Pith Number

pith:NR5DTZGS

pith:2011:NR5DTZGSAJGMLVUM75YBNRRJDU

not attested not anchored not stored refs pending

Differential forms on singular spaces, the minimal model program, and hyperbolicity of moduli stacks

Stefan Kebekus

arxiv:1107.4239 v2 · 2011-07-21 · 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{NR5DTZGSAJGMLVUM75YBNRRJDU}

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	2026-05-18T04:05:59.119732Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6c7a39e4d2024cc5d68cff7016c6291d3ded6e529229a14fcd3d5b9b5a431ee9

Aliases

arxiv: 1107.4239 · arxiv_version: 1107.4239v2 · doi: 10.48550/arxiv.1107.4239 · pith_short_12: NR5DTZGSAJGM · pith_short_16: NR5DTZGSAJGMLVUM · pith_short_8: NR5DTZGS

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/NR5DTZGSAJGMLVUM75YBNRRJDU \
  | 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: 6c7a39e4d2024cc5d68cff7016c6291d3ded6e529229a14fcd3d5b9b5a431ee9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c6dc0538564f384208cc8e0b7b67a0bd3f73f3294046ea43c2cf266634c647ad",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2011-07-21T11:39:55Z",
    "title_canon_sha256": "7199b4a0c10da060095269c9179e529d8f66a22f59c6718e20ba58f510e5669e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.4239",
    "kind": "arxiv",
    "version": 2
  }
}