Pith Number

pith:MMBRQM7Y

pith:2013:MMBRQM7Y3INAS5UJDNDP5UNW2G

not attested not anchored not stored refs pending

Ergodic properties of invariant measures for systems with average shadowing property

Xiaoping Yuan, Xueting Tian, Yiwei Dong

arxiv:1312.0292 v3 · 2013-12-02 · 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{MMBRQM7Y3INAS5UJDNDP5UNW2G}

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	2026-05-18T01:26:32.061745Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

63031833f8da1a0976891b46fed1b6d1b14b0a84a1d279b3c0a7534630990a70

Aliases

arxiv: 1312.0292 · arxiv_version: 1312.0292v3 · doi: 10.48550/arxiv.1312.0292 · pith_short_12: MMBRQM7Y3INA · pith_short_16: MMBRQM7Y3INAS5UJ · pith_short_8: MMBRQM7Y

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/MMBRQM7Y3INAS5UJDNDP5UNW2G \
  | 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: 63031833f8da1a0976891b46fed1b6d1b14b0a84a1d279b3c0a7534630990a70

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "90f07664aca6d075ae79c8cca89723cecb2ac171edb0fa6462e47c570cd2f636",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2013-12-02T00:26:04Z",
    "title_canon_sha256": "94935f4487be3adc4d38228b53e486a8caf8e92813b302708cf312ca8ffce754"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.0292",
    "kind": "arxiv",
    "version": 3
  }
}