Pith Number

pith:7PF5F4OV

pith:2010:7PF5F4OVHQ2AHYW4IESNX4ZAIZ

not attested not anchored not stored refs pending

Extensions of the Stein-Tomas theorem

Andreas Seeger, Jong-Guk Bak

arxiv:1004.4948 v1 · 2010-04-28 · 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{7PF5F4OVHQ2AHYW4IESNX4ZAIZ}

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	2026-05-18T02:24:15.587294Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fbcbd2f1d53c3403e2dc4124dbf3204674cce2bd0e3076b5881c7b8cf492a0fd

Aliases

arxiv: 1004.4948 · arxiv_version: 1004.4948v1 · doi: 10.48550/arxiv.1004.4948 · pith_short_12: 7PF5F4OVHQ2A · pith_short_16: 7PF5F4OVHQ2AHYW4 · pith_short_8: 7PF5F4OV

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/7PF5F4OVHQ2AHYW4IESNX4ZAIZ \
  | 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: fbcbd2f1d53c3403e2dc4124dbf3204674cce2bd0e3076b5881c7b8cf492a0fd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f52006ec87a5072e781a1dd79003517f7e9db6d31da54ee378bb66b5b243dc3a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2010-04-28T04:05:56Z",
    "title_canon_sha256": "5624d2543e480ab96840df8b25f0cd5dc80d8e5291630517b32dd199e6a9228b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1004.4948",
    "kind": "arxiv",
    "version": 1
  }
}