Pith Number

pith:YRMNJVBG

pith:2009:YRMNJVBGXRY55POUOIFB2SNTFJ

not attested not anchored not stored refs pending

Euler characteristics of moduli spaces of torsion free sheaves on toric surfaces

Martijn Kool

arxiv:0906.3393 v3 · 2009-06-18 · 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{YRMNJVBGXRY55POUOIFB2SNTFJ}

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	2026-05-18T01:21:03.223544Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c458d4d426bc71debdd4720a1d49b32a703bd98c4692406f3975734c90eea491

Aliases

arxiv: 0906.3393 · arxiv_version: 0906.3393v3 · doi: 10.48550/arxiv.0906.3393 · pith_short_12: YRMNJVBGXRY5 · pith_short_16: YRMNJVBGXRY55POU · pith_short_8: YRMNJVBG

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/YRMNJVBGXRY55POUOIFB2SNTFJ \
  | 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: c458d4d426bc71debdd4720a1d49b32a703bd98c4692406f3975734c90eea491

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6704841322b1b0e7ce7988697a6f2d7d8d0e42645d3256ca7799aaed935ec3f3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2009-06-18T09:52:06Z",
    "title_canon_sha256": "fd3b54d12f5f2acab5dfc287ed9579d4d93f58f5e768d5f146fe56332a7a85bf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0906.3393",
    "kind": "arxiv",
    "version": 3
  }
}