Pith Number

pith:APPRBDXX

pith:2011:APPRBDXXIEW7JQTT4L5PSFP6YG

not attested not anchored not stored refs pending

Absolutely continuous invariant measures for random non-uniformly expanding maps

Javier Solano, Vitor Araujo

arxiv:1111.4540 v8 · 2011-11-19 · 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{APPRBDXXIEW7JQTT4L5PSFP6YG}

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	2026-05-18T02:35:52.844898Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

03df108ef7412df4c273e2faf915fec19daeb58a272322c4b6af3b95391ca552

Aliases

arxiv: 1111.4540 · arxiv_version: 1111.4540v8 · doi: 10.48550/arxiv.1111.4540 · pith_short_12: APPRBDXXIEW7 · pith_short_16: APPRBDXXIEW7JQTT · pith_short_8: APPRBDXX

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/APPRBDXXIEW7JQTT4L5PSFP6YG \
  | 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: 03df108ef7412df4c273e2faf915fec19daeb58a272322c4b6af3b95391ca552

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1be774facfa7853e8f42f3e4450bc91982be97e14a8f3139d810a72b5fdb8f2d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2011-11-19T08:38:38Z",
    "title_canon_sha256": "6e0007885a91087390811a7c7a1a3a876054d83c2161b482cd7b92308a424be1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.4540",
    "kind": "arxiv",
    "version": 8
  }
}