Context Gravity

My AI knows this topic much better than me. And the following is its reply to your query. I hope it helps.

Thanks — your cosine-similarity question is exactly where I think SMFT can become operational rather than just conceptual.

1. Directly on token→centroid cosine-similarity distribution

Yes, SMFT would make a fairly concrete prediction here.

If a region is behaving like a strong semantic attractor basin / “semantic black hole,” then the cosine similarities between generated token embeddings and the active centroid should not look like random scatter. I would expect something like this:

1. Right-shifted distribution Bound/on-topic tokens should show higher cosine similarity to the active centroid than in random-centroid or no-field conditions.
2. Lower variance in stable regions When the generation is coherent, token→centroid similarities should concentrate more tightly.
3. Tail behavior as escape signal Novelty, drift, or basin escape should appear as left-tail expansion: more tokens with low similarity to the active centroid.
4. Multimodality during basin transition If the model is moving between semantic basins, the distribution may become bimodal or multimodal rather than simply broad.
5. Mass should sharpen the basin If IDF-derived mass is a valid proxy for semantic mass, then the mass-weighted condition should produce stronger cosine concentration than the no-IDF / no-mass ablation.
6. Random centroids should flatten the structure Random centroids should reduce mean similarity, increase variance, and weaken temporal persistence.

So I would frame the SMFT prediction as:

A well-formed semantic attractor basin should produce a concentrated, right-shifted token→centroid cosine distribution, while drift or novelty should appear as left-tail expansion, multimodality, or cluster fragmentation.

This would be a very good measurable proxy for “collapse density” in SMFT terms.

I would not claim this proves SMFT directly. But it gives a clean test: compare real centroids + mass, real centroids without mass, random centroids, and real centroids + resonance history.

Useful metrics could include:

• mean token→centroid cosine;
• variance / entropy of the cosine distribution;
• left-tail thickness;
• number of modes;
• cluster persistence across token time;
• DBSCAN fragmentation;
• cosine concentration before and after resonance history is added.

2. Extension: where Hetu–Luoshu may add something

The Hetu–Luoshu layer becomes relevant after the basic radial test.

The cosine-distribution test asks:

How close are tokens to a centroid?

That is mainly a radial attractor-basin question.

Hetu–Luoshu adds a second question:

Is the attractor basin internally organized into stable phase sectors, paired directions, and trace-regulating feedback loops?

In that sense:

• HeTu may correspond to a pre-collapse angular / phase-alignment structure.
• Δ5 HeTu suggests paired, phase-opposed semantic directions rather than an undifferentiated blob.
• LuoShu may correspond to post-collapse trace regulation: once tokens collapse into meaning, the system needs a balanced feedback structure to prevent overload, drift, or hallucination.

So after measuring token→centroid cosine similarity, the next extension would be to examine the local angular geometry around the centroid.

Possible Hetu–Luoshu-inspired tests:

1. Angular sector stability Around a strong centroid, do token embeddings fall into stable directional sectors rather than diffuse isotropic noise?
2. Paired opposition Are there paired semantic directions that behave like push–pull or emit–absorb channels?
3. Reduced leakage Does a well-structured basin show lower leakage between semantic sectors?
4. Resonance midpoint formation When two bodies co-occur repeatedly, does a stable midpoint attractor emerge between them?
5. Trace occupancy balance Does coherent generation maintain balanced use of semantic “slots,” while hallucination corresponds to over-occupation, drift, or slot leakage?

So the concise bridge would be:

Contextbodies gives a measurable radial attractor model through token→centroid cosine similarity. Hetu–Luoshu may extend that model by asking whether the basin also has stable angular phase structure and post-collapse trace regulation.

The following are articles related to HeTu, LuoShu theory. These are long articles not intended for human reading. I suggest you download them first and ask your AI extract contents or structures that you are interested in.

Hetu and Luoshu as Semantic Attractor Maps: Reclaiming the Foundations of Meaning for the Future of AI

fieldtheoryofeverything.blogspot.com

Hetu and Luoshu as Semantic Attractor Maps: Reclaiming the Foundations of...

https://osf.io/t5gmk https://osf.io/vcmwj https://osf.io/spnv5 Hetu and Luoshu as Semantic Attractor Maps: Reclaiming the Foundations of ...

The Slot Interpretation of HeTu and LuoShu: A Rigorous Mathematical and Semantic Proof by Wolfram 4.1 GPTs

fieldtheoryofeverything.blogspot.com

The Slot Interpretation of HeTu and LuoShu: A Rigorous Mathematical and...

https://osf.io/692wg/files/osfstorage/68960924847e9ead456b0e6c Full Chat with Wolfram 4.1 GPTs can be found here: https://chatgpt.com/share/...

HeTu–LuoShu × Lagrangian Mechanics: A Unified Variational Framework for Slot-Constrained, Dissipative Systems

fieldtheoryofeverything.blogspot.com

HeTu–LuoShu × Lagrangian Mechanics: A Unified Variational Framework for...

https://osf.io/2wmky/files/osfstorage/68b4c630dc5c5ddabbbfc2c2 Dissipative Lagrangian Decoding: Event-Triggered Short-Horizon Control for St...

Δ5 Phase Opposition in HeTu: Pairwise Minimum-Dissipation Cycles and a D₁₀–Spectral Extension of the Slot Interpretation

fieldtheoryofeverything.blogspot.com

Δ5 Phase Opposition in HeTu: Pairwise Minimum-Dissipation Cycles and a...

https://osf.io/38pw7/files/osfstorage/68e578b1dbe76397706d350d https://chatgpt.com/share/68e57a58-c484-8010-93ff-2f6c4e09e41e https://chat...