Pith Number

pith:GD5GPGAG

pith:2005:GD5GPGAGXJB6LNJMLU7ERPJRE3

not attested not anchored not stored refs pending

Tropical Algebraic Sets, Ideals and An Algebraic Nullstellensatz

Zur Izhakian

arxiv:math/0511059 v3 · 2005-11-02 · math.AC · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GD5GPGAGXJB6LNJMLU7ERPJRE3}

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	2026-05-18T04:42:44.919714Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

30fa679806ba43e5b52c5d3e48bd3126fb5600110127afaf1be0f804e37c607b

Aliases

arxiv: math/0511059 · arxiv_version: math/0511059v3 · doi: 10.48550/arxiv.math/0511059 · pith_short_12: GD5GPGAGXJB6 · pith_short_16: GD5GPGAGXJB6LNJM · pith_short_8: GD5GPGAG

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/GD5GPGAGXJB6LNJMLU7ERPJRE3 \
  | 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: 30fa679806ba43e5b52c5d3e48bd3126fb5600110127afaf1be0f804e37c607b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a03caacfee3287e4215bd1d47c395da79f0a8b944cf1e7989e5b7a1a819d2de0",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2005-11-02T19:05:25Z",
    "title_canon_sha256": "67001799cbbdecb6a2a31a616b389bdbd521b92c72b6fc7b8ec1c0c0039ee9c0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0511059",
    "kind": "arxiv",
    "version": 3
  }
}