Pith Number

pith:PRHDHEBZ

pith:2011:PRHDHEBZYN2YUYOXUMRSWW2ULL

not attested not anchored not stored refs pending

Modulare Koszul-Dualit"at

Wolfgang Soergel

arxiv:1109.0563 v2 · 2011-09-02 · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PRHDHEBZYN2YUYOXUMRSWW2ULL}

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	2026-05-18T03:45:23.238552Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7c4e339039c3758a61d7a3232b5b545ad75723662c1697115d0867f289648d3b

Aliases

arxiv: 1109.0563 · arxiv_version: 1109.0563v2 · doi: 10.48550/arxiv.1109.0563 · pith_short_12: PRHDHEBZYN2Y · pith_short_16: PRHDHEBZYN2YUYOX · pith_short_8: PRHDHEBZ

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/PRHDHEBZYN2YUYOXUMRSWW2ULL \
  | 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: 7c4e339039c3758a61d7a3232b5b545ad75723662c1697115d0867f289648d3b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e3c51d157c3c9ef0acc0ee628dd75bab46a65007e8ed2095299f5430cfb06e38",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2011-09-02T21:40:11Z",
    "title_canon_sha256": "95871a18ee79b38f1dafe34e452077c1eeb5422db60c3d091ade4ff9dc2fd5dc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.0563",
    "kind": "arxiv",
    "version": 2
  }
}