Pith Number

pith:O2LBN2O7

pith:1993:O2LBN2O7B5TASGOZJTESAZLEDW

not attested not anchored not stored refs pending

Every coseparable group may be free

Alan H. Mekler, Saharon Shelah

arxiv:math/9305205 v1 · 1993-05-15 · math.LO · math.RA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{O2LBN2O7B5TASGOZJTESAZLEDW}

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	2026-05-18T01:05:52.183220Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

769616e9df0f660919d94cc92065641dac3bdda26e425e4ac56d156352526d2b

Aliases

arxiv: math/9305205 · arxiv_version: math/9305205v1 · doi: 10.48550/arxiv.math/9305205 · pith_short_12: O2LBN2O7B5TA · pith_short_16: O2LBN2O7B5TASGOZ · pith_short_8: O2LBN2O7

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/O2LBN2O7B5TASGOZJTESAZLEDW \
  | 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: 769616e9df0f660919d94cc92065641dac3bdda26e425e4ac56d156352526d2b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4c4a18b7ff53738e359484555ed23b38e0c9be942f8025c58f4421e35494107e",
    "cross_cats_sorted": [
      "math.RA"
    ],
    "license": "",
    "primary_cat": "math.LO",
    "submitted_at": "1993-05-15T00:00:00Z",
    "title_canon_sha256": "f64a1a642e43c66e22deaaad51fabe0164ea941e85b0fde4794fce61e06a4ee0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9305205",
    "kind": "arxiv",
    "version": 1
  }
}