Pith Number

pith:2EXIZ6NF

pith:2001:2EXIZ6NF37VWD5OUOWEKJCTCW3

not attested not anchored not stored refs pending

Multiplicity of closed characteristics on symmetric convex hypersurfaces in $\R^{2n}$

Chaofeng Zhu, Chun-gen Liu, Yiming Long

arxiv:math/0109171 v1 · 2001-09-23 · 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{2EXIZ6NF37VWD5OUOWEKJCTCW3}

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	2026-05-18T02:47:13.483487Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d12e8cf9a5dfeb61f5d47588a48a62b6c82abf19c5c68d29325ebbdcc8aeb608

Aliases

arxiv: math/0109171 · arxiv_version: math/0109171v1 · doi: 10.48550/arxiv.math/0109171 · pith_short_12: 2EXIZ6NF37VW · pith_short_16: 2EXIZ6NF37VWD5OU · pith_short_8: 2EXIZ6NF

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/2EXIZ6NF37VWD5OUOWEKJCTCW3 \
  | 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: d12e8cf9a5dfeb61f5d47588a48a62b6c82abf19c5c68d29325ebbdcc8aeb608

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a2ea50845bdbe72dacda6b4d1bd188bf07cfb99d6b357b5f2cf1f57e2f9c5902",
    "cross_cats_sorted": [
      "math.SG"
    ],
    "license": "",
    "primary_cat": "math.DS",
    "submitted_at": "2001-09-23T13:06:38Z",
    "title_canon_sha256": "77444faf502ddc691b58ce53fb49935dfd1a903ff69bfad6cc745cb4b20e26c1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0109171",
    "kind": "arxiv",
    "version": 1
  }
}