Pith Number

pith:WNJSF2BC

pith:2012:WNJSF2BCOW5BSUL7F7NHKMCNL6

not attested not anchored not stored refs pending

A Bellman function proof of the $L^2$ bump conjecture

Alexander Reznikov, Alexander Volberg, Fedor Nazarov, Sergei Treil

arxiv:1202.2406 v3 · 2012-02-11 · math.CA · 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{WNJSF2BCOW5BSUL7F7NHKMCNL6}

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	2026-05-18T02:54:39.804552Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b35322e82275ba19517f2fda75304d5f9c2772417857b25a0d07e47ff07f9c07

Aliases

arxiv: 1202.2406 · arxiv_version: 1202.2406v3 · doi: 10.48550/arxiv.1202.2406 · pith_short_12: WNJSF2BCOW5B · pith_short_16: WNJSF2BCOW5BSUL7 · pith_short_8: WNJSF2BC

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/WNJSF2BCOW5BSUL7F7NHKMCNL6 \
  | 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: b35322e82275ba19517f2fda75304d5f9c2772417857b25a0d07e47ff07f9c07

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bd8c821908c6f91f68c3c453a75ba45dfe86193a5f0ee2bc24fc78c8df415500",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2012-02-11T03:47:46Z",
    "title_canon_sha256": "317c875a3ed376ba390e665ac36e2d0ac1904c530b246aafddb1b4ec15521491"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1202.2406",
    "kind": "arxiv",
    "version": 3
  }
}