Pith Number

pith:5JZV6RCX

pith:2012:5JZV6RCXNIUMQTQHTMGH6KYBZA

not attested not anchored not stored refs pending

An optimal bound on the number of interior spike solutions for Lin-Ni-Takagi problem

Jing Zeng, Juncheng Wei, Weiwei Ao

arxiv:1209.2824 v1 · 2012-09-13 · math.AP · math.CA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5JZV6RCXNIUMQTQHTMGH6KYBZA}

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	2026-05-18T03:45:40.858600Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ea735f44576a28c84e079b0c7f2b01c8250e26c652d4ed88277277d2708a5826

Aliases

arxiv: 1209.2824 · arxiv_version: 1209.2824v1 · doi: 10.48550/arxiv.1209.2824 · pith_short_12: 5JZV6RCXNIUM · pith_short_16: 5JZV6RCXNIUMQTQH · pith_short_8: 5JZV6RCX

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/5JZV6RCXNIUMQTQHTMGH6KYBZA \
  | 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: ea735f44576a28c84e079b0c7f2b01c8250e26c652d4ed88277277d2708a5826

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f339689fa315201742eba96439f0ea5057c06aa2c258415c54671f4f49710399",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2012-09-13T09:13:45Z",
    "title_canon_sha256": "dea81b7b20a6a543104e447f42f9453c253113b23c95ad076e4abd3b44e9fc17"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.2824",
    "kind": "arxiv",
    "version": 1
  }
}