Pith Number

pith:MKURUNC3

pith:2009:MKURUNC3MJ6XNVR5CFZ7EXG5OY

not attested not anchored not stored refs pending

Adams inequalities on measure spaces

Carlo Morpurgo, Luigi Fontana

arxiv:0906.5103 v4 · 2009-06-29 · 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{MKURUNC3MJ6XNVR5CFZ7EXG5OY}

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	2026-05-18T04:31:12.064639Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

62a91a345b627d76d63d1173f25cdd7624f28a8c828aa59f5d34f3b63fcb4ca7

Aliases

arxiv: 0906.5103 · arxiv_version: 0906.5103v4 · doi: 10.48550/arxiv.0906.5103 · pith_short_12: MKURUNC3MJ6X · pith_short_16: MKURUNC3MJ6XNVR5 · pith_short_8: MKURUNC3

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/MKURUNC3MJ6XNVR5CFZ7EXG5OY \
  | 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: 62a91a345b627d76d63d1173f25cdd7624f28a8c828aa59f5d34f3b63fcb4ca7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0346ac45b726809090a9ccebf80287e3a0bfecbecea44301836e800e168f236d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2009-06-29T07:53:22Z",
    "title_canon_sha256": "1a36a0fae2b9e21dbbe4661c9a10b622789eabe4532a4ff0fe480ee81df8e327"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0906.5103",
    "kind": "arxiv",
    "version": 4
  }
}