Pith Number

pith:6O75NLP3

pith:2009:6O75NLP3YMKNTOIUXBLBV3JIGJ

not attested not anchored not stored refs pending

Minimal half-spaces and external representation of tropical polyhedra

Ricardo D. Katz, Stephane Gaubert

arxiv:0908.1586 v2 · 2009-08-12 · math.OC · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6O75NLP3YMKNTOIUXBLBV3JIGJ}

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	2026-05-18T04:24:43.962989Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f3bfd6adfbc314d9b914b8561aed28326ea00da3d4db22b9da88c56869c46231

Aliases

arxiv: 0908.1586 · arxiv_version: 0908.1586v2 · doi: 10.48550/arxiv.0908.1586 · pith_short_12: 6O75NLP3YMKN · pith_short_16: 6O75NLP3YMKNTOIU · pith_short_8: 6O75NLP3

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/6O75NLP3YMKNTOIUXBLBV3JIGJ \
  | 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: f3bfd6adfbc314d9b914b8561aed28326ea00da3d4db22b9da88c56869c46231

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "edcc0f74a418638e933418dd425a10422d45fb31369b13bdf230ec48a6da4d3d",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2009-08-12T07:55:12Z",
    "title_canon_sha256": "122c06762b97c4c7b308c902a9fa4b97d0391cbb899b3e385cd748f8231d85e0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0908.1586",
    "kind": "arxiv",
    "version": 2
  }
}