Pith Number

pith:QJWD2TLP

pith:2010:QJWD2TLPFUBQMG4KTN6UIT2BJQ

not attested not anchored not stored refs pending

Matrix factorizations and singularity categories for stacks

Alexander Polishchuk, Arkady Vaintrob

arxiv:1011.4544 v1 · 2010-11-20 · 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{QJWD2TLPFUBQMG4KTN6UIT2BJQ}

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	2026-05-18T04:35:05.924277Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

826c3d4d6f2d03061b8a9b7d444f414c231dd0eee747612732bfb4c3457c103a

Aliases

arxiv: 1011.4544 · arxiv_version: 1011.4544v1 · doi: 10.48550/arxiv.1011.4544 · pith_short_12: QJWD2TLPFUBQ · pith_short_16: QJWD2TLPFUBQMG4K · pith_short_8: QJWD2TLP

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/QJWD2TLPFUBQMG4KTN6UIT2BJQ \
  | 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: 826c3d4d6f2d03061b8a9b7d444f414c231dd0eee747612732bfb4c3457c103a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "da9b6ed944d97c7e7f0cda319e6c498f927db289c94f2dc9589628af91ea6119",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2010-11-20T01:00:28Z",
    "title_canon_sha256": "0d39d0c07eccfe39e69492d52e9f4b809cecb59431ad2260ca3963057e4df2e1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1011.4544",
    "kind": "arxiv",
    "version": 1
  }
}