Pith Number

pith:IZLCRMPK

pith:2007:IZLCRMPK3O2KSKAVIYZPJFMYF2

not attested not anchored not stored refs pending

The characteristic quasi-polynomials of the arrangements of root systems and mid-hyperplane arrangements

Akimichi Takemura, Hidehiko Kamiya, Hiroaki Terao

arxiv:0707.1381 v3 · 2007-07-10 · math.CO · math.RT

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Add to your LaTeX paper

\usepackage{pith}
\pithnumber{IZLCRMPK3O2KSKAVIYZPJFMYF2}

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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

2 papers in Pith

Equivariant version of the characteristic quasi-polynomials of root systems

Receipt and verification

First computed	2026-05-18T04:19:41.415867Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

465628b1eadbb4a928154632f495982eae230f9b5e86160df08f2dea9db439e6

Aliases

arxiv: 0707.1381 · arxiv_version: 0707.1381v3 · doi: 10.48550/arxiv.0707.1381 · pith_short_12: IZLCRMPK3O2K · pith_short_16: IZLCRMPK3O2KSKAV · pith_short_8: IZLCRMPK

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/IZLCRMPK3O2KSKAVIYZPJFMYF2 \
  | 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: 465628b1eadbb4a928154632f495982eae230f9b5e86160df08f2dea9db439e6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0b654b71bce09dba975c98694179917a93c08fd3b33cc532ac052a282a9d9469",
    "cross_cats_sorted": [
      "math.RT"
    ],
    "license": "",
    "primary_cat": "math.CO",
    "submitted_at": "2007-07-10T08:33:45Z",
    "title_canon_sha256": "f9f618414b0a1af332884fad1ef62028d3042b9141c76af9a6cf748fe1031595"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0707.1381",
    "kind": "arxiv",
    "version": 3
  }
}