Pith Number

pith:N47MVNWD

pith:2026:N47MVNWD3EFOJCQMDQMT3WBATX

not attested not anchored not stored refs pending

Step Recursion: A Three-Parameter Refinement of the Grzegorczyk Hierarchy

Kirill Osipov

arxiv:2608.04871 v1 · 2026-08-05 · cs.LO · cs.CC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{N47MVNWD3EFOJCQMDQMT3WBATX}

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	2026-08-06T01:47:26.098368Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6f3ecab6c3d90ae48a0c1c193dd8209dc3421e22d5ff762e0d07941cf33e7734

Aliases

arxiv: 2608.04871 · arxiv_version: 2608.04871v1 · doi: 10.48550/arxiv.2608.04871 · pith_short_12: N47MVNWD3EFO · pith_short_16: N47MVNWD3EFOJCQM · pith_short_8: N47MVNWD

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/N47MVNWD3EFOJCQMDQMT3WBATX \
  | 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: 6f3ecab6c3d90ae48a0c1c193dd8209dc3421e22d5ff762e0d07941cf33e7734

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6b8a7c92e6d61ef9ece01fbcfdd4e36239d8f75337212444b81d97be2217d4c3",
    "cross_cats_sorted": [
      "cs.CC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LO",
    "submitted_at": "2026-08-05T14:01:07Z",
    "title_canon_sha256": "57518ef74c429f4929857801d3313dd030307df88ebdab90ab31ba31d0305a7f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.04871",
    "kind": "arxiv",
    "version": 1
  }
}