Pith Number

pith:6K7IU3ZX

pith:2006:6K7IU3ZXCIPFOPGK6ZWEHDGUTY

not attested not anchored not stored refs pending

Tropical curves, their Jacobians and Theta functions

Grigory Mikhalkin, Ilia Zharkov

arxiv:math/0612267 v2 · 2006-12-11 · 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{6K7IU3ZXCIPFOPGK6ZWEHDGUTY}

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	2026-05-18T04:08:53.073257Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f2be8a6f37121e573ccaf66c438cd49e0c1448c6f62c3732f12f6595ca4c60de

Aliases

arxiv: math/0612267 · arxiv_version: math/0612267v2 · doi: 10.48550/arxiv.math/0612267 · pith_short_12: 6K7IU3ZXCIPF · pith_short_16: 6K7IU3ZXCIPFOPGK · pith_short_8: 6K7IU3ZX

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/6K7IU3ZXCIPFOPGK6ZWEHDGUTY \
  | 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: f2be8a6f37121e573ccaf66c438cd49e0c1448c6f62c3732f12f6595ca4c60de

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dbb7eff33f9a323888f273d81c3be3a07b9f93f376d794340cc7900d3e9d478c",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "",
    "primary_cat": "math.AG",
    "submitted_at": "2006-12-11T14:53:36Z",
    "title_canon_sha256": "f6406df0701058fb53976cdc18a40c9605979f50c59d5622aa0709f6ff5c0f6b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0612267",
    "kind": "arxiv",
    "version": 2
  }
}