Pith Number

pith:FKCPWY25

pith:2012:FKCPWY25ZSH44MHHKHLPHSTULD

not attested not anchored not stored refs pending

Critical points of the Moser-Trudinger functional on a disk

Andrea Malchiodi, Luca Martinazzi

arxiv:1203.1077 v1 · 2012-03-06 · math.FA · 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{FKCPWY25ZSH44MHHKHLPHSTULD}

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	2026-05-18T01:36:15.992342Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2a84fb635dcc8fce30e751d6f3ca7458e60dd4456e1dc4de40d69b3611df9f52

Aliases

arxiv: 1203.1077 · arxiv_version: 1203.1077v1 · doi: 10.48550/arxiv.1203.1077 · pith_short_12: FKCPWY25ZSH4 · pith_short_16: FKCPWY25ZSH44MHH · pith_short_8: FKCPWY25

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/FKCPWY25ZSH44MHHKHLPHSTULD \
  | 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: 2a84fb635dcc8fce30e751d6f3ca7458e60dd4456e1dc4de40d69b3611df9f52

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0a07c9e4c7e83a37a688c47d2a5f2d3b13109ebcd4dc96f55bf642813bce5021",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2012-03-06T00:28:27Z",
    "title_canon_sha256": "df61c7bb688e31f38307c91d67409feb3c70d58870663114d318c3a647664a41"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.1077",
    "kind": "arxiv",
    "version": 1
  }
}