Pith Number

pith:47TGP3PP

pith:2011:47TGP3PPLC4G4ZJN4XYFTXTPRH

not attested not anchored not stored refs pending

On the existence of maximizing measures for irreducible countable Markov shifts: a dynamical proof

Ricardo Freire, Rodrigo Bissacot

arxiv:1109.0062 v3 · 2011-09-01 · 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{47TGP3PPLC4G4ZJN4XYFTXTPRH}

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	2026-05-17T23:53:19.263928Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e7e667edef58b86e652de5f059de6f89ff00030d7a8ef563b25002400ceda3b6

Aliases

arxiv: 1109.0062 · arxiv_version: 1109.0062v3 · doi: 10.48550/arxiv.1109.0062 · pith_short_12: 47TGP3PPLC4G · pith_short_16: 47TGP3PPLC4G4ZJN · pith_short_8: 47TGP3PP

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/47TGP3PPLC4G4ZJN4XYFTXTPRH \
  | 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: e7e667edef58b86e652de5f059de6f89ff00030d7a8ef563b25002400ceda3b6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fab35c2ed5d90edf51c92e4e9765b29484ed0aad80fd5bf59e1fc2a5f95fde03",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2011-09-01T01:24:59Z",
    "title_canon_sha256": "900ca910b6a81395bdfb23d8486f27e1e21c01d012e695a0576bf76e341db8ad"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.0062",
    "kind": "arxiv",
    "version": 3
  }
}