Pith Number

pith:TYXVR4GL

pith:2013:TYXVR4GLB7WN623NGIQKZZSVGU

not attested not anchored not stored refs pending

On the torsion of the first direct image of a locally free sheaf

Andrei Teleman

arxiv:1309.0342 v2 · 2013-09-02 · math.CV · math.AG · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TYXVR4GLB7WN623NGIQKZZSVGU}

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	2026-05-18T02:26:53.073624Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9e2f58f0cb0fecdf6b6d3220ace655352a77623a415ec2e51c79e947ae73b90f

Aliases

arxiv: 1309.0342 · arxiv_version: 1309.0342v2 · doi: 10.48550/arxiv.1309.0342 · pith_short_12: TYXVR4GLB7WN · pith_short_16: TYXVR4GLB7WN623N · pith_short_8: TYXVR4GL

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/TYXVR4GLB7WN623NGIQKZZSVGU \
  | 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: 9e2f58f0cb0fecdf6b6d3220ace655352a77623a415ec2e51c79e947ae73b90f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "82cf52f2aef2b0db4c21282b0d342742beea0fbba0505c46fd636a52a1ed3e4c",
    "cross_cats_sorted": [
      "math.AG",
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CV",
    "submitted_at": "2013-09-02T10:00:30Z",
    "title_canon_sha256": "0efa09f7bcf21458157342241afb70098ceca35ac235a7143c55a33b44072d45"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.0342",
    "kind": "arxiv",
    "version": 2
  }
}