Pith Number

pith:VRGK7I56

pith:2006:VRGK7I56T64QMF6CN2DZU53ZJG

not attested not anchored not stored refs pending

The Halting Probability Omega: Irreducible Complexity in Pure Mathematics

G. J. Chaitin (IBM Research)

arxiv:math/0611740 v1 · 2006-11-23 · math.HO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VRGK7I56T64QMF6CN2DZU53ZJG}

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	2026-07-04T14:57:41.717525Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ac4cafa3be9fb90617c26e879a777949a4aaf74c804c230d33925c2fd70c09ac

Aliases

arxiv: math/0611740 · arxiv_version: math/0611740v1 · doi: 10.48550/arxiv.math/0611740 · pith_short_12: VRGK7I56T64Q · pith_short_16: VRGK7I56T64QMF6C · pith_short_8: VRGK7I56

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/VRGK7I56T64QMF6CN2DZU53ZJG \
  | 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: ac4cafa3be9fb90617c26e879a777949a4aaf74c804c230d33925c2fd70c09ac

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d4f010a3f26e011cc9dfa5a171dda44e4ffccdfc53ad5ae27693af27533071b5",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.HO",
    "submitted_at": "2006-11-23T20:58:53Z",
    "title_canon_sha256": "2186217dfbe85e464508ce06721ef31a0e8f476983a96d4cad045ac52449e251"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0611740",
    "kind": "arxiv",
    "version": 1
  }
}