Pith Number

pith:UW63EHED

pith:2011:UW63EHEDGFHMQ2354TCTAF4GNT

not attested not anchored not stored refs pending

A new bound on the Morse index of constant mean curvature tori of revolution in $\mathbb{S}^3$

Antonio Ca\~nete

arxiv:1102.1565 v1 · 2011-02-08 · 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{UW63EHEDGFHMQ2354TCTAF4GNT}

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	2026-05-18T04:29:52.965284Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a5bdb21c83314ec86b7de4c53017866cd592db0244474f89734eaffc1f55a0e3

Aliases

arxiv: 1102.1565 · arxiv_version: 1102.1565v1 · doi: 10.48550/arxiv.1102.1565 · pith_short_12: UW63EHEDGFHM · pith_short_16: UW63EHEDGFHMQ235 · pith_short_8: UW63EHED

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/UW63EHEDGFHMQ2354TCTAF4GNT \
  | 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: a5bdb21c83314ec86b7de4c53017866cd592db0244474f89734eaffc1f55a0e3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "afc4c279bfbfe59788d96430bf5cbfee627b00b2593fa9ce90f6eca10a94d098",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2011-02-08T10:48:03Z",
    "title_canon_sha256": "eff6d2539f2870975ba2bd1ca2e2ca83f50d49933b3af34c60b0875226232758"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1102.1565",
    "kind": "arxiv",
    "version": 1
  }
}