Pith Number

pith:AJV2NVRN

pith:2010:AJV2NVRNC7ICHJOR3QDPC7ACQF

not attested not anchored not stored refs pending

Lifting Tropical Curves in Space and Linear Systems on Graphs

Eric Katz

arxiv:1009.1783 v3 · 2010-09-09 · 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{AJV2NVRNC7ICHJOR3QDPC7ACQF}

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	2026-05-18T04:15:04.383441Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

026ba6d62d17d023a5d1dc06f17c02815d20f2d4b9ff7bc72a3cf192568ca0fd

Aliases

arxiv: 1009.1783 · arxiv_version: 1009.1783v3 · doi: 10.48550/arxiv.1009.1783 · pith_short_12: AJV2NVRNC7IC · pith_short_16: AJV2NVRNC7ICHJOR · pith_short_8: AJV2NVRN

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/AJV2NVRNC7ICHJOR3QDPC7ACQF \
  | 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: 026ba6d62d17d023a5d1dc06f17c02815d20f2d4b9ff7bc72a3cf192568ca0fd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "42a8828d4be91694c97face626ce839bb022172c3aac32b22b283fe7e5fe4d41",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2010-09-09T14:00:55Z",
    "title_canon_sha256": "54cbbeb3dcb1690c4e420b0fc4efd5e5c61e114ad2b7d61fbbd4a8f92b0873ac"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.1783",
    "kind": "arxiv",
    "version": 3
  }
}