Pith Number

pith:TAJ5GPSZ

pith:2006:TAJ5GPSZKCIZUI2J7PYWKJB54U

not attested not anchored not stored refs pending

Filtration equivalent aleph_1-separable abelian groups of cardinality aleph_1

Lutz Str\"ungmann, Saharon Shelah

arxiv:math/0612241 v1 · 2006-12-09 · 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{TAJ5GPSZKCIZUI2J7PYWKJB54U}

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	2026-05-18T01:08:49.362943Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9813d33e5950919a2349fbf165243de53c4184c8022ef9553852e848fad14c6c

Aliases

arxiv: math/0612241 · arxiv_version: math/0612241v1 · doi: 10.48550/arxiv.math/0612241 · pith_short_12: TAJ5GPSZKCIZ · pith_short_16: TAJ5GPSZKCIZUI2J · pith_short_8: TAJ5GPSZ

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/TAJ5GPSZKCIZUI2J7PYWKJB54U \
  | 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: 9813d33e5950919a2349fbf165243de53c4184c8022ef9553852e848fad14c6c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f97842fd01a4b23cfdd00a0a07edc8f8c1126bfd1bb98fef1d3c61a1766f1650",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.LO",
    "submitted_at": "2006-12-09T19:25:51Z",
    "title_canon_sha256": "a9e61f8e8f86b5872576eda3fc9f763e091e6caf917b76d3dde792317f4065bf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0612241",
    "kind": "arxiv",
    "version": 1
  }
}