Pith Number

pith:QJTDU25E

pith:2012:QJTDU25EP3FPHM4ZOQYEACYSQA

not attested not anchored not stored refs pending

Almost-additive ergodic theorems for amenable groups

Felix Pogorzelski

arxiv:1211.2089 v2 · 2012-11-09 · math.DS · math.FA · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QJTDU25EP3FPHM4ZOQYEACYSQA}

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	2026-05-18T00:32:03.427370Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

82663a6ba47ecaf3b3997430400b128013df539763ea69d18fbf5ae410ae1e03

Aliases

arxiv: 1211.2089 · arxiv_version: 1211.2089v2 · doi: 10.48550/arxiv.1211.2089 · pith_short_12: QJTDU25EP3FP · pith_short_16: QJTDU25EP3FPHM4Z · pith_short_8: QJTDU25E

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/QJTDU25EP3FPHM4ZOQYEACYSQA \
  | 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: 82663a6ba47ecaf3b3997430400b128013df539763ea69d18fbf5ae410ae1e03

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "468e1e2e0893e3be71a779828cbcd25648589351b129604b294b0d720677a376",
    "cross_cats_sorted": [
      "math.FA",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2012-11-09T10:05:04Z",
    "title_canon_sha256": "c216709adf6624fbc50e6421bbe572662e03a364e8ec0b08db5634c4f5aacbc1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.2089",
    "kind": "arxiv",
    "version": 2
  }
}