Pith Number

pith:AL4ZDU3B

pith:2011:AL4ZDU3BV2Q45MLI4QYDU6TMWR

not attested not anchored not stored refs pending

Speedups of ergodic group extensions

Adam Fieldsteel, Andrey Babichev, Robert M. Burton

arxiv:1112.4406 v4 · 2011-12-19 · 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{AL4ZDU3BV2Q45MLI4QYDU6TMWR}

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	2026-05-18T03:59:36.437354Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

02f991d361aea1ceb168e4303a7a6cb464ae1550f36778587136b669282c58c0

Aliases

arxiv: 1112.4406 · arxiv_version: 1112.4406v4 · doi: 10.48550/arxiv.1112.4406 · pith_short_12: AL4ZDU3BV2Q4 · pith_short_16: AL4ZDU3BV2Q45MLI · pith_short_8: AL4ZDU3B

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/AL4ZDU3BV2Q45MLI4QYDU6TMWR \
  | 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: 02f991d361aea1ceb168e4303a7a6cb464ae1550f36778587136b669282c58c0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "840623f448f120714439a1693d71fb42d3931f95dc03c6bdc87f39b5d6c08f07",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2011-12-19T17:05:31Z",
    "title_canon_sha256": "0274da75525aa0609bbc957fa7220871f25eb85bdc476ec718fe67f5d50f36e6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.4406",
    "kind": "arxiv",
    "version": 4
  }
}