Pith Number

pith:5Z2OWPG4

pith:2005:5Z2OWPG4MYCQRAPCFOZBVPFW2E

not attested not anchored not stored refs pending

Computable conditions for the occurrence of non-uniform hyperbolicity in families of one-dimensional maps

Hiroki Takahasi, Stefano Luzzatto

arxiv:math/0508302 v3 · 2005-08-16 · math.DS · math.NA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5Z2OWPG4MYCQRAPCFOZBVPFW2E}

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	2026-05-18T03:41:21.689001Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ee74eb3cdc66050881e22bb21abcb6d114e9e9ef67a8876f49e3a022d39eb861

Aliases

arxiv: math/0508302 · arxiv_version: math/0508302v3 · doi: 10.48550/arxiv.math/0508302 · pith_short_12: 5Z2OWPG4MYCQ · pith_short_16: 5Z2OWPG4MYCQRAPC · pith_short_8: 5Z2OWPG4

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/5Z2OWPG4MYCQRAPCFOZBVPFW2E \
  | 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: ee74eb3cdc66050881e22bb21abcb6d114e9e9ef67a8876f49e3a022d39eb861

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d7bd68c0b5ab3d6f488dec5e2c3982533c552c9259167e1c44e22b29514556e0",
    "cross_cats_sorted": [
      "math.NA"
    ],
    "license": "",
    "primary_cat": "math.DS",
    "submitted_at": "2005-08-16T19:09:18Z",
    "title_canon_sha256": "132d7f93a9020499b8e5df8ecd608d1047c1050ccdd5dad65700962bcd12d807"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0508302",
    "kind": "arxiv",
    "version": 3
  }
}