Pith Number

pith:27QEBXFX

pith:2010:27QEBXFXELM6BT47DBPT3KCHZC

not attested not anchored not stored refs pending

Actions of higher-rank lattices on free groups

Martin R. Bridson, Richard D. Wade

arxiv:1004.3222 v2 · 2010-04-19 · math.GR · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{27QEBXFXELM6BT47DBPT3KCHZC}

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	2026-05-18T04:24:35.245621Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d7e040dcb722d9e0cf9f185f3da847c8b01112cb47cc242a398808ce867e993d

Aliases

arxiv: 1004.3222 · arxiv_version: 1004.3222v2 · doi: 10.48550/arxiv.1004.3222 · pith_short_12: 27QEBXFXELM6 · pith_short_16: 27QEBXFXELM6BT47 · pith_short_8: 27QEBXFX

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/27QEBXFXELM6BT47DBPT3KCHZC \
  | 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: d7e040dcb722d9e0cf9f185f3da847c8b01112cb47cc242a398808ce867e993d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1c3e69ed0d1782842b9738ee65f6c3daba63e8041e1b913a45196793a2d32dac",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2010-04-19T15:08:19Z",
    "title_canon_sha256": "b5e1a39f202c5af4073a4fe16b3ff4ffb44a971d8ede5353072b8c44b0b6df61"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1004.3222",
    "kind": "arxiv",
    "version": 2
  }
}