Pith Number

pith:GQEVEXNC

pith:2009:GQEVEXNCYDG4FUCB77ZUNBZI6A

not attested not anchored not stored refs pending

Moduli stacks and moduli schemes for rank 2 unstable bundles

L. Brambila-Paz, Nitin Nitsure, Osbaldo Mata

arxiv:0911.2301 v2 · 2009-11-12 · 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{GQEVEXNCYDG4FUCB77ZUNBZI6A}

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	2026-05-18T04:27:47.815388Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3409525da2c0cdc2d041fff3468728f02e5969eaaede31b7b2339a79ae09aec6

Aliases

arxiv: 0911.2301 · arxiv_version: 0911.2301v2 · doi: 10.48550/arxiv.0911.2301 · pith_short_12: GQEVEXNCYDG4 · pith_short_16: GQEVEXNCYDG4FUCB · pith_short_8: GQEVEXNC

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/GQEVEXNCYDG4FUCB77ZUNBZI6A \
  | 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: 3409525da2c0cdc2d041fff3468728f02e5969eaaede31b7b2339a79ae09aec6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "39cac8ea826a322b827e3b9d7fe76c0c8b7ff2d4e2c3a45ae7e15cfe8fedcf0d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2009-11-12T07:03:40Z",
    "title_canon_sha256": "5bb3695fa8a7903fe425060eeff3ef215f07c0b18311933bdbe869a04d4cd51d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0911.2301",
    "kind": "arxiv",
    "version": 2
  }
}