Pith Number

pith:CP2P5PWT

pith:2006:CP2P5PWTICB45OJWKJKZ6JGVAA

not attested not anchored not stored refs pending

Averaging sequences and abelian rank in amenable groups

Michael Hochman

arxiv:math/0601432 v1 · 2006-01-18 · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CP2P5PWTICB45OJWKJKZ6JGVAA}

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	2026-05-18T02:42:13.426098Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

13f4febed34083ceb93652559f24d5002d48c47abc6a69634c164e46478abe9a

Aliases

arxiv: math/0601432 · arxiv_version: math/0601432v1 · doi: 10.48550/arxiv.math/0601432 · pith_short_12: CP2P5PWTICB4 · pith_short_16: CP2P5PWTICB45OJW · pith_short_8: CP2P5PWT

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/CP2P5PWTICB45OJWKJKZ6JGVAA \
  | 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: 13f4febed34083ceb93652559f24d5002d48c47abc6a69634c164e46478abe9a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2529e089f3d285311357ea433f519831ac7da6839d3e65a493b2e99a3412148a",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.DS",
    "submitted_at": "2006-01-18T11:16:20Z",
    "title_canon_sha256": "27cd7fcae00cd340ec45c0e0e197b626e9c205d20a4f4a1990fcc8b88d2d00ae"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0601432",
    "kind": "arxiv",
    "version": 1
  }
}