Pith Number

pith:QD72X6YT

pith:2013:QD72X6YTIV47GUHPJXJOTUGHEX

not attested not anchored not stored refs pending

Asymptotic density and the Ershov hierarchy

Carl Jockusch, Paul Schupp, Rod Downey, Timothy H. McNicholl

arxiv:1309.0137 v2 · 2013-08-31 · math.LO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QD72X6YTIV47GUHPJXJOTUGHEX}

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	2026-05-18T02:45:04.803686Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

80ffabfb134579f350ef4dd2e9d0c725c76a9c620be5715ed2edbeb40d9f1c2f

Aliases

arxiv: 1309.0137 · arxiv_version: 1309.0137v2 · doi: 10.48550/arxiv.1309.0137 · pith_short_12: QD72X6YTIV47 · pith_short_16: QD72X6YTIV47GUHP · pith_short_8: QD72X6YT

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/QD72X6YTIV47GUHPJXJOTUGHEX \
  | 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: 80ffabfb134579f350ef4dd2e9d0c725c76a9c620be5715ed2edbeb40d9f1c2f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "349e24fddbc3923f5851848d48b23cec62d4f1b3b0d4d01f1c3c2bf15112d3aa",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.LO",
    "submitted_at": "2013-08-31T17:41:05Z",
    "title_canon_sha256": "a610b6006a98dce84e4f7764d0e5e6dcb0897e6ae277c1a5460c2bd31c6dc249"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.0137",
    "kind": "arxiv",
    "version": 2
  }
}