Pith Number

pith:SAKKKVK3

pith:2019:SAKKKVK3JGGH5UPOEYBGMVQUPW

not attested not anchored not stored refs pending

On strong exceptional collections of line bundles of maximal length on Fano toric Deligne-Mumford stacks

Chengxi Wang, Lev Borisov

arxiv:1907.01135 v2 · 2019-07-02 · 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{SAKKKVK3JGGH5UPOEYBGMVQUPW}

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	2026-05-17T23:40:29.862295Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9014a5555b498c7ed1ee26026656147db46e3d78a8623624ee183e902c03a4e8

Aliases

arxiv: 1907.01135 · arxiv_version: 1907.01135v2 · doi: 10.48550/arxiv.1907.01135 · pith_short_12: SAKKKVK3JGGH · pith_short_16: SAKKKVK3JGGH5UPO · pith_short_8: SAKKKVK3

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/SAKKKVK3JGGH5UPOEYBGMVQUPW \
  | 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: 9014a5555b498c7ed1ee26026656147db46e3d78a8623624ee183e902c03a4e8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "63fee691d43cca115e802eda7cd41cb2f70728e452050a448e9b81381ff6afae",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2019-07-02T03:00:16Z",
    "title_canon_sha256": "9c05e72d6e5e2cc43a9fe7dc4c67ada09cad311015d40646d39405eab2cd0792"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1907.01135",
    "kind": "arxiv",
    "version": 2
  }
}