Pith Number

pith:7TAFRPN2

pith:2012:7TAFRPN2B4LXFBUCZZBVZZ5XFK

not attested not anchored not stored refs pending

Morse indices of multiple blow-up solutions to the two-dimensional Gel'fand problem

Francesca Gladiali, Hiroshi Ohtsuka, Massimo Grossi, Takashi Suzuki

arxiv:1210.1373 v1 · 2012-10-04 · 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{7TAFRPN2B4LXFBUCZZBVZZ5XFK}

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	2026-05-18T03:44:03.768913Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fcc058bdba0f17728682ce435ce7b72abffd980648a2365d6ed15aa857c882c1

Aliases

arxiv: 1210.1373 · arxiv_version: 1210.1373v1 · doi: 10.48550/arxiv.1210.1373 · pith_short_12: 7TAFRPN2B4LX · pith_short_16: 7TAFRPN2B4LXFBUC · pith_short_8: 7TAFRPN2

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/7TAFRPN2B4LXFBUCZZBVZZ5XFK \
  | 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: fcc058bdba0f17728682ce435ce7b72abffd980648a2365d6ed15aa857c882c1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f4aeeca6201ee4213322723a0b99f17ee8f8e70d7a4b0ac2bbad295cccffa142",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2012-10-04T10:32:52Z",
    "title_canon_sha256": "2371c59d6aba0845442a06ba57e38b6ec14274c234ae9e0ec9e1f40a4a5af421"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.1373",
    "kind": "arxiv",
    "version": 1
  }
}