Pith Number

pith:BOCPZXFS

pith:2009:BOCPZXFSNK2SYMAV65UGVS2X7E

not attested not anchored not stored refs pending

Butterflies II: Torsors for 2-group stacks

Behrang Noohi, Ettore Aldrovandi

arxiv:0909.3350 v2 · 2009-09-18 · math.AT · math.AG · math.CT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BOCPZXFSNK2SYMAV65UGVS2X7E}

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	2026-05-18T04:41:16.375986Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0b84fcdcb26ab52c3015f7686acb57f92dfc447f4e8261dd353cbd6b366e74fe

Aliases

arxiv: 0909.3350 · arxiv_version: 0909.3350v2 · doi: 10.48550/arxiv.0909.3350 · pith_short_12: BOCPZXFSNK2S · pith_short_16: BOCPZXFSNK2SYMAV · pith_short_8: BOCPZXFS

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/BOCPZXFSNK2SYMAV65UGVS2X7E \
  | 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: 0b84fcdcb26ab52c3015f7686acb57f92dfc447f4e8261dd353cbd6b366e74fe

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3e96d9b5043d55262e7c0d2ebad1cfffeb9a26a4f7934ba0abfd8c6865fa445b",
    "cross_cats_sorted": [
      "math.AG",
      "math.CT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2009-09-18T03:59:10Z",
    "title_canon_sha256": "b4a40805f35632ba42132c16460c047f91226fbe915cd7f6680f03ce8a49d7a2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0909.3350",
    "kind": "arxiv",
    "version": 2
  }
}