Pith Number

pith:TV4I7W6G

pith:2026:TV4I7W6G2O56KACX34XF7EKX4I

not attested not anchored not stored refs resolved

Orientation in Poisson Cluster Processes via Imaginary Bispectra

Boris Baeumer, Conor Kresin, Ting Wang, Yifu Tang

A nonzero imaginary factorial bispectrum certifies orientation for stationary Poisson branching clusters when the reduced third cumulant is L1-integrable.

arxiv:2605.13004 v1 · 2026-05-13 · math.PR · math.ST · stat.TH

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Record completeness

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4 Citations 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

For stationary Poisson branching clusters, in the L^1 third-cumulant regime, a nonzero imaginary factorial bispectrum certifies orientation.

C2weakest assumption

The process belongs to the stationary Poisson branching cluster family and satisfies the L^1 integrability condition on the reduced third cumulant.

C3one line summary

Nonzero imaginary factorial bispectrum certifies orientation in stationary Poisson branching clusters when the third cumulant is integrable.

References

25 extracted · 25 resolved · 1 Pith anchors

[1] Achab, M., Bacry, E., Gaïffas, S., Mastromatteo, I. and Muzy, J.-F. (2018). Uncovering causality from multivariate Hawkes integrated cumulants.Journal of Machine Learning Research18(192), 1–28 2018

[2] Bacry, E. and Muzy, J.-F. (2016). First- and second-order statistics characterization of Hawkes processes and non-parametric estimation.IEEE Transactions on Information Theory62, 2184–2202 2016

[3] Baddeley, A., Davies, T. M., Hazelton, M. L., Rakshit, S. and Turner, R. (2022). Fundamental problems in fitting spatial cluster process models.Spatial Statistics52, 100709 2022

[4] Bingham, N. H., Goldie, C. M. and Teugels, J. L. (1987).Regular Variation. Cambridge University Press, Cambridge 1987

[5] Brillinger, D. R. (1975). Statistical inference for stationary point processes. In M. L. Puri (ed.),Stochastic Processes and Related Topics, Vol. 1. Academic Press, New York, pp. 55–99 1975

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-18T03:09:00.347296Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9d788fdbc6d3bbe50057df2e5f9157e2042abb866fdc52bff128ebbac4df7eac

Aliases

arxiv: 2605.13004 · arxiv_version: 2605.13004v1 · doi: 10.48550/arxiv.2605.13004 · pith_short_12: TV4I7W6G2O56 · pith_short_16: TV4I7W6G2O56KACX · pith_short_8: TV4I7W6G

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/TV4I7W6G2O56KACX34XF7EKX4I \
  | 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: 9d788fdbc6d3bbe50057df2e5f9157e2042abb866fdc52bff128ebbac4df7eac

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3a2a648d83d3430a5ef46f4ed3371140904058807091c0b4ca72aee04c17bd7c",
    "cross_cats_sorted": [
      "math.ST",
      "stat.TH"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-05-13T04:59:10Z",
    "title_canon_sha256": "f73650591aa85edd25a35cb272c2a55727c94dd74b9211b1c83a6f143e43bc92"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13004",
    "kind": "arxiv",
    "version": 1
  }
}