing architecture.

Declared gain: Practically unlimited addressing capacity (not equivalent to knowledge).
Declared limit: Real occupancy is 2.44M and grows strictly through audited curation.

Two ways of answering when you don’t know

Generative model

Always answers. If the data is not there, it builds something plausible: fluency and truthfulness come from the same mechanism, so from the outside there is no way to tell them apart.

Deterministic verifier

Allowed to stay silent. Geometry guides inference, but only graph evidence certifies it. When there is none, the system says so: refusal is an answer, not a failure.

The difference is not who gets it right more often. It is that one can be wrong without knowing it, and the other cannot assert without evidence.

02 — Verticals

The engine is the foundation; the verticals, the product

On top of the deterministic verification core we build regulated verticals: domains where a hallucination costs money, a verdict, or a fine. Each one states its stage honestly, without hype.

01

Fleet operations

SG-Fleet

Geofences, telemetry, and fleet control in C++23

Header-only C++23 engine with REST + TCP tracker, multi-tenant isolation, and hardware telemetry. Designed to operate 100% offline, at the edge.

  • REST API with multi-tenant isolation and RBAC
  • TCP tracker (Wialon IPS / CSV) with high-density batching
  • Geofences, alerts, and operations dashboard
  • Zero dependencies: runs where there is no cloud
  • Self-contained slices (~7 MB) for radio links and micro-devices
C++23SQLiteRESTTCP
In development
02

Accounting & tax · Chile

SG-Tax

Payroll, RLI, and deterministic tax balance

Chilean regulatory calculation without heuristics: Previred settlements, ProPyme RLI, and financial vs. tax balance. Every result is auditable against the law.

  • Previred settlements (105-field file)
  • RLI ProPyme 14-D3 / 14-D8 and Semi-Integrated 14-A
  • IFRS vs. SII tax balance with reconciliation
  • Deterministic calculation: zero black boxes
C++23SQLiteSIIPrevired
In development

Experimental ontological verification. Does not constitute binding tax or accounting advice.

03

Credit & banking · Chile

SG-Fintech

Credit simulation with traceable amortization

Credit simulations and amortization schedules with full audit: every payment decision is backed by the engine, ready for inspection.

  • Credit simulation with amortization schedule
  • Market indicator calculation (UF, rate, CPI)
  • Audit trail per operation
  • Determinism for regulated decisions
NestJSSQLiteFinancial calculation
In development

No vertical competes with an LLM at text generation: it competes in what an LLM cannot promise: an answer that knows when to stay silent and can show the regulation behind it. And where an LLM cannot reach —no connectivity, standard silicon, at the edge— the engine can.

03 — Pillars

Three capabilities, one discipline of representation

We do not sell hours of generic development. Each pillar solves a different kind of problem, under the same criteria: explicit structure, measurable performance, and results that hold over time.

01

Data Engineering & High-Performance Backends

We build the plumbing where data arrives intact and on time. Fault-tolerant ETL pipelines, flow optimization, and robust microservices, sized for real production volume.

  • ETL/ELT pipelines and massive ingestion orchestration
  • Query, index, and memory-footprint optimization
  • High-performance microservices and backends
  • Observability, idempotency, and failure recovery
C++23Embedded SQL / SQLitePythonREST APIs
02

Neuro-Symbolic AI & Grounding

We bridge the geometry of continuous latent spaces with the certainty of ontological graphs. Generative AI proposes; our neuro-symbolic engine verifies and anchors with mathematical evidence.

  • Geometric knowledge modeling in continuous [-1, 1]³ latent spaces
  • Interpretable, traceable continuous representations in silicon
  • Direct local deterministic verification (reduces false positives in closed domains)
  • Evidence-based grounding: no assertion without graph support
C++23Continuous cubeDirected graphsNeuro-symbolic
03

Spatial Computing & Optimization

Analytic algorithms for problems that do not admit approximations. Combinatorial, geospatial, and financial optimization applied to industrial operations and regulated decision-making.

