Pith Number

pith:N55BEEZL

pith:2005:N55BEEZL7WYT3LQUS56XNYCWFL

not attested not anchored not stored refs pending

The combinatorics of frieze patterns and Markoff numbers

James Propp

arxiv:math/0511633 v5 · 2005-11-25 · 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{N55BEEZL7WYT3LQUS56XNYCWFL}

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.

Cited by

1 paper in Pith

Frieze patterns with coefficients

Receipt and verification

First computed	2026-07-05T01:06:28.912678Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6f7a12132bfdb13dae14977d76e0562aed5d7c3092f7eeb61a862443b88d74d0

Aliases

arxiv: math/0511633 · arxiv_version: math/0511633v5 · doi: 10.48550/arxiv.math/0511633 · pith_short_12: N55BEEZL7WYT · pith_short_16: N55BEEZL7WYT3LQU · pith_short_8: N55BEEZL

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/N55BEEZL7WYT3LQUS56XNYCWFL \
  | 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: 6f7a12132bfdb13dae14977d76e0562aed5d7c3092f7eeb61a862443b88d74d0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a91ec75b8d5f60fe0d46feea9a13770a7a311e8b8bcbef2fd6c935ea1b9a7b7e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2005-11-25T17:13:44Z",
    "title_canon_sha256": "d76268c111dedf332da0b461ed075eb0e9760c3497133505cee2bb1d55cdbcfb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0511633",
    "kind": "arxiv",
    "version": 5
  }
}