Pith Number

pith:GD7BRCOM

pith:2016:GD7BRCOMZJCIEY4BE7YTVZWLRU

not attested not anchored not stored refs pending

The Morse index of the critical catenoid

Detang Zhou, Graham Smith

arxiv:1609.01485 v2 · 2016-09-06 · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GD7BRCOMZJCIEY4BE7YTVZWLRU}

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	2026-05-18T00:44:37.023918Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

30fe1889ccca4482638127f13ae6cb8d0e3121eaa7c24f9833e39311ccded62f

Aliases

arxiv: 1609.01485 · arxiv_version: 1609.01485v2 · doi: 10.48550/arxiv.1609.01485 · pith_short_12: GD7BRCOMZJCI · pith_short_16: GD7BRCOMZJCIEY4B · pith_short_8: GD7BRCOM

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/GD7BRCOMZJCIEY4BE7YTVZWLRU \
  | 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: 30fe1889ccca4482638127f13ae6cb8d0e3121eaa7c24f9833e39311ccded62f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a66a35e779e20664345e957ab55f684c1f37f991aa1937c304c62ef3e010f54b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2016-09-06T11:05:41Z",
    "title_canon_sha256": "f51c3196b0dc4ac485955a4fc0a88dd06f4f1f38f9666fba9c2eb0888595758b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.01485",
    "kind": "arxiv",
    "version": 2
  }
}