Pith Number

pith:AY27Q3SW

pith:2012:AY27Q3SWOOD7QKWAR67LUGX6XW

not attested not anchored not stored refs pending

On the sharpness of Mockenhaupt's restriction theorem

Izabella Laba, Kyle Hambrook

arxiv:1211.6069 v3 · 2012-11-26 · 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{AY27Q3SWOOD7QKWAR67LUGX6XW}

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	2026-05-18T03:21:31.345721Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0635f86e567387f82ac08fbeba1afebdad7a8506fce3185657fb61fa041c27fc

Aliases

arxiv: 1211.6069 · arxiv_version: 1211.6069v3 · doi: 10.48550/arxiv.1211.6069 · pith_short_12: AY27Q3SWOOD7 · pith_short_16: AY27Q3SWOOD7QKWA · pith_short_8: AY27Q3SW

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/AY27Q3SWOOD7QKWAR67LUGX6XW \
  | 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: 0635f86e567387f82ac08fbeba1afebdad7a8506fce3185657fb61fa041c27fc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dbcd5268bdee86fcb5df280116b4ba994a0c0e25d6a625659266f0ffebaa0f46",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2012-11-26T19:19:07Z",
    "title_canon_sha256": "f443ee0754b563a4dda3b90037274b8a5c023519dae352c6a6095965e0f18ea8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.6069",
    "kind": "arxiv",
    "version": 3
  }
}