Pith Number

pith:OOWYIAIJ

pith:2004:OOWYIAIJ7SF4FEQMCZE6TKBVCU

not attested not anchored not stored refs pending

Amoebas of algebraic varieties and tropical geometry

Grigory Mikhalkin

arxiv:math/0403015 v1 · 2004-02-29 · math.AG · math.GT · math.SG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OOWYIAIJ7SF4FEQMCZE6TKBVCU}

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	2026-07-04T14:38:16.581403Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

73ad840109fc8bc2920c1649e9a835150dc20de37d20440f90528fdd7902467f

Aliases

arxiv: math/0403015 · arxiv_version: math/0403015v1 · doi: 10.48550/arxiv.math/0403015 · pith_short_12: OOWYIAIJ7SF4 · pith_short_16: OOWYIAIJ7SF4FEQM · pith_short_8: OOWYIAIJ

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/OOWYIAIJ7SF4FEQMCZE6TKBVCU \
  | 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: 73ad840109fc8bc2920c1649e9a835150dc20de37d20440f90528fdd7902467f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "98016459df539df7fa4586b3f57db75fe7aafc22af1e16e763398e43dbcb0475",
    "cross_cats_sorted": [
      "math.GT",
      "math.SG"
    ],
    "license": "",
    "primary_cat": "math.AG",
    "submitted_at": "2004-02-29T19:39:55Z",
    "title_canon_sha256": "f97839e8869bc33a4a5b8770e7d5d4d88d6624878a05202a1cb65d68a70a4986"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0403015",
    "kind": "arxiv",
    "version": 1
  }
}