Pith Number

pith:VMVVWSEY

pith:2018:VMVVWSEYTNT5VXCNKAJPFQWKJ3

not attested not anchored not stored refs pending

A New Approach to the Hofstadter $Q$-Recurrence

Nathan Fox

arxiv:1807.01365 v1 · 2018-07-03 · math.NT · 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{VMVVWSEYTNT5VXCNKAJPFQWKJ3}

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	2026-05-18T00:11:29.826276Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ab2b5b48989b67dadc4d5012f2c2ca4eefaa57cda8b35d7c4919cf7f199d4daa

Aliases

arxiv: 1807.01365 · arxiv_version: 1807.01365v1 · doi: 10.48550/arxiv.1807.01365 · pith_short_12: VMVVWSEYTNT5 · pith_short_16: VMVVWSEYTNT5VXCN · pith_short_8: VMVVWSEY

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/VMVVWSEYTNT5VXCNKAJPFQWKJ3 \
  | 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: ab2b5b48989b67dadc4d5012f2c2ca4eefaa57cda8b35d7c4919cf7f199d4daa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "33f5134ae8da64ca5b07ff088ef4026499c839e7cf9c272513f920dd1be3e57b",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2018-07-03T20:40:23Z",
    "title_canon_sha256": "f46592b659552917d5d2ea727892037cbe293608f8464fece4f75f0a083b559c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1807.01365",
    "kind": "arxiv",
    "version": 1
  }
}