Paper Arc 2026 — Map and Plan

#The Papers

Six papers, one argument. Each is self-contained; together they build a complete account of why externalized, organized reasoning scales and how to govern it.

                    ┌─────────────┐
                    │  Paper 0    │
                    │  Ontology   │  "What exists: belongs-to"
                    │  (FOIS)     │
                    └──────┬──────┘
                           │ defines the index
              ┌────────────┼────────────┐
              ▼            ▼            ▼
     ┌────────────┐ ┌───────────┐ ┌──────────┐
     │  Paper 7   │ │  Paper 1  │ │ Paper R  │
     │  Turing    │ │  Library  │ │ Redaction│
     │  (ICML/    │ │  Theorem  │ │ (NeurIPS)│
     │   ICLR)    │ │  (NeurIPS)│ │          │
     └─────┬──────┘ └─────┬─────┘ └────┬─────┘
           │              │             │
           │  capability  │  efficiency │  reflexive
           │              │             │
           └──────────┬───┘             │
                      ▼                 │
              ┌──────────────┐          │
              │   Paper 3    │◄─────────┘
              │  Hippocampus │
              │  (TiCS/Nat   │  "The brain does this too"
              │   Neuro)     │
              └──────┬───────┘
                     │
                     ▼
              ┌──────────────┐
              │  Paper 4+6   │
              │  Governance  │  "Who decides"
              │  (FAccT/Law  │
              │   journal)   │
              └──────────────┘

#Summary Table

#	Title	Core claim	Venue	Proofs	Draft	Blog
0	Belongs-To and Nothing Else	Single-primitive ontology	Applied Ontology / FOIS	✅ 5 modules	v2	—
1	The Library Theorem	Indexed retrieval exp. faster	NeurIPS 2026	✅ 4 modules	LaTeX v6	—
7	External Memory, Not Chain of Thought	Fixed window = FA; + store = TM	ICML / ICLR 2027	✅ Turing.lean	v1	v1
R	Redaction	Extract knowledge from weights	NeurIPS 2026	—	Plan only	—
3	Your Hippocampus Is a Library	Brain implements Library Theorem	Trends Cog Sci / Nat Neuro	—	—	—
4+6	Who Writes the Constitution?	Policy-governed AI + democratic input	FAccT / Law journal	—	4a: detailed plan	—

#Dependency Order

Paper 0 (ontology)         — no dependencies, submit anytime
Paper 1 (library theorem)  — no dependencies, arxiv-ready NOW
Paper 7 (turing)           — cites Paper 1, self-contained
Paper R (redaction)         — cites Papers 0 + 1, needs experiment
Paper 3 (hippocampus)      — cites Papers 1 + 7, needs lit review
Paper 4+6 (governance)     — cites Paper 7, needs Teachout

#Blog Series

Each paper gets a blog post. Anthropic style: clear, first-person, no jargon, one big idea per post. These are the shareable versions — what you send friends, collaborators, potential co-authors.

Blog	Status	Priority
"Your LLM Is a Finite Automaton" (Paper 7)	v1 done	Ship first — sharpest claim
"Why Organization Beats Scale" (Paper 1)	—	Second — supports Paper 7
"One Relation Is Enough" (Paper 0)	—	When draft v3 ready
"What If You Could Read a Model's Mind?" (Paper R)	—	After experiment
"Your Hippocampus Is a Library" (Paper 3)	—	After lit review
"Who Writes the Constitution?" (Paper 4+6)	—	After Teachout conversation

#Website

Blog posts publish to haak.world. Each post links to:

• The paper (PDF or arxiv)
• The Lean proofs (GitHub repo or inline)
• The other posts in the series

Navigation: landing page with the dependency diagram above, linking to each post. Clean, minimal, readable.

#Immediate Next Steps

1. Submit Paper 1 to arxiv — it's ready, don't let new results delay it
2. Publish "Your LLM Is a Finite Automaton" blog — on haak.world
3. Send blog to Zephyr Teachout — opens the governance conversation
4. Draft Paper 7 for ICLR 2027 — May deadline, plenty of time
5. Paper 0 to Applied Ontology — independent track, submit when polished
6. Paper R experiment — run on GCloud, validate the construction

#Lean Proof Library — Current State

11 modules, 35 theorems, 0 sorries.

Module	Paper	Theorems
Library/Basic	1	Config, branching factor, capacity bound
Library/Sequential	1	Ω(N) lower bound (pigeonhole)
Library/Indexed	1	O(log_b N) upper bound (B-tree)
Library/Separation	1	Exponential separation ratio
Library/Reasoning	1, 7	T² vs T·log T, unbounded gap
Library/Turing	7	Bounded cycling, externalization completeness
Ontology/Basic	0	Entity, belonging, co-participation
Ontology/MetaQualities	0	5 meta-qualities, completeness
Ontology/Closure	0	Reflexive closure terminates at depth 1
Ontology/Derived	0	Situation graph: symmetric, grounded, monotone
Ontology/Expressiveness	0	12 BFO/DOLCE reductions, distinctness

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strategy · 2026-03-16 · zach + claude

Strategy 26 — Paper Arc 2026 — Map and Plan — 2026 — Zachary F. Mainen / HAAK