# Frozen Metric Attention and NESS Reset

Matt Gibson · ORCID 0009-0001-4167-201X
DOI: https://doi.org/10.5281/zenodo.22036446
PDF: https://mattgibson.net/papers/frozen-metric-attention.pdf
HTML: https://mattgibson.net/papers/frozen-metric-attention.html

Machine-readable extract of the hosted PDF (same argument). Prefer this file + the SVG figures for ingest.

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Gibson (2026)  ·  Frozen Metric Attention and NESS Reset  ·  v1 concept
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 Frozen Metric Attention and NESS Reset
 A concept note on invariant-seeded language manifolds
 Version: v1 (concept preprint — not submitted to arXiv)  |  Date: 20 August 2026
 Author: Matt Gibson  |  Independent Researcher, Crimson Symphony Media
 ORCID: 0009-0001-4167-201X  |  License: CC-BY-4.0
 Status: Concept. Not a completed empirical paper. Not a claim of machine consciousness.
Provenance (read this first)
This note is one independent version of a concept developed in public discussion on X with Martin
Noirmont (@virakandah), conversation: https://x.com/virakandah/status/2090451727480750527
Noirmont will deposit a companion concept preprint on Zenodo. The two notes are not a joint paper.
They timestamp overlapping ideas under a common open license so each author can cite the other. A
later joint paper, if written, will cite both DOIs.
What is mine here: the Shannon / Landauer split; frozen (not learned-near-identity) metric G as the
architectural object; the entropy-plateau diagnostic; T112 as an optional codebook seed, labeled
doctrine until a SIM uses it.
What is his, and is only cited: RNA/protein NESS in neuronal environments; language as the
boundary of a meaning manifold; the 20 August 2026 toy SIM numbers. I do not restate his
RNA-attractor ontology as my result.
1. One-sentence claim
Standard next-token transformers hallucinate because they decode on an unconstrained Euclidean
channel. A frozen non-trivial metric on the attention manifold, reset by a nonequilibrium (NESS)
loop, is a candidate for keeping latent trajectories inside a thin legal codebook. A small-scale SIM
(Noirmont, 20 Aug 2026) did not confirm this. The null is expected at that scale. The concept is the
protocol that would actually stress it.
2. Two jobs, two sciences
The discussion mixed a codebook with a thermodynamic reset. They share a story. They do not share
a law.
Job
Object
Base
Root invariant
Frozen codebook / metric seed. Off-code strings are not legal
messages.
Shannon (1948)
Physical gate
A driven loop that erases off-code drift so the distribution is not
Boltzmann.
Landauer (1961), NESS /
Prigogine
Shannon. Entropy H(X) is a property of an ensemble, not of a single integer. A checksum is a
constraint that kills almost all of the unconstrained message space. Mutual information with a source
stays high conditional on staying inside the code. Flat attention softmax(QKT/√d) is the
unconstrained channel. Hallucination, on this reading, is off-codebook decoding: the model emits
high-probability web-scrape mass that is not a codeword of the intended manifold.


Gibson (2026)  ·  Frozen Metric Attention and NESS Reset  ·  v1 concept
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Landauer. Irreversible erasure of one bit in a physical system at temperature T dumps at least kT ln 2
of heat. This applies when a physical or computational reset actually erases illegal configurations
(ATP/chaperone cycles, sleep/oscillatory renormalization, an explicit train-time or decode-time
projection). It does not apply to a person declining a hypothesis. Disagreement is not bit-erasure in a
310 K register.
If the hardware (cell or silicon) stops paying the reset cost, the manifold thermalizes. That is the
Boltzmann warning. The energy-driven checksum loop is the Landauer engine. The codebook is
Shannon. Do not fuse them.
3. Architecture (silicon side)
Replace unconstrained attention with a metric kernel
 Attention(Q,K,V) = softmax( Q G KT / √dk ) V
where G is a frozen positive-definite (or structured) metric on the latent space, not a matrix trained from
≈ I.
Related work already exists: relative position representations, rotary embeddings as a structured G,
hyperbolic and product-manifold attention. The present claim is narrower:
1. Learnable G initialized near identity is Euclidean in disguise. The 20 August toy already showed
metric attention is a wash once G stays near I.
2. The constraint must be hard and non-trivial before a “surface-code” analogy is even in play.
Holonomy / topological protection is a metaphor until G has curvature or a discrete packing that
unconstrained softmax cannot absorb.
3. A NESS-style reset (projection, residual penalty, or periodic renormalization of latent drift back onto
the codebook) is the silicon analogue of ATP/sleep. Without it, even a pretty G is a costume on a
Boltzmann decoder.
This is an engineering hypothesis about fault-tolerant semantic geometry. It is not a solution of the
Hard Problem and not a claim that an LLM so modified is conscious.
4. Small-scale SIM (logged null)
Noirmont ran a toy NESS-driven invariant-seeded holonomic transformer (20 August 2026, public on
the X thread). Reported:
 Random entailment ~6%.
 No architecture reliably better; differences inside seed noise.
 Metric attention a wash once G stays near I.
 Checksum / reset terms did not buy consistency at that scale.
 Capacity tiny; learnable G near zero ≈ Euclidean; drift/gen probes collapsed to an EOS policy; two
seeds; one synthetic language.
Reading: negative small-scale result, not a refutation of the idea. Tiny models cheat by ending the
sequence before drift accumulates. EOS collapse means holonomy was never under long-horizon
pressure. I agree with that reading. I do not re-run the same toy and call it confirmation.


