Pith Number

pith:PPUBYRWZ

pith:2013:PPUBYRWZ7BBQMXTZGQAYX3U4XR

not attested not anchored not stored refs pending

Gap phenomena for a class of fourth-order geometric differential operators on surfaces with boundary

Glen Wheeler

arxiv:1302.4165 v1 · 2013-02-18 · math.AP · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PPUBYRWZ7BBQMXTZGQAYX3U4XR}

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	2026-05-18T03:33:23.943201Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7be81c46d9f843065e7934018bee9cbc4fe97019232fe9aae25a5fffb82be0a8

Aliases

arxiv: 1302.4165 · arxiv_version: 1302.4165v1 · doi: 10.48550/arxiv.1302.4165 · pith_short_12: PPUBYRWZ7BBQ · pith_short_16: PPUBYRWZ7BBQMXTZ · pith_short_8: PPUBYRWZ

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/PPUBYRWZ7BBQMXTZGQAYX3U4XR \
  | 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: 7be81c46d9f843065e7934018bee9cbc4fe97019232fe9aae25a5fffb82be0a8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2fb0b94bc80d3dd980e292f24a1e816205717cdbfe04f1cbf1841cf0b11c4d22",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2013-02-18T06:40:36Z",
    "title_canon_sha256": "8c0b7f400e8b3448d5075bac9ab1f20138266bed8bc67c23156c76d51b3d9aa0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1302.4165",
    "kind": "arxiv",
    "version": 1
  }
}