Pith Number

pith:APHZ3SCN

pith:2013:APHZ3SCNBR2QHCZIZEODHYFFQK

not attested not anchored not stored refs pending

Games and Complexes II: Weight Games and Kruskal-Katona Type Bounds

Richard J. Nowakowski, Sara Faridi, Svenja Huntemann

arxiv:1310.1327 v2 · 2013-10-04 · 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{APHZ3SCNBR2QHCZIZEODHYFFQK}

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	2026-05-18T01:33:58.801975Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

03cf9dc84d0c75038b28c91c33e0a58285e6e0e3f141d1fdc28628cc06720ea7

Aliases

arxiv: 1310.1327 · arxiv_version: 1310.1327v2 · doi: 10.48550/arxiv.1310.1327 · pith_short_12: APHZ3SCNBR2Q · pith_short_16: APHZ3SCNBR2QHCZI · pith_short_8: APHZ3SCN

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/APHZ3SCNBR2QHCZIZEODHYFFQK \
  | 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: 03cf9dc84d0c75038b28c91c33e0a58285e6e0e3f141d1fdc28628cc06720ea7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d7a4997df1b1ca58cb89edba83c84bf5d22438e1dc88a9787cf1fb180b28a93f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-10-04T15:57:20Z",
    "title_canon_sha256": "ec0f2aef07371a15520bbc3475d5e6b373f0b12c4fad61f7dadd453ab4a1cd52"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1310.1327",
    "kind": "arxiv",
    "version": 2
  }
}