Pith Number

pith:6CG4BJJU

pith:2003:6CG4BJJUB2KT6ZKLCCW6Z4Z2KL

not attested not anchored not stored refs pending

Extensions with the approximation and cover properties have no new large cardinals

Joel David Hamkins (The City University of New York)

arxiv:math/0307229 v2 · 2003-07-16 · 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{6CG4BJJUB2KT6ZKLCCW6Z4Z2KL}

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	2026-05-18T02:35:38.570687Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f08dc0a5340e953f654b10adecf33a52dc8504a03161292a1afd303b7865b826

Aliases

arxiv: math/0307229 · arxiv_version: math/0307229v2 · doi: 10.48550/arxiv.math/0307229 · pith_short_12: 6CG4BJJUB2KT · pith_short_16: 6CG4BJJUB2KT6ZKL · pith_short_8: 6CG4BJJU

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/6CG4BJJUB2KT6ZKLCCW6Z4Z2KL \
  | 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: f08dc0a5340e953f654b10adecf33a52dc8504a03161292a1afd303b7865b826

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3b80b51772485092660cc465aa847481d9200ac8056bf8a9654850acc2eb9053",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.LO",
    "submitted_at": "2003-07-16T19:56:05Z",
    "title_canon_sha256": "35d57958b42d6dd6739fb4097abc6c2ffef16e637f04ef9a05acbc54b9f00e4b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0307229",
    "kind": "arxiv",
    "version": 2
  }
}