Pith Number

pith:SA33OCXL

pith:2011:SA33OCXLTOBLFX4EJGSVG5T2MB

not attested not anchored not stored refs pending

Riemann-Roch theory for weighted graphs and tropical curves

Lucia Caporaso, Omid Amini

arxiv:1112.5134 v3 · 2011-12-21 · math.CO · 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{SA33OCXLTOBLFX4EJGSVG5T2MB}

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	2026-05-18T03:31:45.120405Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9037b70aeb9b82b2df8449a553767a605ce12fff7e0febf5ee2b69ad347f73a1

Aliases

arxiv: 1112.5134 · arxiv_version: 1112.5134v3 · doi: 10.48550/arxiv.1112.5134 · pith_short_12: SA33OCXLTOBL · pith_short_16: SA33OCXLTOBLFX4E · pith_short_8: SA33OCXL

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/SA33OCXLTOBLFX4EJGSVG5T2MB \
  | 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: 9037b70aeb9b82b2df8449a553767a605ce12fff7e0febf5ee2b69ad347f73a1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "02137a6a80d0051873bb33c1306cec34a67276bf9f33f451aa2af99d197873c1",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-12-21T18:59:28Z",
    "title_canon_sha256": "f673f9b859336f0dd82b82862cf5f2001d09636edc549c0506f0fe98d89b2f89"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.5134",
    "kind": "arxiv",
    "version": 3
  }
}