Pith Number

pith:KZHKWVTR

pith:2014:KZHKWVTRNQEAF25JPH2D7S72CS

not attested not anchored not stored refs pending

Uniformly expanding Markov maps of the real line: exactness and infinite mixing

Marco Lenci

arxiv:1404.2212 v3 · 2014-04-08 · 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{KZHKWVTRNQEAF25JPH2D7S72CS}

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	2026-05-18T00:46:08.589181Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

564eab56716c0802eba979f43fcbfa14a8850674abf6a7a88d8880c7a357c793

Aliases

arxiv: 1404.2212 · arxiv_version: 1404.2212v3 · doi: 10.48550/arxiv.1404.2212 · pith_short_12: KZHKWVTRNQEA · pith_short_16: KZHKWVTRNQEAF25J · pith_short_8: KZHKWVTR

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/KZHKWVTRNQEAF25JPH2D7S72CS \
  | 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: 564eab56716c0802eba979f43fcbfa14a8850674abf6a7a88d8880c7a357c793

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "821bb5cc29908ec9f4836665e24d9b72c1cb415d9c80bcc502ac134122ec435b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2014-04-08T17:04:03Z",
    "title_canon_sha256": "019135485817efadcfc88130c23bd857e83524902a9ff09bbb38a3d2c72fba56"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1404.2212",
    "kind": "arxiv",
    "version": 3
  }
}