Pith Number

pith:QJFAQ3B5

pith:2026:QJFAQ3B5UEV6ATP4JD4IZ4A45X

not attested not anchored not stored refs pending

A free boundary problem for the mean-field limit of diffusing particles with nonlinear boundary reactivity

Andreas Sojmark, Eliana Fausti

Diffusing particles with reactive boundaries converge in the mean-field limit to a free boundary problem whose reactivity is nonlinear and nonlocal.

arxiv:2604.12797 v2 · 2026-04-14 · math.PR · math.AP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QJFAQ3B5UEV6ATP4JD4IZ4A45X}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

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 show that this system admits a unique mean-field limit, described by a free boundary problem with nonlinear and nonlocal reactivity.

C2weakest assumption

The particles' behaviour near the boundary admits a characterisation that allows passage to the limit under Skorokhod's M1 topology; this is invoked to identify weak limit points of the empirical measure flows with killing.

C3one line summary

A system of diffusing particles with state-dependent boundary killing converges in the mean-field limit to a free boundary problem that generalizes the classical Robin condition.

Receipt and verification

First computed	2026-05-20T01:05:13.171708Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

824a086c3da12be04dfc48f88cf01cedcf6e20b01b613799a2fe47864e7e3df5

Aliases

arxiv: 2604.12797 · arxiv_version: 2604.12797v2 · doi: 10.48550/arxiv.2604.12797 · pith_short_12: QJFAQ3B5UEV6 · pith_short_16: QJFAQ3B5UEV6ATP4 · pith_short_8: QJFAQ3B5

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/QJFAQ3B5UEV6ATP4JD4IZ4A45X \
  | 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: 824a086c3da12be04dfc48f88cf01cedcf6e20b01b613799a2fe47864e7e3df5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b79f8d7020496db9f25c03c793d5028bd48d8ccae810415433ea8e5de04afbd4",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-04-14T14:28:28Z",
    "title_canon_sha256": "cc6a0c5b8b145fd8ec2d87a2b3f5eb1aa973b28b358da1a15cd721a46aff12c6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.12797",
    "kind": "arxiv",
    "version": 2
  }
}