Pith Number

pith:K32PB5NE

pith:2010:K32PB5NEUAVD5UBKDDI4RP5OY3

not attested not anchored not stored refs pending

Morse index of a cyclic polygon

Alena Zhukova, Gaiane Panina

arxiv:1007.2740 v2 · 2010-07-16 · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{K32PB5NEUAVD5UBKDDI4RP5OY3}

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	2026-05-18T04:41:26.022680Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

56f4f0f5a4a02a3ed02a18d1c8bfaec6c7259ec0581edf8b00d9faca156226ae

Aliases

arxiv: 1007.2740 · arxiv_version: 1007.2740v2 · doi: 10.48550/arxiv.1007.2740 · pith_short_12: K32PB5NEUAVD · pith_short_16: K32PB5NEUAVD5UBK · pith_short_8: K32PB5NE

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/K32PB5NEUAVD5UBKDDI4RP5OY3 \
  | 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: 56f4f0f5a4a02a3ed02a18d1c8bfaec6c7259ec0581edf8b00d9faca156226ae

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e7f771ace79550cc7e4deecc783167709b1661bbf3dbaa91aba2c1b5a4e2379e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2010-07-16T11:05:28Z",
    "title_canon_sha256": "045adec16a781753c7dbbe3ba595701d403623ed43a164d3ac44c5a78aca6a1a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1007.2740",
    "kind": "arxiv",
    "version": 2
  }
}