Pith Number

pith:PLFWZXC5

pith:2015:PLFWZXC55RCGE2J3JTDVFI6OCJ

not attested not anchored not stored refs pending

Uniform bounds via regularity estimates for elliptic PDE with critical growth in the gradient

Boyan Sirakov

arxiv:1509.04495 v1 · 2015-09-15 · 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{PLFWZXC55RCGE2J3JTDVFI6OCJ}

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	2026-05-18T01:32:58.758990Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7acb6cdc5dec4462693b4cc752a3ce12678e37092c5b8750d128f106043af860

Aliases

arxiv: 1509.04495 · arxiv_version: 1509.04495v1 · doi: 10.48550/arxiv.1509.04495 · pith_short_12: PLFWZXC55RCG · pith_short_16: PLFWZXC55RCGE2J3 · pith_short_8: PLFWZXC5

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/PLFWZXC55RCGE2J3JTDVFI6OCJ \
  | 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: 7acb6cdc5dec4462693b4cc752a3ce12678e37092c5b8750d128f106043af860

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "109b017861f1662a0e1fa0af72c9c37bde168d359294472faa8a4db9340298af",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-09-15T11:24:32Z",
    "title_canon_sha256": "c5ce0a3d2fdf1e6cb5b85dc75f477522cf227e363b4346bc394d5a10fcadc003"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.04495",
    "kind": "arxiv",
    "version": 1
  }
}