Pith Number

pith:YR3QV2GR

pith:2016:YR3QV2GR73SNDBNUUURVYBUFSI

not attested not anchored not stored refs pending

Multiplicity and concentration behavior of solutions to the critical Kirchhoff type problem

Jian Zhang, Wenming Zou

arxiv:1607.03668 v1 · 2016-07-13 · 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{YR3QV2GR73SNDBNUUURVYBUFSI}

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	2026-05-18T00:44:00.690535Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c4770ae8d1fee4d185b4a5235c068592378a28d2332b10a62dd03bcc6c45ab3e

Aliases

arxiv: 1607.03668 · arxiv_version: 1607.03668v1 · doi: 10.48550/arxiv.1607.03668 · pith_short_12: YR3QV2GR73SN · pith_short_16: YR3QV2GR73SNDBNU · pith_short_8: YR3QV2GR

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/YR3QV2GR73SNDBNUUURVYBUFSI \
  | 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: c4770ae8d1fee4d185b4a5235c068592378a28d2332b10a62dd03bcc6c45ab3e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0a6f06c8f6215a3682f07fadcc821a2897140921e9ecf786400195d817ed6cf4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2016-07-13T10:40:35Z",
    "title_canon_sha256": "2bd8c9c25ffa6217289d1192095addde7172f5755753d4633764b9570ca1243f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1607.03668",
    "kind": "arxiv",
    "version": 1
  }
}