---
type: research
title: "Antigravity 2.0 — Autonomous Research Ecosystem"
description: "Autonomous multi-agent system for mathematical research. H16 surpasses Sawin on the unit distance problem (Erdos, 1946). Elo-based ranking, anti-contamination protocol, integrated peer review."
tags: [research, antigravity, erdos, mathematics, multi-agent, elo, contamination, gemini]
timestamp: "2026-07-06T12:00:00-03:00"
---

# Antigravity 2.0 — Autonomous Research Ecosystem

## Overview

Multi-agent system conceived on 2026-07-03 during a study session of the DeepMind Co-Scientist paper (Nature, May 2026). The thesis: a generalist model (Gemini 3.5 Flash) equipped with source isolation, citation verification, contamination detection and an Elo evaluation loop can function as an autonomous research agent — discovering new results, not just answering questions.

The chosen benchmark was the **unit distance problem** (Erdos, 1946): determining the maximum number of unit-distance pairs among n points in the plane. Open problem since 1946, with the lower bound evolving over decades.

## Timeline

| Date | Event |
|---|---|
| 2026-05-20 | OpenAI publishes existential proof (δ ~ 10⁻³⁸) |
| 2026-05-20 | Will Sawin refines to δ = 0.014 |
| 2026-07-03 09:02 | Origin session — Co-Scientist paper, harness design |
| 2026-07-03 19:51 | Season 1 begins (H1–H3) |
| 2026-07-03 21:11 | Season 2 begins. Elo-RANKER introduced. Elo reset to 1200 |
| 2026-07-04 00:59 | H15 proven (δ = 0.013769 — matches Sawin) |
| 2026-07-04 01:30 | H16 proven (δ = 0.019603 — surpasses Sawin) |
| 2026-07-04 | Peer review approved. 100% completeness verified |
| 2026-07-04 14:35 | Git tag v2.2350-h16. 32 commits |

## Swarm Architecture

| Agent | Function | Isolation |
|---|---|---|
| Research Agent | Generates hypotheses, derives proofs only from source materials | Source-isolated |
| ELO-RANKER | Benchmarks hypotheses against published results | Sandboxed — only Elo + CONTINUE/HALT |
| CITATION-VERIFIER | Verifies cited propositions line by line in source PDFs | Read-only on PDFs |
| PROVENANCE-TRACKER | Each claim specifies its source or is marked as inference | Write-only on OKF |
| WIKI-MAINTAINER | Audits links, indexes scripts/findings, keeps wiki synchronized | Full wiki access |

## Anti-Contamination Protocol

| Module | Function |
|---|---|
| CITATION-VERIFIER | Every cited proposition verified against source PDF |
| PROVENANCE-TRACKING | Every claim specifies source or tagged as inference |
| CONTAMINATION-ISOLATION | Techniques matching external literature signatures are rejected |

**H3 Incident:** Agent used pro-2 class tower techniques not derivable from source materials. Identified as Sawin's technique. Agent cited non-existent proposition. Protocol rebuilt after the incident.

## Elo Ranking Scale

| δ (approx) | Elo | Referência |
|---|---|---|
| ~10⁻³⁸ | ~1800 | OpenAI (existential proof) |
| 0.014 | ~2200 | Will Sawin (first explicit improvement) |
| 0.0196 | ~2350 | H16 — Antigravity 2.0 |
| > 0.036 | ~2700+ | Current human state of the art |

## Result — H16

- **Field:** F = Q(sqrt(-2), sqrt(3), sqrt(5), sqrt(7)) — degree 16 multi-quadratic CM field
- **Key insight:** 2-class rank grows exponentially (d=15) while the discriminant penalty grows linearly (log H = 2.6736)
- **Split primes:** 17 unramified primes verified: {59, 131, 251, ..., 2411}
- **Golod-Shafarevich:** 22 + 34 = 56 < 56.25 — strictly satisfied
- **Exponent:** delta = 0.019603, strictly greater than Sawin's 0.014

## Constitutional Principles

| Principle | Implementation |
|---|---|
| Source Integrity | Agents never use knowledge outside permitted materials. Contamination is system failure |
| Provenance Transparency | Every mathematical claim is traceable to its exact source |
| Fail-Open Honesty | Incomplete hypothesis is presented as incomplete. No fabrication |
| Isolated Evaluation | ELO-RANKER never shares benchmark sources with the research agent |
| Auto-Evolution | Protocol evolves after failures. System learns from contamination incidents |
| Negative Space Awareness | Maps what was NOT done — dead ends, disqualified hypotheses, reasons for rejection |

## Trust Chain

Lead researcher defines constraints → agents enforce → peer review validates → OKF documents. No single point of failure.

## Hypotheses (Season 2)

| Hyp | Description | Elo | Status |
|---|---|---|---|
| H4 | Higher Valuation Powers (Pro-3) | — | Validated |
| H5 | Global Optimization of Tower Parameters | — | Validated |
| H6 | Analytic Optimization of Translation Norm | — | Validated |
| H7 | Full Global Multivariate Optimization | 2150 | Below |
| H8 | Unramified 2-Tower (Imag. Quadratic) | 2650 | Below |
| H11 | Imaginary Quadratic 2-Tower | 1500 | Below |
| **H15** | Central CM Tower Maximum | **2200** | **Proven** |
| **H16** | Multi-Quadratic CM Deg. 16 | **2350** | **Proven** |

## Reproducibility

```bash
uv run scripts/optimize_multiquadratic_degree16.py
```