Pith Number

pith:IZHQUYXB

pith:2016:IZHQUYXBLTZAT6CWGYOK4YU7I3

not attested not anchored not stored refs pending

An Endpoint Version of Uniform Sobolev Inequalities

Cheng Zhang, Tianyi Ren, Yakun Xi

arxiv:1612.01056 v2 · 2016-12-04 · math.AP · 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{IZHQUYXBLTZAT6CWGYOK4YU7I3}

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	2026-05-18T00:09:36.777828Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

464f0a62e15cf209f856361cae629f46d206bb58c4460299b0f3e5074cef7b26

Aliases

arxiv: 1612.01056 · arxiv_version: 1612.01056v2 · doi: 10.48550/arxiv.1612.01056 · pith_short_12: IZHQUYXBLTZA · pith_short_16: IZHQUYXBLTZAT6CW · pith_short_8: IZHQUYXB

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/IZHQUYXBLTZAT6CWGYOK4YU7I3 \
  | 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: 464f0a62e15cf209f856361cae629f46d206bb58c4460299b0f3e5074cef7b26

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5c7388982206f4af2534465e98bede68cfe51e6d0237271a2675b1cf15a424bf",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2016-12-04T03:31:13Z",
    "title_canon_sha256": "5ad5511b61da4b6250e4967202519baa72a41f67c1d4fab9fccd92d2c2266b98"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.01056",
    "kind": "arxiv",
    "version": 2
  }
}