Pith Number

pith:HM5SK4W2

pith:2009:HM5SK4W27CCG5DDPYSA2XAA4EH

not attested not anchored not stored refs pending

A ratio ergodic theorem for multiparameter non-singular actions

Michael Hochman

arxiv:0901.3605 v1 · 2009-01-23 · 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{HM5SK4W27CCG5DDPYSA2XAA4EH}

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	2026-05-18T02:42:15.563336Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3b3b2572daf8846e8c6fc481ab801c21c11a726d495f8fc63f92d850eabb80e3

Aliases

arxiv: 0901.3605 · arxiv_version: 0901.3605v1 · doi: 10.48550/arxiv.0901.3605 · pith_short_12: HM5SK4W27CCG · pith_short_16: HM5SK4W27CCG5DDP · pith_short_8: HM5SK4W2

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/HM5SK4W27CCG5DDPYSA2XAA4EH \
  | 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: 3b3b2572daf8846e8c6fc481ab801c21c11a726d495f8fc63f92d850eabb80e3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c0a6c5a87d7eb84c69eba0b327f7341a09df37333e3dea86f20cf20c989ed6fe",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2009-01-23T05:17:58Z",
    "title_canon_sha256": "5d2e245d8cb8dc08ceac442d44b6780af7a2bc84cb12a53c3c176c8a46662f29"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0901.3605",
    "kind": "arxiv",
    "version": 1
  }
}