Pith Number

pith:HVPJ7JPA

pith:2012:HVPJ7JPAXCAIH5CA26ARQBO7TJ

not attested not anchored not stored refs pending

Modular Koszul duality

Geordie Williamson, Simon Riche, Wolfgang Soergel

arxiv:1209.3760 v1 · 2012-09-17 · 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{HVPJ7JPAXCAIH5CA26ARQBO7TJ}

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	2026-05-18T00:58:04.774752Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3d5e9fa5e0b88083f440d7811805df9a6cc7620b303e2a668e0af37fb9339a2e

Aliases

arxiv: 1209.3760 · arxiv_version: 1209.3760v1 · doi: 10.48550/arxiv.1209.3760 · pith_short_12: HVPJ7JPAXCAI · pith_short_16: HVPJ7JPAXCAIH5CA · pith_short_8: HVPJ7JPA

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/HVPJ7JPAXCAIH5CA26ARQBO7TJ \
  | 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: 3d5e9fa5e0b88083f440d7811805df9a6cc7620b303e2a668e0af37fb9339a2e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "370dfef9f2f274032ef07fb6c5569f030ce4c9cbc0fef44250afaae87fff01a8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2012-09-17T19:41:56Z",
    "title_canon_sha256": "d12c6335dba042f025b6920864596d67d9daca0326c08ab4d1a0f4145cdc1bfd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.3760",
    "kind": "arxiv",
    "version": 1
  }
}