Pith Number

pith:4FSHLZDD

pith:2026:4FSHLZDDWKXTHT7YW4WXD5P77Z

not attested not anchored not stored refs pending

Nonconforming Finite Element Approximation and Energy Lower Bound Estimation for the Gross--Pitaevskii Energy Functional

Chen Zhang, Heyan Zhu, Wenbin Chen

arxiv:2605.23334 v1 · 2026-05-22 · math.NA · cs.NA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4FSHLZDDWKXTHT7YW4WXD5P77Z}

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	2026-05-25T02:01:49.395446Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e16475e463b2af33cff8b72d71f5fffe7360317dfadde0ae85dec7174e7a814d

Aliases

arxiv: 2605.23334 · arxiv_version: 2605.23334v1 · doi: 10.48550/arxiv.2605.23334 · pith_short_12: 4FSHLZDDWKXT · pith_short_16: 4FSHLZDDWKXTHT7Y · pith_short_8: 4FSHLZDD

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/4FSHLZDDWKXTHT7YW4WXD5P77Z \
  | 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: e16475e463b2af33cff8b72d71f5fffe7360317dfadde0ae85dec7174e7a814d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b970e43025d843699e67dfd5927c68c548651f4c2123edd267e401e760619586",
    "cross_cats_sorted": [
      "cs.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2026-05-22T07:50:44Z",
    "title_canon_sha256": "1a3ee71ae850c728f2cc0e98b0d88cd161e0a0050dcbc2a166ef7be681e00062"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.23334",
    "kind": "arxiv",
    "version": 1
  }
}