Pith Number

pith:DWZ2QUIF

pith:2010:DWZ2QUIFXHLUVCGWAIQP5VSDKG

not attested not anchored not stored refs pending

Tropical coamoeba and torus-equivariant homological mirror symmetry for the projective space

Kazushi Ueda, Masahiro Futaki

arxiv:1001.4858 v3 · 2010-01-27 · 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{DWZ2QUIFXHLUVCGWAIQP5VSDKG}

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	2026-05-18T02:47:51.435561Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1db3a85105b9d74a88d60220fed6435191f47cba3d75d9bec46eb5af4c58c401

Aliases

arxiv: 1001.4858 · arxiv_version: 1001.4858v3 · doi: 10.48550/arxiv.1001.4858 · pith_short_12: DWZ2QUIFXHLU · pith_short_16: DWZ2QUIFXHLUVCGW · pith_short_8: DWZ2QUIF

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/DWZ2QUIFXHLUVCGWAIQP5VSDKG \
  | 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: 1db3a85105b9d74a88d60220fed6435191f47cba3d75d9bec46eb5af4c58c401

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f79c6e3b2d226b1c7d0014bb56f5a801c81235cb5112ab719ae01a129c341cfd",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SG",
    "submitted_at": "2010-01-27T05:51:07Z",
    "title_canon_sha256": "796cd491f62a4fd0390c7eba0bef5e5aec6b8fa7b48e2402e58a59ee690e1c45"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1001.4858",
    "kind": "arxiv",
    "version": 3
  }
}