Pith Number

pith:AM45KZT6

pith:2026:AM45KZT6FYRVTZQ5IV742NU3HW

not attested not anchored not stored refs pending

Non-linear Stegall's lemma and general Hamilton-Jacobi-Bellman equations on Wasserstein spaces

CEREMADE), Charles Bertucci (CEREMADE), Pierre-Louis Lions (CdF (institution)

arxiv:2606.31297 v1 · 2026-06-30 · math.AP · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AM45KZT6FYRVTZQ5IV742NU3HW}

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	2026-07-01T01:17:58.402264Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0339d5667e2e2359e61d457fcd369b3d922e622fcff3d97a4b49b4b8e107ac47

Aliases

arxiv: 2606.31297 · arxiv_version: 2606.31297v1 · doi: 10.48550/arxiv.2606.31297 · pith_short_12: AM45KZT6FYRV · pith_short_16: AM45KZT6FYRVTZQ5 · pith_short_8: AM45KZT6

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/AM45KZT6FYRVTZQ5IV742NU3HW \
  | 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: 0339d5667e2e2359e61d457fcd369b3d922e622fcff3d97a4b49b4b8e107ac47

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "aa6613a464fd4c73077befaaa405adc95b83d5dd2408c3e8b49417d970c59eb1",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-06-30T08:11:05Z",
    "title_canon_sha256": "67cf580dc13f5595375a262b0f9aeb37f2d35a9aa938ee991e938731700f7f4c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.31297",
    "kind": "arxiv",
    "version": 1
  }
}