Pith Number

pith:2FQ7JCTF

pith:2022:2FQ7JCTFK7ZXIFLOXE2IS2WA5U

not attested not anchored not stored refs pending

On fractal patterns in Ulam words

Andrei Mandelshtam

arxiv:2211.14229 v2 · 2022-11-23 · 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{2FQ7JCTFK7ZXIFLOXE2IS2WA5U}

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

Small gaps in the Ulam sequence

Receipt and verification

First computed	2026-07-05T09:28:44.540063Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d161f48a6557f374156eb934896ac0ed19ee1a3de991f97f23e5e21868d40b9d

Aliases

arxiv: 2211.14229 · arxiv_version: 2211.14229v2 · doi: 10.48550/arxiv.2211.14229 · pith_short_12: 2FQ7JCTFK7ZX · pith_short_16: 2FQ7JCTFK7ZXIFLO · pith_short_8: 2FQ7JCTF

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/2FQ7JCTFK7ZXIFLOXE2IS2WA5U \
  | 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: d161f48a6557f374156eb934896ac0ed19ee1a3de991f97f23e5e21868d40b9d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "23310939160c2bd458121d16253ebe5768bc26413c21e5f4743791f119d7295f",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2022-11-23T09:43:55Z",
    "title_canon_sha256": "d708b5222ec11c0f7ad6fc3a1eb299b6064f07ca255d6f1df45959f954f5649e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2211.14229",
    "kind": "arxiv",
    "version": 2
  }
}