Pith Number

pith:V4QGXEDG

pith:2011:V4QGXEDGOPC73KUZJKUQ7KFQHH

not attested not anchored not stored refs pending

Compact complete null curves in Complex 3-space

Antonio Alarcon, Francisco J. Lopez

arxiv:1106.0684 v2 · 2011-06-03 · 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{V4QGXEDGOPC73KUZJKUQ7KFQHH}

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	2026-05-18T02:21:44.275136Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

af206b906673c5fdaa994aa90fa8b039c28ddb2949e2e976aedc1e118a42ed9d

Aliases

arxiv: 1106.0684 · arxiv_version: 1106.0684v2 · doi: 10.48550/arxiv.1106.0684 · pith_short_12: V4QGXEDGOPC7 · pith_short_16: V4QGXEDGOPC73KUZ · pith_short_8: V4QGXEDG

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/V4QGXEDGOPC73KUZJKUQ7KFQHH \
  | 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: af206b906673c5fdaa994aa90fa8b039c28ddb2949e2e976aedc1e118a42ed9d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "86140c8cd14ab4301dbc2d64a9f6b82dad2bb48f5a5397f21155eb5f9ec5f5cf",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2011-06-03T15:13:31Z",
    "title_canon_sha256": "b6d1b2b198d1fc27e5882e9b2f7219b9bcf26ef51323923809436f52d956bbfe"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1106.0684",
    "kind": "arxiv",
    "version": 2
  }
}