Pith Number

pith:PACI6K6M

pith:2012:PACI6K6MWYOKEIWGXFKGGGZTPV

not attested not anchored not stored refs pending

Subsets of Products of Finite Sets of Positive Upper Density

Konstantinos Tyros, Stevo Todorcevic

arxiv:1211.3948 v1 · 2012-11-16 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PACI6K6MWYOKEIWGXFKGGGZTPV}

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	2026-05-18T03:40:37.488973Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

78048f2bccb61ca222c6b954631b337d62a6a59e44d5c1dd7c945aaf18bb5842

Aliases

arxiv: 1211.3948 · arxiv_version: 1211.3948v1 · doi: 10.48550/arxiv.1211.3948 · pith_short_12: PACI6K6MWYOK · pith_short_16: PACI6K6MWYOKEIWG · pith_short_8: PACI6K6M

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/PACI6K6MWYOKEIWGXFKGGGZTPV \
  | 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: 78048f2bccb61ca222c6b954631b337d62a6a59e44d5c1dd7c945aaf18bb5842

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7f370128a65f14286f2e2831de17bc1b3e785f7991daad399f577517614ace81",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-11-16T16:38:22Z",
    "title_canon_sha256": "86ef486ccf618c44c19025ce43d6acf02b6b28173805e19c9e4007d75eb3bd8b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.3948",
    "kind": "arxiv",
    "version": 1
  }
}