Pith Number

pith:CVPFSLWR

pith:2026:CVPFSLWRY5IG7UZQIYDNZLK53X

not attested not anchored not stored refs resolved

Finite-size scaling of hetero-associative retrieval in continuous-signal-driven Ising spin systems

Andrea Ladiana

A tri-layer Ising hetero-associative network maps continuous signals to spins and retrieves across modalities at an operational capacity near 0.5.

arxiv:2605.14059 v1 · 2026-05-13 · cond-mat.dis-nn · stat.ML

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3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

The operational storage capacity obeys the Amit-Gutfreund-Sompolinsky finite-size correction alpha_c(N)=alpha_c(infinity)-c N^{-1/2}, extrapolating to an asymptotic operational limit alpha_c(infinity) approx 0.50 under macroscopic-basin retrieval, and the architecture reconstructs the macroscopic sleep state on parietal EEG and EOG axes from a single noisy frontal-EEG cue.

C2weakest assumption

That the PCA-whitening plus SimHash encoder preserves sufficient geometry for the pseudo-inverse couplings to produce a thermodynamically unstable equal-weight mixture whose selection by thermal fluctuations yields reliable cross-modal retrieval in the presence of quenched biological disorder.

C3one line summary

A tri-layer Ising hetero-associative memory with PCA-SimHash encoding achieves finite-size capacity scaling to an asymptotic limit near 0.5 and demonstrates cross-modal reconstruction on sleep polysomnography data.

References

40 extracted · 40 resolved · 0 Pith anchors

[1] Layerσ is initialised with a (possibly noisy) copy of an archetypeµ; lay- ers τ and ϕ are initialised to random spin noise

[2] All layers are simultaneously initialised in a symmetric super- position of two archetypes,s(a) t=0 = sign(w1ξµ1,(a) + w2ξµ2,(a))

[3] Easy mixture disentanglement.A baseline pro- tocol that isolates basin stability from symmetry breaking. All layers receive a partial, highly cor- rupted cue drawn from thesamearchetype µ. Be- cause n 2000

[4] The pristine cue is instantly overwritten by noise

[5] Layer τ reads the now-destroyedσ and the noise fromϕ, and remains noise

Receipt and verification

First computed	2026-05-17T23:39:12.546704Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

155e592ed1c7506fd3304606dcad5dddcf4a82b5cba0e56d3f28d798cdd0e470

Aliases

arxiv: 2605.14059 · arxiv_version: 2605.14059v1 · doi: 10.48550/arxiv.2605.14059 · pith_short_12: CVPFSLWRY5IG · pith_short_16: CVPFSLWRY5IG7UZQ · pith_short_8: CVPFSLWR

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/CVPFSLWRY5IG7UZQIYDNZLK53X \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 155e592ed1c7506fd3304606dcad5dddcf4a82b5cba0e56d3f28d798cdd0e470

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8da3dca9aabac842e1037b92d08ba77a7536692ca347d47111d4dbad5b56e04b",
    "cross_cats_sorted": [
      "stat.ML"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cond-mat.dis-nn",
    "submitted_at": "2026-05-13T19:33:51Z",
    "title_canon_sha256": "6ef4d9e19d0ff6eca3404d3aeb028c51c81196e2aadeea750c75ff973133aa0c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.14059",
    "kind": "arxiv",
    "version": 1
  }
}