Pith Number

pith:VHCXSGX7

pith:2015:VHCXSGX7XIEVRH4UHKZYRHDWIV

not attested not anchored not stored refs pending

Ground states of critical and supercritical problems of Brezis-Nirenberg type

Andrzej Szulkin, Angela Pistoia, M\'onica Clapp

arxiv:1501.01519 v1 · 2015-01-07 · 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{VHCXSGX7XIEVRH4UHKZYRHDWIV}

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	2026-05-18T01:09:51.050097Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a9c5791affba09589f943ab3889c764571c73fbeba887437056ba5fe0d6c72fd

Aliases

arxiv: 1501.01519 · arxiv_version: 1501.01519v1 · doi: 10.48550/arxiv.1501.01519 · pith_short_12: VHCXSGX7XIEV · pith_short_16: VHCXSGX7XIEVRH4U · pith_short_8: VHCXSGX7

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/VHCXSGX7XIEVRH4UHKZYRHDWIV \
  | 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: a9c5791affba09589f943ab3889c764571c73fbeba887437056ba5fe0d6c72fd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6a0b923fb429c6323da7e55f23275282487eee55b3d3af8081f36947aee44c8b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-01-07T15:25:20Z",
    "title_canon_sha256": "4fd521191082295e716ec09ec2d5e0db0404a27857cfb10b68808b294b75fe45"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1501.01519",
    "kind": "arxiv",
    "version": 1
  }
}