Pith Number

pith:VKTTBAWK

pith:2011:VKTTBAWKSLCDC4YTYIZGPECMEQ

not attested not anchored not stored refs pending

The defocusing energy-supercritical cubic nonlinear wave equation in dimension five

Aynur Bulut

arxiv:1112.0629 v2 · 2011-12-03 · 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{VKTTBAWKSLCDC4YTYIZGPECMEQ}

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	2026-05-18T01:37:02.734326Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aaa73082ca92c4317313c23267904c2410ed1b7fa542f527c0517924ab08bcc9

Aliases

arxiv: 1112.0629 · arxiv_version: 1112.0629v2 · doi: 10.48550/arxiv.1112.0629 · pith_short_12: VKTTBAWKSLCD · pith_short_16: VKTTBAWKSLCDC4YT · pith_short_8: VKTTBAWK

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/VKTTBAWKSLCDC4YTYIZGPECMEQ \
  | 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: aaa73082ca92c4317313c23267904c2410ed1b7fa542f527c0517924ab08bcc9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d123e861bd81c622067e3e764c53de2863bdcea3cd5be706bdc084c5fca4474d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2011-12-03T07:47:25Z",
    "title_canon_sha256": "d4536d358626219b6dd23c3adb806157b0a47e0a49aacbe2027f57127aecf1df"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.0629",
    "kind": "arxiv",
    "version": 2
  }
}