Pith Number

pith:KABQKIPZ

pith:2022:KABQKIPZKQMYZ6FQIRAEEYAYIA

not attested not anchored not stored refs pending

Shard theory for $g$-fans

Yuya Mizuno

arxiv:2212.10745 v2 · 2022-12-21 · math.RT · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KABQKIPZKQMYZ6FQIRAEEYAYIA}

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

Fans and polytopes in tilting theory III: Classification of convex $g$-fans of rank 3

Receipt and verification

First computed	2026-07-05T09:11:45.002722Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

50030521f954198cf8b04440426018403d7e9229aedf74ecb652e29988a11e35

Aliases

arxiv: 2212.10745 · arxiv_version: 2212.10745v2 · doi: 10.48550/arxiv.2212.10745 · pith_short_12: KABQKIPZKQMY · pith_short_16: KABQKIPZKQMYZ6FQ · pith_short_8: KABQKIPZ

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/KABQKIPZKQMYZ6FQIRAEEYAYIA \
  | 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: 50030521f954198cf8b04440426018403d7e9229aedf74ecb652e29988a11e35

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "59181ccca45d218f52944f18601c9ac9289ea59135d77880b9325da5f38abed9",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2022-12-21T03:29:28Z",
    "title_canon_sha256": "98423d5adff94a6b2aec7d57f8315e36a475d61bafc548a6012a485026e194bd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2212.10745",
    "kind": "arxiv",
    "version": 2
  }
}