Pith Number

pith:FATQCOOG

pith:2015:FATQCOOGHOI3IQOAVHU5ON4SRT

not attested not anchored not stored refs pending

Compact Sobolev embeddings and torsion functions

Berardo Ruffini, Lorenzo Brasco

arxiv:1506.04371 v1 · 2015-06-14 · math.AP · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FATQCOOGHOI3IQOAVHU5ON4SRT}

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	2026-05-18T01:49:54.702437Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

28270139c63b91b441c0a9e9d737928cd64bfd8ef605389cc08149c954bb0d80

Aliases

arxiv: 1506.04371 · arxiv_version: 1506.04371v1 · doi: 10.48550/arxiv.1506.04371 · pith_short_12: FATQCOOGHOI3 · pith_short_16: FATQCOOGHOI3IQOA · pith_short_8: FATQCOOG

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/FATQCOOGHOI3IQOAVHU5ON4SRT \
  | 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: 28270139c63b91b441c0a9e9d737928cd64bfd8ef605389cc08149c954bb0d80

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9bcf802d38dd4b234c13b4295dd5cd42cce0a043cc68b6e46c473dbabfd07baf",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-06-14T09:53:19Z",
    "title_canon_sha256": "38a613b267dbdc93373683f0d36f541943774996654c0b817ca600e568ca251f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1506.04371",
    "kind": "arxiv",
    "version": 1
  }
}