Pith Number

pith:DRLS67RL

pith:2013:DRLS67RLBS625Q3OS3BA4YFCJF

not attested not anchored not stored refs pending

The existence of two closed characteristics on every compact star-shaped hypersurface in ${\bf R}^4$

Hui Liu, Yiming Long

arxiv:1308.3904 v2 · 2013-08-19 · math.DS · math.SG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DRLS67RLBS625Q3OS3BA4YFCJF}

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	2026-05-18T02:48:26.096584Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1c572f7e2b0cbdaec36e96c20e60a2496677bd99b603a3445109d8d5481ebcc5

Aliases

arxiv: 1308.3904 · arxiv_version: 1308.3904v2 · doi: 10.48550/arxiv.1308.3904 · pith_short_12: DRLS67RLBS62 · pith_short_16: DRLS67RLBS625Q3O · pith_short_8: DRLS67RL

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/DRLS67RLBS625Q3OS3BA4YFCJF \
  | 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: 1c572f7e2b0cbdaec36e96c20e60a2496677bd99b603a3445109d8d5481ebcc5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "125a02afe4f26bda45706cd540461f6a9e7e0c51ebf7fafde0cda1f84678cbe0",
    "cross_cats_sorted": [
      "math.SG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2013-08-19T00:51:03Z",
    "title_canon_sha256": "53b8889dfb5d2ca521c24cbc7ddc1669f8bbdb29be814030c727adea48de8b4a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1308.3904",
    "kind": "arxiv",
    "version": 2
  }
}