Pith Number

pith:YVCQ4FHY

pith:2016:YVCQ4FHYFB2TFJ6WZZG33VBBMB

not attested not anchored not stored refs pending

Entire radial and nonradial solutions for systems with critical growth

Christophe Troestler, Francesca Gladiali, Massimo Grossi

arxiv:1612.03510 v1 · 2016-12-12 · 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{YVCQ4FHYFB2TFJ6WZZG33VBBMB}

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	2026-05-18T00:55:19.079688Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c5450e14f8287532a7d6ce4dbdd421607ee35d3f367fdec4b1ea7a3bdd59ab4b

Aliases

arxiv: 1612.03510 · arxiv_version: 1612.03510v1 · doi: 10.48550/arxiv.1612.03510 · pith_short_12: YVCQ4FHYFB2T · pith_short_16: YVCQ4FHYFB2TFJ6W · pith_short_8: YVCQ4FHY

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/YVCQ4FHYFB2TFJ6WZZG33VBBMB \
  | 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: c5450e14f8287532a7d6ce4dbdd421607ee35d3f367fdec4b1ea7a3bdd59ab4b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e27a2ce863b33dc7311b65de624bc899e1913213519d257970d3b72e9721289e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2016-12-12T01:14:54Z",
    "title_canon_sha256": "3a0f66a5b37b3b31782fbcf217ce3340220ab5e7fd3155faad2467d1d989c07e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.03510",
    "kind": "arxiv",
    "version": 1
  }
}