Pith Number

pith:ZZ5OUBD6

pith:1997:ZZ5OUBD6XFWUVKGQWGSQDRDGO3

not attested not anchored not stored refs pending

Almost every real quadratic map is either regular or stochastic

Mikhail Lyubich

arxiv:math/9707224 v1 · 1997-07-15 · 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{ZZ5OUBD6XFWUVKGQWGSQDRDGO3}

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	2026-05-18T01:05:35.000164Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ce7aea047eb96d4aa8d0b1a501c46676e21e26ef7f3e01e2bf39537d3be2a306

Aliases

arxiv: math/9707224 · arxiv_version: math/9707224v1 · doi: 10.48550/arxiv.math/9707224 · pith_short_12: ZZ5OUBD6XFWU · pith_short_16: ZZ5OUBD6XFWUVKGQ · pith_short_8: ZZ5OUBD6

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/ZZ5OUBD6XFWUVKGQWGSQDRDGO3 \
  | 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: ce7aea047eb96d4aa8d0b1a501c46676e21e26ef7f3e01e2bf39537d3be2a306

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1537367df9b9f47c49cf03a9a5cc43dbb8fdfd7571036755344452b986c51ac1",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.DS",
    "submitted_at": "1997-07-15T00:00:00Z",
    "title_canon_sha256": "c8a19156a08008c9d168a0e6ec27c740d1da5503b3bc432450b97e445aa29ad9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9707224",
    "kind": "arxiv",
    "version": 1
  }
}