Pith Number

pith:IAV2QPH2

pith:2026:IAV2QPH254FVCA4C767UIMPHJM

not attested not anchored not stored refs pending

Invariant Gibbs measures and global dynamics for fractional cubic Schr\"odinger equations on the torus

Chenyuan Zhang, Haitian Yue, Lifeng Zhao, Yuzhao Wang

arxiv:2606.30223 v1 · 2026-06-29 · 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{IAV2QPH254FVCA4C767UIMPHJM}

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	2026-06-30T02:17:55.112448Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

402ba83cfaef0b510382ffbf4431e74b2275ea6c7196e9fdb6a009095dcadfe7

Aliases

arxiv: 2606.30223 · arxiv_version: 2606.30223v1 · doi: 10.48550/arxiv.2606.30223 · pith_short_12: IAV2QPH254FV · pith_short_16: IAV2QPH254FVCA4C · pith_short_8: IAV2QPH2

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/IAV2QPH254FVCA4C767UIMPHJM \
  | 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: 402ba83cfaef0b510382ffbf4431e74b2275ea6c7196e9fdb6a009095dcadfe7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c36221ac8b336b243b6b1e7d80e1ee35c6c49b5e3c6722d362cd10357d627c20",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-06-29T12:38:09Z",
    "title_canon_sha256": "1d38aca26f1a92bb1e7f2ca93c9d3c41305ab991c5893e90d5ef9478221a10a7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.30223",
    "kind": "arxiv",
    "version": 1
  }
}