Pith Number

pith:3TWZXXQS

pith:2026:3TWZXXQSCZ4DK7M7HTYKMSUE2U

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Structural identifiability of partially-observed stochastic processes: from single-particle trajectories to total particle density data

Alexander P. Browning, Arianna Ceccarelli, Ruth E. Baker

A new methodology reveals that single-particle trajectories make spatio-temporal stochastic process parameters structurally identifiable, whereas total particle density data makes them only locally identifiable.

arxiv:2605.13504 v1 · 2026-05-13 · stat.ME · math.AP · math.DS · math.PR · q-bio.QM

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\pithnumber{3TWZXXQSCZ4DK7M7HTYKMSUE2U}

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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

We apply our methodology to a model, and show it is identifiable with trajectory data but only locally identifiable with density data, and demonstrate the critical role of initial conditions in the identifiability analysis.

C2weakest assumption

That the differential algebra approach remains valid after deriving the PDE representation from the underlying stochastic process, and that the characteristic-equation Taylor expansion correctly isolates identifiable combinations involving initial conditions.

C3one line summary

A new methodology shows stochastic particle models are structurally identifiable from trajectory data but only locally identifiable from density data, with initial conditions critical to the analysis.

References

65 extracted · 65 resolved · 0 Pith anchors

[1] Bulletin of Mathematical Biology , volume= 2025

[2] A likelihood-based 2026

[3] Mathematical Biosciences , volume= 2014

[4] Dong, R. and Goodbrake, C. and Harrington, H. and Pogudin, G. , title =. SIAM Journal on Applied Algebra and Geometry , doi =. 2023 , volume = 2023

[5] Bioinformatics , volume = 2019

Receipt and verification

First computed	2026-05-18T02:44:24.672743Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dced9bde121678357d9f3cf0a64a84d5044ad66c16aaac63b76c5e4a6a42242e

Aliases

arxiv: 2605.13504 · arxiv_version: 2605.13504v1 · doi: 10.48550/arxiv.2605.13504 · pith_short_12: 3TWZXXQSCZ4D · pith_short_16: 3TWZXXQSCZ4DK7M7 · pith_short_8: 3TWZXXQS

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/3TWZXXQSCZ4DK7M7HTYKMSUE2U \
  | 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: dced9bde121678357d9f3cf0a64a84d5044ad66c16aaac63b76c5e4a6a42242e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "83bf021dbe7c7d516fd30e9656bd4e3a21fd8c801dfd040a1cd248e8383d0834",
    "cross_cats_sorted": [
      "math.AP",
      "math.DS",
      "math.PR",
      "q-bio.QM"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "stat.ME",
    "submitted_at": "2026-05-13T13:24:51Z",
    "title_canon_sha256": "20cb2e12ae1ccbed964ffe44fa12938a679e42ae16e69e16480d11199e5d94a5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13504",
    "kind": "arxiv",
    "version": 1
  }
}