Pith Number

pith:TRZPQFCU

pith:2009:TRZPQFCUDEJOEHBITKRFBK5QTM

not attested not anchored not stored refs pending

Linear Systems on Tropical Curves

Christian Haase, Gregg Musiker, Josephine Yu

arxiv:0909.3685 v1 · 2009-09-21 · math.AG · 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{TRZPQFCUDEJOEHBITKRFBK5QTM}

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	2026-05-18T01:08:31.150014Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9c72f814541912e21c289aa250abb09b1499e3d0efd4c3e1812d71720b0155a0

Aliases

arxiv: 0909.3685 · arxiv_version: 0909.3685v1 · doi: 10.48550/arxiv.0909.3685 · pith_short_12: TRZPQFCUDEJO · pith_short_16: TRZPQFCUDEJOEHBI · pith_short_8: TRZPQFCU

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/TRZPQFCUDEJOEHBITKRFBK5QTM \
  | 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: 9c72f814541912e21c289aa250abb09b1499e3d0efd4c3e1812d71720b0155a0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f30b84d8480d2afabcd0bbc008fbeca4e47515857c3bfbb9a6e6bf84cac89a00",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2009-09-21T05:58:00Z",
    "title_canon_sha256": "bee523434a9995e171503fc83ffc4b697af80a299964e34b454efd3e2f342424"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0909.3685",
    "kind": "arxiv",
    "version": 1
  }
}