Pith Number

pith:PDBTSV5C

pith:2017:PDBTSV5CTTTGKVMCD6HWXURX5Y

not attested not anchored not stored refs pending

Lifting tropical bitangents

Hannah Markwig, Yoav Len

arxiv:1708.04480 v2 · 2017-08-15 · 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{PDBTSV5CTTTGKVMCD6HWXURX5Y}

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.

Cited by

1 paper in Pith

Tropical geometry

Receipt and verification

First computed	2026-07-05T01:59:25.134377Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

78c33957a29ce66555821f8f6bd237ee0627be9203e40e37394b92913ca76b4c

Aliases

arxiv: 1708.04480 · arxiv_version: 1708.04480v2 · doi: 10.48550/arxiv.1708.04480 · pith_short_12: PDBTSV5CTTTG · pith_short_16: PDBTSV5CTTTGKVMC · pith_short_8: PDBTSV5C

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/PDBTSV5CTTTGKVMCD6HWXURX5Y \
  | 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: 78c33957a29ce66555821f8f6bd237ee0627be9203e40e37394b92913ca76b4c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ab3a304631807c2b6fa7da2d3e441e69d37625c83eeb14eafa3bb2d92d44a5fe",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2017-08-15T12:58:32Z",
    "title_canon_sha256": "839aea8dee5cd934dc8f199f64c262f3c4577dedab006fccf980f549a026c01d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1708.04480",
    "kind": "arxiv",
    "version": 2
  }
}