Pith Number

pith:PIWS4ZNF

pith:2003:PIWS4ZNFJ2OY5OACXS4AF3RYZD

not attested not anchored not stored refs pending

Enumerative tropical algebraic geometry in R2

Grigory Mikhalkin

arxiv:math/0312530 v4 · 2003-12-31 · math.AG · math-ph · math.CO · math.GT · math.MP · 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{PIWS4ZNFJ2OY5OACXS4AF3RYZD}

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

2 papers in Pith

Special Lagrangian submanifolds and circle collapse on K3

Nil-Equivariant Tropological Sigma Models on Filtered Geometries

Receipt and verification

First computed	2026-07-04T14:38:08.288786Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7a2d2e65a54e9d8eb802bcb802ee38c8debd6215631b6326c42246663cf37a25

Aliases

arxiv: math/0312530 · arxiv_version: math/0312530v4 · doi: 10.48550/arxiv.math/0312530 · pith_short_12: PIWS4ZNFJ2OY · pith_short_16: PIWS4ZNFJ2OY5OAC · pith_short_8: PIWS4ZNF

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/PIWS4ZNFJ2OY5OACXS4AF3RYZD \
  | 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: 7a2d2e65a54e9d8eb802bcb802ee38c8debd6215631b6326c42246663cf37a25

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c2f3a25215a06feda9433aede4937c7e6119899db754de984ba0065ee751ef14",
    "cross_cats_sorted": [
      "math-ph",
      "math.CO",
      "math.GT",
      "math.MP",
      "math.SG"
    ],
    "license": "",
    "primary_cat": "math.AG",
    "submitted_at": "2003-12-31T20:22:16Z",
    "title_canon_sha256": "00ad05c6848b32e6390bcacaeec57635a20162bcc6887b8e5446fa29e05386a7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0312530",
    "kind": "arxiv",
    "version": 4
  }
}