Pith Number

pith:XN2ZPRIX

pith:2013:XN2ZPRIX7NLYCZPNYNKT7R7Z7P

not attested not anchored not stored refs pending

A closed formula for the topological entropy of multimodal maps based on min-max symbols

Angel Gimenez, Jose M. Amigo

arxiv:1310.8122 v1 · 2013-10-30 · 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{XN2ZPRIX7NLYCZPNYNKT7R7Z7P}

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	2026-05-18T03:08:25.926858Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bb7597c517fb578165edc3553fc7f9fbcd68868dd676c87285c0b3ae7cd21321

Aliases

arxiv: 1310.8122 · arxiv_version: 1310.8122v1 · doi: 10.48550/arxiv.1310.8122 · pith_short_12: XN2ZPRIX7NLY · pith_short_16: XN2ZPRIX7NLYCZPN · pith_short_8: XN2ZPRIX

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/XN2ZPRIX7NLYCZPNYNKT7R7Z7P \
  | 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: bb7597c517fb578165edc3553fc7f9fbcd68868dd676c87285c0b3ae7cd21321

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6c0c72dd45adc2914fe1191e7b2bc8001cebc256e9c95c4bffe3c42c1923f0f5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2013-10-30T12:41:18Z",
    "title_canon_sha256": "e6014f2dbcb2392325cd33658b4553618a3a038831e5b6e3fa914253736dc9cc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1310.8122",
    "kind": "arxiv",
    "version": 1
  }
}