Pith Number

pith:PCNPZPZO

pith:2013:PCNPZPZOLXP72A2A526PHDF4DR

not attested not anchored not stored refs pending

Sub-additive ergodic theorems for countable amenable groups

Anthony H. Dooley, Guohua Zhang, Valentyn Ya. Golodets

arxiv:1310.1198 v2 · 2013-10-04 · 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{PCNPZPZOLXP72A2A526PHDF4DR}

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	2026-05-18T02:30:47.626114Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

789afcbf2e5ddffd0340eebcf38cbc1c48c0aa2895a417b24cfb1a1c6e4c8d85

Aliases

arxiv: 1310.1198 · arxiv_version: 1310.1198v2 · doi: 10.48550/arxiv.1310.1198 · pith_short_12: PCNPZPZOLXP7 · pith_short_16: PCNPZPZOLXP72A2A · pith_short_8: PCNPZPZO

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/PCNPZPZOLXP72A2A526PHDF4DR \
  | 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: 789afcbf2e5ddffd0340eebcf38cbc1c48c0aa2895a417b24cfb1a1c6e4c8d85

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2aa99c70e72c142ec3fc11c48517aa20d0085a09ece7153472949277699449ec",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2013-10-04T08:35:39Z",
    "title_canon_sha256": "c586b17a2bb56d06f35e71fcd0d6004b3d255a704893efcb3d38b551326e9596"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1310.1198",
    "kind": "arxiv",
    "version": 2
  }
}