Pith Number

pith:VUK4XINB

pith:2012:VUK4XINBRIUPCWNOSLDU3MXGWQ

not attested not anchored not stored refs pending

Verified Error Bounds for Isolated Singular Solutions of Polynomial Systems

Lihong Zhi, Nan Li

arxiv:1212.4699 v1 · 2012-12-19 · math.NA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VUK4XINBRIUPCWNOSLDU3MXGWQ}

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	2026-05-18T03:38:11.734748Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ad15cba1a18a28f159ae92c74db2e6b41fb0c6f828c67a14f69b9f7c49ce8f07

Aliases

arxiv: 1212.4699 · arxiv_version: 1212.4699v1 · doi: 10.48550/arxiv.1212.4699 · pith_short_12: VUK4XINBRIUP · pith_short_16: VUK4XINBRIUPCWNO · pith_short_8: VUK4XINB

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/VUK4XINBRIUPCWNOSLDU3MXGWQ \
  | 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: ad15cba1a18a28f159ae92c74db2e6b41fb0c6f828c67a14f69b9f7c49ce8f07

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3c350bb027e34caaf66949701ca99d0aefc6b9b72113a58eef6917d74644f9e9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2012-12-19T15:10:23Z",
    "title_canon_sha256": "fef2658570b6857f823cafb47bb464ce2c4027cc1a385cece37aae09371a2074"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.4699",
    "kind": "arxiv",
    "version": 1
  }
}