Pith Number

pith:PMJFEH2B

pith:2013:PMJFEH2BDDMGBNBLOSB572VBA4

not attested not anchored not stored refs pending

The Bowen's topological entropy of the Cartesian product sets

Ercai Chen, Xiaoyao Zhou

arxiv:1303.3690 v2 · 2013-03-15 · 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{PMJFEH2BDDMGBNBLOSB572VBA4}

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	2026-05-18T03:26:22.359903Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7b12521f4118d860b42b7483dfeaa1070982f92af6ad838532d154a4768addde

Aliases

arxiv: 1303.3690 · arxiv_version: 1303.3690v2 · doi: 10.48550/arxiv.1303.3690 · pith_short_12: PMJFEH2BDDMG · pith_short_16: PMJFEH2BDDMGBNBL · pith_short_8: PMJFEH2B

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/PMJFEH2BDDMGBNBLOSB572VBA4 \
  | 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: 7b12521f4118d860b42b7483dfeaa1070982f92af6ad838532d154a4768addde

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "31cfcd63beffb9ea95a74855adf4c0ee56c7d21d6b6fe0f5df6d4387afc336c6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2013-03-15T06:38:47Z",
    "title_canon_sha256": "0fdd14ac1968e6970deaaa1ecc9fb95dba7aff56d19f37a5fc558c82c6c886bf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1303.3690",
    "kind": "arxiv",
    "version": 2
  }
}