Pith Number

pith:G45UMBN2

pith:2015:G45UMBN257463QTL2K6ITBY2SI

not attested not anchored not stored refs pending

A vanishing theorem for the homology of discrete subgroups of $\mathrm{Sp}(n,1)$ and $\mathrm{F}_4^{-20}$

Benson Farb, Chris Connell, D. B. McReynolds

arxiv:1506.03516 v2 · 2015-06-11 · math.GT · math.DG · 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{G45UMBN257463QTL2K6ITBY2SI}

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	2026-05-18T00:58:55.537702Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

373b4605baeff9edc26bd2bc89871a922c96ff9eec1b4f50b502e86ddd35d181

Aliases

arxiv: 1506.03516 · arxiv_version: 1506.03516v2 · doi: 10.48550/arxiv.1506.03516 · pith_short_12: G45UMBN25746 · pith_short_16: G45UMBN257463QTL · pith_short_8: G45UMBN2

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/G45UMBN257463QTL2K6ITBY2SI \
  | 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: 373b4605baeff9edc26bd2bc89871a922c96ff9eec1b4f50b502e86ddd35d181

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f46c6875d46279bebfb335a03de8a24c9be073f3385dd23edd826f4cb0ff2502",
    "cross_cats_sorted": [
      "math.DG",
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2015-06-11T00:35:54Z",
    "title_canon_sha256": "3a186134fa382d0ac5c0b115ba7e4627e888728b9fe25efd48990a091fea1674"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1506.03516",
    "kind": "arxiv",
    "version": 2
  }
}