Pith Number

pith:ZPCI23HL

pith:2015:ZPCI23HLODWHRMVIJITQ6FHXFB

not attested not anchored not stored refs pending

Brief introduction to tropical geometry

Erwan Brugall\'e, Grigory Mikhalkin, Ilia Itenberg, Kristin Shaw

arxiv:1502.05950 v1 · 2015-02-20 · 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{ZPCI23HLODWHRMVIJITQ6FHXFB}

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	2026-05-18T02:26:44.462601Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cbc48d6ceb70ec78b2a84a270f14f7284c57c5272dc443eac7f8dbbe3530cb92

Aliases

arxiv: 1502.05950 · arxiv_version: 1502.05950v1 · doi: 10.48550/arxiv.1502.05950 · pith_short_12: ZPCI23HLODWH · pith_short_16: ZPCI23HLODWHRMVI · pith_short_8: ZPCI23HL

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/ZPCI23HLODWHRMVIJITQ6FHXFB \
  | 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: cbc48d6ceb70ec78b2a84a270f14f7284c57c5272dc443eac7f8dbbe3530cb92

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "209228e0c7809636a8b99d09106605ee2ba901a8f6d60109b24a9759f2d52954",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2015-02-20T17:45:36Z",
    "title_canon_sha256": "c3acac703238dafca125b667783731bd49dfb5cfd87d0b89582e02d2021020a6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1502.05950",
    "kind": "arxiv",
    "version": 1
  }
}