Pith Number

pith:PS5OMDKE

pith:2009:PS5OMDKEAHAFEX4NGWUQ5FK3QF

not attested not anchored not stored refs pending

Bifurcation of constant mean curvature tori in Euclidean spheres

Luis J. Alias, Paolo Piccione

arxiv:0905.2128 v2 · 2009-05-13 · 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{PS5OMDKEAHAFEX4NGWUQ5FK3QF}

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	2026-05-18T04:34:54.433270Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7cbae60d4401c0525f8d35a90e955b815b3c8fc81ab94fc134a0f580ac41a12c

Aliases

arxiv: 0905.2128 · arxiv_version: 0905.2128v2 · doi: 10.48550/arxiv.0905.2128 · pith_short_12: PS5OMDKEAHAF · pith_short_16: PS5OMDKEAHAFEX4N · pith_short_8: PS5OMDKE

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/PS5OMDKEAHAFEX4NGWUQ5FK3QF \
  | 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: 7cbae60d4401c0525f8d35a90e955b815b3c8fc81ab94fc134a0f580ac41a12c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "99119fa4480627a8f84d8a8666625d99929b388f9ec93927bb63045858ba98f1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2009-05-13T14:46:57Z",
    "title_canon_sha256": "d348d67aff3f99eea30f430ccf0a99624918fd6c6412ba8b42e638ed6c7a8b97"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0905.2128",
    "kind": "arxiv",
    "version": 2
  }
}