Pith Number

pith:WCJSHLEJ

pith:2011:WCJSHLEJCR45QYZ2XPZUHSU2BA

not attested not anchored not stored refs pending

The hierarchy of equivalence relations on the natural numbers under computable reducibility

Joel David Hamkins, Russell Miller, Samuel Coskey

arxiv:1109.3375 v3 · 2011-09-15 · 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{WCJSHLEJCR45QYZ2XPZUHSU2BA}

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	2026-05-17T23:54:48.966916Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b09323ac891479d8633abbf343ca9a08374210bcc4130883b3fa382735cdc7d2

Aliases

arxiv: 1109.3375 · arxiv_version: 1109.3375v3 · doi: 10.48550/arxiv.1109.3375 · pith_short_12: WCJSHLEJCR45 · pith_short_16: WCJSHLEJCR45QYZ2 · pith_short_8: WCJSHLEJ

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/WCJSHLEJCR45QYZ2XPZUHSU2BA \
  | 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: b09323ac891479d8633abbf343ca9a08374210bcc4130883b3fa382735cdc7d2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e8113e12a307843e23904bf15c2fdf7ecc98525334d81f5aecee22c507524bcf",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.LO",
    "submitted_at": "2011-09-15T15:09:28Z",
    "title_canon_sha256": "f15f336d34b12d925d81debbe346ebb54327e61c46b736c68b368cffc5c68dc5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.3375",
    "kind": "arxiv",
    "version": 3
  }
}