Pith Number

pith:F4XY6KYA

pith:2011:F4XY6KYA7MLZJGRB7THI2LEW4I

not attested not anchored not stored refs pending

Moduli Spaces of Sheaves on K3 Surfaces and Symplectic Stacks

Ziyu Zhang

arxiv:1111.6294 v1 · 2011-11-27 · 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{F4XY6KYA7MLZJGRB7THI2LEW4I}

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	2026-05-18T04:07:31.354704Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2f2f8f2b00fb17949a21fcce8d2c96e2160396bfc8b4a7f601f52b60d29b2ea3

Aliases

arxiv: 1111.6294 · arxiv_version: 1111.6294v1 · doi: 10.48550/arxiv.1111.6294 · pith_short_12: F4XY6KYA7MLZ · pith_short_16: F4XY6KYA7MLZJGRB · pith_short_8: F4XY6KYA

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/F4XY6KYA7MLZJGRB7THI2LEW4I \
  | 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: 2f2f8f2b00fb17949a21fcce8d2c96e2160396bfc8b4a7f601f52b60d29b2ea3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e19abdf174e8f233943293473b20301cff15770a084e0c565c936a2e43231324",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2011-11-27T21:03:39Z",
    "title_canon_sha256": "abb300f2b4aa93f615703d28f4ed4d4783f370da69aadbef3cee0e6d4a6fdd50"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.6294",
    "kind": "arxiv",
    "version": 1
  }
}