RESEARCH NOTE · PUBLIC WORKING PAPER · JULY 2026
A research programme in
persistent intelligence.
Most of the field studies how well a model performs. KodaSōken studies what persists when the model is replaced. Those are different questions — and the second is, we believe, closer to mathematics than to engineering.
C. Mundim · KodaSōken Working Paper · Tokyo, July 2026. This study note follows the paper; where we have a formalism, we give it. Where we have only an empirical observation on a single system, we say so.
01 — THE CENTRAL QUESTION
Scale answers one question. Continuity asks another.
A language model is, to first approximation, a function mapping a finite token string to a probability distribution over the next token:
with parameter count N now in the hundreds of billions. But a large model is stateless between invocations and ephemeral across versions. When the weights are replaced, whatever operating identity a deployed agent had — its role, accumulated commitments, relationships, memory of prior decisions — is, by default, destroyed and rebuilt from scratch.
The programme is organised around the complementary question: when the model changes, what must remain — and can what remains be represented, measured and preserved by construction rather than by luck? We call the affirmative hypothesis continuity as an architecture: an agent’s operating identity lives in a governed runtime outside any single model, so models become interchangeable cognitive resources the agent recruits — not the agent itself. If identity is an object living outside the model, it has a representation, a metric, an invariance group and a transfer theory, all only partially understood.
02 — THE AGENT, AND AN UNREASONABLE RATIO
An agent is a governed loop, not a call.
In our usage an agent is a persistent loop hosting a constitution κ (structured, versioned role, boundaries, permissions and unresolved commitments), a three-tier memory M with semantic retrieval, an orchestration policy π that decides per step whether a task is handled deterministically, by a small specialist model, or escalated to a frontier model — and an append-only, hash-chained audit layer. KoLo is the runtime that hosts (κ, M, π, audit) and treats the language model as a pluggable component.
The mathematically interesting empirical fact is the ratio between deterministic coordination and model inference. On a persistent agent we operate, autonomic operations — scheduling, memory consolidation, health checks, policy enforcement — outnumber model inferences by roughly
over a measured interval (35:1–117:1 across roles; Hiro v0.2, self-measured — see the benchmark registry). We do not claim the ratio is optimal or fundamental. We report it because it suggests the quantity of intelligence-bearing computation required to sustain a competent agent is far smaller than the deterministic coordination around it — with obvious implications for cost, energy and edge deployment, and no proper theoretical treatment yet.
03 — CONTINUITY AS A MEASURABLE QUANTITY
Making continuity a number, not a vibe.
If identity persists outside the model, its survival across a model change should be measurable. For a controlled substrate transition — swapping the underlying model of a running agent while holding κ and M fixed — we define an Identity Fidelity score:
C measures constitution preservation, D measures drift of behavioural posture from the pre-swap baseline (so 1 − D rewards low drift), and R measures recall fidelity across the transition. The weighting is a deliberate, documented choice, not a fitted one. On a controlled cross-provider transition we recorded F = 0.961, with the operating lineage preserved across four completed model and provider transitions and 336+ versioned memory states, none lost.
The epistemic status of that number
A careful reader will (correctly) ask. It is an internal, live-system observation, not an externally reproduced benchmark. The four transitions were planned and supervised, not adversarial. F was formally scored on the most recent transition only; the others are attested operationally. C, D and R are operationalised by procedures that are defensible but not canonical. F = 0.961 should therefore be read as: under a specific, disclosed protocol, a specific agent retained most of a specific notion of identity across a real model swap. It is evidence, not proof — and we publish the formula, the conditions and the failures precisely so the claim is adversarially inspectable.
04 — THE LOW-RANK STRUCTURE OF IDENTITY
Disposition may be low-rank. Facts should not be.
The scale-first orthodoxy says: to add a capability, make the model bigger. We pursue the opposite — one open base model plus many small, domain-specialised adapters, trained and served in-house, viable on commodity CPUs, with facts kept in auditable retrieval rather than baked into weights. The mathematical engine is low-rank adaptation: fine-tuning normally updates a weight matrix by a full-rank change; LoRA constrains the update to a low-rank factorisation
so that only r(d + k) parameters are trained instead of dk — at rank r = 8, on the order of 0.22% of the base model’s parameters. Project Nyx asks a sharper question than whether LoRA works: it distinguishes knowledge (facts the model can state) from disposition (the behavioural posture and priorities with which it acts). The working finding — a manuscript, pre-registered write-then-run, not yet externally reproduced — is that disposition is low-rank and localisable, and that it dissociates from factual knowledge, which is better left in retrieval.
