Pith Number

pith:MHLJAMLW

pith:2013:MHLJAMLWNHNAJN5TM74B3DGJBL

not attested not anchored not stored refs pending

On improved fractional Sobolev-Poincar\'e inequalities

Antti V. V\"ah\"akangas, Bart{\l}omiej Dyda, Lizaveta Ihnatsyeva

arxiv:1312.5118 v1 · 2013-12-18 · math.CA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MHLJAMLWNHNAJN5TM74B3DGJBL}

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	2026-05-18T03:04:16.210103Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

61d690317669da04b7b367f81d8cc90af73557f6f5ee8c90aaa56b7692301f1c

Aliases

arxiv: 1312.5118 · arxiv_version: 1312.5118v1 · doi: 10.48550/arxiv.1312.5118 · pith_short_12: MHLJAMLWNHNA · pith_short_16: MHLJAMLWNHNAJN5T · pith_short_8: MHLJAMLW

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/MHLJAMLWNHNAJN5TM74B3DGJBL \
  | 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: 61d690317669da04b7b367f81d8cc90af73557f6f5ee8c90aaa56b7692301f1c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ff7a7453e8635ad5e0a67a9ce0f254046a81362dcd1a3abcb18149ad30c0714c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2013-12-18T12:44:36Z",
    "title_canon_sha256": "0c4b9056240d3d68410f99b19ce85496cdb16b09266f3e55339092658c86bde0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.5118",
    "kind": "arxiv",
    "version": 1
  }
}