Pith Number

pith:GQE4GF5W

pith:2010:GQE4GF5WGFZGXQMO3CI4GYH5PV

not attested not anchored not stored refs pending

Derived Resolution Property for Stacks, Euler Classes and Applications

Jun Li, Yi Hu

arxiv:1009.5109 v2 · 2010-09-26 · 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{GQE4GF5WGFZGXQMO3CI4GYH5PV}

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	2026-05-18T04:39:50.045924Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3409c317b631726bc18ed891c360fd7d5f093ce15582e40b19d91f098d44174b

Aliases

arxiv: 1009.5109 · arxiv_version: 1009.5109v2 · doi: 10.48550/arxiv.1009.5109 · pith_short_12: GQE4GF5WGFZG · pith_short_16: GQE4GF5WGFZGXQMO · pith_short_8: GQE4GF5W

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/GQE4GF5WGFZGXQMO3CI4GYH5PV \
  | 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: 3409c317b631726bc18ed891c360fd7d5f093ce15582e40b19d91f098d44174b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "806f9ecc7c8645291acfc4dc243646e677aff7539df59bca43457fd56fe398ac",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2010-09-26T17:13:45Z",
    "title_canon_sha256": "fdebf6dbaff3e7ba6f882bfedb4ac23e06cad9f07bcf758991fbf7c1cf9accaf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.5109",
    "kind": "arxiv",
    "version": 2
  }
}