Pith Number

pith:5RL6M3ZW

pith:2011:5RL6M3ZWJB2XAHHIPTC3JOTBZJ

not attested not anchored not stored refs pending

Abelian returns in Sturmian words

Finland, Finland), France, Luca Q. Zamboni (Universite de Lyon, Novosibirsk, Russia), Sobolev Institute of Mathematics, Svetlana Puzynina (University of Turku, University of Turku

arxiv:1108.3635 v1 · 2011-08-18 · cs.FL · cs.DM · 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{5RL6M3ZWJB2XAHHIPTC3JOTBZJ}

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	2026-05-18T04:15:15.591346Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ec57e66f364875701ce87cc5b4ba61ca4589661ccd7322202c87bbf82bcfdcb3

Aliases

arxiv: 1108.3635 · arxiv_version: 1108.3635v1 · doi: 10.48550/arxiv.1108.3635 · pith_short_12: 5RL6M3ZWJB2X · pith_short_16: 5RL6M3ZWJB2XAHHI · pith_short_8: 5RL6M3ZW

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/5RL6M3ZWJB2XAHHIPTC3JOTBZJ \
  | 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: ec57e66f364875701ce87cc5b4ba61ca4589661ccd7322202c87bbf82bcfdcb3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0dd9f66b9d1d1c98956c3421dfd41c8c69dd8f7a0258d3f1a19c5fce9e3585c0",
    "cross_cats_sorted": [
      "cs.DM",
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.FL",
    "submitted_at": "2011-08-18T03:54:29Z",
    "title_canon_sha256": "61c976de4f31b5575459219b2e779ee355f154dc15d9dbc5ef6caa3a8d7ef558"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.3635",
    "kind": "arxiv",
    "version": 1
  }
}