Pith Number

pith:AAFWZNPK

pith:2016:AAFWZNPKF34OAHV53KE7JZPWEK

not attested not anchored not stored refs pending

The Moser-Trudinger inequality and its extremals on a disk via energy estimates

Gabriele Mancini, Luca Martinazzi

arxiv:1608.07169 v2 · 2016-08-25 · 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{AAFWZNPKF34OAHV53KE7JZPWEK}

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	2026-05-18T00:45:01.534228Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

000b6cb5ea2ef8e01ebdda89f4e5f6229c01ae66ecd2f05dfc328c933dec32c9

Aliases

arxiv: 1608.07169 · arxiv_version: 1608.07169v2 · doi: 10.48550/arxiv.1608.07169 · pith_short_12: AAFWZNPKF34O · pith_short_16: AAFWZNPKF34OAHV5 · pith_short_8: AAFWZNPK

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/AAFWZNPKF34OAHV53KE7JZPWEK \
  | 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: 000b6cb5ea2ef8e01ebdda89f4e5f6229c01ae66ecd2f05dfc328c933dec32c9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cb1365ca3185961fb7b87d2d579f08d75698fb9c3aea8fc478db352ca68d902f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2016-08-25T14:25:49Z",
    "title_canon_sha256": "566223f400da8a066337c9116d329f51565cd1c644be4796da7cb32b9ddd38ab"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1608.07169",
    "kind": "arxiv",
    "version": 2
  }
}