Pith Number

pith:U6Y3K6TX

pith:2015:U6Y3K6TXXQOWMB5MDKKY367ETM

not attested not anchored not stored refs pending

Equivalence of critical and subcritical sharp Trudinger-Moser-Adams inequalities

Guozhen Lu, Lu Zhang, Nguyen Lam

arxiv:1504.04858 v1 · 2015-04-19 · 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{U6Y3K6TXXQOWMB5MDKKY367ETM}

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	2026-05-18T02:18:24.532711Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a7b1b57a77bc1d6607ac1a958dfbe49b1ea7b12fab246a281e56c50911038e29

Aliases

arxiv: 1504.04858 · arxiv_version: 1504.04858v1 · doi: 10.48550/arxiv.1504.04858 · pith_short_12: U6Y3K6TXXQOW · pith_short_16: U6Y3K6TXXQOWMB5M · pith_short_8: U6Y3K6TX

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/U6Y3K6TXXQOWMB5MDKKY367ETM \
  | 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: a7b1b57a77bc1d6607ac1a958dfbe49b1ea7b12fab246a281e56c50911038e29

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "02bb3d9a2edd356f1bd3a2c0e51ab855c656418d8b4d1572402c948a97de87c9",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-04-19T17:04:31Z",
    "title_canon_sha256": "552dd32d284557582cccdb31f5a72e7e324e068e05f7f9ee7dc4d7aebcea328d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1504.04858",
    "kind": "arxiv",
    "version": 1
  }
}