Gibson (2026)  ·  Frozen Metric Attention and NESS Reset  ·  v1 concept
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5. What would actually test it
Change one axis at a time. Do not stack new poetry on the same SIM.
1. Freeze G. Non-Euclidean and not learned from 0. Candidates: hyperbolic, product manifold, or a
discrete packing with a hard holonomy check. Optional: the triangular codebook in §6 as one such
seed.
2. Kill early EOS. Sequences long enough that unconstrained attention actually wanders.
3. Entropy of latent drift vs step. If a NESS reset is holding, drift should plateau into a bounded
limit cycle, not expand linearly into Boltzmann noise. Loss curves are secondary.
4. Real text, more than two seeds, before any “reliably better.”
Falsification (architectural claim): frozen non-trivial G + long horizon + reset still sits inside seed
noise versus unconstrained attention on the same data and budget. Then the silicon hypothesis fails
and this note stays a concept.
Non-falsification: a pretty figure on a 20-minute toy.
6. Optional seed (doctrine, not a result)
I use a discrete triangular closure T112 = 6328 = 2701 + 3627 (standard Hebrew/Greek letter-values on
Genesis 1:1 and John 1:1; name-sum 26 + 86 = 112) as a candidate frozen codebook — a thin legal
set that could seed G.
 Arithmetic of that closure is checkable and is not at issue.
 Statistical uniqueness versus real language remains an open control (prior Monte Carlo on scrambled
alphabets is not a genre-matched corpus).
 If a SIM cannot expose a hard holonomy check to that closure, it stays my doctrine, not this
paper’s result.
 Dimensionless integers have no units. Nothing here couples T112 to Gμν or to a physical Hilbert space
of tubulin.
Noirmont’s manifold is linguistic/macro-biological, not a claim that aromatic rings remain in
superposition. I do not reintroduce that merge.
7. Consciousness (scope limit)
Noirmont’s working picture: consciousness as persistence of unactualized (linguistically constrained)
possibility, not Hoffman-outside-spacetime and not hardware merely selecting a many-worlds branch. I
do not claim this note solves that. The silicon object is a regularizer. Persistence of unused probability
mass is something every LLM already has. That is not phenomenal experience.
If a later joint paper addresses the Hard Problem, it will be under his RNA/protein / meaning-manifold
framing, with this note cited only for the attention/NESS protocol.
8. Non-claims
This concept note does not claim:
 machine consciousness;


Gibson (2026)  ·  Frozen Metric Attention and NESS Reset  ·  v1 concept
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 a completed empirical win over transformers;
 that Landauer taxes skeptics;
 Orch-OR, microtubule decoherence-free subspaces, or warp/metric engineering;
 that H(X) = 0 for any biblical verse (metaphor, not Shannon bits).
9. How to cite
Until the Zenodo DOI exists, cite the X conversation as the public timestamp. After deposit:
 Gibson, M. (2026). Frozen Metric Attention and NESS Reset: A concept note on invariant-seeded language
manifolds (v1). Zenodo. [DOI]
Companion (replace with his DOI when issued): Noirmont, M. (2026). [title of companion concept
preprint] (v1). Zenodo. [DOI]
Please cite both if you use the shared concept.
References (minimal)
Landauer, R. (1961). Irreversibility and heat generation in the computing process. IBM J. Res. Dev.
5(3), 183–191.
Shannon, C. E. (1948). A mathematical theory of communication. Bell Syst. Tech. J. 27, 379–423,
623–656.
Noirmont, M. & Kukier, P. (2026). The RNA Attractor Hypothesis as a Novel Molecular and Ontological
Great Filter (V1). Zenodo. https://doi.org/10.5281/zenodo.20626522
Noirmont, M. (2026). Toy SIM of a NESS-driven invariant-seeded holonomic transformer. Public figures
posted 20 August 2026 in https://x.com/virakandah/status/2090451727480750527
Related architectural pointers (not claimed as original): Shaw et al., relative position representations;
Su et al., RoPE; hyperbolic / product-manifold attention.
Independent concept preprint. Common open license with a companion Zenodo note by M. Noirmont. Joint authorship, if any, is a
later document.