Pith Number

pith:JDIH2FXY

pith:2026:JDIH2FXYLAFTMNNHC3YUN46TUX

not attested not anchored not stored refs pending

Quantitative Stability of First Laplacian Eigenstates for the Incompressible Euler Equation on a Flat 2-Torus

Fatao Wang, Guodong Wang, Xiaoxue Zhu

arxiv:2606.12973 v1 · 2026-06-11 · 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{JDIH2FXYLAFTMNNHC3YUN46TUX}

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	2026-06-12T01:09:35.832241Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

48d07d16f8580b3635a716f146f3d3a5f70da4c17d0da982118d18e5901265a5

Aliases

arxiv: 2606.12973 · arxiv_version: 2606.12973v1 · doi: 10.48550/arxiv.2606.12973 · pith_short_12: JDIH2FXYLAFT · pith_short_16: JDIH2FXYLAFTMNNH · pith_short_8: JDIH2FXY

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/JDIH2FXYLAFTMNNHC3YUN46TUX \
  | 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: 48d07d16f8580b3635a716f146f3d3a5f70da4c17d0da982118d18e5901265a5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9a8f1b8d4721e4b520d01cb5c169772a394b5285bd920a4c7d6510bca428ac53",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-06-11T07:07:02Z",
    "title_canon_sha256": "b47dafd48d5a3a02b6761c6a9e60bd81ef950cb5d240cf0d09af23d550775d9d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.12973",
    "kind": "arxiv",
    "version": 1
  }
}