Pith Number

pith:67BAWX2E

pith:2010:67BAWX2EFJCQOTBDR4C3EJRDVI

not attested not anchored not stored refs pending

Mirror maps equal SYZ maps for toric Calabi-Yau surfaces

Baosen Wu, Naichung Conan Leung, Siu-Cheong Lau

arxiv:1008.4753 v2 · 2010-08-27 · math.SG · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{67BAWX2EFJCQOTBDR4C3EJRDVI}

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	2026-05-18T02:58:01.878026Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f7c20b5f442a45074c238f05b22623aa21bd83cf08624908c9099c19cfa0657b

Aliases

arxiv: 1008.4753 · arxiv_version: 1008.4753v2 · doi: 10.48550/arxiv.1008.4753 · pith_short_12: 67BAWX2EFJCQ · pith_short_16: 67BAWX2EFJCQOTBD · pith_short_8: 67BAWX2E

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/67BAWX2EFJCQOTBDR4C3EJRDVI \
  | 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: f7c20b5f442a45074c238f05b22623aa21bd83cf08624908c9099c19cfa0657b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0989f83d7d61dc277d4a703068f299d533a6cc8033df0fcc3f0fd6ffee711bca",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SG",
    "submitted_at": "2010-08-27T16:21:03Z",
    "title_canon_sha256": "212c4fac428ef0c85546c741ae35260531ee6e63b7fb32bf0de6b119c8da1bcc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1008.4753",
    "kind": "arxiv",
    "version": 2
  }
}