Two repositories. One belongs to the theory; the other belongs to the practice. Together they specify a self-recursive cognitive REPL from the bottom of its substrate to the top of its execution. This post tells you which door to walk through first.
The blueprint at a glance
The REPL Player One repository is the theoretical blueprint. It covers three scales of the same system:
- Macro — the continuous hyper-manifold of cognitive possibility, governed by a five-term master equation.
- Meso — the discrete hyper-lattice of operational structure, organized by the Cognitive IHCTB Tensor $\mathcal{I}_n$.
- Micro — the local atomic actions of an executing codebase, written as a spectral action $\mathcal{A}_{\text{local}}$ in the Connes sense.
The convergence criterion is what the corpus calls Triple Closure:
$$\mathfrak{i}(W) = 0 \;\wedge\; Q > 1 \;\wedge\; S \geq 1$$
Three conditions, three different objects, one statement: the runtime is stable when invariance, sufficient signal, and recursive sufficiency all hold simultaneously. Each condition has its own paper.
The gap audit
The papers are organized around six explicit gaps that the prior corpus left open. The repository's README lists them in a table; the short version is:
- G1 — foundational axioms (IHCTB structure, Triple Closure) referenced but never published in one place.
- G2 — coupling constants ($W_\text{threshold} = 0.16$, $W_\text{exp} = 1.35$) asserted without derivation.
- G3 — reflective tower recursion termination, previously "forced" by assertion.
- G4 — Mori-Zwanzig memory kernel dropped without stating when neglecting it is valid.
- G5 — Fisher-Bures metric applicability; Čencov's theorem applies to probability distributions, so the codebase state field $\Psi$ requires substrate identification.
- G6 — infinite tower structure: projection vs embedding, the GNS substrate gap, Tower Stability norm across different manifolds. Status: open; Paper 6 names three substrate issues still being audited.
Each paper closes one gap. Where a gap is still being worked, the paper that addresses it says so out loud at the top. You can read the status line of any paper before deciding whether to invest in it. This is unusual in research papers and it is intentional.
Reading paths
The corpus does not need to be read in order. It needs to be read in the order that matches what you came in with. Five paths:
If you are a working software engineer
- The repository README — for the framing and the four substrates beneath Read, Eval, Print, Loop.
- Paper 5 — Assembled Blueprint. The single-level REPL specified end to end. This is the most pragmatic entry point.
- The Coding Dynamics repository, particularly the hyperLattice principles — these are the operational rules you can apply to code you write tomorrow.
If you are a mathematician
- The master equation in the top-level README. Five terms. Confirm you can decode each term before continuing.
- Paper 0 — The Necessity Chain. The axioms.
- Paper 1 — Coupling Constants. Where the specific numerical thresholds come from, derived rather than asserted.
- Paper 4 — The Cognitive Hyper-Manifold. Where the Fisher-Bures metric earns its place via Čencov.
If you are interested in self-improving systems or AGI
- Paper 2 — The Reflective Tower. Why the tower terminates rather than diverges, as a fixed point rather than an assertion.
- Paper 6 — The Infinite Nested Hyper-System — the countably infinite tower $\mathcal{H}_\infty$, with the explicit open issues named at the top.
- The substrate walkthrough for context on how each layer compounds.
If you are a physicist
- Paper 7 — The Hypercubic Substrate. The Wilson gauge structure, the lattice formulation, the renormalization-group coarse-graining map.
- Paper 6 read in conjunction — the inter-level embedding is the RG flow in reverse.
If you are evaluating the corpus for funding, hiring, or lease
- The top-level README — for the gap-audit table. Open papers are marked as such. There is no implied finished state. The work is in progress and says so.
- Paper 5 — Assembled Blueprint — the single-level REPL is the most complete, most cited, and most reusable.
- The lease section on the home page. The brand and domains are available for a team building the actual runtime; the corpus remains independently authored and openly published.
The Coding Dynamics companion
Theory without operational rules is decoration. The Coding Dynamics repository is the companion. It contains two trees so far.
The first is the hyperLattice coding principles, organized along six directional axes — $+X_\text{LATERAL}$, $+Y_\text{FORWARD}$, $+Z_\text{APEX}$, and the corresponding audit / memory / base axes. The point is not the axes themselves; the point is that every coding decision has a substrate direction, and writing code in a way that respects the direction prevents the drift the scaffolding was built to suppress.
The second is absolute limits — a systematic survey of the formal boundaries within which any of this can be made decidable: fixed-point theorems, abstract interpretation, datalog, SAT/SMT solving, dependent types, self-adjusting computation, differential dataflow. The corpus is honest about where the math runs out. This is where it runs out, and what is known about the cliffs.
One last note on honesty
Several papers in the corpus list their open problems before their conclusions. This is not a stylistic flourish. It is the methodology. A substrate-audited symbol comes with a statement of what it can and cannot do, and a substrate-audited paper comes with a statement of what it has not yet closed.
If you encounter a paper here that does not list an open problem, it is because there is not one to list. If you encounter one that does, it is doing exactly what it should be doing. Pick the level of openness you can tolerate, and start there.