Pith Number

pith:GA5IGEQR

pith:2011:GA5IGEQRCT4CTWANYBRUEBEKB6

not attested not anchored not stored refs pending

Sobolev stability of plane wave solutions to the cubic nonlinear Schr\"odinger equation on a torus

Christian Lubich, Erwan Faou (IRMAR, Inria - Irmar), Ludwig Gauckler

arxiv:1109.2407 v2 · 2011-09-12 · 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{GA5IGEQRCT4CTWANYBRUEBEKB6}

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	2026-05-18T03:43:28.650773Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

303a83121114f829d80dc06342048a0fa2b592c988df2a184a9347583a0d8a7a

Aliases

arxiv: 1109.2407 · arxiv_version: 1109.2407v2 · doi: 10.48550/arxiv.1109.2407 · pith_short_12: GA5IGEQRCT4C · pith_short_16: GA5IGEQRCT4CTWAN · pith_short_8: GA5IGEQR

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/GA5IGEQRCT4CTWANYBRUEBEKB6 \
  | 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: 303a83121114f829d80dc06342048a0fa2b592c988df2a184a9347583a0d8a7a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "528179a5779f8c857e0792694fb34ddb23a31b44f4c85915b6006d296902af77",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2011-09-12T09:09:45Z",
    "title_canon_sha256": "ea483eaf5d45bdd0dd79e4516e394dd97210eb95b940d77bb1221db382326407"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.2407",
    "kind": "arxiv",
    "version": 2
  }
}