Pith Number

pith:WMWO5EQZ

pith:2016:WMWO5EQZ2P4WKSHFU7NGPU7IAS

not attested not anchored not stored refs pending

Lectures on tropical curves and their moduli spaces

Melody Chan

arxiv:1606.02778 v3 · 2016-06-08 · 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{WMWO5EQZ2P4WKSHFU7NGPU7IAS}

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	2026-05-18T00:50:57.044774Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b32cee9219d3f96548e5a7da67d3e804afc37fa3befaf74b55c1362ebbfe84fb

Aliases

arxiv: 1606.02778 · arxiv_version: 1606.02778v3 · doi: 10.48550/arxiv.1606.02778 · pith_short_12: WMWO5EQZ2P4W · pith_short_16: WMWO5EQZ2P4WKSHF · pith_short_8: WMWO5EQZ

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/WMWO5EQZ2P4WKSHFU7NGPU7IAS \
  | 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: b32cee9219d3f96548e5a7da67d3e804afc37fa3befaf74b55c1362ebbfe84fb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "13d246c610a054f159e0beba19ffcfcbbf00df1b1bff420c5dccf2f20a59be86",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2016-06-08T22:59:06Z",
    "title_canon_sha256": "26474bdf8205aa7e3095e30397c9803ea3c613c5c723cb22ed46310441489f0f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1606.02778",
    "kind": "arxiv",
    "version": 3
  }
}