Pith Number

pith:O4LC2VWH

pith:2003:O4LC2VWHVE4KWNHFNY6T5TQZ3O

not attested not anchored not stored refs pending

Critical cardinalities and additivity properties of combinatorial notions of smallness

Boaz Tsaban, Saharon Shelah

arxiv:math/0304019 v7 · 2003-04-02 · math.LO · math.CO · math.GN

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{O4LC2VWHVE4KWNHFNY6T5TQZ3O}

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	2026-05-18T04:37:23.193731Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

77162d56c7a938ab34e56e3d3ece19dbad1ed5283eef9ee0670fb4cff7481c4a

Aliases

arxiv: math/0304019 · arxiv_version: math/0304019v7 · doi: 10.48550/arxiv.math/0304019 · pith_short_12: O4LC2VWHVE4K · pith_short_16: O4LC2VWHVE4KWNHF · pith_short_8: O4LC2VWH

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/O4LC2VWHVE4KWNHFNY6T5TQZ3O \
  | 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: 77162d56c7a938ab34e56e3d3ece19dbad1ed5283eef9ee0670fb4cff7481c4a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e93fd2d8f5beb4112e403f90b65a3c07b61e42c5569f4fbd63e2eb2d05d4aab8",
    "cross_cats_sorted": [
      "math.CO",
      "math.GN"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.LO",
    "submitted_at": "2003-04-02T12:43:58Z",
    "title_canon_sha256": "24eaf6421b49bb551ab5df0bee9c2c39090cc0685d263a13a6467708a6c660df"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0304019",
    "kind": "arxiv",
    "version": 7
  }
}