Pith Number

pith:YMTCSWSZ

pith:2013:YMTCSWSZPQS5HF4QHMT7MTZOC7

not attested not anchored not stored refs pending

Branches of non-symmetric critical points and symmetry breaking in nonlinear elliptic partial differential equations

Jean Dolbeault (CEREMADE), Maria J. Esteban (CEREMADE)

arxiv:1304.4000 v2 · 2013-04-15 · 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{YMTCSWSZPQS5HF4QHMT7MTZOC7}

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	2026-05-18T02:57:24.023333Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c326295a597c25d397903b27f64f2e17ea4b33784645c12336a4268277637a29

Aliases

arxiv: 1304.4000 · arxiv_version: 1304.4000v2 · doi: 10.48550/arxiv.1304.4000 · pith_short_12: YMTCSWSZPQS5 · pith_short_16: YMTCSWSZPQS5HF4Q · pith_short_8: YMTCSWSZ

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/YMTCSWSZPQS5HF4QHMT7MTZOC7 \
  | 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: c326295a597c25d397903b27f64f2e17ea4b33784645c12336a4268277637a29

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9edc2b868838f5d7a522d822cf40ea566695cb9ea929b68216ffec5aa17362aa",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2013-04-15T06:55:32Z",
    "title_canon_sha256": "6a2af079fff2fb58b4999b3c370220200a6beb6aca8da7678365fb30a336a606"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1304.4000",
    "kind": "arxiv",
    "version": 2
  }
}