If this holds, the map from training signal to behavioural identity factors through a low-dimensional subspace of parameter space — and one may ask about the geometry of that subspace: its intrinsic dimension, whether it is approximately shared across base models (which would make identity transferable between substrates), and how it deforms under distribution shift. These are questions about the differential geometry of a learned manifold, and they are wide open.
05 — DETERMINISM AS AN ARCHITECTURE
Spend intelligence only where it is required.
An agent is kept alive by deterministic, zero-inference subsystems — analogues of immune response, circadian scheduling, homeostatic monitoring, reflexes and memory consolidation — running continuously and cheaply, with the expensive model recruited only for genuinely novel cognition. This is the structural reason the autonomic-to-cognitive ratio of §02 is so lopsided: robustness and continuity are cheaper and safer when they are deterministic.
Several applied deployments run in high-trust, low-connectivity environments where data cannot leave the building. This forces an architecture we find independently interesting: models small enough to run offline at the edge, retrieval grounded in a local corpus, and deterministic safety gates — decidable predicates a model’s proposal must satisfy — between model output and any consequential action.
The governing principle throughout: the AI prepares; a verifier checks; a human decides; the audit records everything. The model is never the last link in a consequential chain.
06 — THE EVIDENCE DISCIPLINE
Every claim carries its own label.
Demonstrated
Reproducible under a disclosed protocol — for example, a persistent agent operating continuously for 129 days, with a verification pack of hashes, logs and version counters.
Argued
A coherent theoretical case, not yet reduced to an experiment. Much of the identity-transfer theory sits here.
Not claimed
Deliberately outside our assertions. We make no claim of consciousness, subjective experience or personhood for any system we operate. Our questions are non-phenomenological by construction: what computational structures make persistent self-reference and relational continuity possible, and how can they be evaluated without anthropomorphic inference?
This discipline is itself a research artifact — one of our public working papers is a methodology for making claims about persistent-agent architectures adversarially inspectable. Our first weight-transfer pilot produced measurable behavioural displacement and factual confusion; both are on the record. Internal figures such as F = 0.961 and the 68:1 ratio are labelled internal live-system observations, external reproduction pending. The full status-labelled corpus is on the publications registry.
07 — OPEN PROBLEMS
Where a mathematician could actually help.
These are stated as invitations, not as solved.
1 — A theory of continuity metrics
What axioms should a continuity metric satisfy? Candidate desiderata: invariance under relabelling of tokens and embeddings, an upper bound achieved only by the identity transition, monotonicity under composition of transitions, and adversarial robustness — a hostile grader cannot inflate F. Our F = 0.4C + 0.3(1 − D) + 0.3R is a first draft; the right object may be a (pseudo)metric on a space of agent behaviours, or a divergence between induced policies.
2 — The geometry of the disposition subspace
If behavioural identity is captured by a rank-r adapter, what is the intrinsic dimension of the identity manifold? Is it approximately basis-aligned across different base models — is there a natural map that transports an identity from one substrate to another? This is a question about the alignment of learned low-rank subspaces under a change of parameterisation.
3 — Disposition–knowledge dissociation, made precise
Formalise the claim that disposition and factual knowledge live in approximately orthogonal or separable components of the update. Under what conditions on the data-generating process does such a decomposition provably exist?
4 — The autonomic/cognitive frontier
Given a task distribution, what is the minimal fraction of steps that provably require a learned model rather than a deterministic policy? A computational-complexity-flavoured question about the cost of competence.
5 — Continuity under distribution shift
Model the substrate transition as a perturbation of the policy induced by the model; bound the drift D in terms of a distance between the old and new models. When is continuity robust rather than fortunate?
The field spent the last decade making the forward pass larger. We think the next decade belongs to whatever makes it continuous — a subject with far more unsolved mathematics in it than its engineering surface suggests. If any of these read as a problem you would enjoy, we would welcome the conversation.
DISCLOSURE & CITATION
Disclosure. Internal figures — notably F = 0.961 and the 68:1 autonomic-to-cognitive ratio — are internal live-system observations under disclosed protocols; external reproduction is pending, and they are labelled as such throughout. This work makes no claim of machine consciousness, subjective experience or personhood.
Citation. C. Mundim, A Research Programme in Persistent Intelligence, KodaSōken Working Paper, Tokyo, July 2026. Correspondence: cmundim@kodasoken.com · ORCID 0009-0001-5000-7409.