Pith Number

pith:GG7PLZWH

pith:2015:GG7PLZWH24IX4VEOZEMHU3VWYS

not attested not anchored not stored refs pending

Upper bounds for the dimension of tori acting on GKM manifolds

Shintaro Kuroki

arxiv:1510.07216 v2 · 2015-10-25 · math.GT · 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{GG7PLZWH24IX4VEOZEMHU3VWYS}

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	2026-05-17T23:45:53.724943Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

31bef5e6c7d7117e548ec9187a6eb6c4a846c7334f88148df3e7b4d4a45206e6

Aliases

arxiv: 1510.07216 · arxiv_version: 1510.07216v2 · doi: 10.48550/arxiv.1510.07216 · pith_short_12: GG7PLZWH24IX · pith_short_16: GG7PLZWH24IX4VEO · pith_short_8: GG7PLZWH

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/GG7PLZWH24IX4VEOZEMHU3VWYS \
  | 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: 31bef5e6c7d7117e548ec9187a6eb6c4a846c7334f88148df3e7b4d4a45206e6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "19f0b5e667e458b35facbec257dd991a12c6f72999afae62335bd10e2397504b",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2015-10-25T08:08:31Z",
    "title_canon_sha256": "a2576395900d2b6ef68b2ae3643fbc70e0346fe003e88fc56388342ddf00ad31"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.07216",
    "kind": "arxiv",
    "version": 2
  }
}