# Inside the research harness — Catenation > Inside Catenation's research harness: programmable context, AI agents delegated through code, harness refinement, evidence dependencies, exact computation and research scouting, with recorded mathematics and biology campaigns and the research record behind the proof of Nivat's conjecture. Source: https://www.catenation.ai/research.html [Evidence](https://www.catenation.ai/evaluation.html) [Discuss a pilot](mailto:pranavak@mit.edu?subject=Catenation%20research%20pilot) [Back to the homepage](https://www.catenation.ai/) Architecture # Inside the research harness. How Catenation programs context, delegates to AI agents, and carries evidence forward, with the recorded campaigns open to inspect. The harness ## Six mechanisms, step by step. Program the context and delegate through code. Refine the working environment while the evidence carries forward. ### The context is something the agent can program. The model writes Python to inspect sources, call tools, and work with intermediate objects. The kernel retains those objects; selected results return to the model. [Technical notes](https://www.catenation.ai/technical-notes.html#context) External research state - **Papers + source files** read, inspect, transform - **SOTA Context Map** long-context orientation cache - **Knowledge Base** Knowledge Graph / Ontology - **Evidence ledger** retrieve exact dependencies Large working material stays outside the prompt. The agent chooses what to inspect. Turn 1 · select the material Same kernel RLM · persistent IPython Example `from mantis_forge import ctx sources = await ctx. search ( "boundary cases", limit=4) # inspect exact source records source_map = await ctx. cartography ()` Out Selected source records + their relationships Retained namespace - `sources` selected records *new* - `source_map` nodes + typed edges *new* Model window Instructions + selected context + tool results **Model connection** Codex subscription auth API providers Compatible local endpoints [Provider details](https://www.catenation.ai/technical-notes.html#frontier) Python state persists across turns and compaction; kernel failure has a separate recovery path. Campaign gallery ## Open a research campaign. Read the actual threads, tool outputs, and saved work. Each domain brings its own standard of evidence. [Watch the fleet film](https://www.catenation.ai/#runtime) 30 of 30 campaigns Find a campaign biology · B01 Recorded capture B01 / computational biology ### When is a CRISPR lineage recorder a clock? - Captured source audit and review - Astra - 2026-09-21 On a small fixed tree, derive the exact feasible interval under site-rate bounds and one dated anchor; then apply the same code to one processed ConvexML tree using rate bounds estimated from held-out sites. The decisive output is whether any internal node remains materially narrower than [0,T]. [Campaign notes](https://www.catenation.ai/technical-notes.html#biology) Why it matters ## Leave the field with more than an answer. A useful discovery leaves a method someone else can understand, challenge, and reuse. Catenation keeps the arguments, computations, failed approaches, and dependencies that led to a result, so the intermediate work becomes scientific insight and reusable procedural knowledge. Derivation ### Show the derivation Connect claims to the arguments, sources, and exact computations behind them. Obstruction ### Keep the obstruction A counterexample records why an approach fails, so another agent can start beyond it. Method ### Improve the method Carry useful techniques into prompts, skills, memory, and the next campaign. **The transfer test.** With the record, a researcher should solve a related problem, explain a necessary assumption, or repair a broken argument better than with the paper or transcript alone. Further reading - [Terence Tao, Mathematics in the Age of AI (ICM 2026)](https://arxiv.org/abs/2608.16753) - [Terence Tao on proof abundance (April 2026)](https://mathstodon.xyz/@tao/116477351524980995) - [Jeremy Avigad, The Future of Mathematics (October 2026)](https://terrytao.wordpress.com/2026/10/05/the-future-of-mathematics/) - [A severe misalignment of AI in mathematics (September 2026)](https://terrytao.wordpress.com/2026/09/11/a-severe-misalignment-of-ai-in-mathematics/) Research record ## Inside the Nivat campaign. Catenation’s research campaign proved Nivat’s conjecture, open for 29 years. Inspect the original agent work, computations, refuted approaches, and the resulting argument. **Independently verified** by researchers in symbolic dynamics [Read the proof](https://www.catenation.ai/research/nivat-manuscript.pdf) [Lean formalization: the full proof, machine-checked](https://github.com/PranavaKCode/nivat-lean) The question ### Does limited local variety force global order? Imagine sliding a rectangular window over an infinite tiled floor. If it reveals no more distinct patterns than the window contains tiles, must the entire floor repeat in some direction? First posed in [1997](https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2020.14), Nivat’s conjecture became a landmark problem in two-dimensional symbolic dynamics and combinatorics on words: the mathematics of patterns and repetition. The statement Catenation proved A finite-alphabet configuration with at most *k* × *n* distinct patterns of size *k* × *n* has a nonzero period. Example floor 3 × 2 window · 6 tiles Example: a 3 × 2 window slides over a periodic tiled floor. It finds five distinct patterns, no more than its six tiles, and the floor repeats along one direction. Approach families 11 Original agent histories 7 Refuted shortcuts retained 8 Claims in the preserved ledger 46 Choose a part of the argument, then follow its prerequisites. Loading the preserved dependency map… ### The routes that changed the argument. The closing route combines annihilator algebra, directional pattern counting, and defect geometry. The research record preserves the calculations and reviews behind each revision. Exact example #### When fewer walls meant more patterns An exact seven-to-five-wall example increased the number of 2 × 2 patterns from **15 to 16**. Deleting a canceling pair was not a valid shortcut. Counterexample #### A sharper counting argument A counterexample had no rare 2 × 2 patterns but still had a nonzero affine deficit. The closing route instead uses quadratic observables on the same pattern set. Review #### Review that strengthened the argument Review identified a residual step to resolve. The corrected argument passed **two final reviews**, and the proof was then **independently verified**. The campaign’s full research record, preserved for inspection. The explorer traces 20 connected claims and 25 prerequisite relationships from the original proof. [Proof versions and review record](https://www.catenation.ai/evaluation.html#research) [Dependency data](https://www.catenation.ai/nivat-history.json) ## Bring a multi-day research problem. Talk to the founder about a scoped pilot, or read the methods behind the results. [Technical notes](https://www.catenation.ai/technical-notes.html) [Evidence & evaluation](https://www.catenation.ai/evaluation.html) [Discuss a pilot](mailto:pranavak@mit.edu?subject=Catenation%20research%20pilot) [Back to the homepage](https://www.catenation.ai/) Research that compounds. ### Product [How it works](https://www.catenation.ai/#product) [Inside the harness](https://www.catenation.ai/research.html#harness) [Benchmarks](https://www.catenation.ai/#benchmarks) [Recorded runs](https://www.catenation.ai/#runtime) [Campaign gallery](https://www.catenation.ai/research.html#campaigns) ### Research [Nivat’s conjecture](https://www.catenation.ai/#nivat) [Read the proof](https://www.catenation.ai/research/nivat-manuscript.pdf) [Lean formalization](https://github.com/PranavaKCode/nivat-lean) [Papers](https://www.catenation.ai/#papers) [Evidence & evaluation](https://www.catenation.ai/evaluation.html) [Technical notes](https://www.catenation.ai/technical-notes.html) ### Company [Mantis pilot](https://www.catenation.ai/#pilot) [Direction](https://www.catenation.ai/#company) [Team](https://www.catenation.ai/#team) [Mantis Discovery](https://mantis-discovery.vercel.app/) [Contact](mailto:pranavak@mit.edu?subject=Catenation%20research%20pilot) © 2026 Catenation Research isn’t a task.