Pith Number

pith:QSKAKPI6

pith:2015:QSKAKPI63KZ5TU6UUAFEI7HVFX

not attested not anchored not stored refs pending

Paneitz operator for metrics near $S^3$

Fengbo Hang, Paul C. Yang

arxiv:1504.02032 v1 · 2015-04-08 · math.DG · 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{QSKAKPI63KZ5TU6UUAFEI7HVFX}

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	2026-05-18T02:19:17.399686Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8494053d1edab3d9d3d4a00a447cf52dcb98bdf901ab67ffe1e391d4373e3a06

Aliases

arxiv: 1504.02032 · arxiv_version: 1504.02032v1 · doi: 10.48550/arxiv.1504.02032 · pith_short_12: QSKAKPI63KZ5 · pith_short_16: QSKAKPI63KZ5TU6U · pith_short_8: QSKAKPI6

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/QSKAKPI63KZ5TU6UUAFEI7HVFX \
  | 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: 8494053d1edab3d9d3d4a00a447cf52dcb98bdf901ab67ffe1e391d4373e3a06

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "33b0f6e673c8941d149876f1f0c831a7f0b1e6f6a0430a66c26437b3dad86ad5",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2015-04-08T16:47:45Z",
    "title_canon_sha256": "aa484702d0873c3434a663c9f3298478d32cef90ba13008fd179674a3293ae6a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1504.02032",
    "kind": "arxiv",
    "version": 1
  }
}