Pith Number

pith:BPJ2RPHU

pith:2007:BPJ2RPHU5IR6SC2OXR5VFOCY2F

not attested not anchored not stored refs pending

Coverage processes on spheres and condition numbers for linear programming

Felipe Cucker, Martin Lotz, Peter B\"urgisser

arxiv:0712.2816 v3 · 2007-12-17 · math.PR · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BPJ2RPHU5IR6SC2OXR5VFOCY2F}

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	2026-05-18T04:19:54.967644Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0bd3a8bcf4ea23e90b4ebc7b52b858d16a5a25c607e850956f22985650a83538

Aliases

arxiv: 0712.2816 · arxiv_version: 0712.2816v3 · doi: 10.48550/arxiv.0712.2816 · pith_short_12: BPJ2RPHU5IR6 · pith_short_16: BPJ2RPHU5IR6SC2O · pith_short_8: BPJ2RPHU

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/BPJ2RPHU5IR6SC2OXR5VFOCY2F \
  | 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: 0bd3a8bcf4ea23e90b4ebc7b52b858d16a5a25c607e850956f22985650a83538

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9e9266fd8784ca71daf2b58bf6341bbad05e05131b92950f854cd44150d18241",
    "cross_cats_sorted": [
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2007-12-17T20:58:49Z",
    "title_canon_sha256": "f4cb63a2a98a4672a7af6e9a2c6c14c8a625b02c9289c4021f01ee60f83571af"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0712.2816",
    "kind": "arxiv",
    "version": 3
  }
}