Pith Number

pith:34LPIX5L

pith:2012:34LPIX5LUXQ7UXM352RMBUZF5D

not attested not anchored not stored refs pending

Global regularity for the energy-critical NLS on $\mathbb{S}^3$

Benoit Pausader, Nikolay Tzvetkov, Xuecheng Wang

arxiv:1210.3842 v2 · 2012-10-14 · 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{34LPIX5LUXQ7UXM352RMBUZF5D}

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	2026-05-18T03:27:52.276213Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

df16f45faba5e1fa5d9beea2c0d325e8c3334b6b2c40911631219ba87c33f31d

Aliases

arxiv: 1210.3842 · arxiv_version: 1210.3842v2 · doi: 10.48550/arxiv.1210.3842 · pith_short_12: 34LPIX5LUXQ7 · pith_short_16: 34LPIX5LUXQ7UXM3 · pith_short_8: 34LPIX5L

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/34LPIX5LUXQ7UXM352RMBUZF5D \
  | 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: df16f45faba5e1fa5d9beea2c0d325e8c3334b6b2c40911631219ba87c33f31d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "27b54415639fc8ee01d6837ab0fbdfaa46683c8bdd487ab260425e7a8175040a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2012-10-14T21:05:52Z",
    "title_canon_sha256": "981c09060303c7f0f9e068b8b7bbf0262911f24c7c9665246f9b396a6a09a624"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.3842",
    "kind": "arxiv",
    "version": 2
  }
}