Pith Number

pith:VPKMMYYM

pith:2009:VPKMMYYM6RBUMUWDZX2LAUGUCA

not attested not anchored not stored refs pending

$Q_2$-free families in the Boolean lattice

Jacob Manske, Maria Axenovich, Ryan R. Martin

arxiv:0912.5039 v3 · 2009-12-26 · math.CO

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

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	2026-05-18T01:14:18.714093Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

abd4c6630cf4434652c3cdf4b050d4102b3ab33978e715f909f4e17af165605f

Aliases

arxiv: 0912.5039 · arxiv_version: 0912.5039v3 · doi: 10.48550/arxiv.0912.5039 · pith_short_12: VPKMMYYM6RBU · pith_short_16: VPKMMYYM6RBUMUWD · pith_short_8: VPKMMYYM

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/VPKMMYYM6RBUMUWDZX2LAUGUCA \
  | 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: abd4c6630cf4434652c3cdf4b050d4102b3ab33978e715f909f4e17af165605f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "55624edcd1d8d0c69981d7bbb0ccfe3184739bbfeb7b5ca36b356f9c50267569",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2009-12-26T20:27:08Z",
    "title_canon_sha256": "c2999a66e079d03e5024a6e72ae205f5f310b3afa6631270f8f2bc4d901d5477"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0912.5039",
    "kind": "arxiv",
    "version": 3
  }
}