Pith Number

pith:OSP7XGJE

pith:2016:OSP7XGJEWHFPBRBNQ5NWJPNFS5

not attested not anchored not stored refs pending

A criterion for zero averages and full support of ergodic measures

Christian Bonatti, Jairo Bochi, Lorenzo J. Diaz

arxiv:1609.07764 v1 · 2016-09-25 · 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{OSP7XGJEWHFPBRBNQ5NWJPNFS5}

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	2026-05-18T01:03:55.502543Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

749ffb9924b1caf0c42d875b64bda59758f6b91d9957a37fc9380a51d002ac09

Aliases

arxiv: 1609.07764 · arxiv_version: 1609.07764v1 · doi: 10.48550/arxiv.1609.07764 · pith_short_12: OSP7XGJEWHFP · pith_short_16: OSP7XGJEWHFPBRBN · pith_short_8: OSP7XGJE

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/OSP7XGJEWHFPBRBNQ5NWJPNFS5 \
  | 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: 749ffb9924b1caf0c42d875b64bda59758f6b91d9957a37fc9380a51d002ac09

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f4f2aa25b9433c1df2aeaccee8d53152ceb4a019398d1f5f866dd3a933a89788",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2016-09-25T16:07:27Z",
    "title_canon_sha256": "a94fd5286b8c89a560fdaa1e95c23100dc1b5ab1b3012ec9f53336c673c35118"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.07764",
    "kind": "arxiv",
    "version": 1
  }
}