Pith Number

pith:FAQ3E4C3

pith:2012:FAQ3E4C3Q4UZU43O7MGWV76STW

not attested not anchored not stored refs pending

Asymptotic stability in the energy space for dark solitons of the Gross-Pitaevskii equation

Didier Smets (LJLL), Fabrice B\'ethuel (LJLL), Philippe Gravejat (CMLS-EcolePolytechnique)

arxiv:1212.5027 v2 · 2012-12-20 · 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{FAQ3E4C3Q4UZU43O7MGWV76STW}

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	2026-05-18T03:18:51.583063Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2821b2705b87299a736efb0d6affd29dae6301f6e1de4baae9ca84e0deb964dc

Aliases

arxiv: 1212.5027 · arxiv_version: 1212.5027v2 · doi: 10.48550/arxiv.1212.5027 · pith_short_12: FAQ3E4C3Q4UZ · pith_short_16: FAQ3E4C3Q4UZU43O · pith_short_8: FAQ3E4C3

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/FAQ3E4C3Q4UZU43O7MGWV76STW \
  | 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: 2821b2705b87299a736efb0d6affd29dae6301f6e1de4baae9ca84e0deb964dc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "312c502be9e207599a0ccbbf7b5bfad0c5aa67eede4094ec7e2fc8aa249921e2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2012-12-20T13:31:38Z",
    "title_canon_sha256": "86097b7d498b3d51361d817437cae0fecbaee9e0fe3a980137978ff7c3e498d9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.5027",
    "kind": "arxiv",
    "version": 2
  }
}