Pith Number

pith:QQTYQ5W5

pith:2007:QQTYQ5W56RXNHOU2XRPPD24SI2

not attested not anchored not stored refs pending

Isoperimetric profile and random walks on locally compact solvable groups

Romain Tessera

arxiv:0706.4257 v4 · 2007-06-28 · math.GR · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QQTYQ5W56RXNHOU2XRPPD24SI2}

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	2026-05-18T04:34:09.176651Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

84278876ddf46ed3ba9abc5ef1eb924680452d2a0f451e49945ba974c5737412

Aliases

arxiv: 0706.4257 · arxiv_version: 0706.4257v4 · doi: 10.48550/arxiv.0706.4257 · pith_short_12: QQTYQ5W56RXN · pith_short_16: QQTYQ5W56RXNHOU2 · pith_short_8: QQTYQ5W5

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/QQTYQ5W56RXNHOU2XRPPD24SI2 \
  | 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: 84278876ddf46ed3ba9abc5ef1eb924680452d2a0f451e49945ba974c5737412

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bd18682ae9ba79607f88f076c702b179eb47e8bfeb9dfc7187a1cf7f02c07224",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2007-06-28T15:28:59Z",
    "title_canon_sha256": "066154f636439d1ac04b86ae6c94d1d93d99fe9f4eafe2293ba98cf739485589"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0706.4257",
    "kind": "arxiv",
    "version": 4
  }
}