Pith Number

pith:MMXAT2FB

pith:2013:MMXAT2FBGPJ3FTRJPPD2OYLOXI

not attested not anchored not stored refs pending

Topological Entropy and Algebraic Entropy for group endomorphisms

Anna Giordano Bruno, Dikran Dikranjan

arxiv:1308.4019 v1 · 2013-08-19 · math.GN · math.DS · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MMXAT2FBGPJ3FTRJPPD2OYLOXI}

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	2026-05-18T03:15:35.060926Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

632e09e8a133d3b2ce297bc7a7616eba04c8de64d6252544740b99429986e058

Aliases

arxiv: 1308.4019 · arxiv_version: 1308.4019v1 · doi: 10.48550/arxiv.1308.4019 · pith_short_12: MMXAT2FBGPJ3 · pith_short_16: MMXAT2FBGPJ3FTRJ · pith_short_8: MMXAT2FB

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/MMXAT2FBGPJ3FTRJPPD2OYLOXI \
  | 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: 632e09e8a133d3b2ce297bc7a7616eba04c8de64d6252544740b99429986e058

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "40ef89ef6b4964a40234812892034091a33e4855626363af3ace494094facd71",
    "cross_cats_sorted": [
      "math.DS",
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GN",
    "submitted_at": "2013-08-19T13:37:13Z",
    "title_canon_sha256": "63ec43d3b4f04bf343225305869e00672b6ab1d84b997967d832dfd1eaaf9aba"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1308.4019",
    "kind": "arxiv",
    "version": 1
  }
}