Pith Number

pith:UY6QCJXQ

pith:2012:UY6QCJXQWDR2M3HQEWLU2J4YUM

not attested not anchored not stored refs pending

Brennan's conjecture for composition operators on Sobolev spaces

Alexander Ukhlov, Vladimir Gol'dshtein

arxiv:1212.3999 v3 · 2012-12-17 · math.CV

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UY6QCJXQWDR2M3HQEWLU2J4YUM}

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	2026-05-18T03:33:39.621725Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a63d0126f0b0e3a66cf025974d2798a302f86db4cc55949e29ac399d89eca61d

Aliases

arxiv: 1212.3999 · arxiv_version: 1212.3999v3 · doi: 10.48550/arxiv.1212.3999 · pith_short_12: UY6QCJXQWDR2 · pith_short_16: UY6QCJXQWDR2M3HQ · pith_short_8: UY6QCJXQ

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/UY6QCJXQWDR2M3HQEWLU2J4YUM \
  | 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: a63d0126f0b0e3a66cf025974d2798a302f86db4cc55949e29ac399d89eca61d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dc81dca029bea9074d8fbdf8dfb3de9c1189005952b59c4101758d04321314c1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CV",
    "submitted_at": "2012-12-17T14:17:35Z",
    "title_canon_sha256": "59dfe14a8cc954276dbcce02a75e415c9d816eab3d6242e03f7a964672fb8697"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.3999",
    "kind": "arxiv",
    "version": 3
  }
}