Pith Number

pith:H5Z6BSLV

pith:2020:H5Z6BSLVALZGAT2TKXT3WEWOUI

not attested not anchored not stored refs pending

Cohomology with integral coefficients of stacks of shtukas

Cong Xue

arxiv:2001.05805 v2 · 2020-01-16 · math.AG · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{H5Z6BSLVALZGAT2TKXT3WEWOUI}

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	2026-07-05T06:45:55.741803Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3f73e0c97502f2604f5355e7bb12cea208237309a10db8d1597aa99ea6181d8a

Aliases

arxiv: 2001.05805 · arxiv_version: 2001.05805v2 · doi: 10.48550/arxiv.2001.05805 · pith_short_12: H5Z6BSLVALZG · pith_short_16: H5Z6BSLVALZGAT2T · pith_short_8: H5Z6BSLV

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/H5Z6BSLVALZGAT2TKXT3WEWOUI \
  | 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: 3f73e0c97502f2604f5355e7bb12cea208237309a10db8d1597aa99ea6181d8a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8e012a7fc1304c2a9c36fe8a8d7db37878a007e87677db0ff949b0d70f3ac8ac",
    "cross_cats_sorted": [
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2020-01-16T14:06:05Z",
    "title_canon_sha256": "9ce73b4bdd6c8556615bdb6099e4aa5641dbc1ad976e36e4c5549683e29effe3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2001.05805",
    "kind": "arxiv",
    "version": 2
  }
}