Pith Number

pith:ZHQSNK55

pith:2012:ZHQSNK55VMNFWB7YZR5IX7UBTO

not attested not anchored not stored refs pending

Sobolev regularity for Monge-Amp\`ere type equations

Alessio Figalli, Guido De Philippis

arxiv:1211.2341 v1 · 2012-11-10 · 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{ZHQSNK55VMNFWB7YZR5IX7UBTO}

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	2026-05-18T03:41:03.698692Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c9e126abbdab1a5b07f8cc7a8bfe819bae03f42130ef8b450c917778a1c24813

Aliases

arxiv: 1211.2341 · arxiv_version: 1211.2341v1 · doi: 10.48550/arxiv.1211.2341 · pith_short_12: ZHQSNK55VMNF · pith_short_16: ZHQSNK55VMNFWB7Y · pith_short_8: ZHQSNK55

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/ZHQSNK55VMNFWB7YZR5IX7UBTO \
  | 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: c9e126abbdab1a5b07f8cc7a8bfe819bae03f42130ef8b450c917778a1c24813

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a6fd328ecbdbcad29ba1a4712e54ab570fdd1ae1fdca43e420b9f97d263eed79",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2012-11-10T18:09:56Z",
    "title_canon_sha256": "da88b7beeafb81c5f8c58ec8701c6ad3b84de9481e3d7e6cffacb58d5d02ac90"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.2341",
    "kind": "arxiv",
    "version": 1
  }
}