Pith Number

pith:LWXEBVIX

pith:2020:LWXEBVIX4CZVT6SZFOL5COFGYY

not attested not anchored not stored refs pending

Invariant Gibbs measures for the three-dimensional wave equation with a Hartree nonlinearity II: Dynamics

Bjoern Bringmann

arxiv:2009.04616 v4 · 2020-09-10 · math.AP · math-ph · math.MP · 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{LWXEBVIX4CZVT6SZFOL5COFGYY}

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.

Cited by

1 paper in Pith

On the parabolic and hyperbolic Liouville equations

Receipt and verification

First computed	2026-07-05T11:13:03.757322Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5dae40d517e0b359fa592b97d138a6c6071ac390f3c6877a5e8b1d61e050f350

Aliases

arxiv: 2009.04616 · arxiv_version: 2009.04616v4 · doi: 10.48550/arxiv.2009.04616 · pith_short_12: LWXEBVIX4CZV · pith_short_16: LWXEBVIX4CZVT6SZ · pith_short_8: LWXEBVIX

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/LWXEBVIX4CZVT6SZFOL5COFGYY \
  | 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: 5dae40d517e0b359fa592b97d138a6c6071ac390f3c6877a5e8b1d61e050f350

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5e95073652023c043f4ea52ed1812f251afdbf4a9dc75b8d292a9e512cd3008f",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2020-09-10T00:42:24Z",
    "title_canon_sha256": "fad972f670e6af5600816e0d3ab234e45077abcafa4e26eab14dfa41dda0e9eb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2009.04616",
    "kind": "arxiv",
    "version": 4
  }
}