Pith Number

pith:YNKCJAGV

pith:2026:YNKCJAGVSR663USMAFYKONTZY6

not attested not anchored not stored refs resolved

Matrix-Product Belief Propagation for continuous-state-space variables

Alfredo Braunstein, Federico Florio

Matrix-Product Belief Propagation extends to continuous variables through a Hilbert basis expansion.

arxiv:2605.14522 v1 · 2026-05-14 · cond-mat.stat-mech · cond-mat.dis-nn

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Record completeness

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2 Internet Archive

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

A generalization of this method to models with continuous or mixed continuous/discrete degrees of freedom is presented, using a tunable expansion in a Hilbert function basis.

C2weakest assumption

That a finite expansion in the chosen Hilbert basis (e.g., Fourier) can accurately represent the continuous degrees of freedom with controlled error for the target models.

C3one line summary

Generalizes matrix-product belief propagation to continuous variables using Hilbert basis expansions, enabling linear-cost computation of dynamics and large deviations in mixed-state kinetic Ising models.

References

19 extracted · 19 resolved · 0 Pith anchors

[1] N. Antulov-Fantulin, A. Lancic, H. Stefancic, M. Si- kic, and T. Smuc, Statistical Inference Framework for Source Detection of Contagion Processes on Arbitrary Network Structures, in2014 IEEE Eighth I 2014

[2] A. Braunstein, G. Catania, L. Dall’Asta, M. Mariani, and A. P. Muntoni, Inference in conditioned dynamics through causality restoration, Scientific Reports13, 7350 (2023) 2023

[3] Aurell, Dynamic mean-field and cavity methods for diluted Ising systems, Physical Review E85, 10.1103/PhysRevE.85.031119 (2012) 2012 · doi:10.1103/physreve.85.031119

[4] B. Karrer and M. E. J. Newman, Message passing ap- proach for general epidemic models, Physical Review E 82, 016101 (2010) 2010

[5] A. Braunstein, G. Catania, L. Dall’Asta, M. Mariani, F. Mazza, and M. Tarabolo, Small-coupling dynamic cav- ity: A Bayesian mean-field framework for epidemic infer- ence, Physical Review Research7, 02 2025

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-17T23:39:06.055224Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c3542480d5947dedd24c0170a73679c79f1a930ec470725eb985c5ab58bcff46

Aliases

arxiv: 2605.14522 · arxiv_version: 2605.14522v1 · doi: 10.48550/arxiv.2605.14522 · pith_short_12: YNKCJAGVSR66 · pith_short_16: YNKCJAGVSR663USM · pith_short_8: YNKCJAGV

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/YNKCJAGVSR663USMAFYKONTZY6 \
  | 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: c3542480d5947dedd24c0170a73679c79f1a930ec470725eb985c5ab58bcff46

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "02a3253f390cab4e5e31e259b684042cf41c24491609953472353ace75097e69",
    "cross_cats_sorted": [
      "cond-mat.dis-nn"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cond-mat.stat-mech",
    "submitted_at": "2026-05-14T08:06:32Z",
    "title_canon_sha256": "e4b2500c08acad6145ae6f827b9981e3b5587b86ad9d998d38de4c16746668e9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.14522",
    "kind": "arxiv",
    "version": 1
  }
}