Pith Number

pith:IB6LEH23

pith:2020:IB6LEH234Y2KX7TQSB2BLUW4IW

not attested not anchored not stored refs pending

Smoothness of cohomology sheaves of stacks of shtukas

Cong Xue

arxiv:2012.12833 v1 · 2020-12-23 · math.AG · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{IB6LEH234Y2KX7TQSB2BLUW4IW}

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	2026-07-05T02:01:42.893511Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

407cb21f5be634abfe70907415d2dc45abef126f328cfc954ede5bb39680658f

Aliases

arxiv: 2012.12833 · arxiv_version: 2012.12833v1 · doi: 10.48550/arxiv.2012.12833 · pith_short_12: IB6LEH234Y2K · pith_short_16: IB6LEH234Y2KX7TQ · pith_short_8: IB6LEH23

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/IB6LEH234Y2KX7TQSB2BLUW4IW \
  | 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: 407cb21f5be634abfe70907415d2dc45abef126f328cfc954ede5bb39680658f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "16c423070500528be2ea54a1a2928bf7d1acfc93ff7e0887c0cea62e25e59669",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2020-12-23T17:52:54Z",
    "title_canon_sha256": "9d744f3d74f53a933775a515751f3895b2ff67ed2e036068afdf61aa4bd286ca"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2012.12833",
    "kind": "arxiv",
    "version": 1
  }
}