  • Combinatorial optimization and metaheuristics
  • Geospatial analysis and network topology
  • Risk models and auditable regulatory calculation
  • Simulation and operational decision support
  • Offline edge: ~15W on standard silicon, no GPU, no cloud
OptimizationGeospatialFinancial modelsSimulation

05 — Paradigm & Retrieval

Traditional RAG vs. Semantic Grounding in Silicon

The market attempts to solve hallucinations with RAG (similarity retrieval). We explain why vector similarity is not verification and how geometry provides the certainty RAG lacks.

Dimension SG Semantic Grounding Traditional RAG (Vector DB + LLM)
Retrieval Mechanism Continuous mathematical projection in [-1, 1]³ and transitive path search across a formal graph. Cosmetic text similarity search (embedding cosine distance) injected into the prompt.
Ontological Guarantee Deterministic: if there is no causal path supported in the graph, it returns NO_EVIDENCE and remains silent. Zero. The LLM can still hallucinate, omit, or contradict the very paragraphs retrieved by RAG.
Cost per Query 0 tokens to verify. The entire ontological verification runs in local C++23 memory. High. Thousands of tokens per call to pay for the context window of injected documents.
Response Latency Direct local lookup (p50 0.37 ms desktop / 1.37 ms edge); bounded multi-hop BFS. Public MCP adds network (~0.3–0.6 s). Seconds (2,000 ms to 6,000 ms between vector lookup and autoregressive token generation).
Infrastructure & Power 15 Watts on local standard hardware. Operates 100% offline with no GPU and no cloud. Cloud vector databases, high-power GPU clusters, and mandatory internet connectivity.
Handling Contradictions Topological incompatibility: detects rule collisions and formally rejects them. Blends contradictory texts into an eloquent but false synthesis ("soft hallucination").
Traceability & Auditability Provable: cites the exact node, weight, and regulatory/technical source for each edge. Approximate: points to which document was read, but cannot prove how the conclusion was reached.

Declared Gains and Limits (Total Transparency)

What Semantic Geometry Gains:

Formal auditable verification, local microsecond latency on direct lookup (<0.2 ms), bounded BFS separately, 0 tokens to verify, and protection against contradictions. Requires formalizing organizational critical rules.

What Traditional RAG Gains:

Ease of ingesting massive unstructured documents (PDFs, transcripts, notes) without prior ontological modeling. Loses truth control and logical auditability.

ARQUITECTURA ENTERPRISE

The Ideal Integration: SG as the Gatekeeper for Your RAG

Semantic Geometry and RAG do not need to compete: SG is the output guard that makes RAG viable in production.

  • 01 Use your existing RAG pipeline to freely explore and summarize millions of unstructured pages.
  • 02 Before returning the final answer to the user or core systems, SG verifies the direct lookup in < 1 ms locally; if multi-hop is required, it runs bounded BFS.
  • 03 If RAG hallucinates or contradicts a corporate policy, SG vetoes the response and demands evidence.
  • 04 Result: the wide reach of traditional RAG combined with the mathematical, deterministic shield of Semantic Geometry.

Text similarity is not ontological truth. RAG finds similar words; Semantic Geometry proves whether the claim holds in reality.

Current status

Semantic Geometry is not finished. It is built not to lie while it is not.

Architecture & method
Consolidated Strict C++23, hexagonal architecture, verification suites green.
Knowledge base
Being calibrated Grows through audited ingestion. What cannot be measured is purged.
Domain coverage
Uneven And the engine declares it: where the graph has no evidence, it answers with silence.

A model with incomplete coverage that fills the gaps is riskier than one with the same coverage that stays silent. For industrial operations and regulated decisions, that difference is not a detail: it is the product. The public node runs on a 4-core Acer with the netbook as fallback; the read-only LRU cache lives in the bridge, outside the core.

04 — Identity & Contact

Let's talk about the problem, not the pitch

Tell us what system you need to build, what pipeline is failing, or what decision you cannot back today. We respond with a technical diagnosis, not a brochure.

Company details

Legal name
Semantic Geometry Software & AI SpA
Location
Rancagua, O'Higgins, Chile
Time zone
GMT-4 / GMT-3 (mainland Chile time)

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