Pith Number

pith:2ISLH35R

pith:2016:2ISLH35RM7NJCNWGQF67IMZU6Y

not attested not anchored not stored refs pending

Relative hard Lefschetz for Soergel bimodules

Ben Elias, Geordie Williamson

arxiv:1607.03271 v2 · 2016-07-12 · math.RT · math.AG · math.QA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2ISLH35RM7NJCNWGQF67IMZU6Y}

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.

Cited by

1 paper in Pith

Idempotents, traces, and dimensions in Hecke categories

Receipt and verification

First computed	2026-05-18T00:30:55.467275Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d224b3efb167da9136c6817df43334f63021d88878e04f6890bef629bb2e2003

Aliases

arxiv: 1607.03271 · arxiv_version: 1607.03271v2 · doi: 10.48550/arxiv.1607.03271 · pith_short_12: 2ISLH35RM7NJ · pith_short_16: 2ISLH35RM7NJCNWG · pith_short_8: 2ISLH35R

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/2ISLH35RM7NJCNWGQF67IMZU6Y \
  | 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: d224b3efb167da9136c6817df43334f63021d88878e04f6890bef629bb2e2003

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f5faefb61572dc9364f1d9e3d7befd2be680d679162e028cc005826179b57b53",
    "cross_cats_sorted": [
      "math.AG",
      "math.QA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2016-07-12T09:02:48Z",
    "title_canon_sha256": "79e62fed071399843ae8b08f2dc21bc8858765243172d27bb3d0e683d9439683"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1607.03271",
    "kind": "arxiv",
    "version": 2
  }
}