Pith Number

pith:2JOPVZ5F

pith:2016:2JOPVZ5FQE6F7YYJPBQRNLQBB4

not attested not anchored not stored refs pending

Nash multiplicities and isolated points of maximum multiplicity

Beatriz Pascual-Escudero

arxiv:1609.09008 v3 · 2016-09-28 · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2JOPVZ5FQE6F7YYJPBQRNLQBB4}

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	2026-05-18T00:05:34.683425Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d25cfae7a5813c5fe309786116ae010f0b14fdeee38eedc6620b3171b6fddbde

Aliases

arxiv: 1609.09008 · arxiv_version: 1609.09008v3 · doi: 10.48550/arxiv.1609.09008 · pith_short_12: 2JOPVZ5FQE6F · pith_short_16: 2JOPVZ5FQE6F7YYJ · pith_short_8: 2JOPVZ5F

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/2JOPVZ5FQE6F7YYJPBQRNLQBB4 \
  | 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: d25cfae7a5813c5fe309786116ae010f0b14fdeee38eedc6620b3171b6fddbde

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bd5cf6a2eee1dff3ecfc115d8d2f45cf8a2e01f9ae84009ecc3dde02333b4705",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2016-09-28T17:05:39Z",
    "title_canon_sha256": "a6edaa0ed43d5fae07b7e9936cf66dcafcac0a628c9571d5a005b9e61e9a9ee1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.09008",
    "kind": "arxiv",
    "version": 3
  }
}