Pith Number

pith:EUIRGMX3

pith:2016:EUIRGMX3NVM7J4HHINY7JLSZGB

not attested not anchored not stored refs pending

Exponential Mixing and Smooth Classification of Commuting Expanding Maps

Lei Yang, Ralf Spatzier

arxiv:1608.02295 v1 · 2016-08-08 · 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{EUIRGMX3NVM7J4HHINY7JLSZGB}

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	2026-05-18T01:09:40.549358Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

25111332fb6d59f4f0e74371f4ae59304348016d7afc5ccbd135cd0086a4fa91

Aliases

arxiv: 1608.02295 · arxiv_version: 1608.02295v1 · doi: 10.48550/arxiv.1608.02295 · pith_short_12: EUIRGMX3NVM7 · pith_short_16: EUIRGMX3NVM7J4HH · pith_short_8: EUIRGMX3

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/EUIRGMX3NVM7J4HHINY7JLSZGB \
  | 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: 25111332fb6d59f4f0e74371f4ae59304348016d7afc5ccbd135cd0086a4fa91

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3837c308177665eda0461ced1d4933332dc619e15d9615c08f7284ccdc068907",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2016-08-08T02:19:11Z",
    "title_canon_sha256": "6e2bd72dafdbd5335b9a3c86f67c1df0937d687f19c8a6aac7afd28a2bf1afdf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1608.02295",
    "kind": "arxiv",
    "version": 1
  }
}