Pith Number

pith:BAT6TFJ3

pith:2015:BAT6TFJ3BO57UWQ3HPKE734WDX

not attested not anchored not stored refs pending

Hankel Matrices for the Period-Doubling Sequence

Cor Kraaikamp, Jeffrey Shallit, Robbert J. Fokkink

arxiv:1511.06569 v4 · 2015-11-20 · math.CO · cs.DM · cs.FL

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BAT6TFJ3BO57UWQ3HPKE734WDX}

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	2026-05-18T01:12:12.873163Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0827e9953b0bbbfa5a1b3bd44fef961decda78610c6f85152131f614c5b7d10c

Aliases

arxiv: 1511.06569 · arxiv_version: 1511.06569v4 · doi: 10.48550/arxiv.1511.06569 · pith_short_12: BAT6TFJ3BO57 · pith_short_16: BAT6TFJ3BO57UWQ3 · pith_short_8: BAT6TFJ3

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/BAT6TFJ3BO57UWQ3HPKE734WDX \
  | 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: 0827e9953b0bbbfa5a1b3bd44fef961decda78610c6f85152131f614c5b7d10c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "12d30d0b6ff5c8ef6e58eb72a0ced4bb683a637ca3499fc3499aa4a452678645",
    "cross_cats_sorted": [
      "cs.DM",
      "cs.FL"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-11-20T12:09:46Z",
    "title_canon_sha256": "786b7b3abc070f4bac355907f95958a82a79a979c373c0ded9345691977994d4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.06569",
    "kind": "arxiv",
    "version": 4
  }
}