Pith Number

pith:XXCRQU4B

pith:2024:XXCRQU4BB5GOVCO3VHDJURFCUK

not attested not anchored not stored refs pending

Unique ergodicity for random noninvertible maps on an interval

Hanna Oppelmayer, Sara Brofferio, Tomasz Szarek

arxiv:2401.12361 v2 · 2024-01-22 · math.DS · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XXCRQU4BB5GOVCO3VHDJURFCUK}

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	2026-07-05T07:57:49.012606Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bdc51853810f4cea89dba9c69a44a2a2896350a420990eae1cea22d8d7698e28

Aliases

arxiv: 2401.12361 · arxiv_version: 2401.12361v2 · doi: 10.48550/arxiv.2401.12361 · pith_short_12: XXCRQU4BB5GO · pith_short_16: XXCRQU4BB5GOVCO3 · pith_short_8: XXCRQU4B

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/XXCRQU4BB5GOVCO3VHDJURFCUK \
  | 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: bdc51853810f4cea89dba9c69a44a2a2896350a420990eae1cea22d8d7698e28

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "98a295b4180dbb1035efb62ce302fc7ce6261520cc4972885a462cd312002e5a",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://creativecommons.org/licenses/by-sa/4.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2024-01-22T21:10:26Z",
    "title_canon_sha256": "19af407db5eabf9c022e560bbeeef5e55e8c40c53065fd5f3b27e090be388a55"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2401.12361",
    "kind": "arxiv",
    "version": 2
  }
}