Pith Number

pith:4OMUYZYC

pith:2012:4OMUYZYC6QW5OEGYHS7MMTE357

not attested not anchored not stored refs pending

Abelian returns in Sturmian words

Luca Q. Zamboni, Svetlana Puzynina

arxiv:1204.5755 v1 · 2012-04-25 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4OMUYZYC6QW5OEGYHS7MMTE357}

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	2026-05-18T03:56:59.709222Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e3994c6702f42dd710d83cbec64c9beffe534f31e5ca10c64e15c0230e03366b

Aliases

arxiv: 1204.5755 · arxiv_version: 1204.5755v1 · doi: 10.48550/arxiv.1204.5755 · pith_short_12: 4OMUYZYC6QW5 · pith_short_16: 4OMUYZYC6QW5OEGY · pith_short_8: 4OMUYZYC

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/4OMUYZYC6QW5OEGYHS7MMTE357 \
  | 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: e3994c6702f42dd710d83cbec64c9beffe534f31e5ca10c64e15c0230e03366b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fa95a958ee1abbf958563c1fd50cde934020922db9336799ea2c31b1e0112b6f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-04-25T20:06:55Z",
    "title_canon_sha256": "61c976de4f31b5575459219b2e779ee355f154dc15d9dbc5ef6caa3a8d7ef558"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1204.5755",
    "kind": "arxiv",
    "version": 1
  }
}