Pith Number

pith:7ZZWHKIH

pith:2013:7ZZWHKIHRJPAXTW7KCGDVR7B6T

not attested not anchored not stored refs pending

The birational geometry of moduli space of sheaves on the projective plane

Aaron Bertram, Cristian Martinez, Jie Wang

arxiv:1301.2011 v1 · 2013-01-10 · 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{7ZZWHKIHRJPAXTW7KCGDVR7B6T}

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	2026-05-18T03:36:48.533210Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fe7363a9078a5e0bcedf508c3ac7e1f4e770db30febf23bb757e1db857750099

Aliases

arxiv: 1301.2011 · arxiv_version: 1301.2011v1 · doi: 10.48550/arxiv.1301.2011 · pith_short_12: 7ZZWHKIHRJPA · pith_short_16: 7ZZWHKIHRJPAXTW7 · pith_short_8: 7ZZWHKIH

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/7ZZWHKIHRJPAXTW7KCGDVR7B6T \
  | 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: fe7363a9078a5e0bcedf508c3ac7e1f4e770db30febf23bb757e1db857750099

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a3312b500fc39966899503af5af763fdea339f41a098c603939f1772d869d990",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2013-01-10T00:41:35Z",
    "title_canon_sha256": "10565eb30ae50a1d111490e15b8b7f9ac0ee6cbfa15445e81b4dd99046a794cd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1301.2011",
    "kind": "arxiv",
    "version": 1
  }
}