A five-paper series on the claim that the agent harness has a formal theory. Under stated assumptions there is a structure-preserving interpretation of the four pillars of agent externalization (memory, skills, protocols, harness) in the ArchAgents Architecture triple (G, Know, Phi), and three production systems realise that interpretation on identifiable fragments: ContextFS for memory, AgentHero for skills and for the harness, and CatDB for protocols. Each Part states the laws its layer must satisfy, checks them against the code at a pinned commit, and records where they fail. The synthesis composes the four layers and argues, with Cao (2026), that agentic engineering is the engineering of wiring, certificates and realisation, while code, schemas, migrations and tests remain durable artifacts that live inside G and Know.
Website: https://agent-engineering-pearl.vercel.app
| Part | Title | Pillar | System (commit) | Pages | Read | |
|---|---|---|---|---|---|---|
| Synthesis | The End of Software Engineering and the Rise of Agentic Engineering | all | ContextFS, AgentHero, CatDB | 38 | web | |
| I | Coalgebraic Memory | Memory | ContextFS (a93035d) | 42 | web | |
| II | Operadic Skill Composition | Skills | AgentHero (1c3ad24) | 38 | web | |
| III | Typed Protocol Wiring | Protocols | CatDB (7cc9341a) | 35 | web | |
| IV | Harness Architecture | Harness | AgentHero (1c3ad24) | 42 | web |
The Parts are written to be read in order. Part I is self-contained. Part II imports Part I's state object as a possible port type. Part III compares its wiring operad with Part II's skills operad and shows that their concrete colour sets differ, with only a lossy type erasure checked between them. Part IV imports all three and adds the Know and Phi components. The synthesis adds one theorem of its own (a support criterion for strength of the interpretation) and a section on where the triple is load-bearing and where it is only descriptive.
Part I Part II Part III Part IV
Memory Skills Protocols Harness
ContextFS AgentHero DAGs CatDB AgentHero runtime
(S, alpha) --> coloured operad --> wiring operad W --> (G, Know, Phi)
lineage on substitution- typed ports with receipt-shaped
one time axis closed composition typed refusal certificates,
on a restricted replay-checked
colour set
\ | | /
\__________________|____________________|___________________/
|
Synthesis
named composition is partial at every layer; the side
condition is always disjointness of names in a shared
namespace; strength of the interpretation holds exactly
when the factors' resource footprints are disjoint
The series order is a presentation order. Two dependencies run against it: skill operations can read and write memory state, and a wiring can carry skills as nodes. Each Part states these where they apply.
Part I proves that ContextFS lineage is a coalgebra on a single time axis and is not bitemporal in Snodgrass's sense: two histories that differ only in valid time have identical recordings. Three of eight law clauses hold. Part II shows that AgentHero's DAG ports are string-keyed JSON values, so the operad reading holds only on a restricted colour set, and that multi-output nodes push the structure toward a properad. Part III proves field confinement for CatDB's accepted plans and shows that CatDB carries its policy and provenance material in the port types and reason sets rather than in a separate Know component. Part IV finds that AgentHero's certificates are receipt-shaped rather than theorem-shaped, that the interpretation is lax on the durability fragment because a shared sequence co-orders receipts of independent applications, and that the receipt-sequencing abstraction is strong on the hook fragment whose fence tokens are per row. The hook result does not model scope-based event eligibility. Seven harness laws are stated: five hold, one holds partially, one fails.
Every claim about code names a repository, a path, an identifier, a line range and a commit. Each Part ends with a code evidence appendix, and code/MAPPING.md collects all of those rows in one table. code/<part>/EXCERPTS.md quotes the cited lines verbatim from the pinned commits. Runtime properties (replay, idempotency, fencing, refusal) are stated as implementation-level claims established by source inspection, not as observed behaviour. The two framing papers (Banu, arXiv:2605.12239; Cao, arXiv:2606.05608) are linked from sources/README.md and are not redistributed.
papers/latex/ LaTeX sources of the five papers
papers/pdf/ compiled PDFs
docs/papers/ HTML versions produced by pandoc with the pre and post passes in scripts/
code/ code evidence map and verbatim excerpts at the pinned commits
reviews/ external review rounds for every paper (Gemini peer review, Codex formatting and evidence audits)
team/ interface contracts, shared notation, prospectus, integration report and the team board
website/ Next.js static site (mobile first, server-side KaTeX)
posts/ social media drafts per platform
scripts/ tex-prepass.py, html-postpass.py, latex2html.py
Compile a paper:
cd papers/latex
pdflatex -interaction=nonstopmode memory-coalgebra.tex
pdflatex -interaction=nonstopmode memory-coalgebra.tex
Regenerate the HTML for the website (numbers the bibliography, links citations, resolves cross-references, gives theorem environments their LaTeX numbers):
python3 scripts/tex-prepass.py papers/latex/memory-coalgebra.tex /tmp/memory-coalgebra.pandoc.tex
pandoc /tmp/memory-coalgebra.pandoc.tex --to html5 --mathjax --toc --toc-depth=3 --number-sections --no-highlight --wrap=none -o docs/papers/memory-coalgebra.html
python3 scripts/html-postpass.py docs/papers/memory-coalgebra.html /tmp/memory-coalgebra.pandoc.tex.numbering.json
Build the website:
cd website
npm install
npm run build
Matthew Long The YonedaAI Collaboration, YonedaAI Research Collective Chicago, IL matthew@yonedaai.com, https://yonedaai.com
Repository: https://github.com/YonedaAI/agent-engineering