Pith Number

pith:U3ODH7NI

pith:2017:U3ODH7NI4UWKTHU6QU2TCG5KS3

not attested not anchored not stored refs pending

Topological entropy, sets of periods and transitivity for graph maps

Jorge Groisman, Liane Bordignon, Llu\'is Alsed\`a

arxiv:1712.00104 v2 · 2017-11-30 · 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{U3ODH7NI4UWKTHU6QU2TCG5KS3}

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	2026-05-18T00:11:32.363600Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a6dc33fda8e52ca99e9e8535311baa96f5f62b02194ea3b74521a4cb89f83b04

Aliases

arxiv: 1712.00104 · arxiv_version: 1712.00104v2 · doi: 10.48550/arxiv.1712.00104 · pith_short_12: U3ODH7NI4UWK · pith_short_16: U3ODH7NI4UWKTHU6 · pith_short_8: U3ODH7NI

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/U3ODH7NI4UWKTHU6QU2TCG5KS3 \
  | 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: a6dc33fda8e52ca99e9e8535311baa96f5f62b02194ea3b74521a4cb89f83b04

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f0980b8296e1181d69981e4db38477438b05fdaa4a45fcc3af356825264f0130",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2017-11-30T22:25:34Z",
    "title_canon_sha256": "fca7062614027af16b5843dae9d4116db6d75ea765ba0a0ae9c03b953fce823c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1712.00104",
    "kind": "arxiv",
    "version": 2
  }
}