Pith Number

pith:2ONGAPGJ

pith:2021:2ONGAPGJD5U4HQPU7GPPF7MGR5

not attested not anchored not stored refs pending

Complex ellipsoids and complex symmetry

Javier Bracho, Jorge Arocha, Luis Montejano

arxiv:2111.14280 v1 · 2021-11-29 · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2ONGAPGJD5U4HQPU7GPPF7MGR5}

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	2026-07-05T03:35:41.110241Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d39a603cc91f69c3c1f4f99ef2fd868f4a11a26e9768e3c36757447ed9218102

Aliases

arxiv: 2111.14280 · arxiv_version: 2111.14280v1 · doi: 10.48550/arxiv.2111.14280 · pith_short_12: 2ONGAPGJD5U4 · pith_short_16: 2ONGAPGJD5U4HQPU · pith_short_8: 2ONGAPGJ

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/2ONGAPGJD5U4HQPU7GPPF7MGR5 \
  | 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: d39a603cc91f69c3c1f4f99ef2fd868f4a11a26e9768e3c36757447ed9218102

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6eb469f4100d380e9846666021a030023e7bf5fe4993c248da33f11712f6a9af",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2021-11-29T00:40:10Z",
    "title_canon_sha256": "485b9898ee2d583178f92a8b3a2d03160b3338fa73a33a4d002b5d81b64588c9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2111.14280",
    "kind": "arxiv",
    "version": 1
  }
}