Pith Number

pith:7Y6GIWRK

pith:2009:7Y6GIWRKHYGNLYKLRIPPQZCABR

not attested not anchored not stored refs pending

Quasi-Invariants of Complex Reflection Groups

Oleg Chalykh, Yuri Berest

arxiv:0912.4518 v2 · 2009-12-23 · math.RT · math-ph · math.MP · 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{7Y6GIWRKHYGNLYKLRIPPQZCABR}

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	2026-05-18T03:02:44.488277Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fe3c645a2a3e0cd5e14b8a1ef864400c6a7630598ff25c5e82c0ef7c5602410c

Aliases

arxiv: 0912.4518 · arxiv_version: 0912.4518v2 · doi: 10.48550/arxiv.0912.4518 · pith_short_12: 7Y6GIWRKHYGN · pith_short_16: 7Y6GIWRKHYGNLYKL · pith_short_8: 7Y6GIWRK

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/7Y6GIWRKHYGNLYKLRIPPQZCABR \
  | 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: fe3c645a2a3e0cd5e14b8a1ef864400c6a7630598ff25c5e82c0ef7c5602410c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8c026323fb7ae0a25d0ce93cc0ea858a621c3c66eb3f24a8861f1a5addda01ff",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.QA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2009-12-23T16:34:08Z",
    "title_canon_sha256": "a1af60faede0176d7c32a7f54ce4cd673cf9cf05e5bca0092d74a2a4077e2d1e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0912.4518",
    "kind": "arxiv",
    "version": 2
  }
}