Pith Number

pith:SYZ3XUXV

pith:2011:SYZ3XUXV57RDWNHSIFHECBUVRX

not attested not anchored not stored refs pending

Critical points of the Moser-Trudinger functional

Andrea Malchiodi, Francesca De Marchis, Luca Martinazzi

arxiv:1108.5576 v2 · 2011-08-29 · 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{SYZ3XUXV57RDWNHSIFHECBUVRX}

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	2026-05-18T04:12:54.294904Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9633bbd2f5efe23b34f2414e4106958dfa180dc0924118a4290ec837852b12b8

Aliases

arxiv: 1108.5576 · arxiv_version: 1108.5576v2 · doi: 10.48550/arxiv.1108.5576 · pith_short_12: SYZ3XUXV57RD · pith_short_16: SYZ3XUXV57RDWNHS · pith_short_8: SYZ3XUXV

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/SYZ3XUXV57RDWNHSIFHECBUVRX \
  | 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: 9633bbd2f5efe23b34f2414e4106958dfa180dc0924118a4290ec837852b12b8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "438573b2bbfb251c0624e796154d98a0851274e773fc8161456a59a5f2651a8a",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2011-08-29T14:38:53Z",
    "title_canon_sha256": "69ba2aec70502fffd72cc180c8a4947994d2be5d607058611d62f50e64fc6daa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.5576",
    "kind": "arxiv",
    "version": 2
  }
}