Pith Number

pith:XDV335CZ

pith:2009:XDV335CZTYZQ3SEJ3QR6QJRHPT

not attested not anchored not stored refs pending

Tropical curves with a singularity in a fixed point

Eugenii Shustin, Hannah Markwig, Thomas Markwig

arxiv:0909.1827 v3 · 2009-09-10 · 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{XDV335CZTYZQ3SEJ3QR6QJRHPT}

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	2026-05-18T03:59:25.916360Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b8ebbdf4599e330dc889dc23e826277ceeb1894b3f362e00bccf0d2886be8f27

Aliases

arxiv: 0909.1827 · arxiv_version: 0909.1827v3 · doi: 10.48550/arxiv.0909.1827 · pith_short_12: XDV335CZTYZQ · pith_short_16: XDV335CZTYZQ3SEJ · pith_short_8: XDV335CZ

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/XDV335CZTYZQ3SEJ3QR6QJRHPT \
  | 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: b8ebbdf4599e330dc889dc23e826277ceeb1894b3f362e00bccf0d2886be8f27

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0f3715b6d5727b2c7c405c72701a06d06161f0148d96c695157a4fb0c7df340b",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2009-09-10T19:02:42Z",
    "title_canon_sha256": "202d8694db5c454d41dd1a05b92b7e506cb86ca624d553467789859fdf072151"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0909.1827",
    "kind": "arxiv",
    "version": 3
  }
}