Pith Number

pith:64VW3VLQ

pith:2009:64VW3VLQLTHPACZOZR2OCF2LHZ

not attested not anchored not stored refs pending

The number of extreme points of tropical polyhedra

Ricardo D. Katz, Stephane Gaubert, Xavier Allamigeon

arxiv:0906.3492 v1 · 2009-06-18 · math.CO · 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{64VW3VLQLTHPACZOZR2OCF2LHZ}

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	2026-05-18T04:37:20.855341Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f72b6dd5705ccef00b2ecc74e1174b3e70ce4960574f5aebe6fa42762bf7d60b

Aliases

arxiv: 0906.3492 · arxiv_version: 0906.3492v1 · doi: 10.48550/arxiv.0906.3492 · pith_short_12: 64VW3VLQLTHP · pith_short_16: 64VW3VLQLTHPACZO · pith_short_8: 64VW3VLQ

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/64VW3VLQLTHPACZOZR2OCF2LHZ \
  | 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: f72b6dd5705ccef00b2ecc74e1174b3e70ce4960574f5aebe6fa42762bf7d60b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b4c3d8c5601d41f053b0075ce1bf2519bd27c6b5710a430a5c548d01aeac7a9b",
    "cross_cats_sorted": [
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2009-06-18T18:07:24Z",
    "title_canon_sha256": "e106b6e3161def4aebd022fe92683f906bc707ac2f3b02a36f8232a8ddaa81ba"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0906.3492",
    "kind": "arxiv",
    "version": 1
  }
}