Pith Number

pith:QWY3HCT4

pith:2015:QWY3HCT455ERIPRZAE4TJ4MDW7

not attested not anchored not stored refs pending

Mean-field interaction of Brownian occupation measures, I: uniform tube property of the Coulomb functional

Chiranjib Mukherjee, Wolfgang Koenig

arxiv:1509.06672 v2 · 2015-09-22 · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QWY3HCT455ERIPRZAE4TJ4MDW7}

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.

Receipt and verification

First computed	2026-05-18T00:32:15.396852Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

85b1b38a7cef49143e39013934f183b7d7bb1db756c357056a93bdc316cbfbeb

Aliases

arxiv: 1509.06672 · arxiv_version: 1509.06672v2 · doi: 10.48550/arxiv.1509.06672 · pith_short_12: QWY3HCT455ER · pith_short_16: QWY3HCT455ERIPRZ · pith_short_8: QWY3HCT4

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/QWY3HCT455ERIPRZAE4TJ4MDW7 \
  | 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: 85b1b38a7cef49143e39013934f183b7d7bb1db756c357056a93bdc316cbfbeb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5251b4f3d1f3f6ccb0fdcc96a22732804478241c029447b4028767d4b68f0c2e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-09-22T16:32:12Z",
    "title_canon_sha256": "26be67d1a7b2f6b3262f4752a00eaf7f45065640ce18515e514ee2f735fd22e4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.06672",
    "kind": "arxiv",
    "version": 2
  }
}