Pith Number

pith:VP5YYDO2

pith:2023:VP5YYDO2HQ74GVY67YAN7DFCME

not attested not anchored not stored refs pending

Mapping class groups of exotic tori and actions by ${\rm SL}_d(\mathbb Z)$

Alexander Kupers, Bena Tshishiku, Manuel Krannich, Mauricio Bustamante

arxiv:2305.08065 v2 · 2023-05-14 · math.GT · math.AT · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VP5YYDO2HQ74GVY67YAN7DFCME}

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	2026-07-05T09:07:43.411156Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

abfb8c0dda3c3fc3571efe00df8ca2612e92c7ce372a279c4f780205de461919

Aliases

arxiv: 2305.08065 · arxiv_version: 2305.08065v2 · doi: 10.48550/arxiv.2305.08065 · pith_short_12: VP5YYDO2HQ74 · pith_short_16: VP5YYDO2HQ74GVY6 · pith_short_8: VP5YYDO2

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/VP5YYDO2HQ74GVY67YAN7DFCME \
  | 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: abfb8c0dda3c3fc3571efe00df8ca2612e92c7ce372a279c4f780205de461919

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "182b563c9440420e66479e7eb68ebdacee6e568add55a578f2239f218073a6bb",
    "cross_cats_sorted": [
      "math.AT",
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2023-05-14T04:28:05Z",
    "title_canon_sha256": "02b6e1590c33e59d2e2c06162d52c84aada358c51f037db7dc946225b8e9c67b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2305.08065",
    "kind": "arxiv",
    "version": 2
  }
}